1. technology and computing
2. programming languages
3. c and c++

Computer Languages for Engineers
Book of Examples
2015
University of Duisburg-Essen
Faculty of Engineering
Department of Civil Engineering
Structural Analysis and Construction
Dr. E. Baeck
9.6.2015
Contents
I
FORTRAN
1
1
Development Tools
3
1.1
The Development Toolchain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.2
Some History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.2.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.2.2
FORTRAN’s History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.3
The Fixed FORTRAN Format and it’s Roots . . . . . . . . . . . . . . . . . . . . . . . .
6
1.4
Some free FORTRAN Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.5
The Open Watcom Development Suite . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.6
The MinGW Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
1.6.1
Running Compilers of the MinGW Package . . . . . . . . . . . . . . . . . . . .
10
1.6.2
Installing the MinGW Package . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
1.7
The G95 Compiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
1.8
The Code::Blocks IDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
2
FORTRAN Basics
17
2.1
Structure of a FORTRAN Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
2.2
Format and Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.3
Character Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.4
Available Data Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
2.4.1
Negative Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
2.4.2
Endianness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
Data Types, Variables and Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.5.1
Data Types of FORTRAN 77 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.5.2
Data Types, Constants and KIND in FORTRAN 90 . . . . . . . . . . . . . . . .
23
2.5.3
Representation of a Float Number . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.5.4
Data Ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.5.5
Declaration of Variables and Constants in FORTRAN 77 . . . . . . . . . . . . .
26
2.5.6
Declaration of Variables and Constants in FORTRAN 90 . . . . . . . . . . . . .
27
2.5.7
Complex Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.6.1
Unary Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.6.2
Arithmetic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.6.3
Comparison Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
File IO, Screen and Keyboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
2.7.1
32
2.5
2.6
2.7
Open a File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iii
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65
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78
Linear Algebra, Vectors and Matrices
4.1 Helper Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Outlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Reset and List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
85
85
85
2.8
2.9
2.10
2.11
2.12
2.13
2.14
3
4
Computer Languages for Engineering - SS 15
2.7.2 Writing Texts, write Statement . . . . . . . . . . . . . . . . . . . . .
2.7.3 Formatting, FORMAT Statement . . . . . . . . . . . . . . . . . . .
2.7.4 Read from Keyboard or File . . . . . . . . . . . . . . . . . . . . . .
2.7.5 Close a File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8.1 Explicit Loops with Counter in 66, 77 and 90+ . . . . . . . . . . . .
2.8.2 Simple Nested Loop Example . . . . . . . . . . . . . . . . . . . . .
2.8.3 Quit a Cycle or a Loop . . . . . . . . . . . . . . . . . . . . . . . . .
2.8.4 Implicit, General Loop without a Control Structure in 90+ . . . . . .
2.8.5 Factorial in FORTRAN 90++ . . . . . . . . . . . . . . . . . . . . .
Branching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9.1 if Statement, Fortran 66 like . . . . . . . . . . . . . . . . . . . . . .
2.9.2 Implementation of a Quadratic Equation Solver . . . . . . . . . . . .
2.9.2.1 Some Theory . . . . . . . . . . . . . . . . . . . . . . . .
2.9.2.2 A Flow-Chart of the QuadSolver . . . . . . . . . . . . . .
2.9.2.3 Quadratic Equation, Solver Implementation Fortran 66 like
2.9.2.4 Quadratic Equation, Solver Implementation Fortran 90 like
Subroutines and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10.1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10.2 Subroutines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10.3 Functions as Parameters . . . . . . . . . . . . . . . . . . . . . . . .
Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11.1 Static Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11.2 Dynamical Array . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11.3 Automatic Array . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11.4 A little Array Example . . . . . . . . . . . . . . . . . . . . . . . . .
2.11.5 Pseudo Dynamic Arrays in FORTRAN77 . . . . . . . . . . . . . . .
Global Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.12.1 Classical Fortran and Common . . . . . . . . . . . . . . . . . . . . .
2.12.2 Some Aspects of the Module Concept of FORTRAN90 . . . . . . . .
2.12.3 Using global Data . . . . . . . . . . . . . . . . . . . . . . . . . . .
Memory Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Commandline Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Some Examples
3.1 Hello World . . . . . . . . . . . . . . . . . .
3.2 Simple Sum . . . . . . . . . . . . . . . . . .
3.3 Calculation of real*4/8 Precision . . . . . . .
3.4 Relative Precision with Functions . . . . . .
3.5 Newton’s Algorithm to calculate a Root . . .
3.6 Matrix Product with 77-Main and 90-Library
E. Baeck
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CONTENTS
4.2
II
5
4.1.3
LU-Extract, MatMult and DiffMat . . . . . . . . . . . . . . . . . . . . . . . . .
89
4.1.4
Text Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
4.1.5
Memory Manager . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
4.1.6
Multi Matrix Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
4.1.7
Tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Gauss-LU-Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.2.1
Gauss Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.2.2
Memory Manager . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.2.3
LU-Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2.4
Tracing and Memory Pointers . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.2.4.1
Tracing gaussLU
4.2.4.2
Preparing Main . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.2.5
Gauss FB-Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.2.6
Linare Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
C/C++
123
Development Tools
5.1
6
Page v
127
The Code::Blocks IDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Basics of C/C++
131
6.1
The Preprocessor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.2
Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.3
Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.4
Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.4.1
Assignment Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.4.2
Arthmetic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.4.3
Compound Arithmetic Assignment . . . . . . . . . . . . . . . . . . . . . . . . 133
6.4.4
Increment - Decrement Operators . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.4.5
Relational and Equality Operators . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.4.6
Logical Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.4.7
Bitwise Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.4.8
Compound Bitwise Assignment . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.4.9
Explicit Type Casting Operator . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.4.10 sizeof Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.4.11 Address and Value Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.4.12 C++ operator synonyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.5
Taking about the Hello . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.6
Line Output with printf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.7
A For Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.8
Static Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.9
Branching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.9.1
if Branching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.9.2
switch Branching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.10 Exceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
9.6.2015
Page vi
6.11 OOP with Classes . . . . . . . . . . . .
6.11.1 Some UML Diagrams . . . . .
6.11.2 C++ Class . . . . . . . . . . . .
6.11.2.1 Declaration . . . . .
6.11.2.2 Implementation . . .
6.11.2.3 Structures and Classes
7
III
Computer Languages for Engineering - SS 15
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Profile Example
7.1 Class Concept for the Tin-Walled Approach
7.2 Implementation . . . . . . . . . . . . . . .
7.2.1 Base, the Base Class of all Classes .
7.2.2 Node Class for Model Nodes . . . .
7.2.3 Checking the Node Class . . . . . .
7.2.4 Element Class for Model Elements .
7.2.5 Checking the Element Class . . . .
7.2.6 Profile Class for Model Profiles . .
7.2.7 Checking the Profile Class . . . . .
7.2.8 H-Profile Class for Model Profiles .
7.2.9 Checking the HProfile Class . . . .
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148
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149
149
151
152
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157
157
157
159
161
163
165
169
171
180
183
186
Appendix
A The Console’s Friends
A.1 Directory Commands . . . . . . . . . . . .
A.1.1 Selecting a Drive . . . . . . . . . .
A.1.2 Listing the Content of a Directory .
A.1.3 Creating and Removing a Directory
A.1.4 Browsing through Directories . . .
A.2 File Commands . . . . . . . . . . . . . . .
A.3 Environment Commands . . . . . . . . . .
189
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191
196
196
196
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197
197
198
B Code::Blocks’s first Project
201
C Some Theory
C.1 Section Properties . . . . . . . . . . . . . . . . . . . . . . . .
C.1.1 The Area of a Profile Section . . . . . . . . . . . . . .
C.1.2 First Moments of an Area . . . . . . . . . . . . . . .
C.1.3 Second Moments of an Area . . . . . . . . . . . . . .
C.1.4 Center of Mass . . . . . . . . . . . . . . . . . . . . .
C.1.5 Moments of Inertia with Respect to the Center of Mass
C.1.6 Main Axis Transformation . . . . . . . . . . . . . . .
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D Conventions
213
D.1 The Java Code Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
E. Baeck
Part I
FORTRAN
1
1
Development Tools
1.1
The Development Toolchain
To develop a computer program there are three possible program types.
• Interpreted Programs
An interpreted program file is compiled, i.e. translated, into machine code at run time. That
means, that repeated statements are compiled not only ones. To execute a interpreted program1 the
source code is interpreted, i.e. compiled, line by line by an interpreter. A very simple interpreted
program is a batch statement in the console window. The Basic language originally was designed
as an interpreted language. The MS-Dos of the first years was shipping a Basic interpretor as
development tool. Today we know the Basic language as Visual Basic for Application mostly
from the MS software packages like MS Office.
• Compiled Programs
To create a compiled program, also called executable, there are some steps necessary. After
having created the source files with an editor each of this source files has to be compiled by
the so-called compiler into an object module. The object consists of binary native code, code
which can be understood by the processor of the destination platform. Within a second step all
object modules and the the used libraries are linked to an executable by the so-called linker. The
libraries, especially the system libraries, are used to access the system resources like keyboard,
screen and discs. This code is part of the develop system and can be used in an own application
by linking. If you are developing software for a windows system (MS-Window, X-Windows, etc.)
in an additional last step system resources are linked to the executable by an resource linkder.
Program languages which are used to build an native executable are for example FORTRAN, C,
C++2 .
• Programs running on virtual machines
Languages which are designed for bytecode are compiled in an neutral format. This format is not
directly running an the processor. The compiled module can be executed on a real processor using
a virtual machine, which translates the bytecode just in time before executing it. So bytecode may
1
An interpreted program often is called script.
The languages C and C++ are very important, because the operating systems Linux and Windows are written in C, new
parts of Windows are written in C++ and C# too
2
3
Page 4
Computer Languages for Engineering - SS 15
often be either directly executed on a virtual machine (i.e. interpreter), or it may be further compiled into machine code for better performance. Languages which are designed for the execution
of bytecode are Java, Smalltalk, Python, Forth, TCL and C#.
1.2
1.2.1
Some History
Motivation
To understand the importance of the development of the FORTRAN language, the code for the calculation
of the nth fibunacci number is given in machine and assembler code.
The fibunacci number are defined as follows.
fn = fn−1 + fn−2
for n > 2, with f0 = 1 and f1 = 1
(1.1)
The implementation of the calculation of the nth fibunacci numberis given below in machine code
1
2
3
4
8B542408
FA027706
B9010000
C84AEBF1
83FA0077 06B80000 0000C383
B8010000 00C353BB 01000000
008D0419 83FA0376 078BD98B
5BC3
The implementation of the calculation of the nth fibunacci numberis given below in x86 assembler.
1
2
3
4
5
6
fib:
mov edx, [esp+8]
cmp edx, 0
ja @f
mov eax, 0
ret
7
8
9
10
11
12
@@:
cmp edx, 2
ja @f
mov eax, 1
ret
13
14
15
16
17
@@:
push ebx
mov ebx, 1
mov ecx, 1
18
19
@@:
20
lea
cmp
jbe
mov
mov
dec
jmp @b
21
22
23
24
25
26
27
28
29
30
E. Baeck
@@:
pop ebx
ret
eax,
edx,
@f
ebx,
ecx,
edx
[ebx+ecx]
3
ecx
eax
1.2. SOME HISTORY
1.2.2
Page 5
FORTRAN’s History
The first compiler was written by Grace Hopper, in 1952, for the A-0 System language, which today has
no relevance any more.
The computer language FORTRAN (= FORmular TRANslator) was developed form IBM for the computer Type 704 in 1954-1957 (see figure 1.13 ) and was the first computer language which was able
to handle mathematical formulas in nearly mathematical notation. In the time before FORTRAN only
machine code or assembler was available. Therefore FORTRAN is a very important milestone in programming.
The computer Type 704 was able to perform 4000 integer multiplications per second. A modern computer is able to perform
some 100 millions of integer multiplications.
The 1st FORTRAN version was followed in 1958 by FORTRAN II. FORTRAN IV was published in 1962 and became
ANSI-standard as FORTRAN 66.
The next standardized version is called FORTRAN 77. Today
FORTRAN 77 is often used as computer language in engineering, especially in ad don software packages like ISML or NAG.
Figure 1.1: IBM Type 704 [1]
FORTRAN 90 was the next revision after FORTRAN 77. The concept of object orientated programming
(OOP) was introduced in the FORTRAN language as well as the usual more flexible free format. Furthermore dynamical memory management, build in matrix arithmetic and the possibility of recursive
functions were implemented.
With FORTRAN 95 the next revision was published. Obsolete constructs are removed and besides automatic deallocation of arrays which go out of scope some new key words are introduced.
With FORTRAN 2003 a better interoperability with the C programming language was introduced. A
better integration into the host operating system is given (access to command line arguments and environment variables).
The last revision is the revision FORTRAN 2008 which introduces Co-Arrays, a parallel processing
model and the data type BIT.
Since FORTRAN has been in use for more than fifty years, there is a vast body of FORTRAN in daily use
throughout the scientific and engineering communities. It is the primary language for some of the most
intensive supercomputing tasks, such as weather and climate modeling, computational fluid dynamics,
computational chemistry, computational economics, plant breeding and computational physics. Even
today, half a century later, many of the floating-point benchmarks to gauge the performance of new
computer processors are still written in FORTRAN (e.g., CFP2006, the floating-point component of the
SPEC CPU2006 benchmarks).
3
Note: The programmer sitting in front of his operator panel is not the author in his young days.
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1.3
Computer Languages for Engineering - SS 15
The Fixed FORTRAN Format and it’s Roots
The fixed FORTRAN format is a child of
the punching cards time. Each line of code
was punched onto one card. You had to
punch n cards for a source code with n lines
of code. To handle the cards in a batch, i.e.
to avoid chaos in the order, the cards were
numbered in the last 8 columns (see figure
1.2). Therefor in fixed FORTRAN format
Figure 1.2: IBM FORTRAN Punching Card
the last 8 columns of 80 available columns
are columns of comment. Their information is not considered in the compile step. The leading 5 columns are columns for label numbers and
must not used for statements. The column 6 is the column for the continuation line flag.
A card punch (see figure 1.3) such as the
IBM 3525 (not to be confused with keypunch), is an electronically mechanized
output device used to punch data into
punched cards. Sometimes combined with
card readers and other functions to form
multifunction machines, such as the IBM
2540 card reader-punch, such devices were
attached to a computer.
If you look at the properties of a console
window on WindowsXP, you will find a
buffer size per line for 80 characters as
Figure 1.3: IBM Card Punch
standard. The 80 character line length results from the format of a punch card with it’s 80 columns.
E. Baeck
1.4. SOME FREE FORTRAN TOOLS
1.4
Page 7
Some free FORTRAN Tools
Commercial FORTRAN compilers are often expensive and there for we try to find an open source development package for our lecture. Fortunately there are many FORTRAN development tools available for
free in the Internet some of them are discussed below. If you use one of this packages it is recommended
to update it from the original project site.
• Watcom Fortran 77
Open Watcom is a project of the open source community to maintain and enhance the Watcom
C, C++, and Fortran cross compilers and tools. An Open Source license from Sybase allows free
commercial and non-commercial use of Open Watcom. More information about Open Watcom’s
features, details about Open Watcom’s history and the supported platforms are given on the project
site http://www.openwatcom.org/index.php.
• MinGW Package
MinGW 4 provides a complete Open Source programming tool set which is suitable for the development of native MS-Windows applications, and which do not depend on any 3rd-party C-Runtime
DLLs (only the Microsoft C runtime, MSVCRT). More informations about MinGW are available
on the project page http://www.mingw.org/.
• G95 Package
G95 is based on the G77 of the MinGW package. G95 provides a FORTRAN compiler for the
versions 77, 90, 95 and 2003. The extension of source file selects the FORTRAN version. More
informations about G95 are available on the project page http://g95.org/.
• Code::Blocks
Code::Blocks provides a cross-platform IDE for Linux, Mac-OS and Windows supporting a width
range of available compilers and debuggers. More informations about Code::Blocks are available
on the project site http://www.codeblocks.org.
1.5
The Open Watcom Development Suite
The first FORTRAN 77 compiler of the Watcom Suite was published in 1985 for the IBM PC. Since 2003
the FORTRAN 77 and the C/C++ compilers are available as an open source project under Open Watcom.
The Open Watcom IDE5 consists of the following three main modules.
• IDE Project Manager
Within the Project Manager application projects are initialized. The application type is set. Source
files are added to the project. Tools are started out of the manager application.
• Editor
The Editor can be used to write source files for a project.
4
5
Minimalist GNU for Windows package is a porting of the LINUX development tools.
IDE means Integrated Development Environment.
9.6.2015
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Computer Languages for Engineering - SS 15
• Debugger
To check an application the executable can be started within a debugger program. The common
features of a debugger are supported.
The disadvantage of the Open Watcom suite is, that the three regarded components are not integrated
within one application. Figure 1.4 shows the one and only source file of the famous hello world appliaction. Double clicking the source file in the manager will start the editor application (see figure 1.4).
Figure 1.4: Watcom-IDE-Manager
If standard FORTRAN 77 is used, formating could be a problem, because Open Watcom6 does not support
any formating highlightings. So we use a formating comment, which marks the first 7 columns of source
line. You have to be careful too with the comment columns starting with column 73. This comment
columns also are not marked within the coding.
If the program sources are compiled, the linker creates the executable linking the object files7 with the
libraries. To check the executable the debugger can be started from the Watcom-IDE-Manager. Figure
1.6 shows a debugger session to check our famous startup example hello world.
6
7
Here we talk about the version 1.8.
Object files are compiled source files, created by the compiler.
E. Baeck
1.5. THE OPEN WATCOM DEVELOPMENT SUITE
Page 9
Figure 1.5: Watcom-Editor Session to write the hello world
Figure 1.6: Watcom-Debugger Session to check the hello world
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1.6
Computer Languages for Engineering - SS 15
The MinGW Package
The MinGW package is a porting of the development tools which are by standard available on the
Linux/Unix platform. It’s no longer necessary to use a Linux emulating layer like cygwin8 . MinGW
contents above all compilers, a linker, a debugger and a make utility. There is no IDE available within
the MinGW package. That means if you want to use the pure MinGW package to develop applications
you have to start the tool-chain manually. Because some of the tools are spawning other tools as helper
application you have setup the correct path access to the MinGW binary folder.
If we want to use the MinGW tools from the console window, we have to setup the correct path access.
This is shown in figure 1.7. The MinGW binary folder is chained to the actual search path. There are
a lot of compiler options which are supported by the MinGW compilers. Unfortunately there is no help
page starting the compiler with the usual help option. So you have to read the manual or download some
helping informations.
Figure 1.7: Setup MinGW Path Access
If we want to compile FORTRAN sources, we can use the G77 or the GFortran compiler. The GFortran
compiler is the successor of the G77 and supports also the newer FORTRAN languages, FORTRAN 90,
FORTRAN 95 and FORTRAN 2003 and parts of FORTRAN 2008.
1.6.1
Running Compilers of the MinGW Package
Figure 1.8 shows a simple compiler call of the GFortran compiler, which compiles the FORTRAN source
file and links it with the used libraries.
Figure 1.8: Create an Executable with one Compiler Call
After having called the compiler, we check the existents of the executable with a dir call. Then the
8
More information about cygwin is available on the project site http://www.cygwin.com/.
E. Baeck
1.6. THE MINGW PACKAGE
Page 11
executable is called and prints it’s legendary hello world to the screen. The most simple call of the
compiler is shown in figure 1.8. The file hello.f is selected by the input filter *.f. The output file is set by
the option -o.
1.6.2
Installing the MinGW Package
If you have an archive file of the MinGW package you can simple extract the package files into a folder.
It’s highly recommended to select a folder name, which is free from blanks. A blank usually is used
to separate command line parameters, which are passed to programs to control their run-time behavior.
Therefore blanks would break path names, if the module call is not set into double quotes.
A second kind of installation is given by the MinGW Installation Manager, which you get, if you download newer installations. The installation manager comes with a dialog, where you should select the kind
of installation you want (see figure 1.9).
For our requirements we should install the following packages from the section Basic Setup.
• minqw-32-base, the basic package is used, if we use the code::blocks IDE.
• minqw-32-gcc-fortran, this is used for the Fortran part of the lecture.
• minqw-32-gcc-g++, this is used for the C++ part of the lecture.
You click them right and mark them for installation. After have marked all items to install, you start the
function Apply Changes from the menu Installation. Using the MinGW Intallation Manager provides
the advantage that we can easily select only the packages we really need. They only will be installed and
updated if some newer versions are available.
Figure 1.9: MinGW Installation Manager
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1.7
Computer Languages for Engineering - SS 15
The G95 Compiler
Alternative to the GFortran compiler you can use the G95 compiler, which provides nearly the same
features as the GFortran compiler.
G95 determines how an input file should be compiled based on its extension. Allowable file name
extensions for Fortran source files are limited to .f, .F, .for, .FOR, .f90, .F90, .f95, .F95, .f03 and .F03.
The filename extension determines whether Fortran sources are to be treated as fixed form, or free format.
Files ending in .f, .F, .for, and .FOR are assumed to be fixed form source compatible with old f77 files.
Files ending in .f90, .F90, .f95, .F95, .f03 and .F03 are assumed to be free source form. Files ending in
uppercase letters are pre-processed with the C preprocessor by default, files ending in lowercase letters
are not pre-processed by default. The basic options for compiling Fortran sources with g95 are:
-c Compile only, do not run the linker.
-v Show the actual programs invoked by g95 and their arguments. Particularly useful for tracking
path problems.
-o Specify the name of the output file, either an object file or the executable. An .exe extension is
automatically added on Windows systems. If no output file is specified, the default output file is
named a.out on unix, or a.exe on Windows systems.
Informations about the compiler package are available on the project site http://g95.org.
1.8
The Code::Blocks IDE
Code::Blocks was developed as a free C++ cross platform IDE. A FORTRAN version of Code::Blocks
was initiated by Darius Markauskas with his project site http://darmar.vgtu.lt/. In 2014 Markauskas’s
FORTRAN plugins for the Code::Blocks IDE were implemented and shipped with the standard version
of Code::Blocks, which is version 13.13. So this is the version ore a junger version we should use to
work on our FORTRAN and C++ projects.
Code::Blocks is not written for a specific development package. The IDE provides a very general interface which is able to support a wide variety of compilers.
Figure 1.10 shows the starting page of Code::Blocks. You can create a new project or can open an already
existing project. You can also select one project from the recent list.
To configure the compiler settings the menu command Settings/Compiler and debugger... should be
executed. The first line selects the compiler for the file respectively the project. The tab compiler flags
shows all supported compiler flags. Within the tab Toolchain executable the compiler, linker and make
utility executable are set.
Figure 1.12 shows the hello world FORTRAN source file in an editor window. The coloring supports
the FORTRAN syntax. There are FORTRAN key-word lists for a fast completion of key words writing
source files. Within the left browser window all files of the project are listed in tree mode. Within the right
window you find the editor window and below the editor window the output section with information
concerning the build tool chain execution.
E. Baeck
1.8. THE CODE::BLOCKS IDE
Page 13
Figure 1.10: Starting Code::Blocks
To check the execution of an application, a breakpoint is set on the first source line 1.13. The debugging
session is started with the menu command Debug/Start or with the F8 key. The execution is stopped at
the first breakpoint, that is the second line of code. The yellow arrow shows the execution position of the
program.
The execution of the compiled and linked application is started with the menu command Build/Run or
with the Ctrl-F10 key (see figure 1.14). The program is executed within a console window and stops at
the end of execution. The window will be closed with any key.
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Computer Languages for Engineering - SS 15
Figure 1.11: Setup the Projects Compiler Settings
Figure 1.12: Code::Blocks Editor with hello world Source
E. Baeck
1.8. THE CODE::BLOCKS IDE
Page 15
Figure 1.13: Debugging the hello world Application
Figure 1.14: Run the hello world Application
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E. Baeck
Computer Languages for Engineering - SS 15
2
FORTRAN Basics
The description of FORTRAN 77 can be taken from the WATCOM FORTRAN Language Reference[2].
A detailed description of all statements is given there. The description of G95 and GFortran is available
on the info.server1 with the documents G95Manual.pdf and GFortran.pdf.
2.1
Structure of a FORTRAN Program
A FORTRAN program consists of a mixture of executable and non executable statements, which must
occur in a specific order. So the FORTRAN program is divided into three sections.
• The Declaration Section
The first section is the declaration section with it’s non executable statements of declaration. Here
all variables and constants or parameters are declared. Variables are optional initialized.
• The Execution Section
The second section is the execution section with it’s executable statements. This is the mostly the
largest section, because this section contains all the statements, which describe what’s to do. And
mostly there is a lot to do.
• The Termination Section
The termination section consists of statements, which stop the execution of the program and telling
the compiler, that the program is complete.
All FORTRAN statements should satisfy this requirements. If statements are found in the wrong section,
the compiler stops compiling and the executable will not be build.
1
See http://info.statik.uni-due.de module Lehre/CM-CLFE. Actual versions are available on the project’s site.
17
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2.2
Computer Languages for Engineering - SS 15
Format and Comments
Comment lines are denoted by placing a ”C” or ”*” in column one of the line. Blank lines are treated
as comment lines too. Comment lines may be placed anywhere in the program source (i.e., they may
appear before a FORTRAN statement, they may be intermingled with continuation lines, or they may
appear after a statement). There is no restriction on the number of comment lines. Comment lines may
contain any characters from the processor character set.
Watcom FORTRAN 77 and the standardized with FORTRAN 90 allow end-of-line comments. If a ”!”
character appears in column 1 or anywhere in the statement portion of a source line, the remainder of
that line is treated as a comment unless the ”!” appears inside quotation marks or in column 6, if it’s a
fixed format file.
The FORTRAN 77 has by default the format shown in table 2.1.
Columns Remarks
01 - 05
Column for label numbers (1 to 99999). Column 1 is also used to set comment lines.
06
Column 6 marks a continuation line for the previous line. The mark character can be
every character of the FORTRAN character set but not zero or a blank. By default
there are up to 19 continuation lines available.
07 - 72
Column for statements.
73 - 80
Comment Column. And are used in the days of the punch cards as card number field.
Table 2.1: Fixed Fortran Format
Some source of errors related to the fixed format are discussed below.
• You should check the length of the code line. If the code line runs into the numbering field, i.e. into
the columns 73 to 80, the code will be truncated and this can produce a very subtle error situation.
• If the code is shifted into the header section of a line, i.e. into the columns 1 to 6, the code also
will be truncated, but it’s more probable, that the compiler will detect this error.
In free format FORTRAN which is introduced by standard with the FORTRAN 90 the sources are no
more restricted by some fixed column positions. So the ”C” - comment character is no more available
and the continuation column as well. A comment is always starting with the exclamation mark ”!” and
a continuation line is introduced by the continuation character ”&” of the previous line which should be
continued.
The following example shows an implementation of the helloworld application which only will write it’s
hello to the screen in a fixed formatted coding. The first line is a comment line, note the ”c” character in
the first column. The third line is a continuation line, note the used continuation column 6. So the ”Hello
again!” is printed directly behind the ”Hello World”. The last line closes the program code.
Listing 2.1: Print one Hello
1
2
3
c234567 this is a comment
write ( * , * ) ’Hello World!’
end
E. Baeck
2.3. CHARACTER SET
Page 19
Listing 2.2: Print a second Hello
1
2
3
4
c234567 this is a comment
write ( * , * ) ’Hello World’,
&
’ Hello again!’
end
The next implementation of the Hello Word application uses the FORTRAN 90 free format.
Listing 2.3: Print two Hellos with 90
1
2
3
4
!234567 this is a comment
write ( * , * ) ’Hello World’, &
! this is a 2nd comment
’ Hello Again to 90!’
end
You see within the first line of code the ”c” character was substituted by an exclamation mark ”!”. All
code is shifted to the 1st column. A line end comment is used in the 2nd line using the exclamation mark
”!”. Right before the line end comment the line continuation character ”&” is set. The code position in
the 3rd line is arbitrary. The end statement again closes the code.
2.3
Character Set
The character set of FORTRAN 77 is the following.2
• upper case letter A - Z
• 10 digits 0 - 9
• the 12 special characters: + - * / = ( ) : , . ’ $ and the space character.
The character set of FORTRAN 90/95 is the following.3
• upper case letter A - Z
• lower case letter a -z
• 10 digits 0 - 9
• Miscellaneous common symbols, such as + - * / = ( ) : , . ’ $ ” { } [ ] !
• and any special letter of symbol required by the language, such as a¨ , o¨ , u¨ .
2
Modern FORTRAN 77 compiler support also lower case letters.
The ASCII coding system which is used in computing stores one character in one byte. So ASCII is able to code maximal
256 characters. To support languages with more then 256 characters the Unicode coding, a multibyte coding, was developed,
which is also supported by the actual FORTRAN 90/95.
3
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2.4
Computer Languages for Engineering - SS 15
Available Data Formats
The types of data format available on a computer are depending on the hardware. General there are
some integer formats for integer values available. Standard is a short type with 2 bytes and a long type
with 4 bytes. With the development of the 64 bit operating systems also 8 byte integers are available.
Especially this is necessary to access to large files with a size larger then 2 GB or to be able to handle
memory blocks with a size above 2 GB. On Windows32 with some provider depending tricks this was
already possible, but according to a standard it was not till 64 bit systems are available.
For floats general two formats are available, a 4 byte real and a 8 byte real. In the case of complex
calculations as solving a linear equation system it is strongly recommended to use the 8 byte float.
Within the following table data types are listed with there specific properties.
Type
Size
Restriction
INTEGER
2 Bytes
Range −215 · · · 215 − 1 = 32767
INTEGER
4 Bytes
Range −231 · · · 231 − 1 = 2147483647 ≈ 2.14 · 109
INTEGER
8 Bytes
Range −263 · · · 263 − 1 = 9, 22 · 1018
REAL
4 Bytes
Exponent range −38 · · · 38, 7 digits precision
REAL
8 Bytes
Exponent range −308 · · · 308, 15 digits precision
CHARACTER 1 Byte
one byte character
Table 2.2: General Data Types with their Restrictions
2.4.1
Negative Numbers
Negative numbers can be represented by complements of the positive number. Each digit of then positive number and it’s complement gives the maximum value of the digit. This would be 1 within the
binary system. Table 2.3shows the scheme for the construction of a negative number for 7 using the
b-complement.
Comments
0000|01112 0716 , the positive number has the value 7
1111|10002 F 816 , number complement of 7
12 b-complement = complement +1, F 916
+
1111|10012 b-complement or negative number
Check of the b-complement to be the searched negative number
0000|01112 positive number
+
1111|10012 b-complement or negative number
1|0000|00002 The overflowing bit will be truncated and therefor the sum vanishes.
Table 2.3: Construction of a negative Number
E. Baeck
2.4. AVAILABLE DATA FORMATS
2.4.2
Page 21
Endianness
A data type commonly consists of more then one byte, so the order of storing this bytes in memory
becomes important. There is not only one order which is used to store this bytes. The terms endian and
endianness, refer to how this bytes are stored in memory.
Big-endian systems are systems in which the most significant byte is stored in the smallest address given
and the least significant byte is stored in the largest address. This is shown in right part of figure 2.1.
In contrast to this in the Little Endian order, the most significant byte is stored at the largest address
and the least significant byte is stored in the smallest address. This is shown in left part of figure 2.1.
Big Endian is like a German time stamp: hour-minute-second and Little Endian is like a German date:
day-month-year.
Figure 2.1: Little and Big Endian
The Little Endian was introduced by Intel’s x86 processors. Therefor this Endian is very popular on
all the Intel related computers. On the other hand the Big Endian was introduced by IBM processor
architecture and is also used in the network like the IPv6.
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2.5
Computer Languages for Engineering - SS 15
Data Types, Variables and Constants
Within the following section we will discuss the available data types for the variables of FORTRAN 77
and FORTRAN 90 and above. We will discuss how to declare and initialize variables and constants.
2.5.1
Data Types of FORTRAN 77
Table 2.4 shows the available data types of FORTRAN 77 under standard.
Type
Comment
Example
INTEGER
Integer number
15, -100, 2500
REAL
Floatingpoint number, single precision 3.1415, -5.5, .7E3, 12.5E-5
DOUBLE PRECISION Floatingpoint number, double preci- 3.1415D0, -5.5D0, .7D3, 12.5D-5
sion
COMPLEX
Complex numbers, (two REAL num- (3.1415, -5.5), (1.4, 7.1E4)
bers)
LOGICAL
Logical values
.TRUE., .FALSE.
Table 2.4: Fortran 77 Data Types
Because the standard FORTRAN 77 only supports this few data types, the de facto standard of the
FORTRAN 77 implementation supports some data types more, which are defined by the number of used
bytes too.
INTEGER*1, LOGICAL*1
INTEGER*2, LOGICAL*2
INTEGER*4, REAL*4, LOGICAL*4, (default on 32 bit platforms)
INTEGER*8
REAL*8 (on 32 bit platforms the same as DOUBLE PRECISION)
COMPLEX*16 (complex numbers with two DOUBLE-PRECISION numbers)
1 byte
2 bytes
4 bytes
8 bytes
8 bytes
16 bytes
In FORTRAN77 the data type for characters or strings are the following.
• A character like ’A’ can be stored in the data type CHARACTER or CHARACTER*1.
• A string of n characters like ’The End!’ can be stored in the data type CHARACTER*n.
E. Baeck
2.5. DATA TYPES, VARIABLES AND CONSTANTS
2.5.2
Page 23
Data Types, Constants and KIND in FORTRAN 90
Table 2.5 shows the available intrinsic buildin data types of FORTRAN 90 under standard.
Type
Comment
Example
INTEGER
Integer number
15, -100, 2500
REAL
Floatingpoint number, single precision
3.1415, -5.5, .7E3, 12.5E-5
COMPLEX
Complex numbers, (two REAL numbers)
(3.1415, -5.5), (1.4, 7.1E4)
LOGICAL
Logical values
.TRUE., .FALSE.
CHARACTER String variable with given length
’This is a string! Hey!’
Table 2.5: Fortran 90 Data Types
Because there are de facto so many special data types in FORTRAN 90 a new concept was introduced
to setup the desired byte length of a data type with the so called KIND number. The KIND number is
depended of the implementation of the FORTRAN 90, that means that the byte length is not generally
known, if the KIND number is given. The KIND number of a given value can be evaluated by the function
KIND.
The data type of a constant in FORTRAN90 can be specified by the extension [number of bytes]. The
number of bytes in general are 1,2, 4 and 8 on a 64 bit platform. So we can check this with the following
code snippet.
Listing 2.4: Constants and it’s Check with KIND
1
2
3
4
5
6
7
! check the
write(*,’("
write(*,’("
write(*,’("
write(*,’("
write(*,’("
write(*,’("
kind of constants created with a literal
constant 2_1 kind:",i2)’) kind(2_1)
constant 2_2 kind:",i2)’) kind(2_2)
constant 2_4 kind:",i2)’) kind(2_4)
constant 2_8 kind:",i2)’) kind(2_8)
constant 2._4 kind:",i2)’) kind(2._4)
constant 2._8 kind:",i2)’) kind(2._8)
The code in listing 2.4 will print the following output.
1
2
3
4
5
6
constant
constant
constant
constant
constant
constant
2_1
2_2
2_4
2_8
2._4
2._8
kind:
kind:
kind:
kind:
kind:
kind:
1
2
4
8
4
8
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The following FORTRAN 90 code evaluates the KIND number of 0.0 and 0.0d0, i.e. of single and double
precision for the gfortran compiler on 32 bit Windows XP.4
Listing 2.5: Evaluating the Kind Number 90
1
2
3
4
5
6
7
! Program to evaluate the kind number of
! - single precision (REAL)
! - double precision (DOUBLE PRECISION)
program kinds
write( * ,’(" Kind of single precision:",i2)’) kind(0.0)
write( * ,’(" Kind of double precision:",i2)’) kind(0.0d0)
end program
! it’s single
! it’s double
Figure 2.2 shows the compile and execution step of the Kind application. And you can see from the
output, that single precision gives a KIND number of 4, double precision a KIND number of 8 like real*4
and real*8 in the case FORTRAN 77 standard extension (see above).
Figure 2.2: Evaluating the Kind Numbers
Constant values can also be set in binary, octal and hexadecimal number system. This we can do using
the prefixes b, o and x and appending the number with the universal kind of number representation.
Listing 2.6: Constants in Some Number Systems
1
2
3
4
c234567
integer i_b /b’1101’/
integer i_o /o’12’/
integer i_x /x’ff’/
The code in listing 2.6 assigns the value 13 in binary, the number 10 in octal and the number 255 in
hexadecimal and will print the following output. We can also see, how a variable in old FORTRAN can
be initialized. The initialization value is put in between two slashes.
1
2
3
4
i_b = 13
i_o = 10
i_x = 255
You see, that in FORTRAN 90 a program starts with the key word program <program name> and ends with end program.
E. Baeck
2.5. DATA TYPES, VARIABLES AND CONSTANTS
2.5.3
Page 25
Representation of a Float Number
Float number can be described by the following equation.
x = s · m · be
s
b
e
m
where
(2.1)
is one bit for the sign
is the base (floats according IEEE 754 use a base of 2)
is the exponent (can overflow)
is the mantissa
Float numbers are stored according to the IEEE Standard for Floating-Point Arithmetic (IEEE 754). This
technical standard for floating-point computation was established in 1985 by the Institute of Electrical
and Electronics Engineers (IEEE).
The representation of some floats are given in the table below5 .
