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/* mathews/adaquad.f -- translated by f2c (version 20050501).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* NUMERICAL METHODS: FORTRAN Programs, (c) John H. Mathews 1994 */
/* To accompany the text: */
/* NUMERICAL METHODS for Mathematics, Science and Engineering, 2nd Ed, 1992 */
/* Prentice Hall, Englewood Cliffs, New Jersey, 07632, U.S.A. */
/* This free software is complements of the author. */
/* Algorithm 7.5 (Adaptive Quadrature Using Simpson's Rule). */
/* Section 7.4, Adaptive Quadrature, Page 389 */
/* add missing variable F in Refine subrutine. */
/*< SUBROUTINE AdaptQuad(F,A,B,Tol,SRmat,Integral,ErrBdd,M,State) >*/
/* Subroutine */ int adaptquad_(
v3p_netlib_doublereal (*f)(v3p_netlib_doublereal*),
doublereal *a, doublereal *b,
doublereal *tol, doublereal *srmat, doublereal *integral, doublereal *
errbdd, integer *m, integer *state)
{
/* System generated locals */
integer i__1;
doublereal d__1;
/* Local variables */
integer j, k, n, iterating;
doublereal sum1, sum2;
integer done;
doublereal srvec[11];
extern /* Subroutine */ int srule_(
v3p_netlib_doublereal (*f)(v3p_netlib_doublereal*),
doublereal *, doublereal *,
doublereal *, doublereal *),
refine_(v3p_netlib_doublereal (*f)(v3p_netlib_doublereal*),
integer *, doublereal * , integer *, integer *);
/*< INTEGER M,State >*/
/*< DOUBLE PRECISION A,B,Tol,SRmat,Integral,ErrBdd >*/
/*< INTEGER J,K,N,Iterating,Done >*/
/*< DOUBLE PRECISION Sum1,Sum2,SRvec >*/
/*< DIMENSION SRmat(1:101,1:11),SRvec(1:11) >*/
/*< EXTERNAL F >*/
/*< Iterating = 0 >*/
/* Parameter adjustments */
srmat -= 102;
/* Function Body */
iterating = 0;
/*< Done = 1 >*/
done = 1;
/*< CALL Srule(F,A,B,Tol,SRvec) >*/
srule_(f, a, b, tol, srvec);
/*< DO K=1,11 >*/
for (k = 1; k <= 11; ++k) {
/*< SRmat(1, K) = SRvec(K) >*/
srmat[k * 101 + 1] = srvec[k - 1];
/*< ENDDO >*/
}
/*< M = 1 >*/
*m = 1;
/*< State = Iterating >*/
*state = iterating;
/*< DO WHILE (State .EQ. Iterating) >*/
while(*state == iterating) {
/*< N = M >*/
n = *m;
/*< DO J=N,1,-1 >*/
for (j = n; j >= 1; --j) {
/*< CALL Refine(F,J,SRmat,M,State) >*/
refine_(f, &j, &srmat[102], m, state);
/*< ENDDO >*/
}
/*< ENDDO >*/
}
/*< Sum1 = 0 >*/
sum1 = 0.;
/*< Sum2 = 0 >*/
sum2 = 0.;
/*< DO J=1,M >*/
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
/*< Sum1 = Sum1 + SRmat(J, 8) >*/
sum1 += srmat[j + 808];
/*< Sum2 = Sum2 + Abs(SRmat(J, 9)) >*/
sum2 += (d__1 = srmat[j + 909], abs(d__1));
/*< ENDDO >*/
}
/*< Integral = Sum1 >*/
*integral = sum1;
