Supplementary Lecture Note
by
Aborisade D.O.

Repetitive Structures
Do Loop
While Loop
Do While
 Array
Sample FORTRAN Programs on Two dimensional
array
Sample FORTRAN programs on Multidimensional
array.
References



FORTRAN programming offers us three basic
Control Structures:
(i)Sequence (ii) Selection and Repetition.
Repetition structure or loop makes possible the
repeated execution of one or more statements,
called the body loop. There are two basics
types of repetition structures:

Repetition controlled by a counter: in which the
body of the loop is executed once for each value of
some control variable in a specified range of values .
e.g Do Loop
- Repetition controlled by a logical expression in which
the
decision to continue or to terminate repetition is
determined
by the value of some logical expression. e.g While
Loop.
. While loop is a repetition in which logical
expression controls the loop, in that as long as the
logical expression remain true, the loop continues,
but when it is false, the loop terminates.
false
WHILE
logical
expression
true
Statement
sequence
•
DO WHILE forms:
DO WHILE (logical expression)
statement sequence
END DO
OR
- WHILE (logical expression) DO
statement sequence
END WHILE
–
INTEGER NUMBER, SUM, LIMIT
*Read LIMIT AND initialize NUMBER and SUM
PRINT *, ‘ENTER VALUE 1+2+ ………+ ? IS TO EXCEEED’
READ *, LIMIT
NUMBER=0
SUM=0
DO WHILE (SUM .LE. LIMIT)
NUMBER=NUMBER+1
SUM=SUM+NUMBER
END DO
*Print the results
PRINT *, ‘1+…………..+’, NUMBER, ‘ =‘, SUM, ‘>’, LIMIT
END


An array is a data structure in which a fixed
number of data values of the same type are
organized in a sequence, and direct access to each
value is possible by specifying its position in
sequence.
In a program, an array element can be referenced
by using the array subscripted variable formed by
appending a subscript (or index) enclosed in
parentheses to the array variable e.g.
NTIMES(2),SUM(20). The subscript specifies the
position of an element in the array.
•
Types of Arrays:
One-dimensional arrays
– Two multidimensional arrays
– Multidimensional arrays
• Arrays are declared using DIMENSION statement.
Array declaration format:
DIMENSION list (where list is a list of array
declarations of the form array name(1:u) separated by
commas, the pair 1:u must be a pair of integer constants or
parameters).
–
•
•
e.g DIMENSION COUNT(20)
INTEGER COUNT
OR
DIMENSION COUNT(1:20)
INTEGER COUNT
Dimension in array declaration can be specified by
parameters example the array FAILTM can be
declared by
INTEGER LLIM, ULIM
PARAMETER (LLIM=1, ULIM=50)
REAL FAILTM(LLIM:ULIM)
•
There are three ways by which a one
dimensional array can be read or displayed
use a Do loop containing an input/output statement.
– use only the array name in an input/output
statement.
– use an implied Do loop in an input/output
statement.
Example 1: Input/Output using a Do loop
–
INTEGER LIMIT, NUMVEL, I
PARAMETER (LIMIT=50)
REAL VELOC(LIMIT)
*Read the list of velocities
PRINT *, ‘ENTER THE NUMBER OF VELOCITES:’
READ *, NUMVEL
PRINT *, ‘ENTER THE VELOCITY VALUES, OE PER
LINE:’
DO 10 I=1, NUMVEL
READ *, VELOC(I)
10 CONTINUE
*Print the list of velocities
PRINT 20
20 FORMAT(/1X, ‘LST OF VELOCITIES: ‘/1X,18(‘=‘))
DO 40 I=1, NUMVEL
30
40
PRINT 30, I, VELOC(I)
FORMAT(1X, I3, ‘:’,F10.1)
CONTINUE
END
Example 2: Input/Output using the Array Name
INTEGER LIMIT
PARAMETER(LIMIT=10)
REAL VELOC(LIMIT)
* Read the list of velocities
PRINT *, ‘ENTER THE VELOCITY VALUES AS MANY AS
DESIRED:’
READ *, VELOC
* Print the list of velocities
PRINT 20
20 FORMAT(/1X, ‘LIST OF VELOCITIES:’ / 1X, 18(‘=‘)/)
PRINT 30, VELOC
30 FORMAT(1X, 5F10)
END
Example 3: Input/Output using Implied Do Loops. An implied Do
loop in an input/output statement provides the most flexible method
for reading the elements of an array. It enables a programmer to
specify that only a portion of the array be transmitted and to specify
the arrangement of the values to be read or displayed.
INTEGER LIMIT, NUMVEL, I
PARAMETER(LIMIT=50)
REAL VELOC(LIMIT)
* Read the list of velocities
PRINT *, ‘ENTER THE NUMBER OF VELOCITIES:’
READ *, NUMVEL
PRINT *, ‘ENTER THE VELOCITY VALUES AS MANY AS MANY PER
LINE:’
READ *, (VELOC(I), I=1, NUMVEL)
* Print the list of velocities
PRINT 20, NUMVEL
20 FORMAT(/1X, ‘LIST OF’, 13, ‘VELOCITIES:’ / 1X, 21(‘=‘))
PRINT 30, VELOC(I), I=1, NUMVEL)
30 FORMAT(1X, 5F10.1)
END