Name
Common name
binary16
Half precision
2
binary32
Single precision
binary64
Double precision
binary128 Quadruple precision
Base Digits
E min
E max
Decimal digits Decimal E max
10+1
−14
+15
3.31
4.51
2
23+1
−126
+127
7.22
38.23
2
52+1
−1022
+1023
15.95
307.95
2
112+1 −16382 +16383
34.02
4931.77
The number of decimal digits, the approximate precision in decimal is given by digits · log10 (base).
The maximal decimal exponent is given by Emax · log10 (base).
Figure 2.3 shows the usage of the bits in a Single Precision data type according to the IEEE-754. The
sign V is stored in the highest bit. The next 8 lower bits are used for the exponent and the rest is used for
the mantissa.
Figure 2.3: Single Precision Float
2.5.4
Data Ranges
If you select a data type for an implementation, then you should know the available data range of that
data type. The data range can be depended of the installed operating system and from the processor
himself. So an integer of the Windows3 has half the range as the integer from WindowsXP, if the range
is not explicit set using the * version of the data type. If a not properly data type is selected, then the
code will be inefficient if the data range is larger than needed. If the data range is smaller then needed,
the code will not run properly because the data will go out of range, which will result an overflow with
all it’s unpredictable consequences6 .
5
E is used for exponent.
If you will implement a complex calculation algorithm with a lot of operations like the triangulation of a matrix, then you
should use the double precision data types, to avoid a losses of information.)
6
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The following table shows the ranges of the FORTRAN 77 data types.
Daten Type
Bytes Data Range
INTEGER*1
1
−128 · · · + 127
INTEGER*2
2
−32768 bis +32767 = 215 − 1
INTEGER*4
4
−231 bis +231 − 1 ≈ 2 · 109
REAL*4
4
±10±38 , precision of 7 digits.
REAL*8
8
±10±308 , precision of 16 digits.
2.5.5
Declaration of Variables and Constants in FORTRAN 77
With an explicit declaration the data type of variables and parameter (constants) is set. The declarations
should be made in the header section of a program or a subprogram, which is the section before the first
executable statement is made (like an assignment or a write statement).
The declaration is given by: Data Type [List of Variables]
The list of variables contents one or more variable names, which are separated by commas.
The following example shows the declaration of the variables V1,V2 and V3, which are declared as
REAL*4. The variables I1,I2 and I3 are declared as INTEGER*2.
Listing 2.7: Declaration in 66/77
1
2
3
c234567
REAL*4
V1,V2,V3
INTEGER*2 I1,I2,I3
Constants are called PARAMETER in FORTRAN 77. A constant is declared by an additional PARAMETER statement. The PARAMETER defines the value of the constant. This value is set by compilation
and can not changed at run time (therefor it’s called a constant).
The parameter is set by: PARAMETER (name = value)
The following example declares three real variables and three integer parameters.
Listing 2.8: Declaration and Parameters in 66/77
1
2
3
4
5
6
c234567
REAL*4
INTEGER*2
PARAMETER
PARAMETER
PARAMETER
V1,V2,V3
I1,I2,I3
(I1 = 4)
(I2 = 8)
(I3 = I1+I2)
Within the declaration section of a program variable can be initialized with the statement DATA, which
follows the declaration of the variables to be initialized.
Listing 2.9: Declaration and Initialization in 66/77
1
2
3
4
c234567
REAL*4
V1,V2,V3
INTEGER*2 I1,I2,I3
DATA
I1 /4/, I2 /8/, I3 /12/
E. Baeck
2.5. DATA TYPES, VARIABLES AND CONSTANTS
2.5.6
Page 27
Declaration of Variables and Constants in FORTRAN 90
The declaration of variables in FORTRAN 90 is slightly different from the FORTRAN 77 format and is
given by the following statement.
Data Type :: List of Variables
In the following example the three integer variables month, day and year are declared. In the second
line the real variable seconds is declared. The character variables which should store some strings
should be declared with a properly length. The first declaration shows the declaration with an explicit
length parameter, the second declaration uses only the value of the length.
Listing 2.10: Declaration in 90++
1
2
3
4
INTEGER :: day, month, year
REAL :: seconds
CHARACTER(len = 10) :: prename
CHARACTER(20) :: famname
In the following example you can see how to initialize the just declared variables. This is like declaration
and initialization in the language C simply within one step. So the obsolete statement DATA is no longer
needed and can be canceled from modern FOTRAN 90 sources (see also section 2.5.5).
Listing 2.11: Declaration and Initialization in 90++
1
2
3
4
INTEGER :: day = 16, month = 10 , year = 2010
REAL :: seconds = 10.5
CHARACTER(len = 10) :: prename = ’Ernst’
CHARACTER(20) :: famname = ’Baeck’
The following example shows, how to declare parameters (constants). You see the code is very simular
compared with the previous code. Only the attribut PARAMETER was added. Within the first code the
content of the variables can be changed by an assignment. Within the second code, we have declared
parameters and the content of this parameters can not be changed, because a parameter is fixed. So you
see, that the FORTRAN 77 statement PARAMETER, now obsolete, is also no longer necessary and can
be deleted from modern FORTRAN 90 code (see also section 2.5.5).
Listing 2.12: Declaration and Parameters in 90++
1
2
3
4
2.5.7
INTEGER, PARAMETER :: day = 16, month = 10 , year = 2010
REAL, PARAMETER :: seconds = 10.5
CHARACTER(len = 10), PARAMETER :: prename = ’Ernst’
CHARACTER(20), PARAMETER :: famname = ’Baeck’
Complex Data
As we already have seen Fortran provides in contrast to many languages a complex data type. The
complex data type is like a vector with two components, the real part and the imaginary part. The parts
itself consists of Single Precision floats in the case of COMPLEX*8 and of Double Presision floats in the
case of COMPLEX*16.
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Computer Languages for Engineering - SS 15
The following code snipped 2.13 shows how to declare a complex variable, initialize it and do some basic
calculations. It is shown too, how to get a square root of an arbitrary complex number, which can also
be a negative real. Especially this is used in the example to solve the quadratic equation using complex
variables. The programs output is shown in figure 2.4. We see in the first step the square root of −1 is
calculated giving the imaginary unit i.
Listing 2.13: Playing with Some Complex Numbers
1
2
program complexNumbers
implicit none
3
4
5
6
complex(8) :: c1,c2,c3
c1 = (-1., 0.)
write (*,*) "c1 = ",c1
! here we use the double precision (kind 8)
c2 = cdsqrt(c1)
write (*,*) "c2 = ",c2
! cd: is Complex Double precision
c3 = c1 + c2
write (*,*) "c3 = ",c3
! add two complex numbers
c3 = cmplx(1.2,3.4)
write (*,*) "c3 = ",c3
! create a new complex value with the cmplx function
c3 = c3/(-c2)
write (*,*) "c3 = ",c3
! division
c3 = c3/2. +1
write (*,*) "c3 = ",c3
! division and subtraction
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
end program
Figure 2.4: Console Oupt of the Complex Data Example
E. Baeck
2.6. OPERATORS
2.6
Page 29
Operators
Fortran offers a set of operators, which are offered from the most computer languages. Fortran uses
the same precedence as we know form the mathematics. The power operation has the strongest binding
followed by the point operators (products and divisions) followed by the line operators (plus and minus).
Unary operators will always be applied first. To change the standard precedence of the operators we use
like in mathematics parenthesis to dictate the way a formula should be evaluated.
2.6.1
Unary Operators
Unary operators are working only on one value, therefor unary. In all Fortran dialects there are the
following unary operators available.
Operator Comment
2.6.2
Example
+
plus operator
-
minus operator a = 2 >>> x = -a >>> -2
.not.
logical inverse a = .false. >>> x = .not.a >>> .true.
a = 2 >>> x = +a >>> +2
Arithmetic Operators
Fortran offers the following arithmetic operators. You should be careful with the usage of data types
especially within divisions. If you use integers, the result generally will be truncated.
The following operators are available in all Fortran dialects.
Operator Comment
Example
+
sum operator
x = 2+3 >>> 5
-
subtraction operator
x = 4-2 >>> 2
*
product operator
x = 2*4 >>> 8
/
division operator
x = 9/2 >>> 4
x = 9./2. >>> 4.5
**
power operator
//
concatenate of strings x = "hello"//"world" >>> "hello world"
x = a**2
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2.6.3
Computer Languages for Engineering - SS 15
Comparison Operators
Boolean operators are used to branch and to make decisions. The comparing operators of Fortran 90 are
now nearly identical to the C comparing operators.
The following operators are available in all Fortran dialects.
Operator Comment
Example
.lt.
less than
x = 23 .lt. 13 >>>
.false.
.le.
less equal
x = 23 .le. 23 >>>
.true.
.gt.
greater
x = 23 .gt. 13 >>>
.true.
.ge.
left shift of bits x = 23 .ge. 23 >>>
.true.
.eq.
equal
x = 23 .eq. 23 >>>
.true.
.ne.
not equal
x = 23 .ne. 13 >>>
.false.
Within Fortran 90 there also the following C like comparing operators available.
Operator Comment
Example
<
less than
x = 23 <
<=
less equal
x = 23 <= 23 >>>
.true.
>
greater
x = 23 >
13 >>>
.true.
>=
left shift of bits x = 23 >= 23 >>>
.true.
==
equal
x = 23 == 23 >>>
.true.
/=
non equal
x = 23 /= 23 >>>
.false.
13 >>>
.false.
The result of a boolean expression like above are the boolean values .false. or .true..
E. Baeck
2.6. OPERATORS
Page 31
To combine comparing expressions the following logical operators can be used.78 This operators are
available in all FORTRAN dialects. There are no C-like boolean operators available of this type.
Operator Comment
Example
.and.
logical and x = 1 .lt. 2 .and. 2 .lt. 3 >>>
.true.
.or.
logical or
x = 1 .lt. 2 .or.
.true.
.equ.
logical or
x = .true. >>> y = .false. >>> x .eqv. y
>>>
.false.
x = .true. >>> y = .false. >>> x .neqv. y
>>>
.true.
.nequ. logical or
.not.
2 .gr. 3 >>>
logical not x = .not. (1 .lt. 2)
>>>
.false.
The truth table for the AND operator ∧ is given as follows.
.true. ∧ .true. = .true.
(2.2)
.true. ∧ .false. = .false.
.false. ∧ .true. = .false.
.false. ∧ .false. = .false.
The truth table for the OR operator ∨ is given as follows.
.true. ∨ .true. = .true.
(2.3)
.true. ∨ .false. = .true.
.false. ∨ .true. = .true.
.false. ∨ .false. = .false.
The precedence of the operators, i.e the order of evaluation is given in the following list.
1
2
3
4
5
6
7
8
9
10
highest precedence
|
|
|
|
|
|
|
V
highest precedence
**
*
+
+
//
.EQ.
.NOT.
.AND.
.OR.
.EQV.
/
-
unary operators
.NE.
.LT.
.LE.
.GT.
.GE.
.NEQV.
7
To make expressions clear parenthesis should be used. A term within a parenthesis is evaluated first and it’s result then is
used in further evaluations outside the parenthesis. With parenthesis the order of the evaluation can be set.
8
The logical operator .NEQV. implements the exclusive OR.
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Computer Languages for Engineering - SS 15
File IO, Screen and Keyboard
To communicate with the program the two statements read and write are necessary. In the most simple
case we read the input data from the keyboard and write the output data into a console window. A simple
output gives us the example helloworld, see section 2.2.
2.7.1
Open a File
The open statement assigns a file name to a channel number. Every read or write access to this file uses
this channel number. An open statement also has to set up the access type with the status parameter.
The opening of a file should be checked by the iostat parameter.
Some status values of the open statement are discussed in the table below. In Fortran77 only ’new’
and ’old’ are available.
status
Comment
’old’
The file must exist
’new’
A new file is created. No file with this name must exist.
’replace’ A new file is created. No matter whether there is an old file or
not.
’scratch’ A temporary file is created, a file name is not needed. if the file is
closed, the file is automatically removed
’unknown’ The same as ’replace’. It’s a pre Fortran90 statement and
should be replaced by ’replace’
The access type can be specified with the ’action’ parameter. The available values are discussed in
the table below. This is only available in Fortran90.
action
Comment
’read’
The file is opened only for read access.
’write’
The file is opened only for write access.
’readwrite’ This ’action’ is set if the parameter is not given. The file is
opened for reading and writing.
With the parameter ’position’ the write position can be specified. By default the write position of a
text file is set to the beginning of the file. Sometimes it is needed to append information to a text file, for
example, if data should be written into a log file.
position
Comment
’append’ The file is opened and the write position is set to the file’s end.
In example 2.14 shows a snipped to open an existing file. If the file is not available or an open error
occur, the error handler will set the iostat variable to a value no equal zero. In this case the program will
stop.
E. Baeck
2.7. FILE IO, SCREEN AND KEYBOARD
Page 33
Listing 2.14: Open a file in 90++ with error Handler
1
2
3
4
5
2.7.2
open(ioin,file=infile,status=’old’,iostat=ioerr)
if (ioerr /= 0) then
write(*,*) "error: file ’",infile(1:len_trim(infile)),"’ not found."
stop
endif
Writing Texts, write Statement
The write statement has two parameters and a data list.
1
WRITE (<parameter1>,<parameter2>) <data list>
Parameter 1 sets up the output channel. If we use the value *, the output is written into the console. If
we use an integer number, we have to open a channel before for writing and assign this channel with the
desired channel number. The following example shows the usage of the console window and the output
into a used channel.
1
2
write ( *,*) ’Hallo my Channel’
write (10,*) ’Hallo Channel 10’
! output into the console
! output into channel 10
Parameter 2 sets up the output format. If we use the value *, a standard format is used. Strings are
written in total length and values, integer or floats, are written with full precision.
In example 2.15 we see, how to open a new file and write some formated data into it. The file will be
created, if not existing, in the current folder, because we have not specified an path.
Listing 2.15: Open a file and write some data
1
2
3
4
open(10,file="MyFile.txt",status=’replace’)
write(10,100) "Let’s write the number",10," into a file!"
100 format(a,i3,a)
close(10)
If we opne the file MyFile.txt, we will see the following content.
1
Let’s write the number 10 into a file!
Further details to format types are found int the next section.
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2.7.3
Computer Languages for Engineering - SS 15
Formatting, FORMAT Statement
If data should be formatted, we can use the format statement or we can use the parameter of the format
statement as string as parameter 2 of the write statement. The general form of an output format is
[m]Tw[.n].
1. Format Type T
• I, integer decimal format.
• Z, integer hexadecimal format.
• O, integer octal format.
• B, integer binary format.
• F, float format with fixed decimal point.
• E, float format with exponential representation, single precision.
• D, float format with exponential representation, double precision.
• A, text format, the with of the format is optional.
• X, output of spaces
• /, a new line, linebreak
2. repeat factor m
3. width of the output field w
4. number of significant digits n within float formatting.
If n is used in integer formattings, the leading blanks are filled with zeros.
Formats can also be iterated by iteration factors. If more complex formats should be iterated, the format
block must be bracketed by round parentheses. Within the following example the output of 3 variable
values a, b and c should be written. We use one format with an iteration of 3. The format starts with
2 blanks (2x). Then a text will be written, (a format) and at the end the value of the variable should
be written using a fixed float format (f). The output should have a width of 10 with 2 digits after the
decimal point.
Listing 2.16: Writing some formatted Values to the Screen in F77
1
2
3
4
c
W| 1
2
3
4
5
6
7
c23456789012345678901234567890123456789012345678901234567890123456789012
write(*,8000) ’a=’,a,’b=’,b,’c=’,c
8000 format(3(2x,a,f10.2))
E. Baeck
2.7. FILE IO, SCREEN AND KEYBOARD
2.7.4
Page 35
Read from Keyboard or File
The read statement is similar to the write statement. We simply exchange source and destination.
The first parameter of the read statement passes the io channel. The second parameter passes the input
format. If a * is given, the format is free. That is, the input information units are separated by blanks
(white spaces). Optionally a read io error can be handled by the iostat parameter.
1
READ (<channel>, <format> [,<iostat=errvariable>]) <variable list>
Example 2.17 shows, how to read data from a text file. We will read two integer numbers using a free
formatting, i.e. the numbers in the file have to be separated by white spaces (i.e. blanks or tabs). If an
error occur, the error handler will set an error value not equal to zero. An error for example can occur, if
there are no numbers in this textfile, so that a format clashing will happen.
Listing 2.17: Read two numbers from a text file with a free formatting
read(20,*,iostat=ioerr) n1,n2
if (ioerr /= 0) then
write(*,*) ’*** error reading numbers from file!’
endif
1
2
3
4
The following line will be read correctly.
1
1
2
If we would read the following line, the error handler will throw an exception, because we can not convert
text into numbers.
1
2.7.5
Hello world without any numbers!
Close a File
If an open file is no longer needed, the file should be closed. Optionally with the status parameter the
file can be deleted (’delete’) or saved. If the status parameter is not given, a standard file is kept
(’keep’).
1
CLOSE (<channel>, [<status = ’keep’/’delete’>])
Listing 2.18: Deleting a file by open/close calls in F77
1
2
3
4
c
W| 1
2
3
4
5
6
7
c23456789012345678901234567890123456789012345678901234567890123456789012
open(ioin,file=infile,status=’old’,iostat=ioerr)
if (ioerr .eq. 0) close(ioin,status=’delete’)
9.6.2015
Page 36
2.8
Computer Languages for Engineering - SS 15
Loops
Within this section we discuss the explicit loop statement. Until the FORTRAN 90 there are no statements
to cancel the loop or to cancel a cycle to start the next one immediately. Within the FORTRAN versions
up to 77 this statements have to be implemented by explicit jumps using goto statements.
2.8.1
Explicit Loops with Counter in 66, 77 and 90+
A loop that executes a block of statements a specified number of times is called an iterative DO loop or
counting loop. A counting loop construct has the following form in FORTRAN 66, where index is the
counting variable, which starts with the value istart and iterates up to the value iend. After each cycle
the counting variable is incremented by inc. If inc is not given, inc is set to 1. In FORTRAN 66 the DO
statement needs an ending label number (in this example 100). The loop executes all lines of code until
the line with the given label number.
1
2
3
4
5
c DO loop in FORTRAN66
c234567
do 100 index = istart, iend [, inc]
<Block of statements>
100 continue
In FORTRAN 77 the labeled DO is substituted by a DO ... END DO construct. Single loop cycles as well
as the total loop can be broken by a goto statement jumping to an appropriate label.
1
2
3
4
5
c DO loop in FORTRAN90
c234567
do index = istart, iend [, inc]
<Block of statements>
end do
A loop cycle can be broken by the statement cycle. The cycle statement breaks the actual cycle
and starts the next one, if a new cycle should be executed. The total loop can be broken by an exit
statement.
If we want apply the FORTRAN 90 we use the free format.9
1
2
3
4
! DO loop in FORTRAN90
do index = istart, iend [, inc]
<Block of statements>
end do
9
Please note, that there are a lot of non standardized loop constructions, which are added to some Fortran 77 implementations like Watcom77. The Basic like loop structure with LOOP...UNTIL (BOOLEAN EXPRESSION) is not supported by
standard and so it should be substituted by the new Fortran 90 loop version.
E. Baeck
2.8. LOOPS
2.8.2
Page 37
Simple Nested Loop Example
Within the following example all we have a loop from 1 to 10 and an nested loop form 1 to 5. The
numbers of the counter variables should be printed and their product to. The implementation ist given in
FORTRAN 66, FORTRAN 77 and FORTRAN 90.
The FORTRAN 66 is given as follows. The outer loop is labeled by 100 and the inner loop is labeled by
50. Note that each loop needs his own unique counter variable and nested loops must be nested totally,
i.e. they must not overlap.
Listing 2.19: A nested 66-Loop Example
1
2
3
4
5
6
7
c234567
do 100 i=1,10
do 50 j=1,5
write( * , * ) ’i=’,i,’ j=’,j,’ i * j=’,i * j
50 continue
100 continue
end
The FORTRAN 77 version differs from the FORTRAN 66 version only by removing the label and closing
the loop with an end do statement.
Listing 2.20: A nested 77-Loop Example
1
2
3
4
5
6
7
c234567
do 100 i=1,10
do 50 j=1,5
write( * , * ) ’i=’,i,’ j=’,j,’ i * j=’,i * j
end do
end do
end
Using an indent of code blocks in loops can be problematic because in FORTRAN 77 we only have the
columns from 7 to 72. A much more nicer code can be received, if we use the FORTRAN 90 version
with it’s free formating. Now FORTRAN has the look of a realy modern language. We start with the 1st
column and we have enough space for indenting. The problem of truncating the code with the comment
region is no longer existing.
Listing 2.21: A nested 90-Loop Example
1
2
3
4
5
6
7
program loop90
do i=1,10
do j=1,5
write( * , * ) ’i=’,i,’ j=’,j,’ i * j=’,i * j
end do
end do
end loop90
9.6.2015
Page 38
2.8.3
Computer Languages for Engineering - SS 15
Quit a Cycle or a Loop
In FORTRAN 66 everything is done using an goto statement, so in this dialect we use goto too to quit
a cycle or a the entire loop.
Listing 2.22: Breaking a 66-Loop
1
2
3
c234567................................................................
do 100 i = 1,10
write(*,*)"Begin of a cycle!"
4
5
c
for i=3 the cycle should not be executed
if (i.eq.3)
goto 100
c
break the entire loop for all i > 5
if (i.gt.5)
goto 110
6
7
8
9
10
11
12
13
14
write(*,*)"i=",i
100 continue
110 write(*,*)"End of the loop!"
end
With FORTRAN 90 two very helpful statements came into picture to avoid explicit jumps using goto.
• cycle cancels the current cycle and starts the next
• exit cancels the entire loop
Listing 2.23: Breaking an explicit 90-Loop
1
2
3
program loopescape
do i = 1,10
write(*,*)"Begin of a cycle!"
4
! for i=3 the cycle should not be executed
if (i.eq.3)
cycle
5
6
7
! break the entire loop for all i > 5
if (i.gt.5)
exit
8
9
10
write(*,*)"i=",i
end do
11
12
13
14
15
write(*,*)"End of the loop!"
end program loopescape
E. Baeck
2.8. LOOPS
2.8.4
Page 39
Implicit, General Loop without a Control Structure in 90+
In Fortran 90 the do ... end do statement can be used without any control elements too, so the
break condition of the look has to be implemented manually by the usage of an if statement (see section
2.9 too). If we compare the listings 2.23 with 2.24, we see, that incrementing the loop counter has to be
done manually as well as it’s initialization. Using an implicit (general) loop we have to be careful with
the break condition, so that we avoid hanging in an endless loop.
Listing 2.24: Breaking a general 90-Loop
1
2
3
4
5
program GeneralLoop
i = 0
do
i = i+1
write(*,*)"Begin of a cycle!"
6
7
8
! for i=3 the cycle should not be executed
if (i.eq.3)
cycle
9
10
11
! break the entire loop for all i > 5
if (i.gt.5)
exit
12
13
write(*,*)"i=",i
14
15
end do
16
17
18
write(*,*)"End of the loop!"
end program GeneralLoop
9.6.2015
Page 40
2.8.5
Computer Languages for Engineering - SS 15
Factorial in FORTRAN 90++
The factorial of n is defined iteratively by
n! =
n
Y
i
(2.4)
i=1
so we can translate the product easily into a loop. A
Q
P
product symbol or a sum
will be represented in a
programming language by a loop. The counter variable
of the loop is given by the index range of the product
or sum symbol. The result of a product or a sum will
be assigned to a result variable.
Start
p = 1;
i = 1;
p = p·i
A flowchart for the factorial algorithm is given in figure
2.5.
After having initialized the product variable p and the
loop variable i which is used as a factor in every loop
cycle, we multiply the product variable p by the loop
variable i and assign this new product value to our product variable. After the product step we have to check
whether we have reached the end, i.e. if i is equal to
n which is given as the argument of our factorial function.
i = i +1
no
i =n
yes
print results
End
Figure 2.5: The Factorial’s Flowchart
Listing 2.25: Implementation of the Factorial
1
2
3
4
! calculating the factorial
!
!
analysing effects of the data type size
!
using the factorial
5
6
7
8
9
program factorial90
! integer(2)
:: f
! integer(4)
:: f
! real(4)
:: f
! result value integer 2 bytes
! result value integer 4 bytes
! result value real 4 bytes
10
11
12
13
real(8)
:: f
integer(2) :: i
integer(2) :: n
! result value real 8 bytes
! loop index variable
! input value
14
15
16
n = 200
write(*,*) ’n = ’,n
17
18
19
f = 1
do i = 1,n
20
21
22
23
24
E. Baeck
!new
old
f
=
f * i
write(*,*) i,’! = ’,f
end do
2.8. LOOPS
25
Page 41
end program
Within this example you can check the range of the available data types. If p is set to integer 4 bytes
are used to store the factorial. The larges integer within 4 bytes can be calculated as follows.10
max = 231 − 1 = 2147483647 ≈ 2, 147 · 109
(2.5)
Figure 2.6 shows the problem of an overflow, if the numbers to store exceeds the limit of the data type.
The factorial von 12 looks like plausible. But the next must be wrong, because 4 · 13 6= 19. If we
check the next factorials, we will see, that the numbers not really exceed 2 · 109 . Thats the 2GB Problem.
Furthermore we see, that some numbers become negative. This obvious is also wrong and a consequence
of the overflow situation.
Figure 2.6: Factorial using INTEGER with 4 Bytes
For larger numbers the choice of a real data type is recommended. Within a real data type only the
exponent can overflow. The mantissa can not overflow, because it’s independent of the number’s size. If
we use the largest available data type double precision11 , we will get the situation of figure 2.7.
We see, that with the 8 byte real the factorial reaches 170!. The next result is indicated as Infinity. This
happens, if the memory for the exponent overflows. A 4 byte real has an exponent range of −38 · · · + 38,
a 8 byte real has an exponent range of −308 · · · + 308. We see, that the largest occurring exponent is
+306.
10
This is also known as 2GB problem. This problem occur for example, if a file exceeds the size of 2GB, because a 4 byte
integer is used to address the file’s bytes reading or writing them. A similar problem occur, if you want to have more then 256
columns in MS-EXCEL2003, that’s a one byte limit, or if you need more then 65536 rows in MS-EXCEL2003, that’s a 2 byte
limit.
11
The data type double precision with FORTRAN 90 is obsolete, see also section 2.5.2, but can be used, if you want.
9.6.2015
Page 42
Computer Languages for Engineering - SS 15
Figure 2.7: Factorial using Real with 8 Bytes
2.9
Branching
Branching and decisions can be implemented in Fortran like in the most languages with an if -statement.
The application of if constructs will be discussed using the implementation of the general form of a
quadratic equation. Within a first approach the implementation in a Fortran66 like program is shown.
2.9.1
if Statement, Fortran 66 like
Within the first standardized Fortran version, which will be compiled from modern Fortran compilers
too, the if statement is very rough. It’s like a branch in assembler language, that is, the if statement only
is able to process one statement. Note the two statements in the macro assembler code of section 1.2.1
resumed below. Within a first step, a registers data is compared. In a second step a conditional jump is
performed.
1
2
3
4
...
cmp edx, 2
ja @f
...
< comparing the content of the edx with 2
< jump, if equal
Listing 2.26: Syntax of the if Statement
1
IF (<logical expression>) <statement>
Because of the similar structure of assembler branches and branches in Fortran 66 the developed Fortran
code will be very similar to the assembler code comparing their case structures.
An example to implement an implicit loop with an if statement and a backward jump to calculate the
relative precision is given in section 3.3.
E. Baeck
2.9. BRANCHING
2.9.2
Page 43
Implementation of a Quadratic Equation Solver
The solver of a generall quadratic equation is a vell known problem, we know from our school days. The
implementation whowever requires the solution of a set of subproblems, which indeed is a very good
example to show branching.
2.9.2.1
Some Theory
The following example implements the solver for a general quadratic equation.
a · x2 + b · x + c = 0
(2.6)
We have the following cases.
• a =0∧b =0∧c =0
Infinite solutions. x can be set arbitrary.
• a = 0 ∧ b = 0 ∧ c 6= 0
No solution possible.
• a = 0 ∧ b 6= 0
Linear case, x = −c/b.
• a 6= 0
Quadratic case,
√
1
(−b + b 2 − 4ac).
x1 = 2a
√
1
x2 = 2a
(−b − b 2 − 4ac).
9.6.2015
Page 44
Computer Languages for Engineering - SS 15
2.9.2.2
A Flow-Chart of the QuadSolver
The following flow chart shows all the case, which we have to handle. The algorithm is given for a real
arithmetic, i.e. no complex data types are used. The relevant source code will be developed within the
next section.
Start
yes
a=0
c=0
no
no
yes
x1,2 =
yes
infinit
solutions
Stop
no
x = − bc
d = b2 − 4 · a · c
d <0
yes
b=0
Stop
√
−b±i −d
2·a
no solution
Stop
Stop
no
x1,2 =
2.9.2.3
√
−b± d
2·a
Stop
Quadratic Equation, Solver Implementation Fortran 66 like
The first implementation in strict Forteran 66 shows the subsequent solution of the above discussed
cases. Because the if statement can only process one statement, the inverse case should be checked to
jump over the succeeding code. After the code block a further jump should be performed to the last
statement of the program.
Listing 2.27: Implementation of a 66-Quad-Solver
1
2
3
4
5
6
7
8
9
10
11
12
c quadratic equation
c a*x**2 + b*x + c =
c
c a,b,c are arbitray input parameters
c
c explicit declaration should be done
c
c234567
implicit none
c
c
input parameters
double precision a,b,c
13
14
c
working variables
double precision d,p
c
output float values
double precision x1,x2
15
16
17
18
19
E. Baeck
2.9. BRANCHING
20
Page 45
c
output complex values
double precision x1r,x2r,x1i,x2i
c
Initialization
p = 1.d-15
a = 1.d0
b = 0.d0
c = 4.d0
21
22
23
24
25
26
27
28
29
c
c
30
31
32
33
34
35
36
37
c
c
38
39
40
41
input parameters from the keyboard
write(*,*) ’input of a:’
read(*,*) a
write(*,*) ’input of b:’
read(*,*) b
write(*,*) ’input of c’
read(*,*) c
list input
write(*,*)
write(*,*)
write(*,*)
write(*,*)
parameters for checking
’ Input parameters:’
’ a = ’,a
’ b = ’,b
’ c = ’,c
42
43
c
linear, constant branch
if (dabs(a) .gt. p) goto 500
c
contant branch
if (dabs(b) .gt. p) goto 400
44
45
46
47
48
if (dabs(c) .gt. p)
1write(*,*) ’No solution found, constant case.’
49
50
51
if (dabs(c) .le. p)
1write(*,*) ’Infinit solutions found, constant case.’
52
53
54
goto 600
55
56
57
c
58
59
60
61
linear branch
400 continue
x1 = -c/b
write (*,*) ’Linear case: x = ’, x1
goto 600
62
63
64
65
66
c
quadratic branch
500 continue
c
calculating the discriminante
d = b**2 -4.d0*a*c
67
68
69
c
reel branch
if (d .lt. 0.) goto 550
70
71
72
73
d = dsqrt(d)
x1 = (-b +d)/(2.e0*a)
x2 = (-b -d)/(2.e0*a)
74
75
write(*,*) ’quadratic case, reel values’
9.6.2015
Page 46
Computer Languages for Engineering - SS 15
write(*,*) ’ x1 = ’,x1
write(*,*) ’ x2 = ’,x2
76
77
78
goto 600
79
80
81
c
82
complex branch
550 continue
83
d
x1r
x2r
x1i
x2i
84
85
86
87
88
=
=
=
=
=
dsqrt(-d)
-b/(2.e0*a)
x1r
d/(2.e0*a)
-d/(2.e0*a)
89
write(*,*) ’quadratic case, complex values’
write(*,*) ’ x1 = ’,x1r,’ +i ’,x1i
write(*,*) ’ x2 = ’,x2r,’ +i ’,x2i
90
91
92
93
600 continue
end
94
95
2.9.2.4
Quadratic Equation, Solver Implementation Fortran 90 like
The following code implements the solution of a quadratic equation (see equation 2.6) in a Fortran 90
version. Note, that we are able to implement the case tree without any goto jumps, which were essential
in an 66 approach. In contrast to solution 2.27 in the following code 2.28 we use a complex data type for
the solutions of the quadratic case. So we can waive the last branching concerning the complex case.
Listing 2.28: Implementation of a 90-Quad-Solver
1
2
3
! Solver for a quadratic equation
! Implementation in Fortran90
program quadequation
4
5
implicit none
! only explicit declarations
real(8)::a, b, c
real(8)::d
real(8)::p
real(8)::x
complex(8)::c1,c2
!
!
!
!
!
6
7
8
9
10
11
parameters of the equation
discriminant
precision
for the linear solutions
for the quadratic solutions
12
13
14
15
16
17
! setup
a =
b =
c =
p =
the parameters for the quadratic equation
1.
0.
4.
1.d-15
18
19
20
! print parameters values to the screen
write(*,’(3(a,F10.3))’) ’a=’,a,’ b=’,b,’ c=’,c
21
22
23
24
E. Baeck
! case a=0: it’s not a quadratic equation!
if (dabs(a) < p) then
2.9. BRANCHING
25
26
Page 47
! subcase b=0: => infinit solutions or no solution
if (dabs(b) < p) then
27
! subcase c=0: Trival case => infinit solutions
!
it’s independent of x
if (dabs(c) < p) then
write(*,*) ’Trivial solution, infinit solutions for x.’
28
29
30
31
32
! subcase c!=0: Trivial solution => no solution
!
it’s independent of x
else
write(*,*) ’No solution found.’
33
34
35
36
37
endif
38
39
40
41
42
43
! subcase b!=0 => linear case -> one solution
else
x = -c/b
write(*,’(a,f10.4)’) ’Linear case: x=’,x
44
45
endif
46
47
48
49
50
! a!=0 => quadratic problem -> two solutions
!
if we solve the problem with reals, we have to handle
!
the real and the complex subcase.
else
51
52
53
! calculate the discriminant to make the case check
d = b**2 -4.*a*c
54
55
56
c1 = 1./(2.*a)*(-b +cdsqrt(dcmplx(d,0.d0)))
c2 = 1./(2.*a)*(-b -cdsqrt(dcmplx(d,0.d0)))
57
58
59
60
61
! positive discriminant -> 2 real roots
if (d >= 0.) then
write(*,’(a,f10.4," +i",f10.4)’) ’Quadratic real case, x1=’,c1
write(*,’(a,f10.4," +i",f10.4)’) ’
x2=’,c2
62
63
64
65
66
67
! negative discriminant -> 2 complex roots
else
write(*,’(a,f10.4," +i",f10.4)’) ’Quadratic complex case, x1=’,c1
write(*,’(a,f10.4," +i",f10.4)’) ’
x2=’,c2
endif
68
69
70
endif
end program
In line 55 the function cdsqrt is applied. The leading character c specifies that it is a complex function.
The second character d specifies the kind of the real respectively the imaginary part (see section 2.5.2).
9.6.2015
Page 48
2.10
Computer Languages for Engineering - SS 15
Subroutines and Functions
A very important feature of a programming language is the possibility to encapsulate code into reusable
packages. Such a package is called in Fortran Subroutine or Function. The only difference between
a function and a subroutine is the return value of the function. So a function can be called within
an expression like sin(ϕ) or cos(ϕ). A function as well as a subroutine in general receives a list of
parameters, which are called formal parameters. A parameter can be used to pass information from the
calling program into the function or the subroutine. Then the parameter is called input parameter. A
parameter can be used as well to pass information out of the function or the subroutine into the calling
program. Then the parameter is called output parameter.
2.10.1
Functions
The implementation of a function is given in Fortran66/77 as follows.
Listing 2.29: Syntax of a 66/77-Function
1
2
3
4
5
6
7
c234567
<type> FUNCTION <name> ([<Parameter list>])
[<Declaration Block>]
[<Code Block>]
<name> = <return value>
RETURN
END
The implementation of a function is given in Fortran90+ as follows. Note that the end of a function is
set by the statement end function.
Listing 2.30: Syntax of a 90-Function
1
2
3
4
5
6
<type> FUNCTION <name> ([<Parameter list>])
[<Declaration Block>]
[<Code Block>]
<name> = <return value>
RETURN
END FUNCTION [<name>]
The function Test1 in listing 2.31 calculates the function value of a line. The lines parameter and the
x-value are passed by the list of the formal parameters.
Listing 2.31: A Function and it’s Testing Environment
1
2
3
! Main program as testing environment for function calls
program functions
implicit none
4
5
6
7
8
9
10
11
E. Baeck
real(8)::Test1
real(8)::p1,p2,x1
real(8)::x0
real(8)::xD
real(8)::t
integer::i
!
!
!
!
!
!
function’s return data type
the function’s parameters
initial value
increment
function’s value
loop counter
2.10. SUBROUTINES AND FUNCTIONS
Page 49
! initialize x0 and xDel
x0 = -2.
xD = 0.25
12
13
14
15
! set function parameters
p1 = 2.
p2 = -1.
x1 = x0
16
17
18
19
20
do i=1,16
t = Test1(p1,p2,x1) ! calculating the function value
write(*,’(2(a,f12.6))’)’ x=’,x1,’ f(x)=’,t
x1= x1 + xD
! increment the function parameter
end do
21
22
23
24
25
26
27
end program
28
29
30
31
32
33
34
! function to calculate some values
real(8) function Test1(a,b,x)
implicit none
! we have to declare everything explicitly
real(8)::a,b,x ! declaring the parameters of the function
Test1 = a*x +b ! calculating and asigning the return value
end function Test1 ! the end of function Test1
2.10.2
Subroutines
The implementation of a subroutine is given in Fortran66/77 as follows. You see, there is no return value.
