An Introduction to Fortran

Transcription

1 An Introduction to Fortran Sylvia Plöckinger March 10, 2011 Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

2 General Information Find this file on: Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

3 Outline 1 Literature 2 History 3 Fortran 90 4 Declaration Part 5 Execution Part 6 Modules 7 Back to F77 8 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

4 Literature Literature in the Astronomy Library: Fortran 90/95 for Scientists and Engineers, Stephen J. Chapman Introduction to Programming with Fortran, I. Chivers, J. Sleightholme Fortran for the 90s, Stacey L. Edgar Fortran 90 Programming,T. M. R. Ellis, I. R. Philips, T. M. Lahey Fortran 90 Language Guide, Wilhelm Gehrke Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

5 History The early days... Up tp 1954 Machine language (0,1 - binary) Assembler (mnemonics) Problem: Machine dependent + Higher-level language should be understandable by both humans and machines IBM team led by John Backus developed the first higher level language: Fortran (Formula Translator) very successful First standard Fortran Relatively machine independent Was widely available Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

6 History Next standard: Fortran 77 Column 1-6 1: Line is a comment if a c or a * is inserted 2-5: Labels for GOTO or FORMAT statements 6: Any symbol beside blank or 0 line continues Column 7-72 Actual Fortran statements Column Comments, not read by compiler, originally for sequence numbers of punched cards Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

7 History General Remarks: Your program should be: efficient (in both CPU time and memory) readable (documentation, variable names, indentation,...) portable (machine independent, compiler independent) modular (subroutines can be used otherwise) Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

8 Fortran 90 Fortran 90 Program A program consists of modules, like Program Subroutine Function Interface Module Fortran 90 Modules Every module consists of (Documentation) Header Declaration Part (variable declaration, use statements) Execution Part End Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

9 Declaration Part Declaration Part Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

10 Declaration Part Declaration Part - Variables and Constants Variable names are symbolic references for positions within the memory. They are reserved already by the compiler, but get their values assigned at runtime. The memory for constants is already filled with the value at compilation. Declare all variables and constants explicitly! (Implicit: I-N - Integer, A-H and O-Z - Real) Fortran 77 IMPLICIT NONE INTEGER c REAL ix,x,y,z CHARACTER*10 name LOGICAL a DOUBLE PRECISION b Fortran 90 IMPLICIT NONE INTEGER (kind=4) :: c REAL (kind=4) :: ix, x, y, z CHARACTER (len=10) :: name LOGICAL :: a REAL (kind=8) :: b Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

11 Declaration Part A quick side note on the binary system Integer values: 16 bit (2 byte): [ , ] up to bit (4 byte): [ , ] up to = = 3 Floating point values: = = Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

12 Declaration Part Floating Point numbers SINGLE PRECISION (32 bit or 4 byte) DOUBLE PRECISION (64 bit or 8 byte) Sign: Exponent: Significand: Size = 1 bit Size = 8 bit (single), 11 bit (double) Size = 23 bit (single), 52 bit (double) Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

13 Declaration Part Floating Point numbers Roundoff error Finite accuracy of number representation Decimal: π, 2, 1 3 Binary: 0.1 Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

14 Declaration Part Machine Accuracy ɛ m The smallest number that can be added to 1. and gives as a result a number that is different to 1. For a real number (4 byte) typically For example: 1.E = 1.E07 no matter how often you perform this calculation Error estimation For a randomly distributed error, after N operations: Nɛ m Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

15 Declaration Part KIND - A side mark to the topic of portability It is up to each compiler configuration to decide what kind numbers are associated with each type and kind variation kind value on its own should not be used across platforms! To make sure the accuracy of you program is machine independent use the intrinsic functions: INTEGER, PARAMETER :: intkind = SELECTED INT KIND (2) INTEGER, PARAMETER :: realkind = SELECTED REAL KIND(P=15,R=307)! P... Precision (f.e. 15 significant digits), R... Range (f.e. [10 307, ] ) INTEGER (KIND = intkind) :: i REAL (KIND = realkind) :: a, b, c Error / accuracy / range estimation: KIND(x) Returns the kind type HUGE(x) Returns the largest number PRECISION(x) Returns the decimal precision EPSILON(x) Smallest difference between two reals Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

