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FortranFortran --33

Arrays and FunctionsArrays and Functions

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Arrays (matrices)Arrays (matrices)

Array elements are numbered 1, 2, 3,Array elements are numbered 1, 2, 3, and are stored in consecutive locations ofand are stored in consecutive locations ofmemory.memory.

A(1)

A(2)

A(3)

A(4)

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Declaration of ArrayDeclaration of Array

REALREAL, DIMENSION (10) ::, DIMENSION (10) ::AA LOGICALLOGICAL, DIMENSION(5) ::, DIMENSION(5) :: TRUTHTRUTH

Character(lenCharacter(len

=15)=15)

, DIMENSION(100) ::, DIMENSION(100) ::

NAMESNAMES

Integer, dimension(10,10)Integer, dimension(10,10) :: B:: B

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Declaration (contd.)Declaration (contd.)

One can use named constants inOne can use named constants indeclaration. This is useful in changingdeclaration. This is useful in changingmatrix sizes.matrix sizes.

Integer, Parameter :: dim=10Integer, Parameter :: dim=10

Real ::Real ::A(dimA(dim))

Integer ::Integer :: B(dim,dimB(dim,dim)) Real :: C(2*dim)Real :: C(2*dim)

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Initialization of ArraysInitialization of Arrays An array element behaves like an ordinaryAn array element behaves like an ordinary

variable which has the same type as thevariable which has the same type as thedeclared array type.declared array type.

Array can be initialized by defining everyArray can be initialized by defining every

element :element :

Integer, Dimension (5) :: AInteger, Dimension (5) :: A

Do I=1,5Do I=1,5A(I) = 0A(I) = 0

End DoEnd Do

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Initialization of ArrayInitialization of Array

It is also possible to initialize array in theIt is also possible to initialize array in thedeclaration statement itselfdeclaration statement itself

Real, Dimension(5) :: A=(/1.,2.,3.,4.,5./)Real, Dimension(5) :: A=(/1.,2.,3.,4.,5./)

Initialization may be done with READInitialization may be done with READstatement from terminal or from a filestatement from terminal or from a file

Initialize through an implicit doInitialize through an implicit dointeger, dimension(5):: A=(/(i, i=1,5)/)integer, dimension(5):: A=(/(i, i=1,5)/)initializes A= 1,2,3,4,5initializes A= 1,2,3,4,5

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Changing array rangeChanging array range

The default range of an array is from 1 to N.The default range of an array is from 1 to N.However, sometimes it is useful to change theHowever, sometimes it is useful to change the

range. For instance, if we want to store salesrange. For instance, if we want to store sales

figure of years from 2001 to 2007, it may befigure of years from 2001 to 2007, it may bebetter if we definedbetter if we defined

Real, Dimension(2001:2007) :: SalesReal, Dimension(2001:2007) :: Sales

Internally, computer will subtract 2000 from theInternally, computer will subtract 2000 from theargument to arrive at correct reference.argument to arrive at correct reference.

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Matrix operationsMatrix operations

Fortran 90 allows whole matrix operationsFortran 90 allows whole matrix operations

between matrices of the same shape andbetween matrices of the same shape andoperations like addition, subtraction andoperations like addition, subtraction and

multiplication, division etc. will be done onmultiplication, division etc. will be done onelement to element basis,element to element basis, i.e. ani.e. anoperation C= A+B implies C (I , J)= A(I,J)operation C= A+B implies C (I , J)= A(I,J)

+B(I,J) or C= A*B implies C(I,J) =+B(I,J) or C= A*B implies C(I,J) =A(I,J)*B(I,J) andA(I,J)*B(I,J) and NOT usual matrixNOT usual matrixmultiplication.multiplication.

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Bubble SortBubble Sort

Read N Data as an array of N numbersRead N Data as an array of N numbers For each I check if A(I) > A(J) for J= I+1For each I check if A(I) > A(J) for J= I+1to N. If yes, swap.to N. If yes, swap.