The only difference between subroutine and function is the keyword subroutine instead of function, the
missing return type, and the missing assignment of the return value.
Listing 2.32: Syntax of a 66/77-Subroutine
1
2
3
4
5
6
c234567
SUBROUTINE <name> ([<Parameter list>]):
[<Declaration Block>]
[<Code Block>]
RETURN
END
The implementation of a subroutine is given in Fortran90+ as follows. Note that the end of a subroutine
is set by the statement end subroutine.
Listing 2.33: Syntax of a 90-Subroutine
1
2
3
4
5
SUBROUTINE <name> ([<Parameter list>])
[<Declaration Block>]
[<Code Block>]
RETURN
END SUBROUTINE [<name>]
9.6.2015
Page 50
2.10.3
Computer Languages for Engineering - SS 15
Functions as Parameters
if a function should be used as a parameter, the functions should be declared with the return data type and
the attribute external. A typical and nice example is the implementation of Newton’s algorithm to calculate the roots of an arbitrary equation (see section 3.5). The following example shows the implementation
of the numerical calculation of a function’s derivative, which is used within the Newton’s algorithm. The
function is passed as parameter to the derivative function fs. Within the function’s code the function f
is declared as a real(8) function. To distinguish a function from a variable the function’s symbolic
name can be declared with an external attribute.
Listing 2.34: Passing a Function as a Parameter
1
2
3
4
5
6
function to calculate the deviation of a function
real(8) function fs (f,x,h)
real(8), external:: f
real(8):: x,h
fs = (f(x +h/2) - f(x -h/2))/h
end function
Subroutines may also be passed to procedures as calling arguments. if a subroutine is to be passed as
a calling argument, it must be declared in an external statement. The corresponding dummy argument
should appear in a call statement in the procedure.
2.11
Arrays
An array is a compound of data of the same type. The items of the array are addressed by an index value.
A static array is declared by the definition of the data type and the index range of an array.
2.11.1
Static Array
An static array is declared in FORTRAN77 with the following statements. One really big problem in
FORTRAN77 is, that there are only static arrays, i.e. the developer has to decide about the size of an
array. If the array size is to small, the code must be recompiled. So a FORTRAN77 software in general
is not able to fit to the problems size.
Listing 2.35: Array Declaration in 66/77
1
2
3
4
5
6
<data type> <arrayname>
DIMENSION
<arrayname> (<range-1>,<range-2>,..,<range-n>)
...
... or ...
...
<data type> <arrayname> (<range-1>,<range-2>,..,<range-n>)
E. Baeck
2.11. ARRAYS
Page 51
Listing 2.36 shows a little example code to calculate the scalar product of the vectors v1 and v2. The
vectors are allocated using static arrays.
Listing 2.36: Allocating Static Arrays in FORTRAN66/77
1
2
3
4
5
c1234567
real*8 v1(3), v2(3), s
c
... initialize the variables
do 100 i=1,3
100 s = s + v1(i)*v2(i)
In Fortran90 we declare a statical array with the following format.
Listing 2.37: Array Declaration in 90
1
<data type>, dimension(<range-1>,<range-2>,...,<range-n>):: <arrayname>
Listing 2.38 shows the example 2.36 in a FORTRAN90 style.
Listing 2.38: Allocating Static Arrays in FORTRAN90
1
2
3
4
5
6
7
real(8), dimension (3)::v1 ! vector 1
real(8), dimension (3)::v2 ! vector 2
real(8)::s
! result value
! ... initialize the variables
do i=1,3
s = s + v1(i)*v2(i)
end do
2.11.2
Dynamical Array
A dynamical array can be allocated, i.e. created at run time. So first we can evaluate the necessary
array size and then we can allocate the used memory for the array. This feature is available starting from
FORTRAN90.
Listing 2.39: Dynamical Array Declaration only in 90
1
2
3
4
5
6
7
8
9
<data type>, allocatable, dimension(:,:,...,:):: <arrayname>
...
... next step we allocate the array
...
allocate(<arrayname>(<range-1>,<range-2>,...,<range-n>) [,stat=<statname>])
...
... after the usage we deallocate the memory
...
deallocate(<arrayname>,[stat=<statname>])
After having declared the array name, the array can be allocated by the allocate statement. After the
allocation the array items can be accessed. If an array item is accessed before the array is allocated, the
program in general will crash. If the memory of an dynamical array is no longer needed, the array should
be deallocated with the deallocate statement.
Example 2.40 shows how to allocate and deallocate a double indexed array dynamically. We also see a
memory handler, which prevents crashing in the case of allocation problems.
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Computer Languages for Engineering - SS 15
Listing 2.40: Array Declaration in 90
1
2
real(8),allocatable,dimension(:,:)::a
integer::nDim
! declar a as a dynmical array
! this variable controls the array dimension
3
4
5
6
7
8
9
10
11
! allocate the array a, an allocation error is handled
nDim = 3
allocate(a(nDim,nDim),stat=memstat)
if (memstat /= 0) then
write (*,*) ’*** Error: array a is not allocatable.’
else
deallocate(a,stat=memstat)
end if
2.11.3
Automatic Array
An automatic array will be created automatic in a function or in a subroutine. If the function or subroutine
is exited the automatic array is deallocated automatically. The dimensions of an automatic array are
passed into the function or the subroutine as formal parameters.
Example 2.41 shows the usage of an automatic array. This feature is only available in FORTRAN90
and newer. If we compare this to an implementation in FORTRAN66/77 we would see, that in the old
FORTRAN situation, the array has to be allocated in the main program as a static array and has to be
passed by a parameter to the subroutine. In FORTRAN90++ the array is allocated within the scope of the
sub program automatically without any allocation code. Leaving the sub program the automatic array
automatically is deallocated without any additional code.
Listing 2.41: Usage of an Automatic Array in FORTRAN90
1
2
3
4
5
program AutoArray
implicit none
integer::nDim = 3
call UseAutoArray(nDim)
end program
6
7
8
9
subroutine UseAutoArray(nDim)
integer::nDim, i
real(8),Dimension(nDim)::a;
10
! set automatic array
do i=1,nDim
a(i) = i
end do
! print content of automatic array
write(*,*) (a(i),i=1,nDim)
11
12
13
14
15
16
17
18
end subroutine
E. Baeck
2.11. ARRAYS
2.11.4
Page 53
A little Array Example
The following code shows how to work with static, dynamic and automatic array in a more complex
situation.
Listing 2.42: Static, Dynamic and Automatic Arrays in FORTRAN90
1
2
3
4
! This example shows the 3 types of array available in
! Fortran 90++
program Arrays
implicit none
5
6
7
8
9
10
11
integer::
integer::
integer::
integer::
integer::
integer::
i,j
nDim
memstat
ioerr
ionr = 10
nDim1,nDim2
!
!
!
!
!
!
loop counter
used as matrix dimension
used as memory error flag
used as file io error flag
channel number
dimensions of the matrx in file
12
13
14
! if we use functions, we have to declare their retruns
integer:: iwritemat,ireadmatdim,ireadmat
15
16
17
real(8),dimension(3,3)::a
real(8),allocatable,dimension(:,:)::b
! static array
! dynmical array
18
19
character(256)::logname
! name of the output file and input file
logname = "arrays.log"
! initialize the filename
! note: the file is written into the
! projects folder
20
21
22
23
24
25
26
27
28
29
30
31
! open the log file as a new blank file
open(ionr,file=logname,status=’replace’,iostat=ioerr)
!
.ne.
if (ioerr /= 0) then
write (*,*) ’*** Error: log file not opened!’
stop
endif
32
33
34
35
36
37
38
! allocate the array b, an allocation error ist handled
nDim = 3
allocate(b(nDim,nDim),stat=memstat)
if (memstat /= 0) then
write (*,*) ’*** Error: array b is not allocatable.’
end if
39
40
41
42
43
44
! allocation check: if b is not allocated, we stop
if (.not. allocated(b)) then
write (*,*) ’*** Error: array b not allocated’
stop
end if
45
46
47
48
! initialize array a and b with a special number pattern
! - over the rows (1st index)
do i=1,3
49
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50
51
52
53
54
Computer Languages for Engineering - SS 15
! - over the columns
do j=1,3
a(i,j) = i*10 +j
b(i,j) = i*10 +j +100 ! +100, because we want to
end do
! know, thats the b
55
56
end do
57
58
59
60
! print array data of a and b to the sceen
write(*,’(3(f10.3,1x))’) ((a(i,j),j=1,3),i=1,3)
write(*,’(3(f10.3,1x))’) ((b(i,j),j=1,3),i=1,3)
61
62
63
64
65
! and
! for
ioerr
ioerr
write the array data of a and b into the log file
later readings
= iwritemat(ionr,a,3,3)
= iwritemat(ionr,b,3,3)
66
67
68
69
70
! if not longer needed, free the memory of array b
deallocate(b,stat=memstat)
! close log file
close(ionr)
71
72
73
74
75
76
77
! open the log file to read the data of the first matrix
open(ionr,file=logname,status=’old’,iostat=ioerr)
if (ioerr /= 0) then
write(*,*) ’*** Error: file ’,logname,’ not found!’
stop
endif
78
79
80
! read the matrix dimension
if (ireadmatdim(ionr,nDim1,nDim2) == 0) then
81
82
83
84
! Check the dimensions: size < 1 is not valid
if (nDim1 < 1 .or. nDim2 < 1) then
write (*,*) ’*** Error: wrong dimensions ’,nDim1,’ ,’,nDim2
85
86
87
88
89
90
91
! dimensions ok
else
! now we reallocate the array b
allocate(b(nDim1,nDim2),stat=memstat)
! and read the matrix data from the file
ioerr = ireadmat(ionr,b,nDim1,nDim2)
92
93
endif
94
95
96
97
98
99
else
! wrong format -> close the file and stop it
close(ionr)
stop
endif
100
101
102
! close the input file
close(ionr)
103
104
105
E. Baeck
! now we print the read data into the screen
write(*,*) ’Data of the first matrix in file:’,logname
2.11. ARRAYS
106
107
108
Page 55
do i=1,nDim1
write(*,’(10(f10.3,1x))’) (b(i,j),j=1,3)
enddo
109
110
111
! and deallocate the matrix b
deallocate(b,stat=memstat)
112
113
114
115
116
117
! the usage of an automatic array of the dimension 4x5
! is shown in the next call. Only the dimension of the array
! ist passed, the array is allocated automatically in the
! suboutine
call checkautomat(4,5)
118
119
end program Arrays
120
121
122
123
124
! print matrix data into a file
!
integer function iwritemat(io,m,n1,n2)
implicit none
125
126
127
128
129
130
integer::io
! io channel number
integer::n1
! number of rows
integer::n2
! number of columns
real(8), dimension(n1,n2):: m ! matrix data
integer::ioerr, i, j
131
132
133
134
135
136
137
write(io,*,iostat=ioerr) n1,n2 ! write the dimensions
if (ioerr /= 0) then
write(*,*) ’*** Error: writing not possible’
iwritemat = -1
! exit, if io error
return
endif
138
139
140
141
142
! over the rows
do i=1,n1
write(io,*) (m(i,j),j=1,n2)
enddo
143
144
145
iwritemat = 0
end function iwritemat
! 0 return: everything ok
146
147
148
! Read the dimension of a matrix from a file
integer function ireadmatdim(io,n1,n2)
149
150
151
152
integer::io
integer::n1,n2
integer::ioerr
! io channel
! dimensions of the matrix
! error flag
153
154
155
156
157
158
159
read(io,*,iostat=ioerr) n1,n2
if (ioerr /= 0) then
! if io-error, perhaps a wrong format
write(*,*) ’*** Error: wrong file format’
ireadmatdim = -1
return
endif
160
161
ireadmatdim = 0
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Computer Languages for Engineering - SS 15
end function ireadmatdim
163
164
165
166
167
! read matrix data from a file
!
integer function ireadmat(io,m,n1,n2)
implicit none
168
integer::io
! io channel number
integer::n1
! number of rows
integer::n2
! number of columns
real(8), dimension(n1,n2):: m
! matrix data
integer::ioerr, i, j
169
170
171
172
173
174
! over the rows
do i=1,n1
read(io,*,iostat=ioerr) (m(i,j),j=1,n2)
if (ioerr /= 0) then
! important to check the read-io
write(*,*)’*** Error: format’
ireadmat = -1
return
endif
enddo
175
176
177
178
179
180
181
182
183
184
185
186
ireadmat = 0
end function ireadmat
187
188
189
! example for an automic array
subroutine checkautomat(nDim1,nDim2)
190
real(8), dimension(nDim1,nDim2)::m
191
! automatic array
192
! initialize the array with a number pattern
do i=1,nDim1
do j=1,nDim2
m(i,j) = i*10 +j
enddo
enddo
193
194
195
196
197
198
199
! print the pattern to the screen
write(*,*) ’M:’,nDim1,’,’,nDim2
do i=1,nDim1
write(*,’(10(f10.3,1x))’) (m(i,j),j=1,nDim2)
enddo
200
201
202
203
204
205
206
end subroutine
2.11.5
Pseudo Dynamic Arrays in FORTRAN77
If we need a dynamic array using FORTRAN77 the only chance to implement this is, to use a static
memory buffer, i.e. a static array which has to be large enough to hold the largest dimension of our
pseudo dynamic array. How to implement this we can see in listing 2.43. The dimension of the vectors
are read in from a text input file.
E. Baeck
2.11. ARRAYS
Page 57
Listing 2.43: Dot Product of Vectors using a Pseudo Dynamic Array
1
2
3
c implementing a pseudo dynamic array in FORTRAN 77
c
implicit none
4
5
6
7
c
8
integer
nDim,i
real*8
GetScalProd
memory buffer
real*8
dBuffer(20)
9
10
c
11
12
13
c
c
14
15
16
c
c
17
18
19
c
c
20
open input file
open(10,file=’SkalProd.in’,status=’old’)
read the dimension
read(10,*) nDim
read the first vector
read(10,*) (dBuffer(i),i=1,nDim)
read the second vector
read(10,*) (dBuffer(i),i=nDim+1,nDim*2)
21
22
23
24
25
26
27
28
29
30
c
print out
write(*,*) ’>> scal product of 2 vectors’
write(*,9000) ’v1
= ’,(dBuffer(i),i=1,nDim)
write(*,9000) ’v2
= ’,(dBuffer(i),i=nDim +1,nDim*2)
write(*,9000) ’v1*v2 = ’,
&GetScalProd(dBuffer(1),dBuffer(nDim+1),nDim)
close(10)
9000 format(a,20f10.3)
end
31
32
33
34
c calculation of the dot product of two vectors
real*8 function GetScalProd(a,b,n)
implicit none
35
36
37
integer i,n
real*8 a(1),b(1)
38
39
40
41
42
GetScalProd = 0.
do 100 i=1,n
100 GetScalProd = GetScalProd + a(i)*b(i)
end
As we can see from line 20 of listing 2.43 the size of the buffer has to be set large enough. If not, the
input data will be read into a memory outside of our buffer, which can produce a lot of ugly side effects.
The second problem will occur, if the pointer calculation is not perfect (line 17, 20 and 27). If we use
incorrect pointers, internal data can be overwritten without provoking any error situation. Side effects
like this are very hard to find and can be avoided using allocatable arrays with FORTRAN90.
9.6.2015
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2.12
Computer Languages for Engineering - SS 15
Global Data
Global data in Fortran are handled with specific access statements.
2.12.1
Classical Fortran and Common
Global data in Fortran classically are handled with so called common blocks. A common block is a
block of memory, which can be used from all routines, which are permitted to do this. A routine will be
permitted to access a common block, if the common block is included into this routine with the statement
common.
Global data can be initialized with the block data statement.
Listing 2.44: common Block and block data
1
2
3
4
c initialization of a common
c
c
| block data’s name
block data global
5
6
7
c
c
8
9
10
name of the common
!
|
start with longest datatype
common /old77/ dOld,nOld
real*8 dOld
integer nOld
11
12
13
data nOld /123/
data dOld /3.14/
14
15
end
In listing 2.44 we see, that global data are introduced with a common statement. The name of the
common in this case is old77. If this statement and the following declarations (lines 8 to 10) are found
within a subroutine ore a function, this common variables are available in terms of global data.
The block data statement, which can be only once in a code, will initialize the variables of a common
block. In this case we assign a value to nOld and dOld.
2.12.2
Some Aspects of the Module Concept of FORTRAN90
Using FORTRAN90, the classical concept of common blocks should be considered as obsolete. Common
blocks can be considered as a source of many possible errors and side effects. With FORTRAN90
common blocks can be substituted by modules.
A module in FORTRAN90 is a compound of data and methods according to the object orientated concept
of modern languages. So using modules we also can develop software in FORTRAN using modern
OOP concepts.12
12
OOP is discussed later in the C++ section, see section 6.11.
E. Baeck
2.12. GLOBAL DATA
Page 59
In listing 2.45 some global constants are introduced and initialized. Further a method is implemented
inside the contains block, to print this constants.
Listing 2.45: A module to Handle Some Constants
1
2
3
! global data in FORTRAN 90
! making common and block data obsolete
module constants
4
implicit none
5
6
! data section
real, parameter::e
= 2.7
character(*), parameter::room = "V15-S03-D03"
integer
::nrtel= 2613
7
8
9
10
11
! methodes section
contains
12
13
14
subroutine printConstants
15
16
write(*,*)
write(*,*)
17
18
"my room..",room
"my telnr.",nrtel
19
end subroutine printConstants
20
21
22
end module constants
2.12.3
Using global Data
A really big benefit in FORTRAN’s history is, that old FORTRAN code can be used in modern FORTRAN
environments with nearly no required changes. This we can see within the next example, which uses the
classical common block of listing 2.44 and the modern module of listing 2.45.
Listing 2.46: Using commons and modules
1
2
3
! example to show the usage of common and module
! within one 90 code
program GlobalData
4
5
use constants
6
7
implicit none
8
9
10
11
12
13
14
! insert the common-code here
!
name of the common
!
|
start with longest datatype
common /old77/ dOld,nOld
real*8 dOld
integer nOld
15
16
17
! print the global common data
call printGlobals
18
19
! change the global common data
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Computer Languages for Engineering - SS 15
nOld = 321
dOld = 4.13
20
21
22
! print the global common data
call printGlobals
! print the global module data
call printConstants
23
24
25
26
27
28
end program
29
30
31
32
! subroutine to print the common data
! to this we have to insert the common code
subroutine printGlobals
33
common /old77/ dOld,nOld
real*8 dOld
integer nOld
34
35
36
37
write(*,*) "nOld = ",nOld
write(*,*) "dOld = ",dOld
38
39
40
41
end subroutine
E. Baeck
2.13. MEMORY MAPPING
2.13
Page 61
Memory Mapping
Especially in old FORTRAN66/77 sources the technique of momory mapping using the equivalence
statement is applied. The problem which should be solved is a dynamic memory management. In
contrast to modern languages like C or C++ there is no possibility of dynamical memory allocation.
If a program without dynamical memory management should be efficient the only solution is, to allocate
a statical memory buffer and try to map all large arrays onto this buffer. Is we can do with the equivalence
statement. In FORTRAN90 sources, where the option of dynamical memory allocation is available, we
should not use memory mapping, because it’s highly prone to errors. We easily can overwrite data simple
by mapping errors, which are only found in general by an incredibly high effort of testing.
The equivalence statement links a list of source memory to their destination memory.
Listing 2.47: Equivalence Statement in FORTRAN66/77
1
equivalence (<destination memory>, <source memory>), [(...)]
So in example 2.48 we introduce a real*8 buffer, which is used as a memory mapping array. On
the other hand we allocate two real*8 arrays v1 and v2 and map them onto the buffer. After having
initialized them we calculate the scalar product of this vectors and print them into the console window.
After this we initialize the integer*4 vectors i1 and i2, which have the same length as the real*8
vectors and were also allocated inside the start up section of the program. We calculate the scalar product
of them and print their values.
After this we again print the content of the real*8 vectors and we can see, that their content totally is
overwritten by the integer*4 vectors. The values, which are printed don’t make any sense, because
it’s a real interpretation of an integer bit pattern.
Listing 2.48: Equivalence of Real and Integer Vectors
1
2
3
4
5
c1234567
c
allocate the memory
integer ndim
parameter (ndim = 3)
real*8 buff(nDim*2)
6
7
c
some real memory
real*8 v1(ndim), v2(ndim), s
c
some integer memory
integer*4 i1(ndim*2), i2(ndim*2), is
c
map v1, v2, s onto the memory buffer
equivalence(buff(1),v1), (buff(ndim+1),v2), (buff(ndim*2+1),s)
c
map i1, i2, is onto the memory buffer
equivalence(buff(1),i1), (buff(ndim+1),i2), (buff(ndim*2+1),is)
c
initialize the buffer
do 100 i=1,ndim*2
buff(i) = i
8
9
10
11
12
13
14
15
16
17
18
19
20
100
21
22
23
c
print the vector’s content
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Computer Languages for Engineering - SS 15
write (*,’(a,3f10.3)’) "v1 =",(v1(i),i=1,ndim)
write (*,’(a,3f10.3)’) "v2 =",(v2(i),i=1,ndim)
24
25
26
27
c
28
29
200
30
31
performe the scalar product and print the result
s = 0
do 200 i=1,ndim
s = s + v1(i)*v2(i)
write (*,’(a,f10.3)’) "s =",s
32
33
c
34
35
300
36
set integer vectors
do 300 i=1,ndim*2
i1(i) = i*2-1
i2(i) = i*2
37
38
c
print the vector’s content
write (*,’(a,6i5)’) "i1 =",(i1(i),i=1,ndim*2)
write (*,’(a,6i5)’) "i2 =",(i2(i),i=1,ndim*2)
c
performe the scalar product and print the result
s = 0
do 400 i=1,ndim*2
is = is + i1(i)*i2(i)
write (*,’(a,i5)’) "is =",is
39
40
41
42
43
44
400
45
46
47
48
49
c
c
50
51
print the real vector’s content again
we see, that the values are obviously overwritten
write (*,’(a,3e10.3)’) "v1 =",(v1(i),i=1,ndim)
write (*,’(a,3e10.3)’) "v2 =",(v2(i),i=1,ndim)
52
53
end
Figure 2.8 shows the output of example 2.48.
Figure 2.8: Output listing
E. Baeck
2.14. COMMANDLINE ARGUMENTS
2.14
Page 63
Commandline Arguments
In old FORTRAN there is by standard no possibility to have access to the commandlines’s parameter
because on the mainframe IBM computers everything concerning the runtime environment was handled
by the so called Job Control Language.
With the advent of the command shells like BASH (Born Again SHell) on LINUX systems, programs
are generally started with a wide set of commandline parameters which are passing input data to the
startup of the application (see section A too). Because the FORTRAN90++ is highly influenced by the C
language the concept of passing commandline arguments is very close to C’s strategy.
In C the commandline parameters are parameters of the main function, i.e. the main program. Unlike
C FORTRAN90 provides a function which returns the number of given parameters called IARGC().
With the given number of parameters we can get the value of each parameter by calling the subroutine
GETARG(I,ARG), where I is the parameter’s index (starting from 1) and ARG is a CHARACTER variable, which will come with the desired value on return. Like in C we get the program’s name with an
index value of 0.
The following example 2.49 shows how to access this commandline parameters.
Listing 2.49: A Commandline Example
1
2
program main
implicit none
3
4
5
6
7
character
integer (
integer (
integer (
( len = 255 ) arg
kind = 4 ) i
kind = 4 ) iargc
kind = 4 ) numarg
8
9
10
11
numarg = iargc ( )
write ( *, ’(a,i8,a)’ ) &
’ Program executed with ’, numarg, ’ commandline options’
12
13
14
15
16
17
write
write
write
write
write
(
(
(
(
(
*,
*,
*,
*,
*,
’(a)’
’(a)’
’(a)’
’(a)’
’(a)’
)
)
)
)
)
’ ’
’ Found commandline options’
’ ’
’ I
ARG ’
’ ’
18
19
20
21
22
23
do i = 0, numarg
call getarg ( i, arg )
write ( *, ’(2x,i3,2x,a20)’ ) i, arg
end do
end
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Computer Languages for Engineering - SS 15
Figure 2.9: Running the Commandline Example
We see in figure 2.9, that we run the application commandline with three commandline options called
option1, option2 and option3. This options we access within our program and print the found
option values into the screen.
E. Baeck
3
Some Examples
3.1
Hello World
One famous application which does n’t make any sense is the program helloworld. There are only two
statements: the first writes the famous text to the screen, the second closes the application.
Listing 3.1: A Startup Hello
1
2
3
4
3.2
c234567
c comment
write(*,*) "Hello World "
end
70
12345
Simple Sum
The second example shows the implementation of a simple loop in FORTRAN66 style. The result of the
loop (do-loop with labeled end) is the sum of all integers from 1 to 10. Each step is printed to the screen.
S=
10
X
i
(3.1)
i=1
Listing 3.2: Sum up all Numbers from 1 to 10
1
2
3
4
5
6
7
c234567
n = 0
! sum variable, set to zero
do 100 i=1,10
! performing the sum in fortran IV style
n = n + i
write (*,’(a,i2,a,i4)’) ’ i = ’,i,’ sum = ’,n ! screen dump
100 continue
! end of loop
end
! end of application
65
Page 66
Computer Languages for Engineering - SS 15
The screen output running example 3.2 will be the following.
i
i
i
i
i
i
i
i
i
i
1
2
3
4
5
6
7
8
9
10
3.3
= 1
= 2
= 3
= 4
= 5
= 6
= 7
= 8
= 9
= 10
sum
sum
sum
sum
sum
sum
sum
sum
sum
sum
=
=
=
=
=
=
=
=
=
=
1
3
6
10
15
21
28
36
45
55
Calculation of real*4/8 Precision
This example calculates the relative precision of a 4 and 8 byte float
arithmetic. In listing 3.3 a strict 66 coding is used, if we forget the
line end comment. The idea of this algorithm is, to divide a variable’s
value of 1 by 2 as long as the sum of 1 and this reduced value is
greater than 1. If we would have an infinite precision, this loop would
be an endless loop. Because we only have a few digits, this reduced
value will vanish with some cycles. The last visible value than will
be our relative precision.
In figure 3.1 the algorithm to calculate the relative precision is shown.
The first part will calculate the relative precision for a 4 byte arithmetic, the second part will calculate the relative precision for the 8
byte arithmetic.
Start
x1 = 1.
x2 = 1.
d = 2.
x2 = x2 /d
s = x1 + x2
no
s = x1
yes
result =
x2 ∗ d
Stop
Figure 3.1: Algorithm’s Flowchart
Listing 3.3: Calculation of the Arithmetic’s Relative Precision
1
2
3
C234567890
real*4 x14, x24, x34, d4
real*8 x18, x28, x38, d8
! variables for real*4 analysis
! variables for real*8 analysis
4
5
c
6
7
8
calculation of real*4 relative precision
x14 = 1.
x24 = 1.
d4 = 2.
9
10
11
12
100 x24 = x24 /d4
x34 = x14 + x24
c
write (*,1001) x34, x24
E. Baeck
! back jump label and increment
! reduction
! dump is disabled
3.4. RELATIVE PRECISION WITH FUNCTIONS
13
14
15
16
17
18
19
c
if (x34 .gt. x14) goto 100
x24 = x24 * d4
output
write (*,1000) x24
Page 67
! if increment still seen next run
! prints result to screen using
! a format statment (1000)
1000 format(’ real*4 relative precision: ’,e10.3)
1001 format(’ x14+x24 = ’,e20.14,’ x24 = ’,e20.14)
20
21
22
23
24
25
26
27
28
29
30
31
32
c
calculation of real*8 relative precision
x18 = 1.
x28 = 1.
d8 = 2.
! now the same for real*8
200 x28 = x28 /d8
! arithmetic
x38 = x18 + x28
c
write (*,2001) x38, x28
! dump is disabled
if (x38 .gt. x18) goto 200
x28 = x28 * d8
c
output
write (*,2000) x28
33
34
35
36
2000 format(’ real*8 relative precision: ’,e10.3)
2001 format(’ x18+x28 = ’,e20.14,’ x28 = ’,e20.14)
end
!
If we run this code, we will get the following screen output.
1
2
real*4 relative precision:
real*8 relative precision:
0.119E-06
0.222E-15
We see, that with 4 byte real we nearly get 7 digits, for a 8 byte real we nearly get 16 digits.
3.4
Function to Calculate the Relative Precision
The following code consists of two routines, the first is the main program, which calls the evaluation
function getRelPrec to get the relative precision. The function is working with one integer parameter.
If the parameter is set to 0, the function evaluates the 4 byte relative precision, if the parameter is set to
any value but not 0, the function evaluates the 8 byte relative precision.
9.6.2015
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Computer Languages for Engineering - SS 15
The main program (line 1 to 7) is a testing environments and performs the calls. The code of the function
is given starting from line 9.
Listing 3.4: Function to Evaluate the Relative Precision for 4 and 8 byte floats
1
2
3
4
5
6
7
! evaluate the relative precision for
! 4 and 8 byte float arithmetic
program getRelPrecMain
real(8) :: getRelPrec, eps
write(*,*) ’4 byte relative precision: ’, getRelPrec(0)
write(*,*) ’8 byte relative precision: ’, getRelPrec(1)
end program getRelPrecMain
8
9
10
11
12
13
14
! function to calculate the relative precision
real(8) function getRelPrec(nBytes) ! function interface
! return type is real*8, name is getRelPrec
integer :: nBytes
! nByte: 0:4 bytes / 1:8 bytes
real(4) :: x14,x24,s4,d4
! 4 byte data
real(8) :: x18,x28,s8,d8
! 8 byte data
15
! calculation for 4 byte arithmetic
if (nBytes == 0) then
x14 = 1.
x24 = 1.
d4 = 2.
do
! implicit loop without a counter
x24 = x24/d4
s4 = x14+x24
if (s4 <= x14) exit
end do
eps = x24*d4
! last division should be canceld
! by multiplication
16
17
18
19
20
21
22
23
24
25
26
27
28
else
x18 = 1.
x28 = 1.
d8 = 2.
do
x28 = x28/d8
s8 = x18+x28
if (s8 <= x18) exit
end do
eps = x28*d8
29
30
31
32
33
34
35
36
37
38
39
! implicit loop without a counter
! last division should be canceld
! by multiplication
endif
40
41
42
43
getRelPrec = eps
end function getRelPrec
E. Baeck
! assigning the return value
! end of function
3.5. NEWTON’S ALGORITHM TO CALCULATE A ROOT
3.5
Page 69
Newton’s Algorithm to calculate a Root
The following example shows, how to pass a function as
a functions parameter. Within the Newton’s algorithm
a root of an equation should be calculated. So we have
to specify the function of interest. The function can be
considered as an input parameter. The function’s name
is passed to the derivative calculator and to the newton
main routine.
So, if we want to calculate the roots of an equation
f (x ) = 0, we can apply the iteration scheme 3.3. The
derivative in the denominator is calculated numerically
in equation 3.2. We see that in both equations we need
the values of the function f . This problem can be solved
by passing the function as a parameter.
Figure 3.2: Scheme of the Newton Algorithm
The derivative - it’s called fs in the code - is calculated numerical as follows.
h
h
df
0
≈ f (x + ) − f (x − ) /h
f (x ) =
dx
2
2
(3.2)
The Newton scheme can be described as follows.
f (x )
xi+1 = xi − 0
f (x )
(3.3)
The same formula we get from the triangle of the slope (see figure 3.2) resolving for xn1 .
f 0 (xn ) =
f (xn )
xn − xn+1
(3.4)
There are three possible situations to handle within the iteration loop.
• The function value is vanishing with respect to our selected precision. The iteration loop will be
broken and the found result is passed back to the caller.
• The slope of the function is vanishing. With a vanishing slope we would divide by zero. With an
infinitesimal slope we would get a nearly infinite jump length, which in every case would not be
helpful. Therefore in this case we simple jump to the side and try it once more.
• During the iteration each cycle is counted. So the iteration loop will be broken, if the maximum
available iterations are reached. The actual values and an error message is passed bake to the caller.
The code consists of a main program which calls the function newton. Within newton the functions
f and fs are called. So we have to implement the following functions.
• Myf, the function of our interest.
• fs, the function which calculates the slope of a given function numerically.
• newton, implements the newton scheme.
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Figure 3.3 shows a flowchart of Newton’s algorithm. First we set the system’s parameter. Then
in the iteration loop we calculate the functions
value and it’s derivative. In the simple Newton
case we handle the three break conditions in an
open loop.
Start
Set Parameters:
x0 ; itmax ; ; ...
Initializing:
x = x0 ; it = 0;
The first checks the function value. If the function value is close enough to zero, we have found
a root and the cycles will stop.
Function Data:
F = f (x ); FS = f 0 (x );
The second checks the function’s slope. We
should not divide by zero, therefor we break, if
the slope comes close to zero.
The third checks the iteration break condition,
i.e. the whether the maximal allowed iteration
number is reached. In this case the loop breaks,
because there is no root found.
If we survive all break conditions, the next iteration step is introduce, i.e the new x value is calculated and the iteration counter is incremented.
it ≥ itmax
yes
No Solution
no
|F | < it = it + 1
yes
Solution
no
The code can be separated in two parts or
modules. The first module, which is called
NewtonMain.f90, contents the specific code,
i.e. the main program and a testing function.
The second module, which is called Newton.f90,
contents the newton scheme and the numerical
calculation of the function’s derivative.
x = x −s
yes
|FS | < no
F
x = x − FS
it = it + 1
Figure 3.3: The Newton’s Flowchart
Listing 3.5: Testing Environment to Check the Newton Function
1
2
! Main program to test the implementation
! of newton’s algorithm
3
4
5
program NewtonMain
implicit none
6
7
8
9
10
11
12
! setup the testing parameters
real(8):: x0
! starting value
real(8):: eps
! precision
integer:: nmax
! maximum number of iterations
real(8), external:: Myf
! declaration of the function
integer, external:: newton ! declaration of the newton function
13
14
integer:: nret
15
16
E. Baeck
real(8):: x
! return of the newton function
! solution
! root
3.5. NEWTON’S ALGORITHM TO CALCULATE A ROOT
17
18
19
real(8):: f0
real(8):: fs0
integer:: nit
!
!
!
x0 = 4.
eps = 1.e-6
nmax= 100
! starting position
! the root’s minimal precison
! available iterations
Page 71
function’s value
slope at root’s position
number of used cycles
20
21
22
23
24
25
26
27
28
29
! print input values
write(*,*) ’ Test program for the newton function’
write(*,’(A,F12.4)’) ’ Starting value..........: ’,x0
write(*,’(A,E12.5)’) ’ Precision...............: ’,eps
write(*,’(A,I6)’)
’ Maximum number of cycles: ’,nmax
30
31
32
33
34
! the newton is implemented as a function, which returns a status
! value. The result values are return by the output parameters
!
--- input ----- -- output -nret = newton(Myf,x0,eps,nmax,x,f0,fs0,nit)
35
36
37
38
39
! solution found
!
.eq. (F66/77)
if (nret == 0) then
! here we use C-like F90 operators
write (*,*) ’ Solution found!’
40
41
42
43
! error: vanishing slope, avoid to divide by zero
else if (nret == 1) then
write (*,*) ’ Vanishing slope, no result found!’
44
45
46
47
48
! maximum cycles reached. Break to avoid an infinit loop
else
write (*,*) ’ No solution found, maximum iterations reached!’
end if
49
50
51
52
53
54
! output section
write (*,’(A,F15.8)’)
write (*,’(A,F15.8)’)
write (*,’(A,F15.8)’)
write (*,’(A,I8)’)
’
"
"
"
Solution value....:’,x
Function’s value..:",f0
Function’s slope..:",fs0
Used cycles.......:",nit
55
56
end program
57
58
59
60
61
62
63
64
! user function is an example to tehst newton’s algorithm
! This function is passed to the newton function.
real(8) function Myf(x)
real(8)::x
Myf = x**2 -1
return
end function Myf
The second module contents the more general code, i.e. the code of Newton’s scheme and the derivatives
calculator. General it’s recommended to encapsulate the general code1 into separate modules. This
modules can also be packed into library files2 .
1
2
This is code, which is general applicable and therefore has no dependence with your application
A library file contents compiled module code and can be linked without any compilation to an application.
9.6.2015
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Computer Languages for Engineering - SS 15
Listing 3.6: Simple Newton Function
1
2
3
! implementation of Newton’s algorithm
integer function newton (f,x0,e,ix,x,fx,fsx,nx)
implicit none
4
5
6
real(8), external:: f
real(8), external:: fs
! user function
! deviation calculator
real(8)::x0
real(8)::e
real(8)::h
real(8)::x
real(8)::fx
real(8)::fsx
real(8)::s = 1.0
integer::ix,nx
!
!
!
!
!
!
!
7
8
9
10
11
12
13
14
15
start value
root precision
deviation step width
result: root value
function’ value at x
function’s deviation at x
jump length
16
! initialization section
x = x0
! initialize the iteration variable
nx = 1
! iteration counter
h = e
! set step width for numerical deviation
17
18
19
20
21
! iteration loop (note it’s a named loop)
mainloop: do
22
23
24
fx = f(x)
fsx= fs(f,x,h)
25
26
! calculating the function’s value
! and the function’s solpe
27
! check the number of cycles, if exceeded return with error
if (nx == ix) then
newton = 2
return
28
29
30
31
32
! check the function value, if success return
else if (dabs(fx) < e) then
newton = 0
return
33
34
35
36
37
! check the slope, if vanishing, jump to the side
else if (dabs(fsx) < e) then
x = x + s
38
39
40
41
! calculating the next x value
else
x = x - fx/fsx
end if
42
43
44
45
46
! count the cycle
nx = nx +1
47
48
49
end do mainloop
50
51
52
end function newton
53
54
! function to calculate the deviation of a function
E. Baeck
3.5. NEWTON’S ALGORITHM TO CALCULATE A ROOT
55
56
57
58
59
60
Page 73
! note, that a vanishing step width is not handled
real(8) function fs (f,x,h)
real(8), external:: f
real(8):: x,h
fs = (f(x +h/2) - f(x -h/2))/h
end function
The second version of the Newton program will be extended by a function iwritefunction, which
should print the function’s values and the derivative of the function in a given range.
