A Quick Fortran 77 Courseheim.ifi.uio.no/~inf3330/INF5660/F77.pdf · Advantages of Fortran 77 F77...

A Quick Fortran 77 CourseHans Petter Langtangen

Simula Research Laboratory

&

Dept. of Informatics, Univ. of Oslo

February 2004

A Quick Fortran 77 Course – p. 1

Advantages of Fortran 77

F77 is a very simple language

F77 is easy to learn

F77 was made for computing mathematical formulasand operating efficiently on plain arrays

F77 is still (and will forever be?) the dominatinglanguage for numerical computing

Lots of well tested and efficient F77 libraries exist

Compilers have 50 years of experience with optimizingF77 loops over arrays

Result: F77 is hard to beat when it comes to arrayoperations


Disadvantages of Fortran 77

The basic variables types are primitive

No struct or class construct in F77

No dynamic memory allocation

Very primitive language for text processing, lists andmore complicated data structures

F77 codes are difficult to extend, maintain and re-use

F90/F95: extension of F77 with classes(but not virtual functions, templates etc.)

The efficiency of F90/F95 is still problematic, and F77programmers move very slowly to F90/F95


My opinion

F77 is attractive for time-critical loops (array operations)

Make the rest of the program in a higher-level language:Python, C++, Java or F95

Python and F77 is an easy-to-use pair!

Note: integration of F77 with C++ or Java is notstraightforward


Formatting rules

Lines starting with a character in column 1 arecomment lines

Program statements must begin in column 7 or later

A character in column 6 indicates continuation of theprevious line

Labels (for “go to”) appear as numbers in column 2-5

Only one statement per line

No use of semicolon after a statement

White space has no meaning (can be omitted)


Example on source code file format

C lines starting with a char in column 1 are commentsC program statements start in column 7

C lines can be continued with a char in column 6:REAL R, S1,

& S2, S3

GO TO 100C label numbers (can be avoided) appear in column 2-5

10 CONTINUE100 CONTINUE

C only one statement can appear at each line

C Traditional F77 used upper-case chars and up to 6 charsC in variable names - most modern compilers allow much longerC variable names

C F77 is not case sensitive


Basic variable types

INTEGER NREAL R

C array A of length N, indices from 1 to N:REAL A(N)

C other arrays:DOUBLE PRECISION B(N,N), Q(-1:N), P(0:N,3,2)

C array sizes: NxN N+2 (N+1)x3x2C array indices start at 1 unless explicitly specified

C boolean variables:LOGICAL ON, CONVGD

C Fortran has full support for complex numbers:COMPLEX Z, Y

C alternative floating-point types:REAL*4 VAR1, VAR2REAL*8 VAR2, BARR(N)


Subroutines

Subroutine (no return value):SUBROUTINE MYFUNC2(F1, F2, N, M)

C first declare the variable types of the arguments:INTEGER N, MREAL*4 F1(N), F2(M,N)

C declare local variables in the routine:REAL*4 A, B, C

C computing statements:...RETURNEND

Example on call:INTEGER P, QREAL*8 A(P), A0(Q,P)...CALL MYFUNC(A, A0, Q, P)...


Functions

Functions return a single value:REAL*8 FUNCTION PTCOOR(COOR, PT, DIR, N)INTEGER N, PT, DIRREAL*8 COOR(N,2)PTCOOR = COOR(PT,DIR)RETURN

C the PTCOOR variable (equals the name of the functionC is returned from this function

Example on call:INTEGER NREAL*8 C...C = PTCOOR(COOR, 8, 1, N)

All arguments to subroutines and functions aretransferred as “pointers” (call by reference) so anychange to COOR, PT, DIR or N above is visible in thecalling code


No dynamic memory allocation

Arrays must be allocated with a length fixed at compiletime

INTEGER LENGTHPARAMETER (LENGTH=10000)

C array with fixed size at compile time:REAL*8 ARR(LENGTH)

CALL MYFUNC(ARR, LENGTH)...

C in a subroutine,C the array can have "variable" size:

SUBROUTINE MYFUNC(A, N)INTEGER NREAL*8 A(N)...