16 Declaration Part Other options in the declaration part PARAMETER INTEGER, PARAMETER :: imax = ! whats the difference to that: INTEGER:: imax = REAL, PARAMETER :: pi = 4. * ATAN (1.) Parameter cannot be changed within the program. Memory gets the value already at runtime. DIMENSION INTEGER :: i, j REAL, DIMENSION (100) :: x, y, temp1d REAL, DIMENSION(100,100) :: temp DO i = 1,100,1 x(i) = REAL(i) y(i) = REAL(i) DO j = 1,100,1 temp(i,j) = * & SIN(x(i)) * COS(x(i)*y(j)) ENDDO ENDDO! Not in F77 : temp1d = 0. temp1d = temp (50,:) Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

17 Declaration Part Other options in the declaration part ALLOCATABLE INTEGER :: i, j, nsteps REAL, DIMENSION (:), ALLOCATABLE :: x, y REAL, DIMENSION(:,:), ALLOCATABLE :: temp write (*,*) how many steps in x and y direction? read (*,*) nsteps allocate (x (nsteps) ) allocate (y (nsteps) ) allocate (temp (nsteps, nsteps) ) DO i = 1,100,1 x(i) = REAL(i) y(i) = REAL(i) DO j = 1,100,1 temp(i,j) = * & SIN(x(i)) * COS(x(i)*y(j)) ENDDO ENDDO deallocate (x) deallocate (y) deallocate (temp) OTHERS INTENT(IN) (OUT) (INOUT) PRIVATE PUBLIC SAVE EXTERNAL INTRINSIC OPTIONAL POINTER TARGET Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

18 Execution Part Execution Part Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

19 Execution Part IF Statement IF <logical expression> THEN... ENDIF Logical Expressions IF (a < b) THEN means: IF ( (a < b) ==.true.) THEN IF <logical expression> THEN... ELSE... ENDIF IF <logical expression> THEN... IF <logical expression> THEN... ELSE IF <logical expression> THEN... ELSE... ENDIF ENDIF (a < b): relational ( < <= > >= == /= ) (.LT..LE..GT..GE..EQ..NE. ) (a < b).and. (c > d): logical (.NOT..AND..OR..EQV..NEQV.) Relational expressions have a higher priority than logical expressions. Question!!What could that mean: IF (a) b=b+1!or that: IF (r < N ) EXIT Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

20 Execution Part CASE Construct... INTEGER (kind=1) :: month... SELECT CASE (month) CASE (12,1,2) write (*,*) Winter CASE (3:5) write (*,*) Spring CASE (6:8) write (*,*) Summer CASE (9:11) write (*,*) Autumn CASE DEFAULT write (*,*) Error: Something is wrong with your date END SELECT Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

21 Execution Part DO Loop INTEGER (kind = 1) :: x INTEGER (kind = 2) :: f x DO x = 1, 10, 2 f x = x*x + 10 write (*,*) x, f x ENDDO INTEGER (kind = 1) :: x INTEGER (kind = 2) :: f x x=1 DO f x = x*x write (*,*) x, f x IF (x > 10) EXIT x = x+2. ENDDO INTEGER (kind = 2) :: ix, iy REAL (kind = 4) :: x, y, f xy DO ix = -30, 30, 1 x = REAL(ix) / 10. DO iy = -30, 30, 1 y = REAL(iy) / 10. f xy = (x** *y**2-yy)*exp(1.-(x**2+y**2)) write (*,*) x, y, f x ENDDO ENDDO Be careful: What is the problem here? INTEGER (kind = 2) :: ix, iy REAL (kind = 4) :: x, y, f xy ix= -30; iy= -30 DO x = REAL(ix) / 10. DO y = REAL(iy) / 10. f xy = (x** *y**2-yy)*exp(1.-(x**2+y**2)) write (*,*) x, y, f x IF (iy.gt. 30) EXIT iy = iy + 1 ENDDO IF (ix.gt. 30) EXIT ix = ix + 1 ENDDO Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