We extend the main module by a log file newtonlog.txt and a static array for the iteration path.
Before we call the newton function the function iwritefunction will be called to print the function
values. The allocated array is passed to the newton function to get the iteration path data.
Listing 3.7: Testing Environment to Check the Newton Function
1
2
! Main program to test the implementation
! of newton’s algorithm
3
4
5
program NewtonMain
implicit none
6
7
8
9
10
11
12
! setup the testing parameters
real(8):: x0
! starting value
real(8):: eps
! precision
integer:: nmax
! maximum number of iterations
real(8), external:: Myf
! declaration of the function
integer, external:: newton ! declaration of the newton function
13
14
integer:: nret
15
16
17
18
19
20
21
22
real(8):: x
real(8):: f0
real(8):: fs0
integer:: nit
character(256)::filename
integer::ioerr
integer::iwritefunction
!
!
!
!
!
!
!
!
!
return of the newton function
solution
root
function’s value
slope at root’s position
number of used cycles
name of the log file
return of the write function
return value of the function
23
24
25
! F66/77 version static array
real(8), dimension(100)::xp ! iteration path, x values
26
27
28
29
x0 = 0.
eps = 1.e-6
nmax= 100
! starting position
! the root’s minimal precison
! available iterations
30
31
filename = ’newtonlog.txt’
32
33
34
35
36
37
! print input values
write(*,*) ’ Test program for the newton function’
write(*,’(A,F12.4)’) ’ Starting value..........: ’,x0
write(*,’(A,E12.5)’) ’ Precision...............: ’,eps
write(*,’(A,I6)’)
’ Maximum number of cycles: ’,nmax
38
39
40
! print the function’s values into the log file
ioerr = iwritefunction(filename,Myf,-10.D0,10.D0,0.5D0)
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Computer Languages for Engineering - SS 15
if (ioerr == 0) then
write(*,’(a)’) ’ No problems writing functions values.’
else
write(*,’(a,i10)’) " Error writing function values, code=",ioerr
endif
41
42
43
44
45
46
! the newton is implemented as a function, which returns a status
! value. The result values are return by the output parameters
!
--- input ----- -- output -nret = newton(Myf,x0,eps,nmax,x,f0,fs0,nit,xp)
47
48
49
50
51
! solution found
!
.eq. (F66/77)
if (nret == 0) then
! here we use C-like F90 operators
write (*,*) ’ Solution found!’
52
53
54
55
56
! error: vanishing slope, avoid to divide by zero
else if (nret == 1) then
write (*,*) ’ Vanishing slope, no result found!’
57
58
59
60
! maximum cycles reached. Break to avoid an infinit loop
else
write (*,*) ’ No solution found, maximum iterations reached!’
end if
61
62
63
64
65
! output section
write (*,’(A,F15.8)’)
write (*,’(A,F15.8)’)
write (*,’(A,F15.8)’)
write (*,’(A,I8)’)
66
67
68
69
70
’
"
"
"
Solution value....:’,x
Function’s value..:",f0
Function’s slope..:",fs0
Used cycles.......:",nit
71
72
end program
73
74
75
76
77
78
79
! user function is an example to tehst newton’s algorithm
! This function is passed to the newton function.
real(8) function Myf(x)
real(8)::x
!
Myf = x**2 -1
! Test 1
80
81
82
83
84
!
Myf = x**2 +1
Myf = x**3 +1
return
end function Myf
! Test 2
! Test 3
The array for the storage of the iteration path data is passed to the newton function. Within the
mainloop the positions on the iteration path are saved into the array xpos. At the end of the module
the function iwritefunction is added to print the function’s values.
E. Baeck
3.5. NEWTON’S ALGORITHM TO CALCULATE A ROOT
Page 75
Listing 3.8: Simple Newton Function
1
2
3
! implementation of Newton’s algorithm
integer function newton (f,x0,e,ix,x,fx,fsx,nx,xpos)
implicit none
4
5
6
real(8), external:: f
real(8), external:: fs
! user function
! deviation calculator
real(8)::x0
real(8)::e
real(8)::h
real(8)::x
real(8)::fx
real(8)::fsx
real(8)::s = 1.0
integer::ix,nx
real(8),dimension(ix)::xpos
!
!
!
!
!
!
!
7
8
9
10
11
12
13
14
15
16
start value
root precision
deviation step width
result: root value
function’ value at x
function’s deviation at x
jump length
17
18
19
20
21
! initialization section
x = x0
! initialize the iteration variable
nx = 1
! iteration counter
h = e
! set step width for numerical deviation
22
23
24
! iteration loop (note it’s a named loop)
mainloop: do
25
26
27
fx = f(x)
fsx= fs(f,x,h)
! calculating the function’s value
! and the function’s solpe
28
29
30
! be sure, that the array is dimensioned properly
xpos(nx) = x
31
32
33
34
35
36
! check the number of cycles, if exceeded return with error
if (nx == ix) then
newton = 2
return
37
38
39
40
41
! check the function value, if success return
else if (dabs(fx) < e) then
newton = 0
return
42
43
44
45
! check the slope, if vanishing, jump to the side
else if (dabs(fsx) < e) then
x = x + s
46
47
48
49
50
! calculating the next x value
else
x = x - fx/fsx
end if
51
52
53
! count the cycle
nx = nx +1
54
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Computer Languages for Engineering - SS 15
end do mainloop
55
56
57
end function newton
58
59
60
61
62
63
64
65
! function to calculate the deviation of a function
! note, that a vanishing step width is not handled
real(8) function fs (f,x,h)
real(8), external:: f
real(8):: x,h
fs = (f(x +h/2) - f(x -h/2))/h
end function
66
67
68
69
! write function values to a file
!
integer function iwritefunction(name,f,xfrom,xto,xstep)
70
71
72
73
74
75
character(256):: name
real(8),external::f
real(8)::xfrom
real(8)::xto
real(8)::xstep
!
!
!
!
!
files name
function
start value
end value
step width
76
77
78
79
integer::ioerror
real(8)::x
real(8)::h
! return status
! actual position
! step width calculating the derivative
80
81
82
83
84
85
86
! check the input parameters
if (xstep < 1.e-6) then
write (*,*) ’ *** Error: xstep not ok!’
iwritefunction = -1
return
endif
87
88
89
90
91
92
93
! open the file
open (10,file=name,status=’replace’,iostat=ioerror)
if (ioerror .ne. 0) then
iwritefunction = ioerror
return
! return if there is an error
endif
94
95
96
97
98
! start with the tables header
!
123456789012345678901234567890
write(10,’(a)’)"
x
f(x)
f’(x)"
write(10,’(a)’)"------------------------------"
99
100
101
102
103
104
! write the function’s values
h = 1.e-6
x = xfrom
do
write(10,’(3(F10.4))’,iostat=ioerror) x,f(x),fs(f,x,h)
105
106
107
108
109
110
E. Baeck
! break the loop, if an error occure
if (ioerror.ne.0) exit
x = x + xstep
if (x > xto) exit
end do
3.5. NEWTON’S ALGORITHM TO CALCULATE A ROOT
Page 77
111
112
113
! close the output file
close(10)
114
115
116
! return the error code
iwritefunction = ioerror
117
118
end function iwritefunction
9.6.2015
Page 78
3.6
Computer Languages for Engineering - SS 15
Matrix Product with 77-Main and 90-Library
Within this section the mix of FORTRAN code of version 77 and 90 are discussed. Because in FORTRAN77 only static arrays are available, a buffer array is introduced. This array is used for the program
memory management.
For the three matrices A, B and C , which we use, index pointers into the buffer array are used for
mapping. The dimensions of matrix A and B are read from an input file.
The matrix product is calculated according to the following formula.
C =A·B
(3.5)
with an matrix element Ci,j
Ci,j =
n
X
Ai,k · Bk ,j = Ai,k · Bk ,j
(3.6)
k =1
The last expression follows the Einstein notation, which means that we sum over the indices which ocrur
in every term.
Listing 3.9: 77 Environment to call subsequent FORTRAN90 Routines
1
2
c Fortran77 example to handle a pseudo dynamical memory
c manager based on a buffer array
3
4
5
6
7
c234567
integer
buffersize
parameter (buffersize = 100)
real*8 buffer(buffersize)
! we use a parameter to
! allocate the work buffer
! statical allocation of the buffer
8
9
10
11
integer
integer
integer
ipA
ipB
ipC
! pointer of array A
! pointer of array B
! pointer of array C
integer
iret
! return code
integer
integer
integer
nDimA(2)! Dimension of arra A
nDimB(2)! Dimension of arra B
nDimC(2)! Dimension of arra C
integer
integer
ionr
ioerr
integer
ireadmatdim,ireadmat,imatmult
12
13
14
15
16
17
18
19
20
! io channel number
! error parameter
21
22
23
character*32
24
InpFile
25
InpFile = ’MatMult77.inp’
ionr
= 10
26
27
! fixed input file name
28
29
c
30
31
32
33
E. Baeck
open the input file
write(*,*) ’> open the file:’,InpFile
open(ionr,file=InpFile,status=’old’,iostat=ioerr)
if (ioerr .ne. 0) then
write(*,*) ’*** Error: open file ’,InpFile
3.6. MATRIX PRODUCT WITH 77-MAIN AND 90-LIBRARY
Page 79
stop
endif
34
35
36
37
c
read dimension of the 1st matrix
iret = ireadmatdim(ionr,nDimA)
if (iret .ne. 0) goto 900
! jump to the error exit
write(*,*) ’> dimension of array 1 read:’,nDimA(1),’,’,nDimA(2)
c
read data of array 1
ipA = 1
iret = ireadmat(ionr,buffer(ipA),nDimA)
if (iret .ne. 0) goto 900
! jump to the error exit
c
and list it’s data
call listmat(’Data of matrix 1:’,buffer(ipA),nDimA)
c
read dimension of the 2nd matrix
iret = ireadmatdim(ionr,nDimB)
if (iret .ne. 0) goto 900
! jump to the error exit
write(*,*) ’> dimension of array 2 read:’,nDimB(1),’,’,nDimB(2)
c
read data of array 2
ipB = ipA + nDimA(1)*nDimA(2)
iret = ireadmat(ionr,buffer(ipB),nDimB)
if (iret .ne. 0) goto 900
! jump to the error exit
c
and list it’s data
call listmat(’Data of matrix 2:’,buffer(ipB),nDimB)
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
c
64
65
66
67
68
69
70
multiply matrix 1 with matrix 2
ipC = ipB +nDimB(1)*nDimB(2)
iret = imatmult(buffer(ipA),buffer(ipB),buffer(ipC),
&
nDimA,nDimB)
if (iret .ne. 0) then
write(*,*) ’*** Error: wrong dimensions for product’
goto 900
! jump to the error exit
endif
71
72
c
print the result
nDimC(1) = nDimA(1)
nDimC(2) = nDimB(2)
call listmat(’Data of product matrix 1x2:’,buffer(ipC),nDimC)
c
no problems therefore jump to the regular end
goto 999
73
74
75
76
77
78
79
80
c
error exit
900 write(*,*) ’> Programm canceled due to an error!’
goto 999
! at last we have to close the input file
c
close the input file
999 close(ionr)
81
82
83
84
85
86
87
88
stop
end
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Computer Languages for Engineering - SS 15
Within the FORTAN77 code some array functions are called. This functions are coded in FORTRAN90+.
You see that using the new GNU FORTRAN compiler, it is possible to mix Fortran77 with FORTRAN90+
without any problems.
Listing 3.10: 90 Library to Perform a Matrix Product
1
2
! Note: every read statements reads exactly one line
!
empty lines are NOT ignored
3
4
5
! read the matrix dimensions
integer function ireadmatdim(io,nDim)
6
integer:: io
integer, dimension(2):: nDim
7
8
! io channel number
! dimension array
9
read(io,*,iostat=ioerr) nDim(1),nDim(2)
if (ioerr /= 0) then
! handle io errors
write(*,*) ’*** Error: reading dimension data!’
ireadmatdim = -1
return
! if not ok, then return
endif
10
11
12
13
14
15
16
! simple check of the dimensions
if (nDim(1) < 1 .or. nDim(2) < 1) then
write(*,*) ’*** Error: invalid dimension data:’,nDim(1),’,’,nDim(2)
ireadmatdim = -2
return
endif
17
18
19
20
21
22
23
ireadmatdim = 0
24
! return code for ok
25
26
end function ireadmatdim
27
28
29
! function for reading a matrix
integer function ireadmat(io,a,nDim)
30
integer::io
integer,dimension(2)::nDim
real(8),dimension(nDim(1),nDim(2))::a
31
32
33
! io channel number
! declare the dimensions
! array
34
! over the rows
do i=1,nDim(1)
read(io,*,iostat=ioerr) (a(i,j),j=1,nDim(2))
35
36
37
38
if (ioerr /= 0) then
! if an error occure, return
write(*,*)’*** Error: reading matrix data!’
ireadmat = -1
return
endif
enddo
ireadmat = 0
39
40
41
42
43
44
45
46
47
end function ireadmat
48
49
50
! print array data to the screen with a comment
subroutine listmat (comment,a,nDim)
E. Baeck
3.6. MATRIX PRODUCT WITH 77-MAIN AND 90-LIBRARY
Page 81
51
52
53
54
character*(*)
comment
integer, dimension(2)::nDim
real(8),dimension(nDim(1),nDim(2))::a
! comment to print
! dimension of the matrix
! array data to print
write(*,*) comment
! write the comment line
55
56
57
58
59
60
61
! over the rows
do i=1,nDim(1)
write(*,*) (a(i,j),j=1,nDim(2))
enddo
62
63
end subroutine listmat
64
65
66
! product of 2 matrices
integer function imatmult(a,b,c,nDimA,nDimB)
67
68
69
70
71
integer, dimension(2)::nDimA,nDimB
real(8),dimension(nDimA(1),nDimA(2))::a
real(8),dimension(nDimB(1),nDimB(2))::b
real(8),dimension(nDimA(1),nDimB(2))::c
!
!
!
!
declare
declare
declare
declare
the dimension arrays
array a
array b
array c
72
73
74
75
76
77
! check the dimension of the matrices
if (nDimA(2) /= nDimB(1)) then
imatmult = -1
return
endif
78
79
80
81
82
83
84
85
86
87
88
89
90
! calculate the product of the matrices
! - over the rows of C
do i=1,nDimA(1)
! - over the columns of c
do j=1,nDimB(2)
c(i,j) = 0.
! initialize it
do k=1,nDimA(2)
c(i,j) = c(i,j) + a(i,k)*b(k,j)
enddo
enddo
enddo
imatmult = 0
91
92
end function imatmult
If the main program is coded in FORTRAN90+, the application can be much more flexible as if it would
be coded in FORTRAN77. One very useful addon coming from FORTRAN90+ is a buildin access to
the command line parameters. With this extension we can pass a for example the name of an input file
through the programs interface. The second extension, which is very important here, is an dynamical
memory management. In our FORTRAN77 - version, we have to introduce a static memory buffer
and have to map all the variables which should be dynamical onto it, i.e. we have to do the memory
management, the OS would provide us by free.
9.6.2015
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Computer Languages for Engineering - SS 15
Listing 3.11: A Dynamical 90+ Version of our first 77 Environment
1
2
3
! dynamical arrays in FORTRAN 90+
program MatMult90
implicit none
4
5
6
integer::ioin
integer::ioout
= 10
= 11
! Input channel
! Output channel
7
8
9
10
! helper variables
integer::ioerr
integer::memerr
! error code for io activities
! error code for allocation
! static
integer,
integer,
integer,
! dimension of matrix A
! dimension of matrix B
! dimension of matrix C
11
12
13
14
15
arrays
dimension(2)::nDimA
dimension(2)::nDimB
dimension(2)::nDimC
16
17
18
19
20
! allocatable arrays
real(8), allocatable, dimension(:,:)::A
real(8), allocatable, dimension(:,:)::B
real(8), allocatable, dimension(:,:)::C
21
22
23
! function’s return values
integer::ireadmatdim,ireadmat,ilistmat,imatmult
24
25
26
27
! some strings
character(256)::infile
character(256)::outfile
! input file name
! output file name
28
29
30
31
! setup standard names
infile = "matmult90.in"
outfile = "matmult90.out"
32
33
34
! start comment
write(*,*) ’ open input file...’
35
36
37
38
39
40
41
! open the input file
open(ioin,file=infile,status=’old’,iostat=ioerr)
if (ioerr /= 0) then
write(*,*) "*** error: file ’",infile(1:len_trim(infile)),"’ not found!"
stop
endif
42
43
44
45
46
47
48
! open the output file
open(ioout,file=outfile,status=’replace’,iostat=ioerr)
if (ioerr /= 0) then
write(*,*) "*** error: file",outfile," not found!"
stop
endif
49
50
!>>>>> get the matrix A <<<<<<<
51
52
53
54
E. Baeck
! read the dimesion of matrix A
if (ireadmatdim(ioin,nDimA) < 0) then
write(*,*) "*** error: no dimension for matrix A available!"
3.6. MATRIX PRODUCT WITH 77-MAIN AND 90-LIBRARY
55
56
Page 83
stop
endif
57
58
write(*,*) "dimension of A: ",nDimA(1),"/",nDimA(2)
59
60
61
62
63
64
65
! allocate the matrix A
allocate(A(nDimA(1),nDimA(2)),stat=memerr)
if (memerr /= 0) then
write(*,*) ’*** error: allocation of matrix A’
stop
endif
66
67
write(*,*) "read matrix data of
A..."
68
69
70
71
72
73
! read the matrix data for A
if (ireadmat(ioin,nDimA,A) /= 0) then
write(*,*) ’*** error: reading matrix data!’
stop
endif
74
75
write(*,*) "print matrix data of
A..."
76
77
78
! print the data of matrix a
ioerr = ilistmat(ioout,’Matrix a’,nDimA,a)
79
80
!>>>>> get the matrix B <<<<<<<
81
82
83
84
85
86
! read the dimesion of matrix B
if (ireadmatdim(ioin,nDimB) < 0) then
write(*,*) "*** error: no dimension for matrix B available!"
stop
endif
87
88
write(*,*) "dimension of B: ",nDimB(1),"/",nDimB(2)
89
90
91
92
93
94
95
! allocate the matrix B
allocate(B(nDimB(1),nDimB(2)),stat=memerr)
if (memerr /= 0) then
write(*,*) ’*** error: allocation of matrix B’
stop
endif
96
97
write(*,*) "read matrix data of
B..."
98
99
100
101
102
103
! read the matrix data for B
if (ireadmat(ioin,nDimB,B) /= 0) then
write(*,*) ’*** error: reading matrix data!’
stop
endif
104
105
write(*,*) "print matrix data of
B..."
106
107
108
! print the data of matrix B
ioerr = ilistmat(ioout,’Matrix b’,nDimB,b)
109
110
!>>>>> perform the the product A*B -> C <<<<<<<
9.6.2015
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Computer Languages for Engineering - SS 15
111
! check the dimension!
if (nDimA(2) /= nDimB(1)) then
write (*,*) "*** dimension error! A*B not possible!"
stop
endif
112
113
114
115
116
117
nDimC(1) = nDimA(1) ! rows of A
nDimC(2) = nDimB(2) ! columns of B
118
119
120
! allocate the matrix C
allocate(C(nDimC(1),nDimC(2)),stat=memerr)
if (memerr /= 0) then
write(*,*) ’*** error: allocation of matrix C’
stop
endif
121
122
123
124
125
126
127
! perform the product
ioerr = imatmult(a,b,c,nDimA,nDimB)
128
129
130
! print the data of matrix C = A*B
ioerr = ilistmat(ioout,’Matrix c = a*b’,nDimC,c)
131
132
133
! deallocate the memory
deallocate(a,stat=memerr)
deallocate(b,stat=memerr)
deallocate(c,stat=memerr)
134
135
136
137
138
write(*,*) "close files..."
139
140
! close the files
close(ioin)
close(ioout)
141
142
143
144
145
146
147
end program
E. Baeck
4
Linear Algebra, Vectors and Matrices
This chapter was written as support for the first lectures only dealing with FORTRAN77 development.
Later FORTRAN90 and C++ were added to the curiculum, so that this chapter can be considered as
obsolete with respect to our current curiculum.
4.1
4.1.1
Helper Functions
Outlines
Within the following sections we will discuss some helper functions which we will use to implement the
gauss decomposition algorithm and its testing environment.
4.1.2
Reset and List a Matrix
To check matrices which are decomposed in a lower and upper triangle for example by GaussLU decomposition its helpful to have some helper functions for checking. The helper function ExtractLU extracts
the upper and lower triangle matrix of an arbitrary matrix.
If we multiply the upper by the lower matrix we should get the original matrix which was decomposed
in triangles.
The following new statements are used.
• include1 , includes a source code file into a main file.
• dimension2 , allocates arrays of items of the same data type.
• subroutine3 , declares a subroutine which could be seen as function without return value.
• call4 , a subroutine can be called by the use of the call statement.
• read5 , the read statement is used to read data from keyboard or file.
1
include statement, Page 108, [2]
dimension statement, Page 51, [2]
3
subroutine statement, Page 166, [2]
4
call statement, Page 26, [2]
5
read statement, Page 145, [2]
2
85
Page 86
Name
Computer Languages for Engineering - SS 15
Comments
ResetMat ResetMat resets the content of a given matrix. The content can be reseted
optionally to the values of a zero matrix and a unity matrix
ListMat
ListMat prints the values of given matrix into the screen window. The values
of the matrix can be titled with an arbitrary comment string.
ExtractLU ExtractLU extracts the values of a LU-decomposed matrix into a normalized
lower triangle matrix and a upper triangle matrix. This function is necessary
to check the decomposed matrix automatically.
MatMult
MatMult performs the multiplication of two arbitrary matrices whose dimensions fit to the multiplication algorithm. We use this function to check the
decomposed matrix automatically.
DiffMat
DiffMat calculates the difference matrix of two matrices and returns the norm
of the greatest deference item. This function will be used to check the the
decomposed matrix.
ReadDim ReadDim is used to read the dimension of the matrices from an input file.
ReadMat
ReadMat reads the matrix values from a text file. This function is used to import test values into the testing environment of the decomposition application.
WriteMat WriteMat writes the matrix values to a text file. This function is used to export
test values from the testing environment of the decomposition application.
Table 4.1: Helper Functions
The global trace flag is part of the common block defined in the header file trace.h.
Listing 4.1: Global Data
1
2
3
c234567
common /trace/ ntrace
integer*4 ntrace
E. Baeck
! global flag
! defined in a header file
4.1. HELPER FUNCTIONS
Page 87
The subroutine ResetMat sets the data of an array optional to zero or to unit matrix.
Listing 4.2: Reset a Matrix’s Data
1
2
3
c subroutine to initialize a matrix (n1xn2)
c if mode = 1 a unit-matrix is set
c in all other cases a zero-matrix is set
4
subroutine ResetMat(rm,n1,n2,mode)
5
6
7
8
c
c
mode = 0 >> zero-matrix
mode = 1 >> unit-matrix
9
10
11
12
integer*4 n1, n2
integer
mode
real*8
rm(n1,n2)
! matrix dimensions
! reset flag
! declaring the passed matrix
column-index
do i=1,n2
! in fortran it’s faster to run first
! over all rows then over all columns
13
14
c
15
16
17
c
18
row-index
do j=1,n1
19
20
c
version 1 with nested ifs
if (i.eq.j) then
if (mode.eq.1) then
rm(j,i) = 1.
else
rm(j,i) = 0.
endif
else
rm(j,i) = 0.
endif
c
c
c
c
c
c
version 2 with only one if without nesting
if (i.eq.j .and. mode.eq.1) then
a(j,i) = 1.
else
a(j,i) = 0.
endif
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
enddo
39
40
enddo
41
42
43
return
end
9.6.2015
Page 88
Computer Languages for Engineering - SS 15
The subroutine ListMat prints the data of a matrix to the console window. Besides the data of a matrix
the subroutine should print a little title.
Listing 4.3: List a Matrix’s Data
subroutine ListMat(com,rm,n1,n2)
1
2
character *(*) com
integer*4 n1, n2
real*8
rm(n1,n2)
3
4
5
! *(*) means with variable length
! matrix dimensions
! matrix to print
6
7
c
loop over all rows
write (*,’(a)’) com
do i=1,n1
! print a little title
! loop over all lines
! implicit loop in write statement
write(*,’(10f10.2)’) (rm(i,j),j=1,n2)
8
9
10
11
12
enddo
13
14
return
end
15
16
To test the helper subroutines ResetMat and ListMat a main program should be developed.
Listing 4.4: Check of previous Routines
1
2
3
c234567
c
Main program for step 1
program matrices1
4
5
real*8 a(dim,dim)
! declaring a matrix
call ResetMat(a,dim,dim,1)
call ListMat(’a-matrix’,a,dim,dim)
read (*,*) i
! initialize matrix
! list matrix values to the screen
! read a value
6
7
8
9
10
11
E. Baeck
end
4.1. HELPER FUNCTIONS
4.1.3
Page 89
LU-Extract, Product and Matrix Compare
In this section we will add some further subroutines and functions to the helper functions library of
section 4.1.2.
If we want to check the LU decomposition
A=L·U
(4.1)
we have to extract the L and U part of a decomposed matrix Ax , which holds the upper triangle and the
diagonal of the U in its upper triangle and it’s diagonal values. The values of the L can extracted form
the lower triangle of Ax . Because the L has only 1 values on it’s diagonal, we don’t need to store this
values.
So we need an extractor subroutine, which creates the L and U matrix. Further we need a subroutine
for the multiplication of matrices which is called MatMult. At the end we will need a subroutine which
searches for the maximum difference of the elements of two matrices which is called DiffMat.
The next coding shows the implementation of the extractor of lower and upper triangle.
Listing 4.5: Extract the Triangle Data of a Matrix
subroutine ExtractLU (a,l,u,n)
1
2
3
4
5
6
c
c
c
c
a:
l:
u:
n:
result matrix form LU decomposition
lower triagle extracted to n x n
upper triagle extracted to n x n
dimension of a,l,n >> n x n
7
integer
real*8
8
9
n
a(n,n),l(n,n),u(n,n)
10
11
c
12
rows
do i = 1,n
13
14
c
15
columns
do j = 1,n
16
17
18
c
c
if upper triangle, the lower is set to 0, the
upper triangle value is taken
if (i.lt.j) then
l(i,j) = 0.
u(i,j) = a(i,j)
c
c
if lower triangle, the upper is set to 0, the
lower triangle value is taken
else if (i.gt.j) then
u(i,j) = 0.
l(i,j) = a(i,j)
c
c
if diagonale the lower is set to 1
the diagonale value is assigned to the upper diagonal
else
l(i,j) = 1.
u(i,j) = a(i,j)
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
9.6.2015
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Computer Languages for Engineering - SS 15
endif
35
36
enddo
37
38
enddo
39
40
return
end
41
42
To calculate the original matrix which was decomposed, we have to calculate the product of equation
4.1. In the first version we only use quadratic matrices.
C =A·B
(4.2)
with an matrix element Ci,j
Ci,j =
n
X
Ai,k · Bk ,j
(4.3)
k =1
Listing 4.6: Product of quadratic Matrices
subroutine MatMult(a,b,c,n)
1
2
include ’tracegl.h’
3
! give access to common block
4
5
6
7
8
c
c
c
c
a:
b:
c:
n:
input matrix
input matrix
a x b matrix
dimension of
n x n
n x n
n x n
quadratic array
9
real*8 a(n,n),b(n,n),c(n,n)
10
11
! Trace Code
if (ntrace.gt.0) write(*,*) ’> MatMult started...’
12
13
14
15
c
16
row index
do i=1,n
17
18
c
19
column index
do j=1,n
20
21
22
23
c
c
c
24
25
26
c
27
28
performing the scalar product of
row vector with column vector
but at first we have to initialize the matrix element c(i,j)
c(i,j) = 0.
do k=1,n
! remember: ’*’-Operator has greater priority
!
then ’+’-Operator like in mathematics
c(i,j) = c(i,j) + a(i,k)*b(k,j)
29
30
31
32
end do
enddo
enddo
33
34
E. Baeck
! Trace Code
! end of k-loop
! end of j-loop
! end of i-loop
4.1. HELPER FUNCTIONS
Page 91
if (ntrace.gt.0) write(*,*) ’> MatMult ended...’
35
36
return
end
37
38
The function DiffMat calculates the norm of the greatest element of a difference matrix.
d = max (|Ai,j − Bi,j |)
(4.4)
Listing 4.7: Difference Matrix of two Matrices
real function DiffMat(a,b,n)
1
2
3
4
integer
real*8
n
a(n,n),b(n,n)
real*8
d
! dimension of the quadratic matrices
! matrices to analyse
5
6
7
8
c
starting value, any of them we use the element (1,1)
d = dabs(a(1,1) -b(1,1))
c
rows
do i=1,n
9
10
11
12
13
14
c
15
columns
do j=1,n
16
17
c
18
19
20
c
if the next is greater then actual take the next
if (dabs(a(i,j) -b(i,j)) .gt. d) then
dabs(x) calculates the norm of x
d = dabs(a(i,j) -b(i,j))
21
22
endif
23
24
25
enddo
enddo
26
27
28
29
DiffMat = d
return
end
! the greatest difference value is passed back
! to the calling program
9.6.2015
Page 92
4.1.4
Computer Languages for Engineering - SS 15
Matrix Import from Input File
In this section we want to read data from a input text file and save it to array variables. Therefor we
implement a integer function called ReadMat. We pass the io channel number, the reference to the array
variable and its rows and column size. We use the read statement6 .
If there happen any error, the function returns an integer of 1. If no error occur then then function returns
a zero value. This return value can be used in a calling code to handle the error situation.
Listing 4.8: Read Matrix Data from a Text File
integer function ReadMat(io,rm,n1,n2)
1
2
integer
integer
integer
real*8
3
4
5
6
io
n1
n2
rm(n1,n2)
!
!
!
!
io-chanal no.
dimension of rm (rows)
dimension of rm (columns)
matrix
7
8
c
row loop
do i=1,n1
9
10
read (io,*,err=900) (rm(i,j),j=1,n2)
11
12
! read row values in an implicit
! loop
enddo
13
14
ReadMat = 0
return
15
16
! no error
! return to calling program
17
18
19
20
900 ReadMat = 1
return
end
! reading error
The testing environment has the following code.
We declare the array variable and the used input function ReadMat. Then we open the input file called
matrices2.inp with the open statement7 . This file is a text file and contains the matrix element data
separated by spaces. The rows of the matrix data are separated by linefeeds. The second file is an output
file. The file will only be created. After having read the data, both files will be closed using the close
statement8 . If the io-statements are not executed with success the error handler will be activated and will
perform a jump to the specified label.
6
read statement, Page 145, [2]
open statement, Page 131, [2]
8
close statement, Page 34, [2]
7
E. Baeck
4.1. HELPER FUNCTIONS
Page 93
Listing 4.9: Checking the Matrix IO-Functions
1
2
c234567
program matrices2
! defining program name for linker
3
4
5
6
integer
real*8
real*8
ReadMat
a(3,3)
r(3)
io = 5
io = 6
>>> keyboard
>>> screen
! declaration of functions
! test matrix
! test vector
7
8
9
c
c
10
io1 = 10
io2 = 11
11
12
! io-number for input
! io-number for output
13
14
c
open files
open(io1,file=’matrices2.inp’,status=’old’,err=900)! open an existing file
open(io2,file=’matrices2.out’,status=’unknown’)
! create a new file
c
Input section
if (ReadMat(io1,a,3,3) .gt. 0) goto 901
call ListMat(’matrix values of a’,a,3,3)
15
16
17
18
19
20
! read from file
! list read data
21
22
23
24
c
close files
800 close(io1,status=’keep’)
close(io2,status=’keep’)
! close input file
! close output file
25
26
27
pause ’press return key...’
stop
! wait for a look
28
29
30
31
900 write(*,*) ’ file matrices2.inp not found!’
pause ’press return key...’
! wait for a look
stop
32
33
34
901 write(*,*) ’ format error, reading matrix a.’
goto 800
35
36
end
9.6.2015
Page 94
4.1.5
Computer Languages for Engineering - SS 15
Memory Manager and Pseudo Dynamical Allocation
In this section a quasi dynamical memory management approach will be shown. This approach will overcome the statical declaration of arrays in FORTRAN overlaying them with a statical declared memory
block.
After having opened the input file matrices3.inp (see figure 4.1) we should read the dimension of the first
matrix from line 1. This is done by a new helper function which is called ReadDim. With well-known
matrix dimensions we can request the used memory form the memory manager. With the calculated
memory block index the matrix can be read form the file. This is done with the helper function ReadMat
of Section 4.1.4.
With ReadMat the matrix values are read line by line.
Figure 4.1: Input data for matrices3
After having read the matrix data ReadDim is called which read the dimension of the vector, i.e. the
dimension of a matrix with only one column. Then the values of the vector are read line by line with the
function ReadMat.
Listing 4.10: Read Matrix’s Dimension from File
integer function ReadDim(io,rows,cols)
1
2
integer
3
io, rows, cols
4
read (io,*,err=900) rows,cols
ReadDim = 0
return
5
6
7
! read the dimensionvalues rows and cols
! from the input file
8
9
10
11
900 ReadDim = 1
return
end
! error branch, error code set if an
! format error is dedected
The main program Marices3 shows an approach to solve the problem of dynamical memory allocation in
FORTRAN. Because at last FORTRAN offers only the possibility of statical memory allocation we have
to develop our own memory manager.
E. Baeck
4.1. HELPER FUNCTIONS
Page 95
Therefor a memory block is allocated statically and the used memory of the matrices is overlaid on it.
If we want to use the memory we have to calculate the index of each overlay. We start at the beginning
of the memory block. So the first array will get the index 1. The index of the second array is calculated
as the total length of all memory which is already assigned (that means in our example the length of the
first matrix) plus 1. This is the first item of the second matrix.
Listing 4.11: Checking Matrix Allocation
1
2
c234567
program Matrices3
! set the applications name
3
integer
maxmem
parameter (maxmem = 1000)
real*8
mem(maxmem)
4
5
6
! define a parameter to allocate
! the memory block statically
! memory block
7
integer
integer
integer
integer
8
9
10
11
n1,n2,n3,n4
np1
np2
ReadDim, ReadMat
!
!
!
!
matrix/vector dimension
position of 1st array
position of 1st vector
declaring the return data type of functions
12
io1 = 10
np1 = 1
13
14
! input channel for input file
! position of 1st matrix on memoryblock
15
16
c
open the input file
open (io1,file=’matrices3.inp’,status=’old’,err=900)
c
reading the dimension of the matrix
if (ReadDim(io1,n1,n2) .gt. 0)
17
18
19
20
goto 901
21
22
c
reading the dimension of the matrix
if (ReadMat(io1,mem(np1),n1,n2) .gt. 0)goto 902
c
write matrix content to output window
call ListMat(’content of 1st matrix’,mem(np1),n1,n2)
c
reading the dimension of the vector
if (ReadDim(io1,n3,n4) .gt. 0)
23
24
25
26
27
28
29
goto 901
30
31
c
reading the dimension of the matrix
np2 = n1*n2 +1
if (ReadMat(io1,mem(np2),n3,n4) .gt. 0)goto 902
c
write vector content to output window
call ListMat(’content of 1st vector’,mem(np2),n3,n4)
c
halt a little bit
pause ’ press return...’
goto 999
32
33
34
35
36
37
38
39
40
! jump to the end
41
42
c
43
44
45
error branch for missing input file
900 write(*,*) ’ file matrices3.inp not found!’
pause ’ press return...’
stop
46
47
c
error branch for incorrect format of dimension line
9.6.2015
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Computer Languages for Engineering - SS 15
901 write(*,*) ’ format error reading the dimension’
pause ’ press return...’
stop
48
49
50
51
52
c
error branch for incorrect format of matrix value line
902 write(*,*) ’ format error reading the matrix’
pause ’ press return...’
stop
c
"this is the end"
999 stop
end
53
54
55
56
57
58
59
The output of the program Matrices3 is shown in figure 4.2.
Figure 4.2: Output screen
In figure 4.3 the memory overlay for our little example are shown. Left-aligned we see the memory of
the 3x3 matrix and at the right of the matrix we see the memory block of the vector. In our case the
parameter memmax must be greater equal 12 to have enough memory to allocate the examples data.
Figure 4.3: Memory overlays
E. Baeck
4.1. HELPER FUNCTIONS
4.1.6
Page 97
Automatic Allocation of a Set of Matrices
In this section the main module of the last example is extended. The error handling is changed to a more
variable one. The matrices are read within a loop. The memory pointer are calculated step by step based
on the read matrix dimensions.
We have added two further vectors to our input data file.
Figure 4.4: Input data for matrices3, version 2
The code of the main program is given below.