Many problems exist in which data to be processed can be
naturally organized as a table . To easily solve problems like these,
2 dimensional arrays are defined to stored to data in rows and
columns for processing.
A 2-dimensional array can be declared using statement such as:
DIMENSION TEMTAB(4,3)
REAL TEMTAB
In a 2-dimensional array, the two subscripts refers to the positions
of data in the array. 4 for row position and 3 for column position.
Example of a two dimensional array.
Time
Location 1
Location 2
Location 3
1
65.5
68.1
64.5
2
78.9
56.6
55.8
3
56.5
43.5
54.6
4
45.6
78.9
65.9
Example: A Program to process data in a 2-dimensional array.
INTEGER MAXTIM, MAXLOC, NTIMES, NLOCS, TIME, LOC
PARAMETER (MAXTIM=24, MAXLOC=10)
REAL TEMTAB(MAXTIM,MAXLOC)
PRINT *, ‘ENTER # OF TIMES TEMPERATURES ARE RECORDED’
PRINT *, ‘AND # OF LOCATIONS WHERE RECORDED:’
READ *, NTIMES, NLOCS
PRINT *, ‘ENTER THE TEMPERATURES AT THE FIRST
LOCATION.’
PRINT *, ‘THEN THOSE AT THE SECOND LOCATION. AND SO
ON:’
READ *, ((TEMTAB(TIME,LOC), LOC=1, NLOCS), TIME=1, NTIMES)
PRINT *
PRINT 100, (LOC, LOC=1, NLOCS)

100 FORMAT(1X, T13, ‘LOCATION’ / 1X, ‘TIME’, 1016)
DO 130 TIME=1, NTIMES
PRINT 110, TIME, (TEMTAB(TIME,LOC), LOC=1, NLOCS)
110 FORMAT(/1X, I3, 2X, 10F6.1/)
130 CONTINUE

This refers to array with more than two dimensions. For example,
suppose that temperature readings are made for one week so that
seven temperature tables such as one depicted below could be
referred as a multidimensional array:
Day 7
Day 2
Day 1
Loc1
Loc2
Loc3
1
78.8
34.6
2
65.5
67.5
67.8
88.0
Loc1 Loc2
Loc 3
3
1
45.6
25.8 25.9
2
35.5
20.5 23.8
3
45.9
34.5 45.9
4
23.0
12.6 48.5
Loc
1
Loc
2
Loc
3
19.5
21.5
27.9
50.5
78.5
56.4
67.9
78.0
78.6

The general form of an array declaration is:
array-name(11:u1, 12:u2,………………………..1k:uk)
where the number k of dimensions is at most seven; and each pair
1:u
must be a pair of integer constants or parameters specifying the
range of values for the ith subscript to be from 11 through u1.
or in DIMENSION statements as:
REAL ALPHA(5,10), BETA(5,5,2), GAMMA(1:2,-1:3), BETA(5:12)
INTEGER COUNT(0:2,0:3,1:2) or
DIMENSION list-of-array-declarations e.g
DIMENSION ALPHA(5,10), BETA(5,5,2)
DIMENSION GAMMA(1:2, -1:3), DELTA(5:12), COUNT(0:2,0:3, 1:2)
REAL ALPHA, BETA, GAMMA, DELTA
INTEGER KAPPA
Example
* Program to solve a linear system using Gaussian elimination
INTEGER LIMROW, LIMCOL
PARAMETER (LIMROW=10, LIMCOL= LIMROW+1)
REAL LIN(LIMROW, LIMCOL), X(LIMROW)
INTEGER N, I, J
LOGICAL SINGUL
* Read coefficients and constants
PRINT *, ‘ENTER NUMBER OF EQUATIONS’
READ *, N
DO 10 I=1, N
PRINT *, ‘ENTER COEFFICIENT AND CONSTANT OF
EQUATION’ ,
+
I, ‘: ‘
READ *, (LIN(I,J), J=1, N+1)
10 CONTINUE
SUBROUTINE GAUSS(LIN, LIMROW, LIMCOL, N, X,
SINGUL)
REAL LIN(LIMROW, LIMCOL), X(LIMROW), TEMP,
MULT, EPSIL
PARAMETER (EPSIL=1E-7)
INTEGER N, PIVROW
LOGICAL SINGUL
SINGUL=.FALSE.
DO 50 I=1, N
* Locate pivot element
ABSPIV=ABS(LIN(I,J))
PIVROW=I
DO 10 K=I+1, N
IF (ABS(LIN(K,I)) .GT. ABSPIV) THEN
ABSPIV=ABS(LIN(K,I))
PIVROW=K
END IF
10 CONTINUE
* Check if matrix is nearly singular
IF (ABSPIV .LT. EPSIL) THEN
SINGUL=.TRUE.
RETURN
END IF
* Interchange row PIVROW and I if necessary
IF (PIVROW .NE. I) THEN
DO 20 J=1, N+1
TEMP= LIN(I,J)
LIN(I,J)= LIN(PIVROW, J)
LIN(PIVROW,J) = TEMP
20 CONTINUE
END IF
* Eliminate Ith unknown from equations I+1, ………N
DO 40 J=I+1, N
MULT= -LIN(J, I)/ LIN(I, I)
DO 30 K=I, N+1
LIN(J,K)=LIN(J,K)+ MULT* LIN(I,K)
30 CONTINUE
40 CONTINUE
50 CONTINUE
* Use subroutine GAUSS to find the solution and then display
the solution
CALL GAUSS(LIN, LIMROW, LIMCOL, N, X,
SINGUL)
IF (.NOT. SINGUL) THEN
PRINT *, ‘SOLUTION IS’
DO 20 I=1, N
PRINT 100, I, X(I)
100 FORMAT(1X, ‘X(‘, I2, ‘) =‘, F8.3)
20
CONTINUE
ELSE
PRINT *, ‘MATRIX IS (NEARLY) SINGULAR’
END IF
END

Larry N. and Sandford L.:FORTRAN 77 for
Engineers and Scientists with An Introduction
to FORTRAN 90 fourth Edition.