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438run.txt
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ian@Ian2:~/438$ ls
438 438-1.f 438.f 438.sh
ian@Ian2:~/438$ chmod U+x 438.sh
chmod: invalid mode: ‘U+x’
Try 'chmod --help' for more information.
ian@Ian2:~/438$ chmod u+x 438.sh
ian@Ian2:~/438$ ./438.sh
./438.sh: line 1: :#!: command not found
ian@Ian2:~/438$
ian@Ian2:~/438$ ./438.sh
./438.sh: line 1: :#!: command not found
shar: will not over-write existing file 'Makefile'
shar: will not over-write existing file 'driver.f'
shar: will not over-write existing file 'res'
shar: will not over-write existing file 'src.f'
ian@Ian2:~/438$ ls
438 438-1.f 438.f 438.sh Fortran
ian@Ian2:~/438$ cd Fortran
ian@Ian2:~/438/Fortran$ ls
Dp
ian@Ian2:~/438/Fortran$ cd Dp
ian@Ian2:~/438/Fortran/Dp$ ls
Drivers Src
ian@Ian2:~/438/Fortran/Dp$ cd Drivers
ian@Ian2:~/438/Fortran/Dp/Drivers$ ls
driver.f Makefile res
ian@Ian2:~/438/Fortran/Dp/Drivers$ make
f77 -c driver.f
make: *** No rule to make target 'src.f', needed by 'src.o'. Stop.
ian@Ian2:~/438/Fortran/Dp/Drivers$ gfortran driver.f
/usr/bin/ld: /tmp/ccHi2wRC.o: in function `test02_':
driver.f:(.text+0x4c0): undefined reference to `p2pgs_'
/usr/bin/ld: /tmp/ccHi2wRC.o: in function `test01_':
driver.f:(.text+0xa6a): undefined reference to `p2pgs_'
collect2: error: ld returned 1 exit status
ian@Ian2:~/438/Fortran/Dp/Drivers$ gfortran driver.f -c
ian@Ian2:~/438/Fortran/Dp/Drivers$ ls
driver.f driver.o Makefile res
ian@Ian2:~/438/Fortran/Dp/Drivers$ cat res
TOMS438_PRB
Test TOMS algorithm 438, product-type
two point Gauss-Legendre Simpson
integration.
TEST01
Integral of F(X) * G(X) from -1 to 1,
with F(X) = 1, G(X) = 1/(1+x**2 )
N VINT
1 5.49020
2 2.47843
3 2.90842
4 2.57255
5 2.69529
6 2.63329
7 2.66030
8 2.64773
9 2.65342
10 2.65082
Exact: 2.65164
TEST02
Integral of F(X) * G(X) from 0 to PI,
with F(X) = EXP(-X), G(X) = COS(X)
N VINT
1 0.390787
2 0.516996
3 0.520913
4 0.521413
5 0.521532
6 0.521572
7 0.521589
8 0.521596
9 0.521600
10 0.521603
Exact: 0.521607
TOMS438_PRB
Normal end of execution.