Listing 4.12: Checking Automatic Memory Manager
1
2
c234567
program Matrices3
! set the applications name
3
4
include ’tracegl.h’
! access to global data, common block
integer
maxmem
parameter (maxmem = 1000)
real*8
mem(maxmem)
! define a parameter to allocate
! the memory block statically
! memory block
integer
maxmat
parameter (maxmat = 7)
! number of matrices
! we want to handle 7 matrices
5
6
7
8
9
10
11
12
13
14
15
integer
integer
integer
nrow(maxmat)
ncol(maxmat)
np(maxmat)
! matrix/vector row dimension
! matrix/vector column dimension
! position of matrix "i"
16
17
18
19
integer
nCode
character*32 cCode
integer
ReadDim, ReadMat,
! error-Code of io functions
! error text
! declaring the return data type of functions
9.6.2015
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Computer Languages for Engineering - SS 15
&
20
21
22
23
WriteMat
io1 = 10
io2 = 11
np1 = 1
! input channel number for input file
! output cannel number for output file
! position of 1st matrix on memoryblock
initalization of tracing
ntrace = 0
! tracing disabled
24
25
c
26
27
28
c
open the input file
cCode = ’*** error: input file not found!’
open (io1,file=’matrices3.inp’,status=’old’,err=900)
c
c
c
c
read trace information from input file
ntrace = 0: tracing disabled
ntrace = 1: tracing level one (start/stop of routines)
ntrace = 2: tracing level two (al trace data)
cCode = ’*** error: traceinfo not found!’
read(io1,*,err=900) ntrace
!
c
open the output file
cCode = ’*** error: output file could not be created!’
open (io2,file=’matrices3.out’,status=’unknown’,err=900)
c
reading the matrix and vector information of 4 matrices
do i =1,4
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
c
setup 1st memory pointer
if (i.eq.1) then
np(i) = 1
c
setup momory pointers starting from the 2nd ...
else
previous + length of previous matrix
np(i) = np(i-1) + nrow(i-1)*ncol(i-1)
endif
47
48
49
50
51
52
c
53
54
55
56
c
57
58
59
&
60
61
62
reading the dimension of the matrix
nCode = ReadDim(io1,nrow(i),ncol(i))
if (nCode .gt. 0) then
write (cCode,’(a,i1,a)’)
! setup error information
’*** error: dimension format of ’,i,’. matrix’
goto 900
endif
63
64
c
65
66
67
&
68
69
70
reading the dimension of the matrix
nCode = ReadMat(io1,mem(np(i)),nrow(i),ncol(i))
if (nCode .gt. 0) then
write (cCode,’(a,i1,a)’)
! setup error information
’*** error: matrix data format of ’,i,’. matrix’
goto 900
endif
71
72
c
73
74
75
E. Baeck
write matrix content to output window
write(cCode,’(a,i1,a)’) ’content of ’,i,’. matrix’
call ListMat(cCode,mem(np(i)),nrow(i),ncol(i))
4.1. HELPER FUNCTIONS
76
c
77
Page 99
write matrix content to output file
nCode = WriteMat(io2,cCode,mem(np(i)),nrow(i),ncol(i))
78
end do
79
80
81
c
82
83
84
85
86
1. product
np(5) = np(4) +nrow(4)*ncol(4)
! setup memory for product matrix
nrow(5)= nrow(1)
! number of rows and columns are given
ncol(5)= ncol(2)
! by the numbers of the other matrices
call MatMult(mem(np(1)),mem(np(2)),mem(np(5)),
&
nrow(1),ncol(1),ncol(2))
87
88
c
write matrix content to output window
write(cCode,’(a)’) ’product matrix of a * r1’
call ListMat(cCode,mem(np(5)),nrow(5),ncol(5))
nCode = WriteMat(io2,cCode,mem(np(5)),nrow(5),ncol(5))
c
halt a little bit
pause ’ press return...’
goto 999
89
90
91
92
93
94
95
! jump to the end
96
97
c
only one error branch, because we have an error text
900 write(*,*) cCode
pause ’ press return...’
stop
c
"this is the end"
999 close(io1)
close(io2)
stop
end
98
99
100
101
102
103
104
105
106
9.6.2015
Page 100
Computer Languages for Engineering - SS 15
Figure 4.5 shows the output screen of the discussed program. In the do loop the matrices are read from
the input file and after that the matrix values are written to the screen. The last matrix output shows the
value of the product of the first and the second matrix. Because the second matrix is the unity vector in
the first component direction, the result matrix is equal to the first column vector of the first matrix.
Figure 4.5: Output Screen
Whats new?
• The write statement can also be used to perform formated output to a string. If we want a formated
output to a string the first parameter - which is usually the io channel number - is used to pass the
destination string.
Listing 4.13: Writing into a String
1
write(cCode,’(a,i1,a)’) ’content of ’,i,’. matrix’
• As an index value for the memory pointer we use a indexed array value, mem(np(i)). The
pointer value np(i) is stored for every used array and is used as an index value to access the
memory block mem.
Listing 4.14: Allocating with Memory Pointers
1
E. Baeck
nCode = ReadMat(io1,mem(np(i)),nrow(i),ncol(i))
4.1. HELPER FUNCTIONS
4.1.7
Page 101
Implementing Tracing
In this section we will implement tracing in our example of section 4.1.7. Therefore we introduce a new
data line in our input file. Its only one value with the following meaning.
0: Tracing is disabled.
1: Tracing is enabled. The start and the end of a subroutine or function call is logged on screen.
2: Tracing is enabled. An extended Tracing is activated. Values of the called subroutines or functions
are logged on screen too.
We have added one further line at the beginning of our input data file.
Figure 4.6: Input data for matrices3, version 3
So we have to introduce a common block as a possibility to access to a global trace flag which is called
ntrace. This common block is stored in the file tracegl.h and is used by an include in all subroutines
and functions which should use tracing.
Listing 4.15: Global Data tracegl.h
1
2
3
c234567
common /trace/ ntrace
integer ntrace
So we insert the following line of code in all subroutines and functions which should have access to the
trace common.
Listing 4.16: Include the global Data Header
1
include ’tracegl.h’
9.6.2015
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Computer Languages for Engineering - SS 15
To initialize tracing we set a default trace value. We have used disabled tracing, that means a value of 0.
Then the first line should be read from the input file, which contents the trace value. The following code
is added to our main program.
Listing 4.17: Implementing Trace Functionality, 77 like
1
2
3
4
5
6
7
8
9
10
11
12
13
...
c initalization of tracing
ntrace = 0 ! tracing disabled
c open the input file
cCode = ’ *** error: input file not found!’
open (io1,file=’matrices3.inp’,status=’old’,err=900)
c read trace information from input file
c ntrace = 0: tracing disabled
c ntrace = 1: tracing level one (start/stop of routines)
c ntrace = 2: tracing level two (all trace data)
cCode = ’ *** error: traceinfo not found!’
read(io1, * ,err=900) ntrace !
...
To implement tracing in our function ReadDim we have to give access to the common block including
the common code. Then we can optionally write trace information to the screen. If ntrace is greater
0, we log the beginning and the end of the routine. If ntrace is greater 1, we log the read dimension
values as well.
Listing 4.18: Read Matrix’s Dimension from File
integer function ReadDim(io,rows,cols)
1
2
include ’tracegl.h’
3
! give access to common block
4
integer
5
io, rows, cols
6
! Trace Code
if (ntrace.gt.0) write(*,*) ’> ReadDim started...’
7
8
9
read (io,*,err=900) rows,cols
10
! read the dimensionvalues rows and cols
11
! Trace Code
if (ntrace.gt.1)
&write(*,’(a,i3,a,i3)’) ’>
12
13
14
rows: ’,rows,’ columns: ’, cols
15
ReadDim = 0
16
! from the input file
17
! Trace Code
if (ntrace.gt.0) write(*,*) ’> ReadDim ended, no errors...’
return
18
19
20
21
22
900 ReadDim = 1
! error branch, error code set if an
23
24
25
26
27
E. Baeck
! Trace Code
if (ntrace.gt.0) write(*,*) ’> ReadDim ended with read error...’
return
! format error is dedected
end
4.1. HELPER FUNCTIONS
Page 103
Like in ReadDim we implement tracing also in the routine ReadMat which is given in the following
code.
Listing 4.19: Read Matrix’s Data from File
integer function ReadMat(io,rm,n1,n2)
1
2
include ’tracegl.h’
3
! give access to common block
4
integer
integer
integer
real*8
5
6
7
8
io
n1
n2
rm(n1,n2)
!
!
!
!
io-chanal no.
dimension of rm (rows)
dimension of rm (columns)
matrix
9
! Trace Code
if (ntrace.gt.0) write(*,*) ’> ReadMat started...’
10
11
12
13
14
c
row loop
do i=1,n1
15
16
read (io,*,err=900) (rm(i,j),j=1,n2)
17
18
! read row values in an implicit
! loop
enddo
19
20
ReadMat = 0
! no error
21
22
23
24
! Trace Code
if (ntrace.gt.0) write(*,*) ’> ReadMat ended without errors...’
return
! return to calling program
25
26
27
28
29
30
900 ReadMat = 1
! reading error
! Trace Code
if (ntrace.gt.0) write(*,*) ’> ReadMat ended with read error...’
return
end
9.6.2015
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Computer Languages for Engineering - SS 15
Figure 4.7 shows the trace output in the output window.
Figure 4.7: Screen Output with Tracing Level 2
E. Baeck
4.2. GAUSS-LU-ALGORITHM
4.2
4.2.1
Page 105
Gauss-LU-Algorithm
Gauss Decomposition with Pivot Search
The following linear equation system is given in matrix notation.
A·x =b
(4.5)
If we write it in components we will get:
 

a1,1 a1,2 . . . a1,n
 

 

 a2,1 a2,2 . . . a2,n  
 

..
..  · 
 ..
..
 .
.
.
.  
 

an,1 an,2 . . . an,n
x1


b1


 

 
x2   b2 

=

 
...   ... 

 
bn
xn
(4.6)
or
n
X
aik · xk − bi = 0
(i = 1, 2, ..., n)
(4.7)
k =1
To decompose the matrix A we can use the following theorem.9
For a regular matrix A there is a permutation matrix P so that the product P · A can be decomposed
into L a lower and U a upper triangle matrix.
P ·A=L·U
(4.8)
If we insert 4.8 into 4.5 after having multiplied with P from the left hand side.
P ·A·x =P ·b
(4.9)
To calculate the solution vector x we introduce the helper vector c.
L·U ·x =P ·b
(4.10)
L·c =P ·b
(4.11)
With the forward substitution we get the helper vector c.10 The permutation matrix has to be considered
on the right hand side.
L·c =P ·b
(4.12)
With the backward substitution we get the solution vector x .11
R·x =c
(4.13)
After having decomposed the matrix A, forward- backward substitution can be done for as many as
desired right sides. So we can calculate the inverse of A column by column with a respective unity
vector as right side.
A·X =1
(4.14)
9
The proof is given in H.R. Schwarz [4] Satz 2.4.
Forward substitution is possible, because the the vector c is multiplied form the left by a lower triangle matrix.
11
backward substitution is possible, because the the vector x is multiplied form the left by an upper triangle matrix.
10
9.6.2015
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4.2.2
Computer Languages for Engineering - SS 15
Step 1: Memory Manager and Main Program
To handle different data types using only one memory block we apply the equivalence statement12 , which
overlays a set of variables. In our example we overlay the real*8 array dmem and the integer*4 array
imem.
Listing 4.20: Setup Memory Manager for GaussLU, 77 like
1
2
3
4
c234567
program GaussLU
c
include ’tracegl.h’
5
6
c
7
memory allocation
integer*4 mem8X
8
parameter (mem8X = 1000)
9
10
11
12
13
c
14
15
real*8
dmem(mem8X)
integer*4 imem(1)
integer*4 imem(mem8X*2)
equivalence(dmem(1),imem(1))
c
16
17
18
character*32
integer*4
integer*4
cCode
nDim
nLC
! dimension of matrix a
! number of load cases (vector b)
integer
integer
integer
nPA
nPS
nPI
! pointer for matrix a
! pointer for scaling vector
! pointer for permutation vector (integer*4)
integer
ReadMat ! function return values
19
20
21
22
23
24
25
26
c
27
initialization
ntrace = 0
! no tracing
io - channels
io1 = 10
io2 = 11
! input
! output
28
29
c
30
31
32
33
c
Read input file
cCode = ’*** error: input file not found!’
open (io1,file = ’gausslu.inp’,status = ’old’,err=900)
c
read 1st line
cCode = ’*** error: format error in 1st line!’
read (io1,*,err=900) nDim, nLC, ntrace
c
memory pointer values
nPA = 1
nPS = nPA + nDim*nDim
nPI = (nDim*nDim + nDim)*2 +1
c
read the matrix from input file
34
35
36
37
38
39
40
41
42
43
44
45
46
12
equivalence statement, Page 84, [2]
E. Baeck
4.2. GAUSS-LU-ALGORITHM
Page 107
nCode = ReadMat(io1,dmem(nPA),nDim,nDim)
if (nCode .gt. 0) then
cCode = ’*** error: format error reading matrix’
goto 900
endif
47
48
49
50
51
52
53
c
close input stream
close(io1)
c
list input values
call ListMat(’Matrix values of A:’,dmem(nPA),nDim,nDim)
54
55
56
57
58
write(*,’(a,i5)’)’ Pointer of matrix..............:’, nPA
write(*,’(a,i5)’)’ Pointer of scaling vector......:’, nPS
write(*,’(a,i5)’)’ Pointer of permutation vector..:’, nPI
59
60
61
62
goto 999
63
64
65
c
error branch
900 write(*,*) cCode
c
end of program
999 continue
66
67
68
69
70
71
72
73
pause ’press enter....’
stop
end
The first input line sets the dimension of the matrix, the number of the right hand sides and the trace flag.
Figure 4.8: Input data
9.6.2015
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Computer Languages for Engineering - SS 15
Figure 4.9 shows the screen output of the first steps main program. After having read the matrix values
the matrix values are listed. Then the real*8 pointer index values of the matrix (1), the scaling vector
(3 · 3 + 1 = 10) and the integer*4 pointer index value ((3 · 3 + 3) ∗ 2 + 1 = 25) are listed.
Figure 4.9: Screen output of step 1
4.2.3
Step 2: Decomposition with Pivot Search
We encapsulate the Gauss LU decomposition in a subroutine of our mathlib module.
Listing 4.21: GaussLU Decomposition, 77 like
1
2
3
4
5
6
7
8
c
c
c
c
c
c
c
c
9
10
c
11
12
13
Interface description
a
: matrix to decompose
n
: dimension of a
ip : permutation vector
d
: scaling vector
flag: 0: singular matrix
1: positiv sign
-1: negativ sign
subroutine gaussLU(a,n,ip,d,flag)
c
c
14
15
16
17
include ’tracegl.h’
! give access to common block
declaration
integer*4 n
real*8
a(n,n)
integer*4 ip(n)
real*8
d(n)
! matrix to decompose
! permutation vector
! scaling vector
18
real*8
real*8
real*8
real*8
19
20
21
22
23
28
! precision
deps = 1.e-7
flag = 1
24
26
! helper variables
c
25
27
s
dh
dF
deps
c
c
c
29
(1) build up the scaling vector for pivot search
- initialization for row i
do i=1,n
30
31
c
32
33
E. Baeck
initialize with original row index
ip(i) = i
4.2. GAUSS-LU-ALGORITHM
34
c
35
36
37
38
39
40
c
c
41
Page 109
calcation of sum of all values in column j of a
s = 0.
do j=1,n
s = s + dabs(a(i,j))
end do
s = 0 ? if yes, then no regular matrix
if (s .lt. deps)
42
43
c
44
45
matrix singular return with error flag
flag = 0
return
46
47
c
else
48
49
50
51
c
c
52
scaling with respect to the column sum
value of column i
d(i) = 1./s
53
endif
54
55
end do
56
57
58
59
c
c
60
(2) decomposition
- loop over all rows
do i =1,n-1
61
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63
c
c
64
65
66
67
68
c
c
c
69
70
71
72
73
74
75
76
77
c
c
78
pivot search
- initalization:
dpvt = dabs(a(i,i)*d(i))
ipvt = i
! scaled diagonal value
! and its position
- no we look at all elements in the matrix below
the actual diagonal element
do j=i+1,n
dh = dabs(a(j,i)*d(j)
if (dh .gt. dpvt) then
! scaled element is greater then
dpvt = dh
! actual pivot, we take this value
ipvt = j
! and its position
endif
end do
check the pivat
if (dpvt .lt. deps) then
! if pivot is less then precision
! we have non regular matrix
79
80
c
81
82
83
84
85
86
87
c
c
c
matrix is singular => return with error
flag = 0
return
end if
if neccesary we swap the matrix lines
i to pivot-line
if (i .ne. ipvt) then
88
89
flag = -flag
! sign information for determinant
9.6.2015
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92
c
c
Computer Languages for Engineering - SS 15
! calculation
to swap data, we need a third variable to avoid
over writing!
93
94
c
swap permutation values
j
= ip(i)
ip(i)
= ip(ipvt)
ip(ipvt)= j
c
swap scaling factors
dh
= d(i)
d(i)
= d(ipvt)
d(ipvt) = dh
c
swap matrix
do j = 1,n
dh
a(i,j)
a(ipvt,j)
end do
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
elements of row i and ipvt
= a(i,j)
= a(ipvt,j)
= dh
110
endif
111
112
113
114
c
c
115
elemination step
for all rows below actual diagonal element
do j = i+1,n
116
117
c
118
119
120
121
c
c
122
123
124
elimination factor
a(j,i) = a(j,i)/a(i,i)
dF
= a(j,i)
for all values at the right hand side of the actual
diagonal elements column
do k = i+1,n
a(j,k) = a(j,k) -dF*a(i,k)
end do ! end of k-loop
column-loop of elemeination step
125
126
127
end do
end do
128
129
130
E. Baeck
return
end
! end of j-loop
! end of i-loop
row-loop of elemination step
global row-loop
4.2. GAUSS-LU-ALGORITHM
4.2.4
Page 111
Step 3: Tracing and Memory Pointers
With this step we implement tracing to be able to check the implemented algorithm.
4.2.4.1
Tracing the Decomposer
To be able to check the decomposer algorithm we introduce some tracing code into the decomposer
routine gaussLU.
We implement the following add ons.
• We will access to the global variable ntrace of the common-block trace.
• We trace the start of gaussLU.
• We trace the break of gaussLU, if a singular matrix is found.
• We trace the sum of the norm of all items of a matrix row and it’s inverse, the row scaling factor.
• Before starting the elimination step we trace the pivot value and the corresponding matrix row.
• If row swapping is needed, we trace the original row index and the pivot row index.
• We trace the modified matrix elements during elimination.
Listing 4.22: GaussLU Decomposition with Tracing, 77 like
1
2
3
4
5
6
7
8
c
c
c
c
c
c
c
c
9
10
c
11
12
13
Interface description
a
: matrix to decompose
n
: dimension of a
ip : permutation vector
d
: scaling vector
flag: 0: singular matrix
1: positiv sign
-1: negativ sign
subroutine gaussLU(a,n,ip,d,flag)
c
c
14
15
16
17
18
include ’tracegl.h’
! give access to common block
declaration
integer*4 n
real*8
a(n,n)
integer*4 ip(n)
real*8
d(n)
integer
flag
!
!
!
!
matrix to decompose
permutation vector
scaling vector
permutation flag
19
real*8
real*8
real*8
real*8
20
21
22
23
24
25
26
s
dh
dF
deps
! helper variables
! precision
c
deps = 1.e-7
flag = 1
27
28
! Trace Code
9.6.2015
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Computer Languages for Engineering - SS 15
if (ntrace.gt.0) write(*,*) ’> GaussLU started...’
29
30
31
32
c
c
c
(1) build up the scaling vector for pivot search
- initialization for row i
do i=1,n
33
34
35
c
initialize with original row index
ip(i) = i
c
calcation of sum of all values in column j of a
s = 0.
do j=1,n
s = s + dabs(a(i,j))
end do
36
37
38
39
40
41
42
43
44
c
c
s = 0 ? if yes, then no regular matrix
if (s .lt. deps) then
45
46
47
c
matrix singular return with error flag
flag = 0
48
49
50
&
51
52
53
if (ntrace.gt.0)
write(*,*) ’> GaussLU ended with vanishing column...’
return
c
else
54
55
56
57
c
c
scaling with respect to the column sum
value of column i
d(i) = 1./s
58
59
60
&
&
61
62
if (ntrace.gt.1)
write (*,’(a,i5,a,e12.5,a,e12.5)’)
’>> row:’,i,’ sum: ’,s,’ scaling value: ’, d(i)
63
endif
64
65
end do
66
67
68
69
c
c
70
(2) decomposition
- loop over all rows
do i =1,n-1
71
72
73
c
c
74
75
76
77
78
c
c
c
79
80
81
82
83
84
E. Baeck
pivot search
- initalization:
dpvt = dabs(a(i,i)*d(i))
ipvt = i
! scaled diagonal value
! and its position
- no we look at all elements in the matrix below
the actual diagonal element
do j=i+1,n
dh = dabs(a(j,i)*d(j))
if (dh .gt. dpvt) then
! scaled element is greater then
dpvt = dh
! actual pivot, we take this value
ipvt = j
! and its position
endif
4.2. GAUSS-LU-ALGORITHM
end do
85
86
87
Page 113
c
c
check the pivat
if (dpvt .lt. deps) then
88
! if pivot is less then precision
! we have non regular matrix
89
90
c
91
92
&
93
94
95
96
matrix is singular => return with error
flag = 0
if (ntrace.gt.0)
write(*,*) ’> GaussLU ended with vanishing pivot...’
return
end if
c
97
&
&
98
99
if (ntrace.gt.1)
write(*,’(a,i5,a,i5,a,e12.5)’)
’>> row:’,i,’ pivot row:’,ipvt,’ pivot value:’,dpvt
100
101
102
103
c
c
c
if neccesary we swap the matrix lines
i to pivot-line
if (i .ne. ipvt) then
104
105
flag = -flag
! sign information for determinant
! calculation
to swap data, we need a third variable to avoid
over writing!
106
107
108
109
c
c
110
111
c
swap permutation values
j
= ip(i)
ip(i)
= ip(ipvt)
ip(ipvt)= j
c
swap scaling factors
dh
= d(i)
d(i)
= d(ipvt)
d(ipvt) = dh
c
swap matrix
do j = 1,n
dh
a(i,j)
a(ipvt,j)
end do
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
elements of row i and ipvt
= a(i,j)
= a(ipvt,j)
= dh
127
128
&
129
130
if (ntrace.gt.1)
write(*,’(a,i5,a,i5)’) ’>> swap of ’,i,’ with ’,ipvt
endif
131
132
133
c
c
134
elemination step
for all rows below actual diagonal element
do j = i+1,n
135
136
c
elimination factor
a(j,i) = a(j,i)/a(i,i)
dF
= a(j,i)
c
for all values at the right hand side of the actual
137
138
139
140
9.6.2015
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Computer Languages for Engineering - SS 15
c
diagonal elements column
do k = i+1,n
a(j,k) = a(j,k) -dF*a(i,k)
end do ! end of k-loop
column-loop of elemeination step
142
143
144
145
146
147
148
&
&
if (ntrace.gt.1)
write(*,’(a,i3,a,i3,2x,10e12.3)’)
’ el.step:’,i,’ row:’,j,(a(j,k),k=j,n)
149
150
151
152
end do
end do
! end of j-loop
! end of i-loop
row-loop of elemination step
global row-loop
153
154
155
if (ntrace.gt.0)
& write(*,*) ’> GaussLU ended with decomposition...’
156
157
158
4.2.4.2
return
end
Preparing the Test Environment
To decompose a matrix using gaussLU and check the result automatically we need memory for the
following arrays.
• real*8 array(n,n) AC, the copy of the matrix to decompose.
• real*8 array(n,n) A, the matrix to decompose.
• integer*4 vector(n) Ip, to store the permutation information.
• real*8 vector(n) S, to store the scaling information for pivot search.
• real*8 array(n,n) L, the lower triangle matrix with zero values in the upper triangle.
• real*8 array(n,n) U, the upper triangle matrix with zero values in the lower triangle.
• real*8 array(n,n) AR, the product matrix of lower and upper triangle.
After having read the input data from the file gausslu.inp we copy the matrix values to a backup matrix
using the subroutine MemCpyR8. The helper function MemCpyR8 will be implemented later.
After having decomposed the matrix A into a lower and upper triangle, the matrices L and U will be
extracted using the helper function extractLU. We now can recalculate the original matrix multiplying L
and U and swapping the matrix rows to the original positions. In a final step we calculate the greatest
difference value of the last and the first matrix. If this value vanishes with respect to the used arithmetic
(precision) the decomposed matrix is checked.
E. Baeck
4.2. GAUSS-LU-ALGORITHM
Page 115
Listing 4.23: Main Program for GaussLU Decomposition with Tracing
1
2
3
4
c234567
program GaussLU
c
include ’tracegl.h’
! access to trace common
5
6
c
7
8
memory allocation
integer*4 mem8X
parameter (mem8X = 1000)
! length of memory block in *8 units
9
10
11
12
c
13
14
c
15
16
17
real*8
dmem(mem8X)
! memory block
integer*4 imem(1)
! integer*4 memory
integer*4 imem(mem8X*2)
! the same as a above
equivalence(dmem(1),imem(1))! dmem and imem, the same memory
!
character*32 cCode
! error code string
integer*4
nDim
! dimension of matrix a
integer*4
nLC
! number of load cases (vector b)
18
19
20
21
integer
integer
integer
nPA
nPS
nPI
! pointer for matrix a
! pointer for scaling vector
! pointer for permutation vector (integer*4)
integer
ReadMat ! function return values
22
23
24
25
c
26
initialization
ntrace = 0
! no tracing
io - channels
io1 = 10
io2 = 11
! input
! output
27
28
c
29
30
31
32
c
Read input file
cCode = ’*** error: input file not found!’
open (io1,file = ’gausslu.inp’,status = ’old’,err=900)
c
read 1st line
cCode = ’*** error: format error in 1st line!’
read (io1,*,err=900) nDim, nLC, ntrace
c
memory pointer values
nPA = 1
nPS = nPA + nDim*nDim
nPI = (nDim*nDim + nDim)*2 +1
33
34
35
36
37
38
39
40
41
42
43
! memory pointer of matrix a
! memory pointer of scaling vector
! memory pointer of permutation vector
44
45
c
read the matrix from input file
nCode = ReadMat(io1,dmem(nPA),nDim,nDim)
if (nCode .gt. 0) then
cCode = ’*** error: format error reading matrix’
goto 900
endif
c
close input stream
close(io1)
46
47
48
49
50
51
52
53
54
9.6.2015
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c
Computer Languages for Engineering - SS 15
list input values for checking
call ListMat(’Matrix values of A:’,dmem(nPA),nDim,nDim)
56
57
write(*,’(a,i5)’)’ Pointer of matrix..............:’, nPA
write(*,’(a,i5)’)’ Pointer of scaling vector......:’, nPS
write(*,’(a,i5)’)’ Pointer of permutation vector..:’, nPI
58
59
60
61
62
c
c
save original matrix: AC = A
call MemCpyR8(dmem(1),dmem(nPAC),nDim*nDim)
63
64
65
c
c
LU-decomposition....: A = (L,U)
call GaussLU(dmem(1),nDim,imem(nPI),dmem(nPS),flag)
66
67
68
69
c
c
c
Extract.L,U-martices: L = extract(L,U), U= extract(L,U)
A
L
U
call ExtractLU(dmem(1),dmem(nPL),dmem(nPU),nDim)
70
71
72
c
c
Product.............: AR = L * U
call MatMult(dmem(nPL),dmem(nPU),dmem(nPAR),nDim,nDim,nDim)
73
74
75
c
c
difference of AC and AR
dif = DiffMat(dmem(nPAC),dmem(nPAR),nDim)
76
77
if (dif .lt. dEpsR) then
write (*,*) ’ LU-Decomposition ok!’
else
write (*,*) ’ Error in LU-Decomposition!’
endif
78
79
80
81
82
83
goto 999
84
85
86
c
error branch
900 write(*,*) cCode
c
end of program
999 continue
87
88
89
90
91
92
93
94
E. Baeck
pause ’press enter....’
stop
end
4.2. GAUSS-LU-ALGORITHM
Page 117
Figure 4.10: Output of gaussLU Tracing
4.2.5
Forward-Backward Substitution
After the decomposition (equation 4.8) the solution of a linear equation system can be calculated using
the so called forward-backward substitution (equations 4.10, 4.12 and 4.13). Equation 4.12 describes the
forward substitution, which calculates the intermediate vector b. Equation 4.13 describes the backward
substitution, which calculates the result vector x .
The code of the forward-backward substitution is given below.
Listing 4.24: Forward Backward Substitution, 77 like
1
2
3
4
5
6
7
8
c
c
c
c
c
c
c
c
9
10
forward / backward substituation
a : decomposed
n : dimension
m : number of load cases
ip: permutation vector
b : right hand side matrix
x : soluton matrix
subroutine SubstFB(a,n,m,ip,b,x)
c
integer
n,m
real*8
a(n,n),b(n,m),x(n,m)
integer*4 ip(n)
11
12
13
14
15
c
16
17
18
19
20
c
c
c
21
helpers
real*8 s
integer ipvt
! original row of load item
over all right hand sides
do k=1,m
22
23
24
25
26
c
spectial case dim = 1
if (n.eq.1) then
x(1,k) = b(1,k)/a(1,1)
goto 100
! next load case
9.6.2015
Page 118
endif
27
28
29
30
Computer Languages for Engineering - SS 15
c
c
c
forward substituation: L*c = P*b
ipvt
= ip(1)
x(1,k) = b(ipvt,k)
31
32
33
do i=2,n
s = 0.
do j=1,i-1
s = s + a(i,j)*x(j,k)
enddo
34
35
36
37
38
39
ipvt
= ip(i)
x(i,k) = b(ipvt,k) -s
enddo
40
41
42
43
44
45
c
c
c
backward substituation: U*x = c
x(n,k) = x(n,k)/a(n,n)
46
47
do i=n-1,1,-1
s = 0.
do j=i+1,n
s = s + a(i,j)*x(j,k)
enddo
48
49
50
51
52
53
x(i,k) = (x(i,k) -s)/a(i,i)
enddo
54
55
56
57
58
100 continue
enddo
! end of load case loop
59
return
end
60
61
4.2.6
Linear Solver
The solution of a linear equation system is performed in two steps. In a first step the equation matrix is
decomposed by a Gauss-LU decomposer. The second step will be performed for every right hand side
calculating the result vector for the selected right hand side.
The input data consist of the system dimension, the matrix data and the data of the right hand sides. An
example is given below.
Listing 4.25: Inputdata to Read from a Text File
1
2
3
4
5
6
7
3 4
2.0
0.7
1.3
1.0
0.0
0.0
E. Baeck
2
1.1 1.3
3.0 -0.7
-3.0 1.5
0.0 1.0 3.0
1.0 2.0 2.0
0.0 3.0 1.0
>> dimension , number of "load cases"
>> start of matrix data
>> 4 vectors of right hand side
4.2. GAUSS-LU-ALGORITHM
Page 119
The main program implementing the solution of a linear equation system is given below.
Listing 4.26: Implementation of a Linear Solver Environment
1
2
C1234567
program LinSolve
3
include ’tracegl.h’
4
5
6
c
memory block
integer*4
mem8X
parameter (mem8X = 1000)
c
Memory
real*8
integer*4
7
8
9
10
11
12
13
c
equivalence(dmem,imem)
14
15
16
c
c
17
18
19
20
21
c
c
22
23
24
25
26
27
28
35
45
51
52
io1
= 10
io2
= 11
ntrace = 0
! input channel
! output channel
nLA
nLB
nLS
44
50
! status code
c
43
49
character*32 cCode
cCode = ’*** error: format error!’
read(io1,*,err=900) nDim, nLC,ntrace1
41
48
! declare the functions
c
40
47
ReadMat
cCode = ’*** error: input file not found!’
open (io1,file = ’linsolve.inp’,status = ’old’,err=900)
38
46
Pointer of A
right hand side matrix pointer
solution matrix pointer
scaling vector pointer
pointer for the product A*X
pointer for permutation information
c
37
42
!
!
!
!
!
!
c
34
39
adress pointer
integer
nPA
integer
nPB
integer
nPX
integer
nPS
integer
nPAX
integer
nPI
integer
33
36
! Systemdimension
! Number of load cases
! Permutation sign
c
31
32
system parameters
integer*4
nDim
integer*4
nLC
integer*4
nFlag
c
29
30
dmem(mem8X)
imem(1)
c
c
= nDim*nDim
= nDim*nLC
= nDim
! number of items in A
! number of items in B,X and A*X
! number of items in scaling vector
calculation of memory pointers
nPA = 1
nPB = nLA +1
nPX = nLA +nLB +1
nPS = nLA +2*nLB +1
nPAX = nLA +2*nLB +nLS +1
!
!
!
!
!
pointer
pointer
pointer
pointer
pointer
of
of
of
of
of
A
B
X
scaling vector
the testing matrix A*X
9.6.2015
Page 120
nPI
53
54
55
Computer Languages for Engineering - SS 15
c
c
= (nLA +3*nLB +nLS)*2 +1
! pointer of permutation vector
reading input data of A
nCode = ReadMat(io1,dmem(nPA),nDim,nDim)
if (nCode .gt. 0) then
cCode = ’*** error: format of matrix A’
goto 900
endif
56
57
58
59
60
61
62
c
reading input data of B
nCode = ReadMat(io1,dmem(nPB),nDim,nLC)
if (nCode .gt. 0) then
cCode = ’*** error: format of matrix B’
goto 900
endif
63
64
65
66
67
68
69
c
c
close input file
close(io1)
70
71
72
c
list of decomposed
call ListMat(’Input matrix:’,dmem(nPA),nDim,nDim)
c
list of right hand side matrix
call ListMat(’Right hand sides:’,dmem(nPB),nDim,nLC)
73
74
75
76
77
78
c
c
decompose A using Gauss-LU-Decomposition
call GaussLU(dmem(nPA),nDim,imem(nPI),dmem(nPS),nflag)
if (nflag.eq.0) then
write(*,*) ’*** error: matrix A is singular!’
goto 999
endif
79
80
81
82
83
84
85
c
c
list of decomposed
call ListMat(’Decomposed matrix:’,dmem(nPA),nDim,nDim)
86
87
88
c
c
forward / backward substituation
call SubstFB (dmem(nPA),nDim,nLC,imem(nPI),dmem(nPB),dmem(nPX))
89
90
91
c
c
list of solution vectors
call ListMat(’Solution vectors:’,dmem(nPX),nDim,nLC)
92
93
94
c
c
jump to the end
goto 999
95
96
97
c
900
98
error output
write(*,*) cCode
99
100
101
c
999
102
103
104
E. Baeck
the end
continue
pause ’press enter...’
stop
end
4.2. GAUSS-LU-ALGORITHM
Page 121
Figure 4.11 shows the output window of the LinSolve program. To check the execution of the program
some test strings were written to the output screen.
Figure 4.11: Outputwindow of LinSolve
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E. Baeck
Computer Languages for Engineering - SS 15
Part II
C/C++
123
Page 125
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language.
It is regarded as a ”middle-level” language, as it comprises a combination of both high-level and low-level
language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell Labs as an enhancement
to the C language and originally named C with Classes. It was renamed C++ in 1983.
As one of the most popular programming languages ever created, C++ is widely used in the software
industry. Some of its application domains include systems software, application software, device drivers,
embedded software, high-performance server and client applications, and entertainment software such
as video games. Several groups provide both free and proprietary C++ compiler software, including the
GNU Project, Microsoft, Intel and Embarcadero Technologies. C++ has greatly influenced many other
popular programming languages, most notably C# and Java.
A nice C++ documentation in the web you get with the link [6].
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E. Baeck
Computer Languages for Engineering - SS 15
5
Development Tools
5.1
The Code::Blocks IDE
We have talked a lot about the Code::Blocks IDE in section 5.1. For our C/C++ codes we use the
Code::Blocks IDE as well. We only need to install the Fortran version of Code::Blocks, because it’s a
simple add on to the original one, which is written for C/C++ developments.
The only thing we should change developing C/C++ projects is the selection of the project type and the
selection of the compiler. This is discussed below.
If we create a new project, to implement C/C++ coding, we have to select the Consol Application from
the project creation wizzards template list (see figure 5.1).
Figure 5.1: Selecting a Console Application, a C/C++-Project
If the template is selected, we have to select the standard type of Consol Application, that means we have
to select a C project or a C++ project. Because the C features are also available in a C++ development,
we select the C++ console application type (see figure 5.2).
If we close the console application type, we get the well known start up form for our project (see figure
5.3). We have to specify the project’s root folder and the project’s name.
Within the next step we have to setup the targets. It’s very important to select now the proper compiler.
127
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Computer Languages for Engineering - SS 15
Figure 5.2: Selecting of a C++ Console Application
Figure 5.3: Selecting of a C++ Console Application
In this case it is the GNU C++ compiler, which is called GCC (see figure 5.4).
If we click on next, we have completed the creation procedure of a console application. If we open
the project browser an load the code file main.cpp, we can study the startup code (see figure 5.5). The
HelloCpp node is inserted into the project tree, like we have seen in the case of Fortran projects. In the
case of C++ project, the code generator creates a file with the name main.cpp. cpp is used as extension
of C++ files. This extension is important to select the GCC compiler building the project’s executable.
main.cpp is used, because a C/C++ application needs a main function. This main function will be called,
if the executable is started.
E. Baeck
5.1. THE CODE::BLOCKS IDE
Page 129
Figure 5.4: Specifying the project targets
Figure 5.5: Startup Code of a C++ Project
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Computer Languages for Engineering - SS 15
6
Basics of C/C++
A detailed description of C and C++ is available in literature or can be downloaded from several web
pages.