Ugly techniques exist for simulating dynamic memoryallocation


Scratch arrays

If you need scratch arrays inside a routine, these mustbe allocated outside (with fixed length) and provided asarguments:

INTEGER NPARAMETER (N=390000)REAL*8 WORK1(N)...CALL MYFUNC3(Q1, Q2, N, WORK1)...

SUBROUTINE MYFUNC3(Q1, Q2, N, SCRATCH)INTEGER NREAL*8 Q1, Q2, SCRATCH(N)...


Main program

The main program starts with PROGRAM:PROGRAM MYPROGINTEGER SIZEPARAMETER (SIZE=100000)REAL*8 COOR(SIZE,2), WORK1(SIZE), WORK2(SIZE)...CALL COMPUTE(COOR, WORK1, WORK2, N)...END

The rest of the code is subroutines or functions


Loops over arrays

For-loops are called do-loops in F77:C i=1,3,5,7,...,N and j=1,2,3,...,N:

DO J = 1, NDO I = 1,N,2A(I,J) = SIN(I*DX + J*DY)

END DOEND DO

Arrays are stored column-wise in Fortran 77 (row-wisein C), so the first index should have the fastest variationin a loop!


If-tests

C comparison operators:C .LT. .LE. .GT. .GE. .EQ.C < <= > >= ==

IF (A .GE. MAX) THENMAX = A

END IF

IF (Q2 .LT. Q1) THENQ2 = Q1

ELSE IF (Q2 .EQ. Q1) THENQ2 = 0.0

ELSEQ1 = 0.0

END IF


Strings

C declare strings with fixed length:CHARACTER BUFFER*200CHARACTER FILENAME*30

CALL FILEREAD(FILENAME)...

SUBROUTINE FILEREAD(NAME)C strings in a subroutine (unknown length):

CHARACTER NAME*(*)..


I/O, standard input/output

WRITE(*,*) ’computed A(’,I,’)=’,A(I,J)WRITE(*,*) ’Give two numbers:’READ(*,*) R1, R2


I/O, files (1)

INFILE=20OPEN(INFILE, FILE=NAME, STATUS=’UNKNOWN’, IOSTAT=IERR,

& FORM=’FORMATTED’)IF (IERR .GT. 0) THEN

C unsuccessful opening of the fileWRITE(*,*) ’Could not open file’, NAME

END IF

READ(INFILE,*) NDO I = 1,NREAD(INFILE,*) A(I)

END DO

C try to read more...DO I = 1, 1.0E+20READ(INFILE, *, IOSTAT=IERR) A(N+I)IF (IERR .LT. 0) THEN

C end of fileAL = N+IGO TO 100

ELSE IF (IERR .GT. 0) THENWRITE(*,*) ’Read error...’

END IFEND DOCLOSE(INFILE)


I/O, files (2)

100 CONTINUEOPEN(21, FILE=’sim.dat’, STATUS=’UNKNOWN’,

& FORM=’FORMATTED’)WRITE(21,*) NDO I = 1,NWRITE(21,*) A(I)

END DOCLOSE(21)


Global variables

Global variables in F77 are stored in (named) commonblocks:INTEGER J1, MREAL*8 A(M)COMMON /DATA1/ J1, M, A

To use a global variable in a routine, the completecommon block must be declared

Most F77 compilers allow a keyword "include" forincluding a file with the definition of a common block(otherwise all declarations of a common block must beconsistent throughtout a program)


Scientific Hello World

program helloworldreal*8 r, swrite(*,*) ’Give a number:’read(*,*) rs = sin(r)write(*,*) ’Hello, World! sin(’,r,’)=’,s

C with format string (A is text, F is float):write(*,1000) ’Hello, World! sin(’,r,’)=’,s

1000 format(A, F6.3, A, F11.8)end


Compiling and using the code

Compiling and linking:g77 -O3 -c hw.f # produces hw.o object fileg77 -o tmp.app hw.o # links to executable tmp.app

Running the program:unix> ./tmp.appGive a number:

0.0001Hello, World! sin( 0.0001)= 9.99999998E-05

Hello, World! sin( 0.000)= 0.00010000


A complete application

We shall show the complete F77 code for a programsolving the differential equation

md2y

dt2+ b

dy

dt+ cf(y) = A cosωt

numerically

Initial conditions:

y(0) = y0,dy

dt

∣

∣

∣

∣

t=0

= 0

Most solution methods require the equation to berewritten as a system of first-order differentialequations:

dy1

dt= y2

dy2

dt=

1

m(A cos ωt − by2 + cf(y1))