ian@Ian2:~/438/Fortran/Dp/Drivers$ cd ~/438/Fortran/Dp/
ian@Ian2:~/438/Fortran/Dp$ ls
Drivers Src
ian@Ian2:~/438/Fortran/Dp$ cd Src
ian@Ian2:~/438/Fortran/Dp/Src$ ls
src.f
ian@Ian2:~/438/Fortran/Dp/Src$ gfortran src.f -c
ian@Ian2:~/438/Fortran/Dp/Src$ cp src.f ~/438/Fortran/Dp/Driver/src.f
cp: cannot create regular file '/home/ian/438/Fortran/Dp/Driver/src.f': No such file or directory
ian@Ian2:~/438/Fortran/Dp/Src$ cp src.f ~/438/Fortran/Dp/Driver/src.f
cp: cannot create regular file '/home/ian/438/Fortran/Dp/Driver/src.f': No such file or directory
ian@Ian2:~/438/Fortran/Dp/Src$ cp src.f ~/438/Fortran/Dp/Driver/
cp: cannot create regular file '/home/ian/438/Fortran/Dp/Driver/': Not a directory
ian@Ian2:~/438/Fortran/Dp/Src$ cd ~/438/Fortran/Dp/Src
ian@Ian2:~/438/Fortran/Dp/Src$ ls
src.f src.o
ian@Ian2:~/438/Fortran/Dp/Src$ cd ~/438/Fortran/Dp/Driver
bash: cd: /home/ian/438/Fortran/Dp/Driver: No such file or directory
ian@Ian2:~/438/Fortran/Dp/Src$ cd ~/438/Fortran/Dp/Drivers
ian@Ian2:~/438/Fortran/Dp/Drivers$ ls
driver.f driver.o Makefile res src.o
ian@Ian2:~/438/Fortran/Dp/Drivers$ gfortran -o 438-run driver.o src.o
ian@Ian2:~/438/Fortran/Dp/Drivers$ ./438-run
TOMS438_PRB
Test TOMS algorithm 438, product-type
two point Gauss-Legendre Simpson
integration.
TEST01
Integral of F(X) * G(X) from -1 to 1,
with F(X) = 1, G(X) = 1/(1+x**2 )
N VINT
1 5.49020
2 2.47843
3 2.90842
4 2.57255
5 2.69529
6 2.63329
7 2.66030
8 2.64773
9 2.65342
10 2.65082
Exact: 2.65164
TEST02
Integral of F(X) * G(X) from 0 to PI,
with F(X) = EXP(-X), G(X) = COS(X)
N VINT
1 0.390787
2 0.516996
3 0.520913
4 0.521413
5 0.521532
6 0.521572
7 0.521589
8 0.521596
9 0.521600
10 0.521603
Exact: 0.521607
TOMS438_PRB
Normal end of execution.
ian@Ian2:~/438/Fortran/Dp/Drivers$ ls
438-run driver.f driver.o Makefile res src.o
ian@Ian2:~/438/Fortran/Dp/Drivers$ cat driver.f
program main
c***********************************************************************
c
cc TOMS438_PRB tests TOMS438.
c
implicit none
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'TOMS438_PRB'
write ( *, '(a)' ) ' Test TOMS algorithm 438, product-type'
write ( *, '(a)' ) ' two point Gauss-Legendre Simpson'
write ( *, '(a)' ) ' integration.'
call test01
call test02
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'TOMS438_PRB'
write ( *, '(a)' ) ' Normal end of execution.'
stop
end
subroutine test01
c***********************************************************************
c
cc TEST01 tests the rule with one factor equal to 1.
c
implicit none
double precision a
double precision b
double precision exact
double precision fn00, gn00
external fn00
external gn00
integer n
double precision vint
a = -4.0D+00
b = 4.0D+00
exact = 2.0D+00 * atan ( 4.0D+00 )
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'TEST01'
write ( *, '(a)' ) ' Integral of F(X) * G(X) from -1 to 1,'
write ( *, '(a)' ) ' with F(X) = 1, G(X) = 1/(1+x**2 )'
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' N VINT'
write ( *, '(a)' ) ' '
do n = 1, 10
call p2pgs ( a, b, n, fn00, gn00, vint )
write ( *, '(2x,i6,2x,g14.6)' ) n, vint
end do
write ( *, '(a)' ) ' '
write ( *, '(a,g14.6)' ) ' Exact: ', exact
return
end
subroutine test02
c***********************************************************************
c
cc TEST02 tests the rule with factors exp(-x) and cos(x).