6.1
The Preprocessor
C and C++ are native languages which are compiled into the native code. Before a code file (cpp-file) is
compiled by the compiler a preprocessing step is performed. The preprocessor includes further files into
a file or substitutes textually so-called macros, which are defined in terms of preprocessor commands. A
further feature of the preprocessor is, the possibility of macro driven optional compiling.
Preprocessor commands in general starts with a # character. In the following box in the first line a file
of the development package is included. If we use the parenthesis < and > the compiler searches for the
files first in the folders of the compiler packages and then in the actual folder. In the second line the file
name is bracketed with the quotes ". Therefore the compiler searches first in the current folder and then
in the folders of the development package. With #define a macro is introduced. With #undefine
the macro can be removed from the macro list. With #ifdef, #elif, #else and #endif optional
compiling can be performed. This preprocessor commands are working like the if, else, endif of
the FORTRAN compiler (section 2.9).
Listing 6.1: Working with Macros
1
2
#include <a_library_file.h>
#include "a_user_file.h"
3
4
5
6
7
8
9
#define MYMACRO
#ifdef MYMACRO
... code, which will be compiled if MYMCRO was defined
#else
... code, which will be compiled if MYMCRO was not defined
#endif
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6.2
Computer Languages for Engineering - SS 15
Comments
The C++ language offers to different comment types. With the classical block comment, which comes
form the C language, we can bracket a part of a line or some lines and make them comments. We start
the comment with /* and close the comment with */. We can put an arbitrary number of characters and
lines in between this brackets.
The second type of comment is a line end comment. This line end comment is set with the character //.
In the following box we see at the beginning a block comment followed by several line end comments.
The one and only statement of this code includes the <stdio.h>, which is the declaration header of
the printf function, which comes from C and is used by standard to print to the screen.
Listing 6.2: Block- and Line End Comment
1
2
3
4
/*
A little comment example
(this is a block comment)
*/
5
6
// ... and this is a line end comment
7
8
9
10
11
// declare the printf function
#include <stdio.h>
// <..> compiler searches first in
// the lib folder
// ".." compiler searches in actual folder
6.3
Data Types
C/C++ offers the following data types, which are also related the the platform. This data types can be
grouped into character, integral, floating point and void types.
type
char
bytes comment
2
character or small integer
range
signed: -128 to 127
unsigned: 0 to 255
short
2
short integer
signed: -32768 to 32767
unsigned: 0 to 65535
int
4
standard integer
signed: -2147483648 to 2147483647
unsigned: 0 to 4294967295
long
4
long integer
signed: -2147483648 to 2147483647
unsigned: 0 to 4294967295
long long
8
64 bit integer
signed: −263 to +263 − 1 ≈ 9, 2218
unsigned: 0 to 264 − 1
float
4
floating point number.
+/- 3.4e +/- 38 ( 7 digits)
double
8
double precision floating point number.
+/- 1.7e +/- 308 ( 15 digits)
E. Baeck
6.4. OPERATORS
Page 133
The integer data type can be modified with the unsigned key.
6.4
Operators
C/C++ offers the following operators.
6.4.1
Assignment Operator
operator comment
Assignment
=
6.4.2
example
i = 5;
Arthmetic Operators
operator comment
example
+
addition
i = 9 +5; ⇒ 14
-
substraction
i = 9 -5; ⇒ 4
*
multiplication
i = 9 *5; ⇒ 45
/
division
i = 9 /5; ⇒ 1
%
modulo
i = 9 %5; ⇒ 4
6.4.3
Compound Arithmetic Assignment
operator comment
example
+=
addition
i = 2; i += 9; ⇒ 11
-=
substraction
i = 3; i -= 1; ⇒ 2
*=
multiplication
i = 2; i *= 4; ⇒ 8
/=
division
i = 6; i /= 2; ⇒ 3
%=
modulo
i = 9; i %= 2; ⇒ 1
6.4.4
Increment - Decrement Operators
operator comment
example
++
incrementation
i = 2; i++; ⇒ 3
--
decrementation
i = 3; i--; ⇒ 2
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6.4.5
Computer Languages for Engineering - SS 15
Relational and Equality Operators
operator comment
example
==
equal to
3 == 2; ⇒ 0
!=
not equal to
3 != 2; ⇒ 1
>
greater
3 > 2; ⇒ 1
<
less than
3 < 2; ⇒ 0
>=
greater equal
3 >= 3; ⇒ 1
<=
less equal
3 <= 4; ⇒ 0
6.4.6
Logical Operators
operator comment
example
!
not
!(3 == 2); ⇒ 1
&&
and
(3 == 2) && (1==1); ⇒ 0
||
or
(3 == 2) || (1==1); ⇒ 1
The following table shows the truth values of the && and the || operator.
Truth tabel of the && operator
6.4.7
Truth tabel of the || operator
a
b
a && b
a
b
a || b
true
true
true
true
true
true
true false
false
true false
true
false true
false
false true
true
false false
false
false false
false
Bitwise Operators
operator comment
example
&
and
0x20 & 0xff; ⇒ 0x20
|
or
0x20 | 0xff; ⇒ 0xff
ˆ
exclusive or
0x20 ˆ 0xff; ⇒ 0xdf
˜
complement
˜0x20; ⇒ 0xffffffdf
<<
shift left
0x20<<1; ⇒ 0x40
>>
shift right
0x20>>1; ⇒ 0x10
E. Baeck
6.4. OPERATORS
6.4.8
Page 135
Compound Bitwise Assignment
operator comment
example
&=
and
i = 0x20; i &= 0xff; ⇒ 0x20
|=
or
i = 0x20; i |= 0xff; ⇒ 0xff
ˆ=
exclusive or
i = 0x20; i ˆ= 0xff; ⇒ 0xdf
<<=
shift left
i = 0x20; i <<=1; ⇒ 0x40
>>=
shift right
i = 0x20; i >>=1; ⇒ 0x10
6.4.9
Explicit Type Casting Operator
The type casting operator converts one type into another type. The destination type is set in between two
round brackets. In the following example an integer -1 is casted into an unsigned character, so the sign
bit is no more interpreted as a sign and becomes part of the one byte number information. Every bit now
is set in the one byte variable and therefore we get 255 as value.
Listing 6.3: Casting an integer to a unsigned char
1
2
3
4
unsigned char i;
int j = -1;
k = (unsigned char)j;
printf("k= %d\n",k);
5
6
7
... output:
k= 255
6.4.10
sizeof Operator
The sizeof operator determines the length of a variable in bytes. In the following example the length is
determined of an unsigned char, an int, a float and a double. So we get the numbers 1, 4, 4
and 8.
Listing 6.4: Evaluating the Size with the sizeof Operator
1
2
3
4
5
unsigned char i
int
j
float
f
double
d
printf("%d, %d,
= 1;
= -1;
= 1.2;
= 3.4;
%d, %d\n",sizeof(i),sizeof(j),sizeof(f),sizeof(d));
6
7
8
... output:
1, 4, 4, 8
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6.4.11
Computer Languages for Engineering - SS 15
Address and Value Operator
The address operator & determines the address of a variable in memory. The value operator * determines
the value of data with a given address. In our example we determine the address of a variable i and then
the value of the second item of an integer array is determined. The address of an array is given by the
arrays name. The address of the second item of an array therefore is given by the name of the array plus
one.
operator comment
example
&
address
printf("%X\n",&i); ⇒ 22FF40
*
value
int s[2] = {1,2}; *(s+1); ⇒ 2
6.4.12
C++ operator synonyms
For some operators there are macros which provides some synonyms for C/C++ operators. Some of
them are given within the following table
6.5
operator synonym
example
&&
and
(3 == 2) and (1==1); ⇒ 0
||
or
(3 == 2) or (1==1); ⇒ 1
!
not
not (3 == 2); ⇒ 1
!=
not_equ
3 not_equ 2; ⇒ 1
&
bitand
0x20 bitand 0xff; ⇒ 0x20
|
bitor
0x20 bitor 0xff; ⇒ 0xff
ˆ
xor
0x20 xor 0xff; ⇒ 0xdf
˜
compl
compl 0x20; ⇒ 0xffffffdf
&=
and_equ
i = 0x20; i and_eq 0xff; ⇒ 0x20
|=
or_equ
i = 0x20; i or_eq 0xff; ⇒ 0xff
ˆ=
xor_equ
i = 0x20; i xor_eq 0xff; ⇒ 0xdf
Taking about the Hello
We have seen, if we create a new project within Code::Blocks IDE a Hello code is created automatically.
From this code we can see how a C/C++ code is buildup.
We see from the following example code, that a C/C++ application has to have a function, which is
called main. A function in C/C++ starts the the type of return, in this case an int, which is an integer.
The type of return is followed by the functions name. In this case the name should be main, because it’s
the main routine. A function, like in FORTRAN, will have some formal parameters, which are listed in
between a pair of brackets. In this case we don’t use parameters, therefore the brackets are empty. The
definition of the function’s interface is followed by a code block. In C/C++ a code block is enclosed
within curled brackets {...code block...}. Every statement, which is an executable or declaring
code, has to be closed by a semicolon. Therefore in general more than one statement can be written into
E. Baeck
6.6. LINE OUTPUT WITH PRINTF
Page 137
one line. Note the line end comments too, which are listed with a green highlighting. We also can see,
that a function can be exited with a return statement. If a function should return a value, then the return
statement is followed by an expression. In this case a value of zero is returned to the operating system,
which is calling the main function.
Listing 6.5: Our First Hello
1
2
// declare the iostream
#include <iostream>
3
4
5
// setup the namespace
using namespace std;
6
7
8
9
10
11
12
6.6
int main()
{
// stream the string to the screen
cout << "Hello world of C++!" << endl;
return 0;
}
Line Output with printf
The C function printf to print something into the console window will get at least one parameter. This
parameter is the text to print. In general there are a lot of data to be filled into this text with so called
escapes. For every escape there is one data item needed. The data items to be filled into the text have to
be passed in the order of their escapes starting from the second argument of the printf function. So the
following printf will print four values into the console window, therefore we have to pass five parameters,
the text with the escapes and the four values which have to be filled into the escapes.
Listing 6.6: printf Example
1
2
3
4
5
int
i = 1;
char
c = ’A’;
float f = 1.2;
double e = 2.4e-4;
printf("Let’s print 4 values: i=%d, c=%c, f=%10.3f and e=%12.3e\n",i,c,f,e);
The consol output is the following.
Listing 6.7: Consol Output of above’s Example
1
2
3
4
5
int
i = 1;
char
c = ’A’;
float f = 1.2;
double e = 2.4e-4;
Let’s print 4 values: i=1, c=A, f=
1.2 and e=
2.400e-004
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Computer Languages for Engineering - SS 15
There is a wide set of escapes. The most used escapes are described below. An escape starts with the %
character and ends with the type specifier. The type specifier selects the data type to print.
1
%[flags][width][.precision][length]specifier
• flags specify the kind of output, for example the justification
• width specify field width, which should be used for the output
• precision specify the number of digits in the case of a floating point item
• length specify data type length, for example a long float
The following table shows the most important specifiers we use in an escape.1
1
specifier output
example
d or i
signed decimal integer
-123
u
unsigned decimal integer
123
o
unsigned octal
771
x
unsigned hexadecimal integer
ff
X
unsigned hexadecimal integer (uppercase)
FF
f
decimal floating point
392.65
e
scientific notation (mantissa/exponent), lowercase
3.9265e+2
E
scientific notation (mantissa/exponent), uppercase
3.9265E+2
g
use the shortest representation: %e or %f
392.65
G
use the shortest representation: %E or %F
392.65
c
character
a
s
string of characters sample
Hello
%
% followed by another % will write a single %
%
A complete description of all escape specifiers si given in http://www.cplusplus.com/reference/cstdio/printf/.
E. Baeck
6.7. A FOR LOOP
6.7
Page 139
A For Loop
The most used loop statement in C/C++ is the for statement. The for statement executes a statement or a
code block. The execution of the loop is controlled by tree expressions.
Listing 6.8: Syntax of a for Loop
1
2
3
4
for ([<initialization>];[<break condition>];[<iterator condition>])
{
[<code block>]
}
• The initialization is executed before the loop is starting.
• The break condition is evaluated after each loop cycle. If the value of the expression is vanishing
the loop will be broken, if not a next cycle will be started.
• The iteration condition is a statement, which is executed after the execution of a cycle.
The following example shows how to iterate an integer starting from 5 up to 50 with a step width of
5. The first step is to declare and initialize the used variables. We declare them all as int to get 4 byte
integers. After the data type - in this case int - the variable optionally can be initialized using an =
operator for the assignment.
After we have declared and initialized the variables, a little header line is printed onto the screen with the
printf function. Here we see, that a constant string in C/C++ is bracketed with double quotes ". A line
break character \n uses the so-called escape character \.
Then the for loop is started with the for key word and it’s control fields. Within the first field the i loop
counter variable is set to the starting value, which we have stored in the variable iFrom. The second
field contents the boolean expression, which should control the cycles. If the loop counter i is less equal
the end value, which is stored in the variable iTo a next cycle is started. Here we use the operator <=,
which is also introduced in FORTRAN90+. The third field adds the value of iStep to the loop counter
i. This is done with the += operator. We also can write instead of the third expression i=i+iStep.
Within the cycle the value of i is printed to the screen using the printf function. The string, which should
be printed to the screen contents the escape %d this is an escape to fill in an integer value. In this case
it’s the value of i, which follows the string as first data parameter. The loop is completed by the closing
parenthesis of the code block.
Listing 6.9: Simple loop Example
1
2
3
4
/*
A little loop example
(this is a block comment)
*/
5
6
// ... and this is a line end comment
7
8
9
10
11
// declare the printf function
#include <stdio.h>
// <..> compiler searches first in
// the lib folder
// ".." compiler searches in actual folder
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Computer Languages for Engineering - SS 15
12
13
// note: every statement has to be closed by an ’;’ character
14
15
16
17
18
19
20
int main()
{
int i;
int iFrom = 5;
int iTo
= 50;
int iStep = 5;
// note: there is no implicit declaration
//
here we use an integer datatype
21
// "\n" : line break
// printf is the standard C print routine, which is declared
// within the stdio.h file of the standard C library
printf("This is a Loop Application\n");
22
23
24
25
26
// run a loop
for (i=iFrom;i<=iTo;i+=iStep)
{
// %d: integer escape
printf("i = %3d\n",i);
}
27
28
29
30
31
32
33
}
Figure 6.1 shows the screen output of the example ALittleLoop.
Figure 6.1: Screen Output of ALittleLoop
E. Baeck
6.8. STATIC ARRAYS
6.8
Page 141
Static Arrays
In this section we will see how to allocate static arrays in C/C++. A static array is like in FORTRAN
a sequence of data of the same data type. The data within the array are accessed by an index. A very
important difference between C/C++ and FORTRAN is, that the first index of an array in C/C++ is zero
and a standard array in FORTRAN starts with the index one.
So if we mix FORTRAN and C/C++ code we should be very careful with the array indexing. To show
the usage of static arrays we will discuss a little example, which calculates the scalar product of two
vectors, which are represented in the code by two arrays.
An array in C/C++ is declared by the data type followed by the arrays name and the arrays dimension.
Listing 6.10: Declaration of a Static Array
1
<data type> <name> [ <index 1>[,<index 2>]...[,<index n>] ];
In our example we use two array with one index and it’s dimension of 3. The data type should be a large
float which in C/C++ is called double.
Within the first part our example declares and initializes the vectors and the result variable sp. If an
array should be initialized, a list of values separated by commas and bracketed into curled brackets is
assigned to the arrays name. Then the result is calculated within a for loop, which runs over all vector
items. See also equation 6.1, which describes how to calculate the scalar product of two vectors ~a and ~b.
The loop counter is initialized with zero, the first array index. The loop runs up to the index 2, which is
the last valid array index. After each cycle the counter i is incremented with the incrementation operator
++.
s = ~a · ~b =
n
X
ai · bi
(6.1)
i=1
After having calculated the scalar product the result is printed to the screen with the printf function. In
this case we use the escape %10.3f. The first number sets the width of the output field, in this case 10
character. The second number sets the decimal places.
Listing 6.11: Multiplying Vectors by a Dot Product
1
2
// declare the printf function
#include <stdio.h>
3
4
5
6
7
8
9
int main()
{
int
double
double
double
i;
s1[3] = {1.1,1.2,1.3};
s2[3] = {2.1,2.2,2.3};
sp = 0.;
//
//
//
//
loop counter
vector 1
vector 2
scalar product
10
11
12
13
14
15
16
// calculate the scalar product
sp = 0.;
// you should initialize everything
for (i=0;i<3;i++)
// over all components of the vector
{
sp += s1[i]*s2[i];
// array access by index
}
17
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Computer Languages for Engineering - SS 15
// print the result
printf("s1*s2 = %10.3f\n",sp);
18
19
// print the result
20
// print the addresses of the arrays. If we do this, the address
// should be casted to an unsigned integer value
// - this is an cast operator: new = (datatype)old
//
it converts the old into the new
printf("address of s1: %X\n",(unsigned int)s1);
printf("address of s2: %X\n",(unsigned int)s2);
21
22
23
24
25
26
27
// calculate the scalar product
// using item pointers, i.e. the address of the data in memory
//
// s1 is the address of the first item in the array s1
// so we add up the index value [0..2] and get all the values
// of the array. The * - operator gets the value which is stored
// at the given address
sp = 0.;
for (i=0;i<3;i++)
{
//
s1[i]
s2[i]
//
----------------sp += (*(s1+i)) * (*(s2+i));
}
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
// print the result (we hope it’s the same as above ;)
printf("s1*s2 = %10.3f\n",sp);
43
44
45
}
Figure 6.2 shows the screen output of the example ScalarProduct.
Figure 6.2: Screen Output of ScalarProduct
E. Baeck
6.9. BRANCHING
6.9
Page 143
Branching
In C/C++ we have the if statement, which is very close to FORTRAN’s if. On the other hand we have
the switch statement, which is not so general because it is only working on comparing variable values of
the type int and char to constant values.
6.9.1
if Branching
Like in FORTRAN too C/C++ provides some statements for branching. The most used and most common branching statement is the if..else if..else statement. The if is followed by an expression. If the expression’s value is zero the assigned code block is not executed. If the expression’s value
is not vanishing the code block is executed. Optionally we can extend the first if by further else if
conditions. At the end an optional else can be introduced with it’s own code block.
Listing 6.12: Syntax of the if Statement
1
2
3
4
5
if
([expression 1]) code block 1
else if ([expression 2]) code block 2
else if ([expression 3]) code block 3
...
else
code block n
The following example shows the usage of the if..else if..else statement and the usage of some
operators, which are discussed in section 6.4.
Listing 6.13: Simple Operator Example Using if
1
2
3
/*
Example to discuss some C/C++ operators
*/
4
5
6
// this we need for printf
#include <stdio.h>
7
8
9
10
11
int main()
{
int
int
i=2, j=-2;
flag;
// two number
// and a flag
12
13
14
15
16
17
18
19
20
21
22
23
// compare two numbers
// 1st if
if
(i == j)
printf("%d is equal %d\n",i,j);
// 2nd if
else if (i == -j)
printf("%d is equal minus %d\n",i,j);
// ... and the else branch
else
{
printf("no if executed!\n");
printf("i = %d, j = %d\n",i,j);
}
24
25
26
// here we use the not equal operator
if (i != j)
printf("%d is not equal %d\n",i,j);
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27
// now there are some very useful bit operators
flag = 0;
28
29
30
// set the 20th bit, coded in a hexdecimal number
flag |= 0x00080000;
// 4 byte number
31
32
33
// we print the number first in hex and then in decimal
printf("flag = 0x%8.8X - %d\n",flag,flag);
34
35
36
// the 20th bit is set and all bits of the lower 2 bytes.
// (if we set all bits we can simple use the F digit)
flag |= 0x0008FFFF;
// 4 byte number
37
38
39
40
// to clear the 2nd bit we first code it in hex 0x02
// and then invert it with the ˜ operator. Then the inverse
// of the second is overlayed bit by bit with the and operator &
flag &= ˜0x2;
41
42
43
44
45
// the result is printed to the screen
printf("flag = 0x%8.8X - %d , inverted 2nd bit: 0x%8.8X\n",flag,flag,˜0x2);
46
47
48
6.9.2
}
switch Branching
An alternative branching can be implemented using the switch statement. This statement preferable is
used to check a variables value’s. We will find this statement for example in message filters of windowed
environments. The statement starts with the switch key followed by a series of case blocks. A case block
is executed either if the case value is found in the switch variable or if the previous case block is not
closed by a break statement. The break statement at the end of a case block is optional and exits the
switch statement.
Listing 6.14: Syntax of the switch Statement
1
2
3
4
5
6
7
8
9
10
11
12
switch (variable)
{
case value1:
code block 1
[break]
case value2:
code block 2
[break]
...
default:
dfault code block
}
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6.9. BRANCHING
Page 145
In example 6.15 a variable i is declared. The value 2 is checked inside the switch statement. Because
there is a unclosed 2 block, the code of the 2 and the following 3 block will be executed. The result is
shown below.
Listing 6.15: Simple switch example
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
// usage of a SWITCH-CASE statement
int var = 2;
....
switch (var)
{
case 1:
printf("this is case 1: var = 1\n");
break;
case 2:
printf("this is case 2 and 3: we will enter next case block\n");
case 3:
printf("this is case 3: var = %d\n",var);
break;
default:
printf("sorry no case available for var = %d\n",var);
}
Listing 6.16: Console Output of above’s Example
1
2
this is case 2 and 3: we will enter next case block
this is case 3: var = 2
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Exceptions
The classical error handling is working with return codes, i.e. a function is called and will return a code
(mostly a number), to show whether the the function had success or not. If we only have a very flat
calling hierarchy, this is not a big work to implement. But if we have a lot of functions to call, the way
back to the master call can be very difficult.
So in modern languages so called error handlers have been implemented, which are working similar to
event handlers, i.e. an error event is created, the function is canceled and the error handler is searching
for a goal to continue with the work. An error event like this is called an exception. The exception will
be thrown in the case on an error.
The error event handler is enabled, if we put the code, which can produce exceptions into an try block.
So, if an error occur in this try block, the error event handler is searching for a snipped of code, which
should treat this event. This codes are put into so called catch blocks, which should catch a thrown
exception.
So the syntax of this error handling is as follows.
Listing 6.17: Syntax of the if Statement
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
// enabling error handling
try
{
... // this code should be executed with an error handler
}
// catch block with exception data
catch(<type> <variable>)
{
... // error code for a specified exception
}
// at the end all unspecified exceptions are handled
catch(...)
{
... // error code for all unspecified exceptions
}
The following example shows how to throw an exception. In line 8 an integer exception is thrown with
the code 123. So the try code is aborted in this line and the catch block in line 23 is executed. If we would
set the first throw an comment, the second would throw an const char* exception, which passes a
simple C string. In this case the catch block starting at line 17 would be executed.
Listing 6.18: Simple Exception Example
1
2
3
4
5
6
7
8
#include <stdio.h>
int main()
{
// try to do something
try
{
// create an integer exception
throw 123;
9
10
11
E. Baeck
// create a string exception
throw "*** kill the startup!";
6.10. EXCEPTIONS
Page 147
12
printf("some unreachable statements....\n");
13
}
14
15
// catch the exception, if something is wrong#include "node.h"
catch(const char* str)
{
printf("*** Exception: ’%s’\n",str);
}
16
17
18
19
20
21
// catch an int exception
catch(int nCode)
{
printf("*** Exception: %d\n",nCode);
}
// catch everything
catch(...)
{
printf("typeless exception\n");
22
23
24
25
26
27
28
29
30
31
}
return 0;
32
33
34
}
The program’s output is
shown in figure 6.3.
We can see the format of the
integer catch block with the
data of the throwing statement 123.
Figure 6.3: Output of the Exception Example
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OOP with Classes
C++ is an object orientated programing language2 . So what is the concept of an object or a class? A
class or an object combines data, called attributes, with functions, called methods. This can be described
by so called UML3
An instance of a class, that is the realization of the class in memory, is created simply by assigning the
class’s name followed by the constructors parameter list to a symbolic name, which than is the pointer or
the reference to this instance. To access member attributes or methods of a class the dot notation is used,
i.e. <instance>.<member>. The instance will be deleted if it runs out of scope.
6.11.1
Some UML Diagrams
UML structure diagrams of the emphasize the things that must be present in the system being modeled.
Since structure diagrams represent the structure they are used extensively in documenting the architecture of software systems. In our description of the examples we want to implement we use the Class
Diagram which describes the structure of a system by showing the system’s classes, their attributes, and
the relationships among the classes.
A UML class diagram (see figure 6.4) consists of a rectangular box, which is divided into three sections. The fist section contents the class’s name. This name
is written centered in bold letters. The second section contents the attribute’s
names of the class and the third section contents the method’s names.
Class Name
attribute 1
attribute 2
method 1
method 2
Figure 6.4: A UML
Class Diagram
A UML note diagram (see figure 6.5) consists of a stylized note sheet which is
filled with some information.
Class Name
attribute 1
attribute 2
method 1
method 2
Figure 6.5: A UML Note
Diagram
This is
Class 1
A UML note diagram (see figure 6.6) will be assigned to an
other component of the diagram scene with a simple line.
Figure 6.6: A UML Note Diagram Assignment
Figure 6.7 shows how to draw diagrams for inheriting classes. An arrow with
a white filled arrowhead points from the inheriting class, the special class, to
the inherited class, the base class. The attributes and the methods of the Base
class are now available in the name space of the inheriting class, i.e. the special
class now has the attributes attributB1, attributB2, attributS1 and
attributS2.
2
This is only
a simple Note
Base Class
attributeB1
attributeB2
methodB1
methodB2
Special Class
attributeS1
attributeS2
methodS1
methodS2
Object orientated Programming is often used with the abbreviation OOP.
Figure 6.7: A UML InThe Unified Modeling Language includes a set of graphic notation techniques to create visual models
of software-intensive
heritance
Diagram
systems. The Unified Modeling Language is an international standard see [7], UML 2.3 was formally released in May 2010.
3
E. Baeck
6.11. OOP WITH CLASSES
Class 1
List A
List B
Page 149
*
method 1
1
2..*
Class A
attribute A1
attribute A2
1..*
Class B
attribute B1
attribute B2
Figure 6.8 shows a aggregation and a composition.
An aggregation is drawn by a white filled rhombus.
An composition is drawn by a black filled rhombus.
Aggregation and compositions describe a container
or a list of several instances of an object, which are
members of a main class. If for example a profile
consists of several parts, the parts can be described as
an composition, if a part only exists within a profile.
If a part exists also without a profile, the parts are
described within the profile with an aggregation.
At the ends of the connecting lines the multiplicities
are noted. The multiplicity gives the range of referFigure 6.8: A UML Diagram for a Composition and enced instances in the form from..to. For the Class A
an Aggregation
we have 2 up to infinite instances in an composition,
therefor at the end of the line we can not have a multiplicity of zero. In our example we have exactly one instance of the class 1. On the other hand Class B
is referred to Class 1 within an aggregation. In our example on instance of Class B can be reverenced by
an undefined number of instances of Class 1. This is shown by the * icon. On the other hand the class
1 references at least on instance of the Class B. Otherwise the number of references is arbitrary. This is
also shown by the * icon.
method A
6.11.2
method B
C++ Class
A C++ class consists of a declaration and an implementation part. The declaration part often lives in a
header file with the class’s name as prefix and h as suffix. The implementation of a class lives often in a
code file which uses the classes name as a prefix and cpp as suffix.
So for example if we want to implement a class with the name MyClass we put the declaration code
into the file MyClass.h and the implementation code into the file MyClass.cpp.4
6.11.2.1
Declaration
A class declaration is introduced by the key word class followed by the class’s name. If a class inherits
base classes, the list of the base classes to inherit follows a colon. The declaration code is bracketed into
curled parenthesizes. With the keys public:, protected: and private: the access permissions
are set. Every item (attribute or method) following an access permission will get this permission. Within
the declaration blocks members are declared like variables and methods are declared like functions.
4
This concept is rigorously applied in the implementation of the Microsoft Foundation Classes MFC.
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The access permissions to an item (attribute or method) are discussed as follows. If it is set to
• public,
all permissions are assigned, i.e. the item is accessible from outside of the class.
• protected,
only the class itself and classes, which are derived from this class, are allowed to access.
• private,
only the class itself is allowed to access the item.
The following example shows a little class declaration with 2 public attributes and methods and 2 protected attributes and methods as well. The declaration starts with the classes’ constructor which is declared without return type. The name of the constructor is given by the classes’ name. In general a
constructor can be used with some parameters for special initializations. The declaration of the constructor is followed by the declaration of the destructor. A destructor is declared without a return type. The
name of the destructor is given by the classes’ name with a leading tilde ˜ character. The class does not
inherit a base class.
Listing 6.19: Declaring a Class
1
2
3
class MyClass: public MyBaseClass
{
public:
4
MyClass(parameter1, parameter2);
˜MyClass();
5
6
// constructor
// destructor
7
8
9
int
int
publicAttribut1;
publicAttribut2;
int
int
publicMethode1();
publicMethode2();
10
11
12
13
protected:
int protectedAttribut1;
int protectedAttribut2;
14
15
16
17
int
int
18
19
20
protectedMethode1();
protectedMethode2();
}
if an attribute is declared as static, the attribute is an object attribute and not an attribute of the instance
of an object, that means, that this attribute only exists once for an object. A non static attribute will be
created however for each single instance of a class.
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6.11. OOP WITH CLASSES
6.11.2.2
Page 151
Implementation
If a class should be implemented in an cpp file, the header file with the class declarations has to be
included in the header section of the cpp file. To avoid multiple inclusion of a header file, the header file
should be protected with a macro #define discussed in section ??.
The implementation file contents in general all implementations of the class’s methods and the implementation of the object attributes, i.e. the attributes with a static property. Every name of a part
of a class, which should be implemented starts with the class name followed by the part’s name. The
class name and the part name are separated by two colons. So an implementation of the above discussed
declaration could be as follows.
Listing 6.20: Implementing a Class
1
#include "MyClass.h"
// include the declaration
2
3
4
5
6
7
// implement the constructor code
MyClass::MyClass(parameter1, parameter2)
{
... lines of code ...
}
8
9
10
11
12
13
// implement the destructor code
MyClass::˜MyClass()
{
... lines of code ...
}
14
15
16
17
18
19
// implement one of MyClass’s methods
int MyClass::publicMethod1()
{
... lines of code ...
}
20
21
...
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Structures and Classes
In example 6.21 we discuss the relation between a struct and a class. We can say, that a struct
is the simplest kind of a class. A struct only has public items and only attributes no methods.
Therefor we can use a struct as a base class of a our class. In this example the struct is introduced
using a typedef statement. With typedef a new name is introduced as an alias (lines 11-16). In our
case we use MYSTRUCT instead of struct tagMYSTRUCT.
Then we inherit from MYSTRUCT the class MyClass. This class comes with a public method f1 and
a private method f2. In addition we introduce a public attribute lValue.
The constructor performs all initializations. We initialize all inherited attributes and the additional class
attribute. Inside the methods we throw an exception and stop the execution of the program.
The attributes of a struct as well as the attributes of a class can be initialized using the fast and very
low leveled function memset. A given byte, in this case the zero byte, is copied into the struct’s
attributes.
The main routine shows how to initialize the struct and how to copy an instance’s data into a
struct’s data using the socalled cast operator. In this case this operator by default is available, because the class is inherited from the struct.
The programs execution is stopped by an exception throw, which is done in one of the called methods.
Listing 6.21: Stuctures and Classes
1
2
3
4
/*
Example to show the relation between a structure
and a class. The program is stopped by an exception
*/
5
6
7
#include <stdio.h>
#include <memory.h>
8
9
10
11
12
13
14
15
16
// declaring a structure with some
// attributes
typedef struct tagMYSTRUCT
{
int
nValue;
double dValue;
float
fArray[2];
} MYSTRUCT;
17
18
19
20
// inhereting this structure by a class
class MyClass : public MYSTRUCT
{
21
22
// methodes
23
24
25
26
27
// visible, accessable from outside
public:
// constructor is called if the instance is created
MyClass();
// no return type
28
29
E. Baeck
// destructor is called if the instance is deleted
6.11. OOP WITH CLASSES
˜MyClass();
30
Page 153
// no return type
31
// method 1
int f1();
32
33
34
35
36
37
38
// not accessable from outside
private:
// method 2
int f2();
39
40
41
42
43
// accessable attributs
public:
long
lValue;
};
44
45
46
47
48
49
// classname :: methode name
// this is called the constructor
MyClass::MyClass()
{
printf("create MyClass instance...\n");
50
// initialization of the attributes
nValue
= 1;
dValue
= 2.;
fArray[0] = 3.1;
fArray[1] = 3.2;
lValue
= 4;
51
52
53
54
55
56
57
}
58
59
60
61
62
63
// this is called the destructor
MyClass::˜MyClass()
{
printf("delete MyClass instance...\n");
}
64
65
66
67
68
69
// method 1 calls private method f2
// and throws an int exception
int MyClass::f1()
{
f2();
70
// integer exception (error!)
throw (123);
71
72
73
}
74
75
76
77
78
79
// method 2 ony throws a char* exception
int MyClass::f2()
{
throw("error form f2");
}
80
81
82
83
84
85
// this is the main routine, which is called
// from the OS
int main()
{
// type name
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MYSTRUCT m;
86
87
// print the struct’s content
printf("1> m: %d %lf %f %f\n",m.nValue,m.dValue,m.fArray[0],m.fArray[1]);
88
89
90
// initialize a struct
// address initvalue
memset(&m , 0,
sizeof(MYSTRUCT));
91
92
93
94
// print the struct’s content
printf("2> m: %d %lf %f %f\n",m.nValue,m.dValue,m.fArray[0],m.fArray[1]);
95
96
97
try
{
98
99
// create an instance of the class MyClass
MyClass c;
100
101
102
// print the instance’s content
printf("3> c: %d %lf %f %f\n",c.nValue,c.dValue,c.fArray[0],c.fArray[1]);
103
104
105
// assign the instances data to the struct
m = (MYSTRUCT)c;
106
107
108
// print the struct’s content
printf("4> m: %d %lf %f %f\n",m.nValue,m.dValue,m.fArray[0],m.fArray[1]);
109
110
111
// call f1 to throw an exception
c.f1();
112
113
114
// print the struct’s content
printf("3> %d %lf %f %f %ld\n",c.nValue,c.dValue,c.fArray[0],c.fArray[1],c.lValue);
115
116
}
117
118
// error handler for integer exceptions
catch(int nError)
{
printf("*** int Error: %d\n",nError);
}
119
120
121
122
123
124
// handle unspecified exceptions
catch(...)
{
printf("*** unhandled error\n");
}
125
126
127
128
129
130
return 0;
131
132
}
E. Baeck
6.11. OOP WITH CLASSES
Page 155
Figure 6.9 shows the console output of program 6.21. We see, that printing the not initialized struct,
we get some arbitrary data pattern from the stack, i.e. data patterns which by accident are found int the
uninitialized variables.
After that the struct is initialized, so that now the items values are zero. Then the instance of the class
is allocated and we assign their values to the struct.
At the end the program stops after a const char* exception is thrown, which obviously not is handled, so that the catch for unspecified exceptions will be used.
Figure 6.9: Output of the Stuct and Classes Example
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7
Profile Example
In this chapter we discuss the implementation of little software project in C++ which implements the
thin-walled approach for some profile types.
7.1
Class Concept for the Tin-Walled Approach
If we want to build up a class library for modeling and describing a problem, it’s recommended to start
with a general base class, which should content all the common features of our classes.
One of this features could be a general logging code, which should be implemented in every class of the
library. The logging code should write informations into a log file. This feature should be available in
every class of the class library. A second feature is an instance counter. Every instance, which is created
should be counted by the base class.
7.2
Implementation
Figure 7.1 shows the class tree of our profile class library. The common base class Base is inherited by
a general profile class Profile. The Profile class contents all common features of a profile like in
our case the model of the thin-walled approach with it’s nodes and elements. A special profile, in our
example an U, H or L profile, then is implemented in the frame of it’s special class, i.e. UProfile,
HProfile or LProfile class.
To show the inheritance we also inherit from the Profile a specialized profile like the UProfile
class. The differences between the UProfile class and the LProfile class for example are obviously
the input parameters. A second difference between the specialized profiles are the methods to create the
geometry of the profile, i.e. the method to create nodes and elements. If now the geometry of the
specialized profile is created, the general method, to calculate the section values in the frame of the TWA
is called from each element and from the base class Profile.1
The thin-walled profile approach is given by a set of nodes and elements which describes the profile part
as lines with a constant thickness. The nodes, described in terms of a Node class, and the elements,
described in terms of a Element class, are created dynamically. The pointer of the nodes and elements
1
Base classes are also called superclass or parent class
157
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Computer Languages for Engineering - SS 15
Node
2..*
1
Base
2..*
1
Element
1..*
1
Profile
UProfile
HProfile
LProfile
Figure 7.1: Class Hierarchy of the Profile Implementation
are stored in the profile class Profile in a pointer array m_pNC and m_pNE.
Because the element should be able to calculate it’s section values, we make the element a collection of
it’s nodes. So a direct access to the node’s data is possible. If we would only store the node numbers in
the element, an element would not be able to calculate it’s section values, because a direct access to the
node’s coordinate values would not be possilble.