Solution methods: forward Euler and 2nd-orderRunge-Kutta


Initialize parameters

subroutine scan2(m_, b_, c_, A_, w_, y0_, tstop_, dt_, func_)C Initialize the data needed in the solver, and store in aC common block /data/, from the arguments to this subroutine.

real*8 m_, b_, c_, A_, w_, y0_, tstop_, dt_character func_*(*)

real*8 m, b, c, A, w, y0, tstop, dtcharacter func*20common /data/ m, b, c, A, w, y0, tstop, dt, func

m = m_b = b_c = c_A = A_w = w_y0 = y0_tstop = tstop_dt = dt_func = func_returnend


Initialize parameters from stdin

subroutine scan1()C Read input data (physical and numerical parameters)C from standard input. The data are stored in a common block.

real*8 m_, b_, c_, A_, w_, y0_, tstop_, dt_character func_*20read(*,*) m_, b_, c_, func_, A_, w_, y0_, tstop_, dt_call scan2(m_, b_, c_, A_, w_, y0_, tstop_, dt_, func_)returnend


Step in forward Euler method

subroutine adv_fe(y, n, t, dt, scratch)C Advance the solution one time step using theC Forward Euler method.

integer n, ireal*8 y(n), t, dt, scratch(n)

call rhs(scratch, y, n, t)C Forward Euler scheme:

do 10 i = 1,ny(i) = y(i) + dt*scratch(i)

10 continuereturnend


Step in 2nd-order Runge-Kutta method

subroutine adv_rk2(y, n, t, dt, scratch1, scratch2)C Advance the solution one time step using aC 2nd order Runge-Kutta method.

integer n, ireal*8 y(n), t, dt, scratch1(n), scratch2(n), t2

call rhs(scratch1, y, n, t)do 10 i = 1,n

scratch2(i) = y(i) + dt*scratch1(i)10 continue

t2 = t + dtcall rhs(scratch2, scratch2, n, t2)do 20 i = 1,n

y(i) = y(i) + 0.5*dt*(scratch1(i) + scratch2(i))20 continue

returnend


Define equations to be solved

The numerical algorithm subroutines call a subroutinethat evaluates the right-hand side of the first-orderdifferential equation system

Code on next slide


Define equations to be solved

subroutine rhs(f, y, n, t)C Define the right-hand side of the ODE system.

integer nreal*8 f(n), y(n), treal*8 cterm

real*8 m, b, c, A, w, y0, tstop, dtcharacter func*20common /data/ m, b, c, A, w, y0, tstop, dt, func

if (func .eq. ’y’) thencterm = y(1)

else if (func .eq. ’siny’) thencterm = sin(y(1))

else if (func .eq. ’y3’) thencterm = y(1) + (y(1)**3)/6.0

elsewrite(*,*) ’Error: spring-term ’,func,’ illegal’cterm = 0.0

endif

f(1) = y(2)f(2) = ( -b*y(2) - c*cterm + A*cos(w*t) )/mreturnend A Quick Fortran 77 Course – p. 28

Putting it all together

subroutine timeloop()C Integrate the ODEs in time by calling adv_fe orC adv_rk2 at every time step.

integer n, nmaxparameter (nmax=2)real*8 time, y(nmax), scratch1(nmax), scratch2(nmax)real*8 m, b, c, A, w, y0, tstop, dtcharacter func*20common /data/ m, b, c, A, w, y0, tstop, dt, func

n = 2C initial conditions:

y(1) = y0y(2) = 0.0

open(21, file=’sim.dat’, status=’unknown’, form=’formatted’)do 10 time = dt, tstop, dt

C call adv_fe (y, n, time, dt, scratch1)call adv_rk2 (y, n, time, dt, scratch1, scratch2)write(21,1000) time, y(1)

10 continueclose(21)return

1000 format(F12.4, F12.4)end A Quick Fortran 77 Course – p. 29

A main program

program oscillator

call scan1()call timeloop()end


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