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Gauss Seidel MethodGauss Seidel Method

Read the coefficient matrix and theRead the coefficient matrix and ther.h.sr.h.s. of each equation. of each equation

The set of equations can be solved iteratively by writing the i-th equation asA

The solution of the i-th variable is

( ) /A

ii i ij j i

j i

i ij j i ii

j i

AX Y

X A X Y

X A X Y

=

+ =

= +

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GaussGauss--SeidelSeidel

The method converges if written inThe method converges if written indiagonally dominant formdiagonally dominant form

Give trial values of XGive trial values of Xii

Solve for each XSolve for each Xii iteratively.iteratively.

ij

j i

( ) ( ( ) sum(I)) / ( , ), wheresum(I)= A X I Y I A I I

=

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Subroutine structureSubroutine structure Similar to main program except for theSimilar to main program except for the

argument listargument list

Subroutine sub (Subroutine sub (argument listargument list))

Declaration sectionDeclaration sectionStatementsStatements

ReturnReturn

End subroutine subEnd subroutine sub

The variables in the argument list match theThe variables in the argument list match thetype and order in thetype and order in the DeclarationDeclaration in Subroutinein Subroutine

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How argument list is usedHow argument list is used Subroutine to calculate range of a projectileSubroutine to calculate range of a projectile

Subroutine RangeSubroutine Range ((init_velinit_vel, angle, time, range1), angle, time, range1)Implicit NoneImplicit None

Real INTENT(IN) ::Real INTENT(IN) :: init_velinit_vel, angle, angle

Real INTENT(OUT) :: range1, timeReal INTENT(OUT) :: range1, timeReal, parameter :: g=9.81Real, parameter :: g=9.81

Real, parameter :: pi=3.14159Real, parameter :: pi=3.14159

Real ::Real :: radian_angleradian_angle

radian_angleradian_angle = angle*pi/180.= angle*pi/180.Range1= (Range1= (init_velinit_vel)**2*sin(2*)**2*sin(2*radian_angle)/gradian_angle)/g

Time =2.*Time =2.* init_velinit_vel**sin(radian_angle)/gsin(radian_angle)/g

ReturnReturn

end subroutine Rangeend subroutine Range

2 sin2VR

g

=

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How a main program calls this subroutineHow a main program calls this subroutine

Program rangefinderProgram rangefinder

real :: u, t, theta, range2real :: u, t, theta, range2

Write(*,*)Write(*,*)Enter initial velocity u , angle ofEnter initial velocity u , angle of

projectionprojection in degrees and time tin degrees and time tRead(*,*)Read(*,*) u,t,thetau,t,theta

CallCall Range(uRange(u, theta, t, range2), theta, t, range2)Write(*,*)Write(*,*)Range=Range=, range,, range,timetime--, t, t

End program rangefinderEnd program rangefinder

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INTENT VariablesINTENT Variables

Dummy arguments in a subroutine canDummy arguments in a subroutine can

have INTENT attributehave INTENT attribute

INTENT(IN), INTENT(OUT),INTENT(IN), INTENT(OUT),

INTENT(INOUT)INTENT(INOUT) Intent attribute of each argument shouldIntent attribute of each argument should

be declared in the subroutine so thatbe declared in the subroutine so thataccidental tampering such arguments doaccidental tampering such arguments donot take place.not take place.

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Passing arrays as argument of a subroutinePassing arrays as argument of a subroutine

Calling argument passes a pointer to theCalling argument passes a pointer to thememory location of the array argument.memory location of the array argument.

There are several ways to pass on arrayThere are several ways to pass on arrayarguments. In this example we use dummyarguments. In this example we use dummyarguments where the arrays have the samearguments where the arrays have the sameshape as in the calling program.shape as in the calling program.

The main program calls a subroutineThe main program calls a subroutine matmultmatmult toto

do the matrix multiplication.do the matrix multiplication.