E. Baeck
7.2. IMPLEMENTATION
7.2.1
Page 159
Base, the Base Class of all Classes
A UML class diagram in figure 7.2 shows the concept of the common
class Base. The class contents three object attributes, the name of
the common log file, a print buffer and the instance counter. This attributes are declared with an static property. Besides the constructor and the destructor, the class has a method which will write the
content of the message buffer to the screen and/or into a log file. The
object method ResetLog deletes an allready existing log file. The
following code gives the declaration header code of the class Base.
Base
− logFile[256]: char
− msg[256]: char
− counter:int
+ Base(): −
− ˜Base(): −
+ appendLog(..): int
+ resetLog(..): int
Figure 7.2: TWD’s Base Class
Listing 7.1: Base Class of All Classes
1
2
#ifndef BASE_H_INCLUDED
#define BASE_H_INCLUDED
// protect against multiple
// inclusion
3
4
5
6
// class declaration
class Base
{
7
8
public:
// can be accessed from everywhere
9
10
11
12
13
// attributes
// ==========
// instance counter
static int counter;
// class attribute
// logfile’s name
static char logFile[256];
// old c string
14
15
16
17
18
19
// string buffer to log
static char msg[256];
20
21
22
23
24
25
26
27
28
// methodes
// ========
Base();
˜Base();
int appendLog(char* str);
static void resetLog();
//
//
//
//
constructor to initalize
destructor to free memory or to close files ...
logging methode
reset log
};
#endif // BASE_H_INCLUDED
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The implementation code of the class Base is given below. Note, that object attributes must be implemented like methods. Therefore in line 6 to 8 we implement the object attributes like global variables.
Listing 7.2: Base Class Implementation
1
2
3
#include "base.h"
// specify the interface
#include <stdio.h> // io functions of the c library
#include <string.h> // string functions of the c library
4
5
6
7
8
// implement class attributes
int
Base::counter = 0;
char
Base::logFile[256] = {0};
char
Base::msg[256] = {0};
// counter
// log file
// message buffer
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
// constructor
// |class name
// |
| method, the contructor
Base::Base()
{
#ifdef _COMMENT
// initialization: it is sufficient to set the first item to 0
logFile[0] = 0;
// ... as number
logFile[0] = ’\0’;
// ... or as character code
#endif
// set the default filename
//
|destination
//
|
|source
if (!logFile[0]) strcpy(logFile,"Base.log");
24
// count the new instance
counter++;
25
26
27
// create the output string
// - print into an char array
sprintf(msg,"> %d instance(s) created.\n",counter);
28
29
30
31
// - print the message into the file
appendLog(msg);
32
33
34
}
35
36
37
38
39
40
// destructor
Base::˜Base()
{
// create message
sprintf(msg,"> Instance %d deleted.\n",counter);
41
// print message
appendLog(msg);
42
43
44
// decrement the counter, because an instance is deleted
counter--;
45
46
47
}
48
49
50
51
// AppendLog prints a message to the log and to the screen
int Base::appendLog(char* pMsg)
{
E. Baeck
7.2. IMPLEMENTATION
Page 161
// print to the screen
printf("%s",pMsg);
52
53
54
// open the log
//
|file structure (like a channel number
//
|file name
//
|
| open mode
FILE* pHnd = fopen(logFile,"a");
55
56
57
58
59
60
// check the file return
// (same as if (pHnd == 0)
if (!pHnd) return 0;
61
62
63
64
// print the message
//
| pointer to the file structure FILE
fprintf(pHnd,"%s",msg);
65
66
67
68
// close the log
fclose(pHnd);
69
70
71
return 1;
72
73
}
74
75
76
77
78
79
7.2.2
// ResetLog deletes an allready existing log-file
void Base::resetLog()
{
remove(logFile);
}
Node Class for Model Nodes
A UML class diagram in figure 7.3 shows the concept of the class
Node. The class contents the node’s number and a double array
to hold the instance’s coordinate data. Besides the constructor and
the destructor, the class has a method List which will write the
instances data to the log using the inherited method of the class
Base::appendLog. To keep it simple all attributes and methods
of the class are declared as public.
In line 6 we can see, that the class inherits it’s base class Base (see
section 7.2.1), therefore we have to include the Base class header file
in line 4.
Node
+ nNo: int
+ dx[2]: double
+ Node(..): −
− ˜Node(): −
+ listData(..): void
Figure 7.3: The Class Node
Listing 7.3: Node Class’s Header
1
2
#ifndef NODE_H_INCLUDED
#define NODE_H_INCLUDED
3
4
5
6
7
#include "Base.h"
// include Base class’s header
//
| inherit from Base
class Node: public Base
{
8
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public:
10
// attribute
int
nNo;
double dx[2];
11
12
13
// node number
// x,y values (vector)
14
15
16
17
public:
// constructor: x,y optional
Node(int nNo, double x = 0., double y = 0.);
18
// destructor
˜Node();
19
20
21
// list the node’s data
void listData();
22
23
24
25
};
#endif // NODE_H_INCLUDED
The implementation code of the class Node is given below. Note, that constructor is used with it’s
parameters to initialize the node coordinates. If coordinate values are passed by the constructor, the
values are assigned to the attributes. The constructor at the end will print the nodes data into the log file.
Listing 7.4: Node Class’s Implementation
1
2
#include "node.h"
#include <stdio.h>
3
4
5
6
7
8
9
10
11
// constructor
//
parameters
call Base class
Node::Node(int nNo, double x, double y) : Base()
{
// assign the coordinates
nNo
= nNo;
dx[0] = x;
dx[1] = y;
12
// print the data
listData();
13
14
15
}
16
17
18
// destructor (nothing to do)
Node::˜Node() { }
19
20
21
22
23
24
25
26
27
// List method, prints Node’s data
void Node::listData()
{
sprintf(msg,
"> node: no = %2d, x = %10.3f y = %10.3f\n",
nNo,dx[0],dx[1]);
AppendLog(msg);
}
E. Baeck
7.2. IMPLEMENTATION
7.2.3
Page 163
Checking the Node Class
To check the node class, we implement a little testing frame, which simple creates some Node instances,
assign some data, print the Node data using it’s List method and deleting the Node instance at the
end. Because we inherit the Base class features, the creation and the deletion of an instance is logged
to the screen, so we can simple check this event.
The testing code is given within the following main steps.
• If we want to use the Node class, we have to declare it with the inclusion of it’s declaration header,
this is done in the first line.
• A simple Node instance is created by declaring a variable N1 of the type Node.
• To initialize with special parameters we assign the return of the constructor to a variable of type
Node, called N2.
• Then we print the data of the created nodes N1 and N2 by calling their method List. This is done
using the dot access (<variable name>.<method>).
• After this we declare an address pointer pN32 of the to a Node instance using the Node* type.
Because there is no valid instance address in N3 we initialize it with a zero value.3
• To assign a valid address of a Node instance to pN3, we create a Node instance dynamically
by the usage of the new operator. The return of the new Node is an address and this address is
assigned to our third Node* variable N3.
• To print the data of the third node we have to use the arrow access because it’s a pointer variable
(<variable name>-><method>).
• After the printing of the content of the third Node instance we remove the instance from memory
using the delete operator. To avoid the access to an invalid address, we check the address pointer
against zero.
The code of the testing frame is given below.
Listing 7.5: Checkenvironment for the Node Class
1
2
#include "Node.h"
#include <stdio.h>
// load Node header
// used for printf
int main()
{
Node
Node
// the main routine
3
4
5
6
7
n1 = Node(1);
n2 = Node(2,1.1,1.2);
// standard coordinates used
// use parameters to initialize
8
9
10
n1.listData();
n2.listData();
// list the data of node 1
// list the data of node 2
11
12
// creating 3rd Node instances dynamically
2
A prefix in the variable name of p shows, that it’s a pointer variable, which means, that the variable contents the address of
the assigned data and not the data itself.
3
A zero address value means, that no memory is referenced to this address pointer.
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Node*
13
14
pN3 = 0;
// address of a Node instance
// 0: no memory assigned
15
// create an instance dynamically with the new operator
printf("now create the instance for pN3\n");
pN3 = new Node(3,2.1,2.2);
16
17
18
19
// list data of node 3. note, we use the ’->’ operator
// if the variable contents an adress an not the data itself
pN3->listData();
20
21
22
23
// delete the Node instance using the delete operator
if (pN3)
delete pN3;
24
25
26
}
The Output of the above discussed code
is given in figure 7.4. If an instance is
created, we see in the log the message
of the Base class constructor, which
counts the instances. This output is
followed by the output of the Node
class constructor, which prints the coordinates of the Node instance. Here
we can see, that the first node will get
the standard zero values and the second
instance will get the coordinates, which
are passed to the constructor.
Figure 7.4: Output of the Node Check Program
Then the created instances’ data are printed using their List methods. Then we create the third instance
and their data are printed like in the previous cases. After that the third Node instance is deleted explicitly
and we see that the instance counter in the Base class destructor is decremented. Closing the program
the destructor of the Base class of the statically created instances N1 and N2 is automatically executed.
So we can see the decrementation of the instance counter down to zero.
E. Baeck
7.2. IMPLEMENTATION
7.2.4
Page 165
Element Class for Model Elements
A UML class diagram in figure 7.5 shows the concept of the class
Element. The Element class get’s the pointer of it’s Node instances. If this pointers (the addresses of the Node instances) are
known, the Element will be able to calculate all it’s sections values.
So we can encapsulate this features into the Element. At the end to
get the profiles total section values we simply have to add up all it’s
Element’s values.
Element
+ nNoX : int
+ nNo : int
+ dt : double
+ pN : Node**
+ dL : double
To get a general implementation, we introduce a simple container for
the Node instance pointers, which is a simple C array. In the general
case we can have elements with an arbitrary number of nodes, so we
introduce the number of Node pointers m_nNoX, which in our case
will be 2. The Node instance pointers will be stored in the array
m_pN, which we have to allocate dynamically.
+ dA : double
Besides the Node instance pointers, our element need to know it’s
thickness. The thickness is stored in the attribute m_dt.
+ initResults() : void
The following attributes will hold the element’s section values.
+ dS[2] : double
+ dI[3] : double
+ Element(..) : −
− ˜Element(): −
+ listDagatList() : void
+ setData() : int
Figure 7.5: The Class Element
• dL, the length of the element. This value is used to calculate the section values.
• dA, the area of the element (see section C.1.1).
• dS, the static moments of the element, [0]: Sy , [1]: Sz (see section C.1.2).
• dI, the moments of inertia of the element, [0]: Iyy , [1]: Izz , [2]: Iyz , (see section C.1.3).
Besides the constructor and the destructor, the class provides a method which will write the instances data
to the log using the inherited method of the class Base::AppendLog. The method InitResults
will initialize all internal and public items of the element, which are used to get and hold the result values.
The method SetData will calculate the elements section values.
The Element class provides only one constructor, i.e only one interface. The constructor comes with
four parameters which will describe a linear element.4
• int nNo, the element’s number.
• Node* pN1, the instance pointer to the element’s starting node.
• Node* pN2, the instance pointer to the element’s terminating node.
• double dt, the element’s thickness.
We have to note, that all element’s methods suppose, that the input data are correct. Error checking will
be performed later, if we create an general TWA profile.
4
Introducing further interfaces, the library can be extended by other element types.
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As we have seen in figure 7.5 the Element class may be considered as composition of Node instances.
One element will have 2 nodes or more.
Element
Node
1
2..*
Figure 7.6: UML-Diagram of the Element Composition
Listing 7.6: Element Class’s Header
1
2
#ifndef ELEMENT_H_INCLUDED
#define ELEMENT_H_INCLUDED
3
4
5
#include "Base.h"
class Node;
// include Base-Class’s header
// we need a Node pointer
6
7
8
9
class Element: public Base
{
public:
10
// attributes
int
nNoX;
// number of Nodes
int
nNo;
// element number
double dt;
// thickness
// adress of the Node instances pointer array (therefore 2 *)
Node** pN;
11
12
13
14
15
16
17
// section attributes
double dL;
//
double dA;
//
double dS[2];
//
double dI[3];
//
18
19
20
21
22
element length
element area
element’s static moments
element’s moments of inertia
23
// methods
// constructor: only with all element data
Element(int no,Node* n1, Node* n2, double t);
24
25
26
27
// destructor
˜Element();
28
29
30
// list the data
void
listData();
31
32
33
// initialize the results
void
initResults();
34
35
36
// calculate results
int
setData();
37
38
39
40
};
#endif // ELEMENT_H_INCLUDED
The implementation code of the class Element is given below. Note, that constructor is used with it’s
parameters to initialize the element data.
E. Baeck
7.2. IMPLEMENTATION
Page 167
Listing 7.7: Element Class’s Implementation
1
2
3
4
#include
#include
#include
#include
"element.h"
<stdio.h>
<memory.h>
<math.h>
//
//
//
//
declare the element class
for printing
used for memory access (memset)
to calculate the root
5
6
#include "node.h"
// we should know the Node too
7
8
9
10
11
// constructor
Element::Element(int nNo, Node* pN1, Node* pN2, double dt)
{
nNoX = 2;
// we only have elements with two Nodes
12
// assigning attributes
this.nNo
= nNo;
this.dt
= dt;
13
14
15
16
// Node address array
// !!! we have allocate it !!!
pN
= new Node*[nNoX];
17
18
19
20
// assign the Node pointers
pN[0] = pN1;
pN[1] = pN2;
21
22
23
24
// initialize the result attributs
initResults();
25
26
27
printf("> element %d created.\n",nNo);
28
29
}
30
31
32
33
34
35
// destructor: note: the Node instances have to be freed outside
Element::˜Element()
{
printf("> element %d deleted.\n",nNo);
}
36
37
38
39
40
41
// initialize the result attributs
void Element::initResults()
{
dL = 0.;
dA = 0.;
42
// initialize an array
//
| destination (array’s address)
//
|
| byte to copy
//
|
|
| number of byte to copy
memset((void*)&dS[0],0,2*sizeof(double));
// dS == &dS[0]
memset((void*)&dI[0],0,3*sizeof(double));
43
44
45
46
47
48
49
}
50
51
52
53
54
// list the elements data
void Element::listData()
{
// print header
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sprintf(msg,"element %2d, t = %10.2f\n",nNo,dt);
appendLog(msg);
55
56
57
// print element’s Node data
for (int i=0;i<nNoX;i++)
{
pN[i]->listData();
}
58
59
60
61
62
63
// list result values
sprintf(msg,"
L..........:
appendLog(msg);
sprintf(msg,"
A..........:
appendLog(msg);
sprintf(msg,"
Sx.........:
appendLog(msg);
sprintf(msg,"
Sy.........:
appendLog(msg);
sprintf(msg,"
Ixx........:
appendLog(msg);
sprintf(msg,"
Iyy........:
appendLog(msg);
sprintf(msg,"
Ixy........:
appendLog(msg);
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
%12.3f mm\n",dL);
%12.3f cmˆ2\n",dA/1.e2);
%12.3e cmˆ3\n",dS[0]/1.e3);
%12.3e cmˆ3\n",dS[1]/1.e3);
%12.3e cmˆ4\n",dI[0]/1.e4);
%12.3e cmˆ4\n",dI[1]/1.e4);
%12.3e cmˆ4\n",dI[2]/1.e4);
}
80
81
82
83
84
85
86
// calculate all supported the section values of an element
int Element::setData()
{
// introduce some helper variables
double dxc[2];
// element center coordinates
double dLp[2];
// projected length of the element
87
88
89
90
91
92
// ... and calculate them
for (int i=0;i<2;i++)
{
// center coordinates
dxc[i] = (pN[1]->dx[i] + pN[0]->dx[i])/2.;
93
// projected length
dLp[i] = pN[1]->dx[i] - pN[0]->dx[i];
94
95
96
}
97
98
99
// calculate the length of the element
dL = sqrt(dLp[0]*dLp[0] + dLp[1]*dLp[1]);
100
101
102
// calculate the area
dA = dL * dt;
103
104
105
106
107
108
// calculate the static moment
for (int i=0;i<2;i++)
{
dS[i] = dxc[(i+1)%2]*dA;
}
109
110
E. Baeck
// calculate the moment of inertia
7.2. IMPLEMENTATION
Page 169
// Ixx, Iyy
int j;
for (int i=0;i<2;i++)
{
j = (i+1)%2;
// index on right side
dI[i] = ( (pow(dLp[j],2)/12.
+ pow(dxc[j],2)) * dA);
}
// Ixy
dI[2] = (dLp[0]*dLp[1]/12. + dxc[0]*dxc[1])*dA;
111
112
113
114
115
116
117
118
119
120
121
return 1;
122
123
7.2.5
// 1==true -> ok!
}
Checking the Element Class
To check the element class, we implement a little testing frame, which simple creates an element to
calculate the section values of a flat steel Fl200x4. The origin of the used coordinate system is in the
center of the element. The element is orientated into the vertical direction, i.e. in the direction of the
second coordinate.
The program executes the following steps.
• Allocate the Node instances.
We create 2 node 1 at the position (0, −100) and node 2 at (0, 100).
• Allocate the Element instances.
Element 1 gets the Node instance pointer 1 and 2 and the element’s thickness.
• Calculate the section values.
• List the element’s data.
• Delete all created instances.
The code of the testing frame is given below.
Listing 7.8: Check Environment for the Node Class
1
2
3
#include <stdio.h>
#include "node.h"
#include "element.h"
// what is a Node
// what is an Element
4
5
6
7
8
9
10
11
12
int main()
{
// create a flat steel Fl 200x4
// we need 2 Nodes for one Element
// the are allocated at the heap
//
No x
y
Node* pN1 = new Node(1, 0., -100.);
Node* pN2 = new Node(2, 0., 100.);
13
14
15
// create one Element on the heap
Element* pE1 = new Element(1,pN1,pN2,4.);
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16
// calculate the values
pE1->setData();
17
18
19
// list element’s data
pE1->listData();
20
21
22
// clear the memory
delete pN1;
delete pN2;
delete pE1;
return 0;
23
24
25
26
27
28
}
The Output of the above discussed code
is given in figure 7.4. If an instance is
created, we see in the log the message
of the Base class constructor, which
counts the instances. This output is
followed by the output of the Node
class constructor, which prints the coordinates of the Node instance.
After this the Element instance is created. The constructor of the element
shows us the element’s number. After the calculation of the section values
Figure 7.7: Output of the Element Check Program
is done, the element’s List method is
called, i.e. we see the element’s number and it’s thickness. Then all node data of this element are listed
and at the end we see the calculated section values.
Because the element is vertical we only get an area of
A = L · t = 200 · 4 mm 2 = 8cm 2
and a moment of inertia of
Ixx =
E. Baeck
1
1
· L3 · t =
· 2003 · 4 mm 2 = 266, 7cm 4
12
12
7.2. IMPLEMENTATION
7.2.6
Page 171
Profile Class for Model Profiles
A UML class diagram in figure 7.8 shows the concept of the class
Profile. The class contents the profile’s name and a container for
the profile’s nodes and profile’s elements. The containers are build by
a simple dynamical array and an integer, which holds the length of
the array.
The methods of the class creates the containers with a specified
length. A Node instance and an Element instance can be added
by an specific Add function. To check the node and element information Check methods are implemented, which checks the existents of the referenced node and element number. Besides the constructor and the destructor, the class has a method which will write
the instances data to the log using the inherited method of the class
Base::appendLog. To keep it simple all attributes and methods
are set to public.
We have the following class attributes. The meaning of the section
values is discussed in section C.1.
• pName[256], the profile’s name
• dA, total area
• dS[2], total static moment’s
Profile
+ pName[256] : char
+ dA : double
+ dS[2] : double
+ de[2] : double
+ dIu[3] : double
+ dIc[3] : double
+ dIm[2] : double
+ dAlpha : double
+ pNC : Node**
+ nNC : int
+ pEC : Element**
+ nEC : int
+ Profile(..) : −
− ˜Profile(): −
+ addNodeContainer(..) : int
+ addElementContainer(..) : int
+ addNode(Node* pN) : int
+ addElement(..) : int
+ listData() : void
• de[2], center of mass coordinates
• dIu[3], moment of inertia in user coordinates
+ deleteNodes() : int
+ deleteElements() : int
+ checkNode(..) : int
• dIc[3], moment of inertia in center of mass coordinates
+ checkElement(..) : int
• dIm[2], moment of inertia in main coordinates
+ resetSectionValues() : void
+ getSectionValues() : int
• dAlpha, main axis angle
+ listSectionValues() : void
• pNC, pointer to Node instance array
+ pTrans() : double
• nNC, length of node container
Figure 7.8: The Class Profile
• pEC, pointer to Element instance array
• nEC, length of element container
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The profile class has the following methods.
methode
parameter type
comment
constructor
Profile
cName
const char profile’s name
˜Profile
destructor
addNodeContainer
create the node container
nLength int
length of the array
create the element container
addElementContainer
nLength int
length of the array
adds a Node pointer into it’s array slot,
error checking is done
addNode
pN
Node*
instance pointer to store
adds an Element pointer into it’s array
slot, error checking is done
addElement
pE
Element*
instance pointer to store
listData
prints all data of the profile
deleteNodes
deletes all nodes and their container
deleteElements
deletes all elements and their container
checkNode
check the data of a node
pN
Node*
Node instance to check
check the data of an element
checkElement
pE
Element*
Element instance to check
resetSectionValues
initialize all section values
getSectionValues
print the section values
pTrans
calculate the principal values of the moment of inertia and the rotation angle
In this version of the implementation the input data is checked only by the Profile class, because in this
context it does not sence to access nodes and elements directly. So all input data runs through the profile’s
input functions.
If errors are detected we give up running backward using error codes. If an item is checked and an error
is detected an exception is thrown. So the applying routine has to catch the exception using the code of
the profile within a try block..
E. Baeck
7.2. IMPLEMENTATION
Page 173
The declaration of the class Profile is given by the following listing.
Listing 7.9: Profile Class’s Header
1
2
#ifndef PROFILE_H_INCLUDED
#define PROFILE_H_INCLUDED
3
4
5
6
#include "Base.h"
class Node;
class Element;
// we should know something about the Base
// we use Node pointers
// we use Element pointers
7
8
9
10
11
// a profile’s class
class Profile: public Base
{
public:
12
13
14
// interface - constructor
Profile(const char* cName);
15
16
17
// destructor
˜Profile();
18
19
20
// create a Node container
int addNodeContainer(int nLength);
21
22
23
// create a Element container
int addElementContainer(int nLength);
24
25
26
// add a Node
int addNode(Node* pN);
27
28
29
// add a Element
int addElement(Element* pE);
30
31
32
// list all values
void listData();
33
34
35
// delete/clear all Nodes
int deleteNodes();
36
37
38
// delete/clear all Nodes
int deleteElements();
39
40
41
// check the Node instance
int checkNode(Node* pN);
42
43
44
// check the Element instance
int checkElement(Element* pE);
45
46
47
48
// methods to calculate the section values
// - reset
void resetSectionValues();
49
50
51
// - calculate the section values
int getSectionValues();
52
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// - list them
void listSectionValues();
53
54
55
// - main axis transformation
double mTrans();
56
57
58
// ----------------------// attributes of the class
// - profile’s name
char pName[256];
59
60
61
62
63
64
65
66
67
68
69
70
71
// - section values
double dA;
double dS[2];
double de[2];
double dIu[3];
double dIc[3];
double dIm[2];
double dAlpha;
//
//
//
//
//
//
//
// Node container
Node**
pNC;
int
nNC;
// Node instance array
// array’s dimension
// Element container
Element** pEC;
int
nEC;
// Element instance array
// array’s dimension
area
static moment
center of mass coordinates
M o I in user coordinates
M o I in main CS
M o I main values
rotation angle
72
73
74
75
76
77
78
79
80
81
};
#endif // PROFILE_H_INCLUDED
The implementation code of the class Profile is given below. Note, that constructor is used with it’s
parameters to initialize the Profile data.
Listing 7.10: Profile Class’s Implementation
1
2
3
4
5
6
/*
Implementation of the Profile class
*/
#include "profile.h"
#include "node.h"
#include "element.h"
7
8
9
10
#include <stdio.h>
#include <string.h>
#include <math.h>
// standard io (printing)
// to use string functions
// to use math functions
11
12
13
14
15
16
17
// constructor
Profile::Profile(const char* pName): Base()
{
// copy name
//
dest.
source
strcpy(pName,pName);
18
19
20
21
E. Baeck
// initialize the container
pNC = 0; // for Nodes
nNC = 0;
7.2. IMPLEMENTATION
pEC = 0;
nEC = 0;
22
23
Page 175
// for Elements
24
// reset the results
resetSectionValues();
25
26
27
}
28
29
30
31
32
33
34
// destructor
Profile::˜Profile()
{
// first delete the content
deleteNodes();
deleteElements();
35
// delete the containers
if (pNC) delete [] pNC;
if (pEC) delete [] pEC;
36
37
38
39
// for Nodes
// for Elements
}
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
// reset the section values
void Profile::resetSectionValues()
{
dA = 0.;
//
destination pointer
//
|
| byte to copy
//
|
|
| number of bytes to copy
memset((void*)dS, 0, sizeof(double)*2);
memset((void*)de, 0, sizeof(double)*2);
memset((void*)dIu, 0, sizeof(double)*3);
memset((void*)dIc, 0, sizeof(double)*3);
memset((void*)dIm, 0, sizeof(double)*2);
dAlpha = 0.;
}
55
56
57
58
59
60
// delete all Nodes
int Profile::deleteNodes()
{
// check the container
if (!pNC)
return 0;
61
// delete the Node instances
for (int i=0;i<nNC;i++)
{
Node* pN = pNC[i]; // get the instance "i"
if (pN) delete pN;
// delete instance "i", if available
}
62
63
64
65
66
67
68
delete [] pNC;
pNC = 0;
nNC = 0;
69
70
71
// delete the container
// NO conaitner
// NO length
72
return 1;
73
74
}
75
76
77
// delete all Elements
int Profile::deleteElements()
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78
Computer Languages for Engineering - SS 15
{
// check the container
if (!pEC)
return 0;
79
80
81
// delete the Node instances
for (int i=0;i<nEC;i++)
{
Element* pE = pEC[i]; // get the instance "i"
if (pE) delete pE;
// delete instance "i", if available
}
82
83
84
85
86
87
88
delete [] pEC;
pEC = 0;
nEC = 0;
89
90
91
// delete the container
// NO conaitner
// NO length
92
return 1;
93
94
}
95
96
97
98
99
100
101
// list all profile attributs
void Profile::listData()
{
sprintf(msg,"Profile ’%s’ (node space: %d, element space: %d)\n",
pName,nNC,nEC);
AppendLog(msg);
102
// list the nodes data
for (int i=0;i<nNC;i++)
{
Node* pN = pNC[i];
if (pN) pN->listData();
}
103
104
105
106
107
108
109
// list the elements data
for (int i=0;i<nEC;i++)
{
Element* pE = pEC[i];
if (pE) pE->listData();
}
110
111
112
113
114
115
116
// list the result values
listSectionValues();
117
118
119
}
120
121
122
123
124
125
126
127
128
129
130
131
132
133
// list the section values
void Profile::listSectionValues()
{
appendLog((char*)"Section values:\n");
sprintf(msg," area.....................:
appendLog(msg);
sprintf(msg," static moment S_y........:
appendLog(msg);
sprintf(msg," static moment S_z........:
appendLog(msg);
sprintf(msg," center of mass y.........:
appendLog(msg);
sprintf(msg," center of mass z.........:
E. Baeck
%10.2f cmˆ2\n",dA/1.e2);
%10.2f cmˆ3\n",dS[0]/1.e3);
%10.2f cmˆ3\n",dS[1]/1.e3);
%10.2f mm\n",de[0]);
%10.2f mm\n",de[1]);
7.2. IMPLEMENTATION
appendLog(msg);
appendLog((char*)"Moment of Inertia in user cooordinates:\n");
sprintf(msg," I_yy.....................: %10.2f cmˆ4\n",dIu[0]/1.e4);
appendLog(msg);
sprintf(msg," I_zz.....................: %10.2f cmˆ4\n",dIu[1]/1.e4);
appendLog(msg);
sprintf(msg," I_yz.....................: %10.2f cmˆ4\n",dIu[2]/1.e4);
appendLog(msg);
appendLog((char*)"Moment of Inertia in centroid cooordinates:\n");
sprintf(msg," I_yy.....................: %10.2f cmˆ4\n",dIc[0]/1.e4);
appendLog(msg);
sprintf(msg," I_zz.....................: %10.2f cmˆ4\n",dIc[1]/1.e4);
appendLog(msg);
sprintf(msg," I_yz.....................: %10.2f cmˆ4\n",dIc[2]/1.e4);
appendLog(msg);
appendLog((char*)"Moment of Inertia in main cooordinates:\n");
sprintf(msg," I_eta....................: %10.2f cmˆ4\n",dIm[0]/1.e4);
appendLog(msg);
sprintf(msg," I_zeta...................: %10.2f cmˆ4\n",dIm[1]/1.e4);
appendLog(msg);
sprintf(msg," alpha....................: %10.2f ˆ
A ◦ \n",dAlpha*45./atan(1.));
appendLog(msg);
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
Page 177
}
157
158
159
160
161
162
// allocate the Node space
int Profile::addNodeContainer(int nLength)
{
// delete the old container
deleteNodes();
163
// create the Node array
pNC = new Node* [nLength];
if (!pNC) return 0;
// no memory available
164
165
166
167
// initialize the memory with Null (0)
//
destination address
//
|
| byte to copy
memset((void*)pNC,0,sizeof(Node*)*nLength);
168
169
170
171
172
// save the length
nNC = nLength;
173
174
175
return nLength;
176
177
}
178
179
180
181
182
183
// allocate the Element space
int Profile::addElementContainer(int nLength)
{
// delete the old container
deleteElements();
184
185
186
187
// create the Element array
pEC = new Element* [nLength];
if (!pEC) return 0;
// no memory available
188
189
// initialize the memory with Null (0)
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Computer Languages for Engineering - SS 15
//
destination address
//
|
| byte to copy
memset((void*)pEC,0,sizeof(Element*)*nLength);
190
191
192
193
// save the length
nEC = nLength;
194
195
196
return nLength;
197
198
}
199
200
201
202
203
204
// Add an element and it’s Nodes
int Profile::addElement(Element* pE)
{
// container available
if (!pEC)
throw "*** Error: no element container!\n";
205
// check element address
if (!pE)
throw "*** Error: no element pointer\n";
206
207
208
// check the instance and throw an exception,
// if there is an error
checkElement(pE);
209
210
211
212
// add the element
pEC[pE->nNo -1]
213
214
= pE;
215
// add the element’s Nodes
pNC[pE->pN[0]->nNo -1] = pE->pN[0];
pNC[pE->pN[1]->nNo -1] = pE->pN[1];
216
217
218
219
return 1;
220
221
}
222
223
224
225
226
227
// check an element instance
int Profile::checkElement(Element* pE)
{
// check instance pointer
if (!pE)
throw "*** Error: invalid element pointer!";
228
229
230
if (pE->nNo < 1 || pE->nNo > nEC)
throw "*** Error: invalid element number!";
231
232
233
234
235
236
237
238
239
240
// check the Node instances
for (int i=0;i<2;i++)
{
Node* pN = pE->pN[i];
if (!pN)
throw "*** Error: Node instance not found!";
if (pN->nNo < 1 || pN->nNo > nNC)
throw "*** Error: Node number invalid!";
}
241
242
243
244
245
E. Baeck
// check Node numbers
if (pE->pN[0]->nNo == pE->pN[1]->nNo)
throw "*** Error: Invalid Node numbers";
7.2. IMPLEMENTATION
return 0;
246
247
Page 179
}
248
249
250
251
252
253
// calculate the section values
int Profile::getSectionValues()
{
// initialization
resetSectionValues();
254
// sum over all elements
for (int i=0;i<nEC;i++)
{
// get element
Element* pE = pEC[i];
255
256
257
258
259
260
// element exists?
if (!pE)
continue;
261
262
263
// calculate Element results
pE->setData();
264
265
266
// sum up the values
dA += pE->dA;
for (int j=0;j<2;j++)
for (int j=0;j<3;j++)
267
268
269
270
dS[j] += pE->dS[j];
dIu[j] += pE->dI[j];
}
271
272
// calculate the center of mass
de[0] = dS[1]/dA;
de[1] = dS[0]/dA;
273
274
275
276
// calculate the principal values
pTrans();
277
278
279
return 1;
280
281
}
282
283
284
285
286
287
288
289
290
// principal axis transformation
// return: angle
double Profile::pTrans()
{
// M o I in CCS (center of mass)
dIc[0] = dIu[0] - de[1]*de[1]*dA;
dIc[1] = dIu[1] - de[0]*de[0]*dA;
dIc[2] = dIu[2] - de[0]*de[1]*dA;
291
292
293
294
295
// helper values
double dIdel = dIc[0] - dIc[1];
double dIsum = dIc[0] + dIc[1];
double dIsqr = sqrt(dIdel*dIdel +4.*dIc[2]*dIc[2]);
296
297
298
299
// M o I in principal coordinate system
dIm[0] = 0.5*(dIsum + dIsqr);
dIm[1] = 0.5*(dIsum - dIsqr);
300
301
// calcualate the rotation angle
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Computer Languages for Engineering - SS 15
dAlpha = 0.5*atan2(2.*dIc[2],dIdel);
302
303
return dAlpha;
304
305
7.2.7
}
Checking the Profile Class
To check the profile class, we implement a little testing frame, which simple creates an profile to calculate
the section values of a flat steel Fl200x4. The origin of the used coordinate system is in one endpoint and
the profile is rotated by 45◦ . We have used this example already to check the element in section 7.2.5.
The program executes the following steps.
• Allocate the Profile instances.
We pass the name of the profile.
• Allocate the containers.
We need a node space of two and an element space of one.
• Create the Node instances.
To check it flexible we use macros to enable or disable this part of code. Because in our case there
is no macro definition, we get the code within the #else branch.
• Create the Element instance.
We pass the element number, the Node instance pointers and the element’s thickness.
• Add the element to the profile.
Adding the element to the profile, the element’s data are checked, so if there will be detected an
error, the routine will be canceled by an exception, we have to handle.
• Calculate the section values and
• list the profiles data.
• At the end we should not forget to clear the memory, deleting the Profile instance.
All the above discussed steps should be done within a try block, so that we can handle detected errors
in the following catch blocks.
• The first catch block will handle our exceptions, because we pass a const char* to the
exception throwing them.
• The second catch block will handle all other exceptions. So, if we divide by zero or if we have
forgotten to check one case, the program is not crashing, an unspecified exception is thrown.
E. Baeck
7.2. IMPLEMENTATION
Page 181
The code of the testing frame is given below.
Listing 7.11: Check Environment for the Profile Class
1
2
3
4
5
#include
#include
#include
#include
#include
<stdio.h>
<math.h>
"profile.h"
"node.h"
"element.h"
// we start with the profile
// and will need some nodes
// and some elements
6
7
8
9
10
11
12
13
14
15
// #define _CENTERED
// disabled, to get the #else branch
int main()
{
// run the code using an exception handler, to
// handle errors detected by the error checker
try
{
// create the profile
Profile* pProf = new Profile("Fl200x4");
16
// add containers
pProf->addNodeContainer(2);
pProf->addElementContainer(1);
17
18
19
20
21
22
23
24
// create the Nodes (double symmetric)
#ifdef _CENTERED
Node* pN1 = new Node(1,0., 100.);
Node* pN2 = new Node(2,0.,-100.);
25
26
#elif
27
28
29
_SHIFTED
// create the Nodes, shifted
Node* pN1 = new Node(1,0.,
0.);
Node* pN2 = new Node(2,0.,-200.);
30
31
#else
// create the Nodes, shifted and rotated
Node* pN1 = new Node(1,0.,
0.);
Node* pN2 = new Node(2, 200./sqrt(2.),-200./sqrt(2.));
32
33
34
35
#endif
// create the Elements
Element* pE1 = new Element(1,pN1,pN2,4.);
36
37
38
// add element
pProf->addElement(pE1);
39
40
41
// calculate the section values
pProf->getSectionValues();
42
43
44
// list profile data
pProf->listData();
45
46
47
// delete the profile
delete pProf;
48
49
50
}
51
52
// handle the errors throwing string exceptsions
9.6.2015
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Computer Languages for Engineering - SS 15
catch(const char* str)
{
printf("Exception: %s\n",str);
}
53
54
55
56
57
// handle all unspecified exceptions
catch(...)
{
printf("Unknow exception!");
}
return 0;
58
59
60
61
62
63
64
}
The Output of the above discussed code
is given in figure 7.9. We see, that we
create four instances (two nodes, one
element and one profile). We see the
test printing of there constructors.
Then after having assembled the profile
the section values are calculated and
printed. We see, that we get the same
area as in the case of the element check
(section 7.2.5).
The center of mas we get at the center
of the element, which is
200
1
= 70.71
ex = · √
2
2
At the end we see, that we will get the
same values for the moment of inertia
in the main coordinate system as we
have calculated in the case of the element check. The calculated rotation
angle is -45◦ as expected.
E. Baeck
Figure 7.9: Output of the Element Check Program
7.2. IMPLEMENTATION
7.2.8
Page 183
H-Profile Class for Model Profiles
A UML class diagram in figure 7.10 shows the concept of the class
HProfile. The class is derived from the class Profile, which
itself is derived from the class Base. The only attributes the class
HProfile gets, are the parameters to describe the profile’s geometry.
Base
Profile
• dh, the height,
• dw, the width
HProfile
• dt, the flange thickness
+ dh : double
+ dw : double
• ds, the web thickness
+ dt : double
The HProfile instance is created with the call of the constructor,
so we put the data checking and the creation of the profile’s geometry
data into the constructor. Therefore with one statement all the things
to do are done. We pass the name of the profile and it’s geometry
parameter to the constructor.