c
implicit none
double precision a
double precision b
double precision exact
double precision gn01, gn02
external gn01
external gn02
integer n
double precision vint
a = 0.0D+00
b = 3.141592653589793D+00
exact = 0.5 * exp ( -b ) * ( sin ( b ) - cos ( b ) )
& - ( 0.5 * exp ( -a ) * ( sin ( a ) - cos ( a ) ) )
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'TEST02'
write ( *, '(a)' ) ' Integral of F(X) * G(X) from 0 to PI,'
write ( *, '(a)' ) ' with F(X) = EXP(-X), G(X) = COS(X)'
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' N VINT'
write ( *, '(a)' ) ' '
do n = 1, 10
call p2pgs ( a, b, n, gn01, gn02, vint )
write ( *, '(2x,i6,2x,g14.6)' ) n, vint
end do
write ( *, '(a)' ) ' '
write ( *, '(a,g14.6)' ) ' Exact: ', exact
return
end
function fn00 ( x )
c***********************************************************************
c
cc FN00 evaluates the function 1.
c
implicit none
double precision fn00
double precision x
fn00 = 1.0D+00
return
end
function fn01 ( x )
c***********************************************************************
c
cc FN01 evaluates the function X.
c
implicit none
double precision fn01
double precision x
fn01 = x
return
end
function gn00 ( x )
c***********************************************************************
c
cc GN00 evaluates the function 1/(1+X**2).
c
implicit none
double precision gn00
double precision x
gn00 = 1.0D+00 / ( 1.0D+00 + x * x )
return
end
function gn01 ( x )
c***********************************************************************
c
cc GN01 evaluates the function exp(-x).
c
implicit none
double precision gn01
double precision x
gn01 = exp ( - x )
return
end
function gn02 ( x )
c***********************************************************************
c
cc GN02 evaluates the function cos(x).
c
implicit none
double precision gn02
double precision x
gn02 = cos ( x )
return
end
ian@Ian2:~/438/Fortran/Dp/Drivers$ cd ~/438/Fortran/Dp/Drivers
ian@Ian2:~/438/Fortran/Dp/Drivers$ ls
438-run driver.f driver.o Makefile res src.o
ian@Ian2:~/438/Fortran/Dp/Drivers$ cd ~/438/Fortran/Dp/Src
ian@Ian2:~/438/Fortran/Dp/Src$ ls
src.f src.o
ian@Ian2:~/438/Fortran/Dp/Src$ cat src.f
SUBROUTINE P2PGS ( A, B, N, FN, GN, VINT )
C
C THIS SUBROUTINE USES THE PRODUCT TYPE TWO-POINT GAUSS-
C LEGENDRE-SIMPSON RULE COMPOUNDED N TIMES TO APPROXIMATE
C THE INTEGRAL FROM A TO B OF THE FUNCTION FN(X) * GN(X).
C FN AND GN ARE FUNCTION SUBPROGRAMS WHICH MUST BE SUPPLIED
C BY THE USER. THE RESULT IS STORED IN VINT.
C
INTEGER I, N, J, K
DOUBLE PRECISION A, AG, AM(2,3), B, F(2), FN, G(3),
& GN, H, VINT, X(2), Y(2)
DATA AM(1,1), AM(2,3) / 2 * 2.732050807568877D0 /,
& AM(1,2), AM(2,2) / 2 * 4.D0 /, AM(1,3), AM(2,1)
& / 2 * -.7320508075688773D0 /
H = ( B - A ) / DBLE ( FLOAT ( N ) )
X(1) = A + .2113248654051871D0 * H
X(2) = A + .7886751345948129D0 * H
Y(1) = A + H / 2.D0
Y(2) = A + H
VINT = 0.D0
G(3) = GN ( A )
DO 4 I = 1, N
G(1) = G(3)
DO 1 J = 1, 2
F(J) = FN ( X(J) )
G(J+1) = GN ( Y(J) )
X(J) = X(J) + H
Y(J) = Y(J) + H
1 CONTINUE
DO 3 J = 1, 2
AG = 0.D0
DO 2 K = 1, 3
AG = AG + AM(J,K) * G(K)
2 CONTINUE
VINT = VINT + F(J) * AG
3 CONTINUE
4 CONTINUE
VINT = H * VINT / 12.D0
RETURN
END
ian@Ian2:~/438/Fortran/Dp/Src$