22 Execution Part DO Loop INTEGER (kind = 1) :: x INTEGER (kind = 2) :: f x DO x = 1, 10, 2 f x = x*x + 10 write (*,*) x, f x ENDDO INTEGER (kind = 1) :: x INTEGER (kind = 2) :: f x x=1 DO f x = x*x write (*,*) x, f x IF (x > 10) EXIT x = x+2. ENDDO Loop Counter Avoid infinite loops : INTEGER (kind = 4), PARAMETER :: imax = INTEGER (kind = 4) :: i i = 0 DO IF (i > imax) EXIT i = i+1 ENDDO INTEGER (kind = 2) :: ix, iy REAL (kind = 4) :: x, y, f xy DO ix = -30, 30, 1 x = REAL(ix) / 10. DO iy = -30, 30, 1 y = REAL(iy) / 10. f xy = (x** *y**2-yy)*exp(1.-(x**2+y**2)) write (*,*) x, y, f x ENDDO ENDDO Corrected version INTEGER (kind = 2) :: ix, iy REAL (kind = 4) :: x, y, f xy ix= -30! ; iy= -30 DO iy= -30 x = REAL(ix) / 10. DO y = REAL(iy) / 10. f xy = (x** *y**2-yy)*exp(1.-(x**2+y**2)) write (*,*) x, y, f x IF (iy.gt. 30) EXIT iy = iy + 1 ENDDO IF (ix.gt. 30) EXIT ix = ix + 1 ENDDO Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

23 Modules F90 Modules Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

24 Modules Subroutines Example: PROGRAM test IMPLICIT NONE INTEGER :: type REAL :: r, p, d, g... call equation of state (type, t, p, d, g)... END PROGRAM test SUBROUTINE equation of state (type, temp, pres, & dens, gamma) IMPLICIT NONE INTEGER :: type REAL :: temp, pres, dens, gamma... END SUBROUTINE equation of state Advantages: Keeps the code structured Test each code segments separately Include already existing segments Numerical Recipes!!! Use a given segment frequently in a code Use a self-written subroutine in different programs Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

25 Modules Functions A function itself needs a variable declaration and gives back a value. Syntax PROGRAM main IMPLICIT NONE REAL :: plummer dens, edge dens, totalmass, & plummer rad, cutoff rad... edge dens = plummer dens(totalmass, plummer rad, cutoff rad) END PROGRAM main FUNCTION plummer dens (totalmass, plummer rad, cutoff rad) IMPLICIT NONE REAL :: plummer dens, edge dens, totalmass, plummer rad, cutoff rad plummer dens =... END FUNCTION plummer dens Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

26 Modules Modules Sharing variables between different routines: Syntax MODULE constants IMPLICIT NONE REAL, PARAMETER :: pi = 4.*ATAN(1.) REAL, PARAMETER :: Msol = E33 REAL, PARAMETER :: parsec = E18 END MODULE constants PROGRAM main USE constants, ONLY: pi WRITE (*,*) Pi =, pi END Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

27 Modules Main program of the powerful FLASH3.2 code program Flash use Driver interface implicit none call Driver initflash() call Driver evolveflash() call Driver finalizeflash() end program Flash Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

28 Back to F77 Back to Fortran 77 Common Block - Syntax PROGRAM main IMPLICIT NONE REAL a, b COMMON /coeff/ a, b CALL solve END PROGRAM main SUBROUTINE solve IMPLICIT NONE REAL a, b COMMON /coeff/ a, b... END SUBROUTINE solve Common Block + Include PROGRAM main INCLUDE main.inc CALL solve END PROGRAM main SUBROUTINE solve INCLUDE main.inc... END SUBROUTINE solve! file main.inc : IMPLICIT NONE REAL a,b COMMON /coeff/ a, b Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

29 Back to F77 Compiler and Linker We use: gfortran <options> <infile 1> <infile 2>... To find out about the options:> man gfortran Some helpful options: -fdefault-integer-8 : Set the default integer and logical types to the 8 byte wide type -fdefault-real-8 : Set the default real type to the 8 byte wide type -fimplicit-none : Equivalent of adding implicit none to the start of every procedure -o <output>: Output file not default (a.out) but <output> The compiler is treating every routine separately no error message when the declarations of values which are exchanged do not fit together! Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

30 Gnuplot Gnuplot Homepage: Freely distributed Command line driven Available for a lot of different platforms Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

31 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

32 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

33 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

34 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

35 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

36 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

37 Gnuplot Try out the following with the 3D data from last week: set pm3d at b set contour base set surface set view 70,60,1.0,1.5 set dgrid3d 50, 50 set hidden3d show contour splot "data3d.dat" u 1:2:3 w line palette Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

38 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

39 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

40 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

41 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

42 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43

43 Gnuplot Sylvia Plöckinger () An Introduction to Fortran March 10, / 43