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Matrix Multiplication subroutineMatrix Multiplication subroutine

Program mainProgram main

Real, dimension (20,20) :: A,B,CReal, dimension (20,20) :: A,B,C

! 20X20 is the maximum size that the! 20X20 is the maximum size that the

multiplication is expected to be handled.multiplication is expected to be handled.Integer :: al, au,Integer :: al, au, blbl,, bubu

!these are actual dimensions of the!these are actual dimensions of thematrices A,B and that of product C, whichmatrices A,B and that of product C, whichwill be passed on. For multiplication au=will be passed on. For multiplication au=blbl

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Multiplication (Contd.)Multiplication (Contd.) Enter the matrix elements of A and BEnter the matrix elements of A and B

CallCall MatmultMatmult (A, B, al, au,(A, B, al, au, blbl,, bubu, C), C)Write CWrite C

Subroutine StructureSubroutine Structure ::

SubroutineSubroutine MatmultMatmult (A1,B1,al,au,bl,bu,C)(A1,B1,al,au,bl,bu,C)! The names of dummy arguments may or may not be! The names of dummy arguments may or may not bethe same as the real argument but their number and thethe same as the real argument but their number and theorder in which they appear must be identicalorder in which they appear must be identical

integer, intent (in) :: al, au,integer, intent (in) :: al, au, blbl,, bubureal,real, intent(inintent(in), dimension(20,20) :: A1,B1), dimension(20,20) :: A1,B1

real,real, intent(outintent(out), dimension(20,20) :: C), dimension(20,20) :: C

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Matrix multiplication (contd.)Matrix multiplication (contd.)

IF (au/=IF (au/=blbl) THEN) THENWrite(*,*)Write(*,*)The matrix is not conformableThe matrix is not conformable

stopstop

END IFEND IF

Carry out multiplication of matrices A1 andCarry out multiplication of matrices A1 and

B1 and store in result in CB1 and store in result in C

ReturnReturn

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FunctionFunction

Result is a single number, logical value aResult is a single number, logical value astring or an arraystring or an array

Intrinsic functions are built inIntrinsic functions are built in sin(xsin(x),),abs(xabs(x))

Here we talk about user defined functionsHere we talk about user defined functions

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FunctionsFunctions

Function definition should define the return type.Function definition should define the return type.This can be done in two ways :This can be done in two ways :

Integer functionInteger function myfunctionmyfunction (I, J)(I, J) OROR FunctionFunction myfunctionmyfunction (I,J)(I,J)

integer ::integer :: myfunctionmyfunction

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Program to calculate volume of a sphere,Program to calculate volume of a sphere,

given radius.given radius.

Main programMain program

Implicit noneImplicit none

Real :: radius, volumeReal :: radius, volume

Read(*,*) radiusRead(*,*) radiusWrite(*,*)Write(*,*)volume=volume=,, volume(radiusvolume(radius))

End MainEnd Main

The function program for volume would look as followsThe function program for volume would look as follows

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Subroutine VolumeSubroutine VolumeReal functionReal function volume(Rvolume(R))

! R is a dummy argument corresponding to radius in main.! R is a dummy argument corresponding to radius in main.implicit noneimplicit none

Real,Real, intent(inintent(in) :: R) :: R

Real, parameter :: pi=3.14159Real, parameter :: pi=3.14159If (r

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RecursionRecursion A function can call itself recursivelyA function can call itself recursively For instance n! = n*(nFor instance n! = n*(n--1)!1)!Recursive function factorial (n)Recursive function factorial (n) Result(facResult(fac))! Note the return value is in Result,! Note the return value is in Result, facfac is the result returnedis the result returned

Integer,Integer, intent(inintent(in) :: n) :: n

Integer ::Integer :: facfac

If (n==0) thenIf (n==0) then

FacFac=1=1

ElseElse

FacFac= n*factorial(n= n*factorial(n--1)1)

End ifEnd if

End Function FactorialEnd Function Factorial