+ ds : double
+ HProfile(..) : −
− ˜HProfile(): −
+ check(): int
+ create() : int
+ listData() : void
The HProfile class therefore will have the following methods.
methode
parameter type
Figure 7.10: The Class HProfile
comment
constructor
HProfile
cName
const char profile’s name, send to the base class
dh
double
profile’s height
dw
double
profile’s width
dt
double
profile’s flange thickness
dw
double
profile’s weg thickness
˜Profile
destructor
check
checks the parameter passed by the constructor call
create
create the geometry of the profile in
terms of nodes and elements
listData
list the profile’s data calling the List
method of the base class too
If errors are detected we give up running backward using error codes. If an item is checked and an error
is detected an exception is thrown. So the applying routine has to catch the exception using the code of
the profile within a try block..
9.6.2015
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Computer Languages for Engineering - SS 15
The declaration of the class HProfile is given by the following listing.
Listing 7.12: HProfile Class’s Header
1
2
#ifndef HPROFILE_H_INCLUDED
#define HPROFILE_H_INCLUDED
3
4
#include "profile.h"
// we have to know something about Profile
5
6
7
8
class HProfile : public Profile
{
public:
9
HProfile(const char* pName,
double dh,
double dw,
double dt,
double ds);
10
11
12
13
14
//
//
//
//
//
profile’s name
height
width
thickness of the flanges
thickness of the web
15
int check();
int create();
void listData();
16
17
18
// check the parameters
// create the profile
// list the data
19
// attributes: profile parameters
double dh;
// height
double dw;
// width
double dt;
// thickness of the flanges
double ds;
// thickness of the web
20
21
22
23
24
25
26
};
#endif // HPROFILE_H_INCLUDED
The implementation code of the class HProfile is given below. Note, that constructor is used with it’s
parameters to initialize the HProfile data.
Listing 7.13: HProfile Class’s Implementation
1
2
3
4
#include
#include
#include
#include
"hprofile.h"
"node.h"
"element.h"
<stdio.h>
// we need the HProfile header
// we will create Nodes
// and Elements
5
6
7
8
9
10
11
12
13
14
15
// constructor
don’t forget to call the base classes constructor
HProfile::HProfile(const char* pName,
double dh, double dw, double dt, double ds) :
Profile(pName)
{
// assign the input data
this.dh
= dh;
this.dw
= dw;
this.dt
= dt;
this.ds
= ds;
16
17
18
// check the data
check();
19
20
21
E. Baeck
// create the profile
create();
7.2. IMPLEMENTATION
22
Page 185
}
23
24
25
26
27
28
29
30
31
32
33
// Check the H-profile’s data, throw an exception if something is not ok
int HProfile::check()
{
double dEps = 0.5;
if (dt < dEps)
throw "error: dt invalid!";
if (ds < dEps)
throw "error: ds invalid!";
if (dw < 2.*ds)
throw "error: dw invalid!";
if (dh < 3.*dt)
throw "error: dh invalid!";
return 1;
}
34
35
36
37
38
39
40
// create the geometry
int HProfile::create()
{
// add node and element space
addNodeContainer(6);
// for 6 nodes
addElementContainer(5); // for 5 elements
41
// create nodes
Node* pN[6];
pN[0] = new Node(1,-dw/2., (dh-dt)/2.);
pN[1] = new Node(2,
0., (dh-dt)/2.);
pN[2] = new Node(3, dw/2., (dh-dt)/2.);
pN[3] = new Node(4,-dw/2.,-(dh-dt)/2.);
pN[4] = new Node(5,
0.,-(dh-dt)/2.);
pN[5] = new Node(6, dw/2.,-(dh-dt)/2.);
42
43
44
45
46
47
48
49
50
// create elements
Element* pE[5];
pE[0] = new Element(1,pN[0],pN[1],dt);
pE[1] = new Element(2,pN[1],pN[2],dt);
pE[2] = new Element(3,pN[3],pN[4],dt);
pE[3] = new Element(4,pN[4],pN[5],dt);
pE[4] = new Element(5,pN[1],pN[4],ds);
51
52
53
54
55
56
57
// bottom flange
// top flange
// web
58
// add elements to the profile
for (int i=0;i<5;i++)
addElement(pE[i]);
59
60
61
return 1;
62
63
}
64
65
66
67
68
69
70
71
72
73
74
75
76
77
// list all profile data
void HProfile::listData()
{
// list input data
sprintf(msg,"profile name........:
appendLog(msg);
sprintf(msg," height.............:
appendLog(msg);
sprintf(msg," width..............:
appendLog(msg);
sprintf(msg," flange thickness...:
appendLog(msg);
sprintf(msg," web thickness......:
%s\n",pName);
%10.2f mm\n",dh);
%10.2f mm\n",dw);
%10.2f mm\n",dt);
%10.2f mm\n",ds);
9.6.2015
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Computer Languages for Engineering - SS 15
appendLog(msg);
78
79
// call the base class’s methode!
Profile::listData();
80
81
82
7.2.9
}
Checking the HProfile Class
To check the profile class, we implement a little testing frame, which simple creates an profile to calculate
the section values of a HEA100 standard profile.
The program executes the following steps.
• Allocate the HProfile instances, specifying all profile parameters.
• Calculate the section values and
• list the profiles data.
• At the end we should not forget to clear the memory, deleting the HProfile instance.
All the above discussed steps should be done within a try block, so that we can handle detected errors
in the following catch blocks.
• The first catch block will handle our exceptions, because we pass a const char* to the
exception throwing them.
• The second catch block will handle all other exceptions. So, if we divide by zero or if we have
forgotten to check one case, the program is not crashing, an unspecified exception is thrown.
The code of the testing frame is given below.
Listing 7.14: Check Environment for the HProfile Class
1
2
3
#include <stdio.h>
#include <math.h>
#include "hprofile.h"
// we start with the hprofile
4
5
6
7
8
9
10
11
12
int main()
{
// run the code using an exception handler, to
// handle errors detected by the error checker
try
{
// check the H-Profile class
HProfile* pProf = new HProfile("HEA-100",96.,100.,8.,5.);
13
14
15
// calculate the section values
pProf->getSectionValues();
16
17
18
19
E. Baeck
// list profile data
pProf->listData();
7.2. IMPLEMENTATION
Page 187
delete pProf;
20
}
21
22
// handle the errors throwing string exceptsions
catch(const char* str)
{
printf("Exception: %s\n",str);
}
23
24
25
26
27
28
// handle all unspecified exceptions
catch(...)
{
printf("Unknow exception!");
}
return 0;
29
30
31
32
33
34
35
}
The Output of the above discussed
code is given in figure 7.11. We see
the input data used and the coordinates of the created nodes. Because
the output given is rather long, we
have split this output into the input
section (upper picture) and the result
section (lower picture).
The lower figure shows the calculated
section values. Because the origin is
in the center of the H-profile, we will
not get any eccentricity, i.e. static moments. If we use this symmetric origin, we see that the moments of inertia
with respect to our three coordinaten
systems are the same.
Figure 7.11: Output of the Element Check Program
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In the following table we compare the calculated values with the values we will find in the book of
standard profiles.5 We see, that the values are on the secure side, i.e. the calculated values are smaller
than the exact value and the error in this case is less than 4%.
value
exact TWA error
[cm 2 ] [cm 2 ]
area
21.2
20.4 −3.4
[cm 4 ] [cm 4 ]
5
[%]
[%]
big moment of inertia
349
338 −3.3
small moment of inertia
134
133
-0.8
Areas are given in cm 2 and moments of inertia are given in cm 4 , according to German standard table books.
E. Baeck
Part III
Appendix
189
Appendix A
The Console’s Friends
If you want to work with a console window you should know the console’s best friends, the commands
to navigate through the folder tree, the commands to create, delete and chance directories, the commands
to setup paths and environment variables and commands to copy and delete files.
And if you want to be happy using the console window, it’s recommended to know something about
assembling so-called batch files, which are in the most simple kind only a list of commands which
should be executed without typing them a dozen times.
The console window can be created with the command cmd from the execution input field in the start
menu of windows. A list of a lot of console commands is given by the command help1 . If you need a
specific information related to a special command, you will get this information calling the help with the
command’s name as parameter. If the command is not part of the command line help you can run the
command with the option /?.
An A-Z Index of the Windows CMD command line
ADDUSERS Add or list users to/from a CSV file
ADmodcmd Active Directory Bulk Modify
ARP
Address Resolution Protocol
ASSOC
Change file extension associations
ASSOCIAT One step file association
AT
Schedule a command to run at a specific time
ATTRIB
Change file attributes
b
BCDBOOT Create or repair a system partition
BCDEDIT Manage Boot Configuration Data
BITSADMIN Background Intelligent Transfer Service
BOOTCFG Edit Windows boot settings
BROWSTAT Get domain, browser and PDC info
c
CACLS
CALL
CERTREQ
CERTUTIL
CD
CHANGE
CHKDSK
1
Change file permissions
Call one batch program from another
Request certificate from a certification authority
Utility for certification authority (CA) files and services
Change Directory - move to a specific Folder
Change Terminal Server Session properties
Check Disk - check and repair disk problems
The list of commands is given in the language of the computer.
191
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CHKNTFS
CHOICE
CIPHER
CleanMgr
CLEARMEM
CLIP
CLS
CLUSTER
CMD
CMDKEY
COLOR
COMP
COMPACT
COMPRESS
CON2PRT
CONVERT
COPY
CSCcmd
CSVDE
Computer Languages for Engineering - SS 15
Check the NTFS file system
Accept keyboard input to a batch file
Encrypt or Decrypt files/folders
Automated cleanup of Temp files, recycle bin
Clear memory leaks
Copy STDIN to the Windows clipboard
Clear the screen
Create or configure a cluster
Start a new CMD shell
Manage stored usernames/passwords
Change colors of the CMD window
Compare the contents of two files or sets of files
Compress files or folders on an NTFS partition
Compress one or more files
Connect or disconnect a Printer
Convert a FAT drive to NTFS
Copy one or more files to another location
Client-side caching (Offline Files)
Import or Export Active Directory data
d
DATE
Display or set the date
DEFRAG
Defragment hard drive
DEL
Delete one or more files
DELPROF Delete user profiles
DELTREE Delete a folder and all subfolders
DevCon
Device Manager Command Line Utility
DIR
Display a list of files and folders
DIRUSE
Display disk usage
DISKPART Disk Administration
DISKSHADOW Volume Shadow Copy Service
DISKUSE Show the space used in folders
DOSKEY
Edit command line, recall commands, and create macros
DriverQuery Display installed device drivers
DSACLs
Active Directory ACLs
DSAdd
Add items to active directory (user group computer)
DSGet
View items in active directory (user group computer)
DSQuery Search for items in active directory (user group computer)
DSMod
Modify items in active directory (user group computer)
DSMove
Move an Active directory Object
DSRM
Remove items from Active Directory
e
ECHO
Display message on screen
ENDLOCAL End localisation of environment changes in a batch file
ERASE
Delete one or more files
EVENTCREATE Add a message to the Windows event log
EXIT
Quit the current script/routine and set an errorlevel
EXPAND
Uncompress CAB files
EXTRACT Uncompress CAB files
f
FC
FIND
FINDSTR
FOR /F
FOR /F
FOR
FORFILES
E. Baeck
Compare two files
Search for a text string in a file
Search for strings in files
Loop command: against a set of files
Loop command: against the results of another command
Loop command: all options Files, Directory, List
Batch process multiple files
Page 193
FORMAT
FREEDISK
FSUTIL
FTP
FTYPE
Format a disk
Check free disk space
File and Volume utilities
File Transfer Protocol
File extension file type associations
GETMAC
GOTO
GPRESULT
GPUPDATE
Display the Media Access Control (MAC) address
Direct a batch program to jump to a labeled line
Display Resultant Set of Policy information
Update Group Policy settings
g
h
HELP
Online Help
HOSTNAME Display the host name of the computer
i
iCACLS
IF
IFMEMBER
IPCONFIG
INUSE
Change file and folder permissions
Conditionally perform a command
Is the current user a member of a group
Configure IP
Replace files that are in use by the OS
LABEL
LOGEVENT
LOGMAN
LOGOFF
LOGTIME
Edit a disk label
Write text to the event viewer
Manage Performance Monitor
Log a user off
Log the date and time in a file
MAKECAB
MAPISEND
MBSAcli
MEM
MD
MKLINK
MODE
MORE
MOUNTVOL
MOVE
MOVEUSER
MSG
MSIEXEC
MSINFO32
MSTSC
Create .CAB files
Send email from the command line
Baseline Security Analyzer
Display memory usage
Create new folders
Create a symbolic link (linked)
Configure a system device
Display output, one screen at a time
Manage a volume mount point
Move files from one folder to another
Move a user from one domain to another
Send a message
Microsoft Windows Installer
System Information
Terminal Server Connection (Remote Desktop Protocol)
NET
NETDOM
NETSH
NETSVC
NBTSTAT
NETSTAT
NOW
NSLOOKUP
NTBACKUP
NTDSUtil
NTRIGHTS
Manage network resources
Domain Manager
Configure Network Interfaces, Windows Firewall & Remote access
Command-line Service Controller
Display networking statistics (NetBIOS over TCP/IP)
Display networking statistics (TCP/IP)
Display the current Date and Time
Name server lookup
Backup folders to tape
Active Directory Domain Services management
Edit user account rights
l
m
n
o
OPENFILES Query or display open files
p
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PATH
Display or set a search path for executable files
PATHPING Trace route plus network latency and packet loss
PAUSE
Suspend processing of a batch file and display a message
PERMS
Show permissions for a user
PERFMON Performance Monitor
PING
Test a network connection
POPD
Return to a previous directory saved by PUSHD
PORTQRY Display the status of ports and services
POWERCFG Configure power settings
PRINT
Print a text file
PRINTBRM Print queue Backup/Recovery
PRNCNFG Display, configure or rename a printer
PRNMNGR Add, delete, list printers set the default printer
PROMPT
Change the command prompt
PsExec
Execute process remotely
PsFile
Show files opened remotely
PsGetSid
Display the SID of a computer or a user
PsInfo
List information about a system
PsKill
Kill processes by name or process ID
PsList
List detailed information about processes
PsLoggedOn Who’s logged on (locally or via resource sharing)
PsLogList Event log records
PsPasswd
Change account password
PsPing
Measure network performance
PsService View and control services
PsShutdown Shutdown or reboot a computer
PsSuspend Suspend processes
PUSHD
Save and then change the current directory
q
QGREP
Query
Query
Query
Query
Search file(s) for lines that match a given pattern
Process / QPROCESS Display processes
Session / QWinsta
Display all sessions (TS/Remote Desktop)
TermServer /QAppSrv List all servers (TS/Remote Desktop)
User
/ QUSER
Display user sessions (TS/Remote Desktop)
r
RASDIAL Manage RAS connections
RASPHONE Manage RAS connections
RECOVER Recover a damaged file from a defective disk
REG
Registry: Read, Set, Export, Delete keys and values
REGEDIT Import or export registry settings
REGSVR32 Register or unregister a DLL
REGINI
Change Registry Permissions
REM
Record comments (remarks) in a batch file
REN
Rename a file or files
REPLACE Replace or update one file with another
Reset Session Delete a Remote Desktop Session
RD
Delete folder(s)
RMTSHARE Share a folder or a printer
ROBOCOPY Robust File and Folder Copy
ROUTE
Manipulate network routing tables
RUN
Start | RUN commands
RUNAS
Execute a program under a different user account
RUNDLL32 Run a DLL command (add/remove print connections)
s
SC
E. Baeck
Service Control
Page 195
SCHTASKS Schedule a command to run at a specific time
SCLIST
Display Services
SET
Display, set, or remove session environment variables
SETLOCAL Control the visibility of environment variables
SETX
Set environment variables
SFC
System File Checker
SHARE
List or edit a file share or print share
ShellRunAs Run a command under a different user account
SHIFT
Shift the position of batch file parameters
SHORTCUT Create a windows shortcut (.LNK file)
SHOWGRPS List the groups a user has joined
SHOWMBRS List the Users who are members of a group
SHUTDOWN Shutdown the computer
SLEEP
Wait for x seconds
SLMGR
Software Licensing Management (Vista/2008)
SOON
Schedule a command to run in the near future
SORT
Sort input
START
Start a program, command or batch file
SUBINACL Edit file and folder Permissions, Ownership and Domain
SUBST
Associate a path with a drive letter
SYSTEMINFO List system configuration
t
TAKEOWN
TASKLIST
TASKKILL
TELNET
TIME
TIMEOUT
TITLE
TLIST
TOUCH
TRACERT
TREE
TSDISCON
TSKILL
TSSHUTDN
TYPE
TypePerf
Take ownership of a file
List running applications and services
End a running process
Communicate with another host using the TELNET protocol
Display or set the system time
Delay processing of a batch file
Set the window title for a CMD.EXE session
Task list with full path
Change file timestamps
Trace route to a remote host
Graphical display of folder structure
Disconnect a Remote Desktop Session
End a running process
Remotely shut down or reboot a terminal server
Display the contents of a text file
Write performance data to a log file
VER
VERIFY
VOL
Display version information
Verify that files have been saved
Display a disk label
WAITFOR
WEVTUTIL
WHERE
WHOAMI
WINDIFF
WINMSDP
WINRM
WINRS
WMIC
WUAUCLT
Wait for or send a signal
Clear event logs, enable/disable/query logs
Locate and display files in a directory tree
Output the current UserName and domain
Compare the contents of two files or sets of files
Windows system report
Windows Remote Management
Windows Remote Shell
WMI Commands
Windows Update
XCACLS
XCOPY
Change file and folder permissions
Copy files and folders
v
w
x
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Comment / Remark
Within the following sections some of the most important commands are discussed which are very helpful, if you are working within the console window. The command’s details should be studied from the
original literature too. Within this short scratch only the most important command options are discussed.
A.1
Directory Commands
A.1.1
Selecting a Drive
Selecting the active drive, the name of the drive should be given as command, like c: to select the
standard drive or d: to select the cd-rom or z: to select the user-drive on a computer of the computerpool. Informations of the drive are listet with the command vol.
A.1.2
Listing the Content of a Directory
To list the content of an directory we can use the command dir. dir lists all files and subdirectories of the
actual directory. You can also call the dir command with some wildcards filtering. Figure A.1 shows a
directory list using a wildcard2 filtering of *.pdf. Note, that the volume information of the actual drive
is also listed. We will get the same listing, if we use the absolute path of the desired directory and start
the command from anywhere.
dir c:\CM\Cm-CLFE\BookOfExamples\*.pdf
Figure A.1: Create a Directory List of all pdf Files
A.1.3
Creating and Removing a Directory
A directory can simply be created with the command mkdir. Figure A.2 shows in the first step a directory
list of the directory c:\cm\commands. Then a new directory is created with the name commands.
After that the creation is checked with a further dir call. You can remove the directory with the inverse
command rmdir.
2
A wildcard is a joker or a filter definition for a command. * means everthing within one section of a file name in between
dots. A ? character is a joker for only one character within a string. So the wildcards t?st.* would filter a file with the name
test.pdf or tost.nothing .
E. Baeck
A.2. FILE COMMANDS
Page 197
Figure A.2: Create a Directory
A.1.4
Browsing through Directories
To browse through directories you can use the command cd, which is also called change directory.
With the command cd .. you step one level up to the root directory. You can specify the directories
name relative then you will jump out from the actual directory to the specified. You also can specify
the directories name absolute. Then you will jump from the roots directory into the specified. Figure
A.3 shows, that we start in the root directory. Then we clime up with relative jumps into the directory c:\cm, c:\cm\commands and at last c:\cm\commands\test. After that we jump back
with one jump into the root with cd \ and then back in our test directory with an absolute jump
cd \cm\commands\test.
Figure A.3: Browsing through the Directories
A.2
File Commands
How can we check the content of a file with a simple command. You can use the type command. Figure
A.4 shows how to pipe3 a screen stream into a file. This can be done by using a pipe character >.
Within a first step the directory list of the actual directory is created with the dir command. This list is
piped into a file with the name dir.lst using the command dir > dir.lst. After having created
the text file with the directory list this list is viewed by the command type. If you have to list larger
files with a lot of lines, you can use the command more to give a list page by page. So you have to
pipe the output of the type command into the postprocessing more command by using the command
type longfile.txt | more.
3
Pipe means, that a output stream of one process is used as an input stream for a following process, | character, or is used as
input stream for a file, > character.
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Figure A.4: Create a Directory
To delete a file the command del can be used. Figure A.5 shows in the first step a directory list. Two files
are found in the directory, dir.lst and helloworld.f90. In the second step the file dir.lst is
deleted by the command del dir.lst. This is shown in the third step giving an actual directory list
with the command dir. You can also use wildcards within the del command, so you can delete all files
from the directory with the wildcard *.*, so in this case we use the command del *.*.
Figure A.5: Create a Directory
A.3
Environment Commands
One of the most important environment commands is the command path which is used to specify the
search path for the executables. If you want to execute a program from the command line, it should be
accessible by the command executer. Therefore the command path should be used to extend the standard
path by the access path of the desired program.
If we want to use the compiler gfortran.exe, which lives in the folder c:\programs\mingw\bin we
should use the following command to extend the search path.
path = %path%;c:\programs\mingw\bin
%path% sets the still active path, which should not be overwitten by the extension.
If you want to check the actual path, then the command path can be given without parameters (see figure
A.6). The figure shows that the MinGW\bin is set and that the installed compiler g95.exe was found.
E. Baeck
A.3. ENVIRONMENT COMMANDS
Page 199
Figure A.6: Checking the System Path
Please note, that no quotes are used to specify the search path of the MinGW package, even if there are
space characters inside the path name. It is astonishing, that the compiler executable is found, if quotes
are used, but the secondary processes can obviously not be executed, so that you will get the following
error message (see figure A.7), if the compiler should compile a source file.
Figure A.7: Compiler Error due to wrong Path Settings
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E. Baeck
Computer Languages for Engineering - SS 15
Appendix B
Code::Blocks’s first Project
Within this chapter the creation of a project with the Code::Blocks IDE for Fortran is discussed as well
as the settings which are essential (see also section 5.1).
A new project can be created following the steps discussed below.
1. Start the IDE
To create a project we start the Code::Blocks application (see figure 1.10).
2. Check the Toolchain
Because the Code::Blocks IDE is a general IDE for a set of compilers, we have to setup the
parameters for the toolchain executable. Especial the compiler’s root directory has to be fitted (see
figure 1.11).
3. Start new Project
Click on the link Create a new project.
4. Select the Fortran Template
Figure B.1 shows the selection of the template to initialize the new project.
5. Setup the Project’s Name and it’s Folder
To setup the project’s name and folder, we have to fill in the project’s name into the first edit
control (see figure B.2). The second edit contents the root folder of our project. We can use the
browser control - the button with the three dots - to browse the folder tree. The third edit contents
the project file. The file name is created automatically. The whole project file with the total path is
created within the fourth edit.
6. Setup the Project’s Configuration
Clicking on next we will see the form to specify the project’s configuration (see figure B.3). Note,
that is very important to select the proper compiler in the first combo. Please select the GNU
Fortran Compiler. If the proper compiler is not selected, the build chain will crash with a strange
error message. It’s recommended to use the standard configurations release and debug. If the
software will work properly, you can build the release version of your software for shipping. If the
software is working faultily or bad the debug version can be used to find the software bugs with
the debugger tool.
201
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Figure B.1: Select the Fortran Template
Figure B.2: Setup the Project’s Name and Folder
7. Project’s Wizard finished
If we click on finish, the wizard is closed and we will see the project within the IDE’s project
browser (see figure B.4). If we open the node Fortran Sources, we find a source module called
hello.f90.
8. Rename the hello by a meaningful Name
To use a meaningful name for our main module we have to rename the hello.f90 by simply clicking
right on it. You select the rename item from the context menu and will get a small form to overwrite
the hello.f90 (see figure B.5). So we overwrite the default name by LittleProjectMain.f90.
E. Baeck
Page 203
Figure B.3: Setup the Project’s Configuration
Figure B.4: The Project now is created
9. Open the Main Module
A module’s source can be loaded into the editor by double clicking it in the source folder tree.
Figure B.6 shows the content of the default source of the renamed module.
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Figure B.5: Overwriting the default source filename
Figure B.6: Open the Main Module
E. Baeck
Page 205
10. Overwrite the Module Source
After having opend the main module, we can overwrite it’s source. In line 6 we implement a call
to the subroutine MySubModule. This source lives in a second module, which should be created
as follows. Figure B.7 shows the overwritten source of the main module.
Figure B.7: Overwriting the Main Module’s Source
11. Create a new Module for the Subroutine
To create a new source file, a new module we use the command file/New/empty file from the main
menu. The new source file is initialized with a standard name, in our case with untitled1. So we
are asked, whether we want to add this new source to our project. The answer should be yes (see
figure B.8).
12. Save the new Module using a meaningful Name
After having added the new module to our project, we should specify the name of the new module
within the standard save as dialog (see figure B.9).
13. Setup the Configuration for the new Module
Before we can start to write the new module’s source we have to set up it’s configuration. We
select both configurations, the release and the debug configuration (see figure B.10).
14. Writing the new Module’s Source
After having installed the new module for our project we can double click it’s node within the
source module tree and load it into the IDE’s editor. Because we want to show how to work with
more than one module our main program should call the subroutine MySubModule which only
should print the content of it’s input string parameter. Figure B.11 shows the source of the sub
module.
15. Build the Executable
The executable now can be build by the command Build/Build from the main menu or by the
acceleration key Ctrl-F9. If you have executed the build you should see a build log like in figure
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Figure B.8: Starting with a new Module
Figure B.9: Save the new Module specifying it’s name
B.12 in the build log window. Before a total build is executed it is recommended to check and
compile each module for it’s own by the acceleration key Ctrl-Shift-F9.
16. Executing the Executable
The executable can be started from the IDE with the command Build/Run or by usage of the
acceleration key Ctrl-F10. The programm starts within a command window and will print it’s
output (see figure B.13).
E. Baeck
Page 207
Figure B.10: Select the Configurations to support
Figure B.11: Writing the Sub Module’s Source
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Figure B.12: Check the Output int the Build Log Window
Figure B.13: Result of our little Project
E. Baeck
Appendix C
Some Theory
C.1
Section Properties
Within this chapter the formulas for the section properties of a thin walled model are given.
A thin walled model for a profile section consists of a set of lines which describes the profile section
geometry at the centerline.
C.1.1
The Area of a Profile Section
The Area is approximately the sum of the areas of the lines of the thin walled model.
Z
A=
eµ · dA ≈
A
with: Li
ti
eµ,i
C.1.2
n
X
eµ,i · Li · ti
(C.1)
i=1
the length of line i
the thickness of line i
the relative elasticity of line i (1 for only one material)
First Moments of an Area
The first moments of an area are the area integrals given below. The (y,z) values are related to an given
coordinate system.
Z
Sy =
eµ · z · dA ≈
A
Z
Sz =
eµ · y · dA ≈
A
with: Ai
yi
zi
n
X
i=1
n
X
eµ,i · z i · Ai
eµ,i · y i · Ai
i=1
the area of a line i
the y coordinate of the center of line i
the z coordinate of the center of line i
209
(C.2)
Page 210
C.1.3
Computer Languages for Engineering - SS 15
Second Moments of an Area or Moments of Inertia
The moments of inertia can be calculated with the formulas below. If we have a given arbitrary coordinate
system in general we have three values of inertia the Iy , the Iz and the mixed Iyz . If we use the main
coordinate system, the mixed moment of inertia is vanishing, so we use the symbols Iξ and Iη .
Z
2
eµ · z · dA ≈
Iy =
A
Z
A
(zb,i − za,i )2 /12) + z 2i · Ai
n
X
eµ,i ·
(yb,i − ya,i )2 /12) + y 2i · Ai
i=1
n
X
Z
eµ · y · z · dA ≈
Iyz =
A
with: Ai
yi
zi
ya,i
za,i
yb,i
zb,i
eµ,i ·
i=1
eµ · y 2 · dA ≈
Iz =
n
X
eµ,i · (((yb,i − ya,i )(zb,i − za,i )/12) + y i · z i ) · Ai ) (C.3)
i=1
the area of a line i
the y coordinate of the center of line i
the z coordinate of the center of line i
the y coordinate of the first point of line i
the z coordinate of the first point of line i
the y coordinate of the second point of line i
the z coordinate of the second point of line i
R
To solve an integral like Iy = A z 2 · dA for a polyline we can split up the integral into the sum of
integrals over the polyline segments.
Z
Iy =
A
z 2 · dA =
n Z
X
i=1
z 2 · dA
(C.4)
Ai
To solve an integral for a polyline segment we simple calculate it for the center of mass, because a simple
shift only will give us an additional term, the Steiner term. If we now want to calculate the polyline
integral at the center of mass we rotate the coordinate system by an angle ϕ into the line’s longitudinal
direction, because the transversal dimension, the thickness, is constant and so the respective integral will
be trivial.
E. Baeck
C.1. SECTION PROPERTIES
Page 211
Thus we make the following substitution.
(y, z ) ⇒ (η, ξ)
(C.5)
z = ξ/cos(ϕ)
(C.6)
With this substitution we will get the following integral.
Z
η=+t
Z
ξ=+L/2
Iy,i =
ξ2
· dη · dξ
cos(ϕ)2
η=−t
ξ=−L/2
Z ξ=+L/2
ξ2
=t·
· dξ
cos(ϕ)2
ξ=+L/2
1 ξ3
=t·
·
3 cos(ϕ)2 ξ=−L/2
ξ=−L/2
=t·
L3
1
·
12 cos(ϕ)2
(zb,i − za,i )2
=
· Ai
12
C.1.4
with t · L = Ai
(C.7)
Center of Mass
The coordinates of the center of mass are calculated with the arithmetic mean. Because the numerator of
the arithmetic mean is identical with the first moment of the area (see section C.1.2) and the denominator
is identical with the area of the profile, which is calculated in section C.1.1 we can use this values.
R
y · dA
Sz
=
yc = AR
A
dA
R A
z · dA
Sy
=
zc = AR
(C.8)
A
A dA
C.1.5
Moments of Inertia with Respect to the Center of Mass
If we know the center of mass coordinates given in section C.1.4 we can calculate the moments of inertia
with respect to the center of mass using Steiner’s Theorem as follows.
Iy,c = Iy − zc2 · A
Iz ,c = Iz − yc2 · A
Iyz ,c = Iyz − yc · zc · A
(C.9)
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C.1.6
Computer Languages for Engineering - SS 15
Main Axis Transformation
To get the moments of inertia Iξ and Iη we have to transform the moments of inertia into the main
coordinate system. Using this coordinate system the mixed moment of inertia is vanishing.
The main axis transformation is given with equation C.10.1
Idel = Iy,c − Iz ,c
Isum = Iy,c + Iz ,c
q
2 + 4 · I2
Isqr = IDel
yz ,c
2 · Iyz ,c
1
· arctan(
)
2
Idel
1
Iξ = · (Isum + Isqr )
2
1
Iη = · (Isum − Isqr )
2
ϕ=
1
(C.10)
The rotation angle ϕ should be shifted into the intervall [−π/2... + π/2]. To avoid a zero division calculating the rotation
angle ϕ a special version of the atan function should be used, which is able to handle the pole problem. In Python like in C this
function is called atan2(y, x ), which calculates the atan( xy ).
E. Baeck
Appendix D
Conventions
D.1
The Java Code Conventions
The following code convention [8] is published by Oracle (successor of Sun Microsystems, Inc). We
apply this convention to choose names for our software items.
1. Classes
Class names should be nouns, in mixed case with the first letter of each internal word capitalized.
Try to keep your class names simple and descriptive. Use whole words-avoid acronyms and abbreviations (unless the abbreviation is much more widely used than the long form, such as URL or
HTML).
2. Methods
Methods should be verbs, in mixed case with the first letter lowercase, with the first letter of each
internal word capitalized.
3. Variables
Except for variables, all instance, class, and class constants are in mixed case with a lowercase first
letter. Internal words start with capital letters. Variable names should not start with underscore _
or dollar sign $ characters, even though both are allowed.
Variable names should be short yet meaningful. The choice of a variable name should be
mnemonic- that is, designed to indicate to the casual observer the intent of its use. One-character
variable names should be avoided except for temporary ”throwaway” variables. Common names
for temporary variables are i, j, k, m, and n for integers; c, d, and e for characters.
4. Constants
The names of variables declared class constants and of ANSI constants should be all uppercase
with words separated by underscores ("_"). (ANSI constants should be avoided, for ease of
debugging.)
213
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E. Baeck
Computer Languages for Engineering - SS 15
Bibliography
[1] Photo: Lawrence Livermore National Laboratory
(Link: http://www.columbia.edu/acis/history/704.html)
[2] Watcom FORTRAN 77 Language Reference Edition 11.0c
[3] Stefen J. Chapman
Fortran 90/95 for Scientists and Engineers, Second Edition
McGraw-Hill, 2004
[4] H.R. Schwarz, N. K¨ockler
Numerische Mathematik
BI Wissenschaftsverlag Mannheim/Wien/Z¨urich, 1988
[5] Wikipedia, The Free Encyclopedia
[6] cplusplus.com - The C++ Resources Network
http://www.cplusplus.com/
[7] ISO/IEC 19501:2005
Information technology – Open Distributed Processing – Unified Modeling Language
(UML) Version 1.4.2
[8] Java Code Conventions
Oracle Inc., Sun Microsystems, Inc., September 12, 1997
215
Index
.AND., 31
.EG., 30
.EQU., 31
.FALSE., 31
.GE., 30
.GT., 30
.LE., 30
.LT., 30
.NE., 30
.NEQU., 31
.NOT., 31
.OR., 31
.TRUE., 31
2GB, 20
A format, 34
ACTION, 32
area, 209
arithmetic mean, 211
array, 50
automatic, 52
dynamical, 51
static, 50
assembler, 4
backward substitution, 105
base class, 157
bash, 63
binary numbers, 20
block data, 58
break, 144
build, 13, 205
bytecode, 4
C, 3, 5, 131
C++, 3, 131
C/C++ projects, 127
C#, 3
CALL, 85
card punch, 6
cast, 152
catch, 146, 172, 183
cd, 197
cdsqrt, 47
center of mass, 211
channel, 33
char, 132
CLOSE, 92
cmd, 191
Code::Blocks, 7, 12, 201
columns, 18
COMMON, 101
common, 58
compiler, 3
complement, 20
complex, 20
console window, 191
constants, 23
contains, 59
CONTINUE, 36
CYCLE, 36
CYGWIN, 10
debugger, 8
del, 198
derivative, 69, 71
dir, 196, 197
DO, 36
double, 132, 141
DOUBLE PRECISION, 22
E format, 34
editor, 7, 12
encapsulating, 108
END DO, 36
end function, 48
end subroutine, 49
endian, 21
endianness, 21
equivalence, 61
216
INDEX
exception, 146, 172, 183
EXIT, 36
exponent, 41
extension, 12
F format, 34
factorial, 40
FB substitution, 117
Fibunacci numbers, 4
first moment, 209
fixed format, 18
float, 20, 132
formal parameters, 48
FORMAT, 34
Forth, 4
FORTRAN 2008, 5
FORTRAN I, 5
FORTRAN II, 5
FORTRAN IV, 5
Fortran66, 36, 37, 42, 65
Fortran77, 18, 19, 22, 36, 37
Fortran90/95, 18, 19, 22, 37
forward substitution, 105
free format, 18
free FORTRAN compiler, 12
free FORTRAN tools, 7
function, 48
G95, 7, 17, 198
GCC C++ compiler, 128
GFortran, 17, 198
Grace Hopper, 5
I format, 34
IBM Type704, 5
IDE, 7
IEEE 754, 25
IF, 42
if, 143
INCLUDE, 85
info.server, 17
input parameters, 48
integer, 20
INTEGER*2, 22
INTEGER*4, 22
interpreter, 3
IPv6, 21
Page 217
ISML, 5
iteration, 69
Java Code Conventions, 213
Job Control Language, 63
kind, 23, 47
label, 36
linear equation system, 105, 118
LINUX, 3, 10, 63
LOGICAL*1, 22
LOGICAL*2, 22
long, 132
long long, 132
machine code, 4
main axis, 212
main function, 136
memory manager, 106
memset, 152
MFC, 149
MinGW, 7, 10, 198
mkdir, 196
module, 58
moment of inertia, 210
MS Excel, 41
NAG, 5
negative numbers, 20
new, 163
Newton, 50
Newton’s Algorithm, 71
OOP, 148
OPEN, 92
output parameters, 48
parent class, 157
path, 198
permissions, 150
piping, 197
POSITION, 32
preprocessor, 131
private, 150
program structure, 17
protected, 150
public, 150
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punch card and 80, 6
Python, 4
Computer Languages for Engineering - SS 15
Watcom, 7, 17
Windows32, 20
WRITE, 32
quadratic equation, 43
X format, 34
READ, 32, 85, 92
REAL*8, 22
return, 137
return code, 146
rmdir, 196
run, 206
second moment, 210
short, 132
Smalltalk, 4
stack, 155
STATUS, 32
struct, 152
SUBROUTINE, 85
subroutine, 48
suffix
cpp, 149
h, 149
superclass, 157
switch, 144
the most famous code, 65
throw, 146, 172, 183
try, 146, 172, 183
type, 197
typedef, 152
UML, 148
aggregation, 149
class diagram, 148
composition, 149
inheritance diagram, 148
note diagram, 148
note diagram assignment, 148
unicode, 19
UNIX, 10
unsigned, 132
upper lower extractor, 85
VBA, 3
virtual machine, 3
void, 132
vol, 196
E. Baeck