/*< ErrBdd = Sum2 >*/
*errbdd = sum2;
/*< RETURN >*/
return 0;
/*< END >*/
} /* adaptquad_ */
/*< SUBROUTINE Refine(F, P,SRmat,M,State) >*/
/* Subroutine */ int refine_(
v3p_netlib_doublereal (*f)(v3p_netlib_doublereal*),
integer *p, doublereal *srmat, integer * m, integer *state
)
{
/* System generated locals */
integer i__1;
doublereal d__1;
/* Local variables */
doublereal a, b, c__;
integer j, k;
doublereal s;
integer iterating;
doublereal s2, fa, fb, fc, err, tol, tol2;
integer done;
doublereal check;
extern /* Subroutine */ int srule_(
v3p_netlib_doublereal (*f)(v3p_netlib_doublereal*),
doublereal *, doublereal *,
doublereal *, doublereal *);
doublereal sr0vec[11], sr1vec[11], sr2vec[11];
/*< INTEGER P,M,State >*/
/*< DOUBLE PRECISION SRmat >*/
/*< INTEGER J,K,Iterating,Done >*/
/*< DOUBLE PRECISION A,B,C,Err,Fa,Fb,Fc,S,S2,Tol,Tol2,Err,Check >*/
/*< DOUBLE PRECISION SR0vec,SR1vec,SR2vec >*/
/*< DIMENSION SRmat(1:101,1:11) >*/
/*< DIMENSION SR0vec(1:11),SR1vec(1:11),SR2vec(1:11) >*/
/*< EXTERNAL F >*/
/*< Iterating = 0 >*/
/* Parameter adjustments */
srmat -= 102;
/* Function Body */
iterating = 0;
/*< Done = 1 >*/
done = 1;
/*< State = Done >*/
*state = done;
/*< DO K=1,11 >*/
for (k = 1; k <= 11; ++k) {
/*< SR0vec(K) = SRmat(P, K) >*/
sr0vec[k - 1] = srmat[*p + k * 101];
/*< ENDDO >*/
}
/*< A = SR0vec(1) >*/
a = sr0vec[0];
/*< C = SR0vec(2) >*/
c__ = sr0vec[1];
/*< B = SR0vec(3) >*/
b = sr0vec[2];
/*< Fa = SR0vec(4) >*/
fa = sr0vec[3];
/*< Fc = SR0vec(5) >*/
fc = sr0vec[4];
/*< Fb = SR0vec(6) >*/
fb = sr0vec[5];
/*< S = SR0vec(7) >*/
s = sr0vec[6];
/*< S2 = SR0vec(8) >*/
s2 = sr0vec[7];
/*< Err = SR0vec(9) >*/
err = sr0vec[8];
/*< Tol = SR0vec(10) >*/
tol = sr0vec[9];
/*< Check = SR0vec(11) >*/
check = sr0vec[10];
/*< IF (Check .EQ. 1) RETURN >*/
if (check == 1.) {
return 0;
}
/*< Tol2 = Tol / 2 >*/
tol2 = tol / 2;
/*< CALL Srule(F, A, C, Tol2, SR1vec) >*/
srule_(f, &a, &c__, &tol2, sr1vec);
/*< CALL Srule(F, C, B, Tol2, SR2vec) >*/
srule_(f, &c__, &b, &tol2, sr2vec);
/*< Err = ABS(SR0vec(7) - SR1vec(7) - SR2vec(7)) / 10 >*/
err = (d__1 = sr0vec[6] - sr1vec[6] - sr2vec[6], abs(d__1)) / 10;
/*< IF (Err .LT. Tol) THEN >*/
if (err < tol) {
/*< SR0vec(11) = 1 >*/
sr0vec[10] = 1.;
/*< ENDIF >*/
}
/*< IF (Err .LT. Tol) THEN >*/
if (err < tol) {
/*< DO K=1,11 >*/
for (k = 1; k <= 11; ++k) {
/*< SRmat(P, K) = SR0vec(K) >*/
srmat[*p + k * 101] = sr0vec[k - 1];
/*< ENDDO >*/
}
/*< SRmat(P, 8) = SR1vec(7) + SR2vec(7) >*/
srmat[*p + 808] = sr1vec[6] + sr2vec[6];
/*< SRmat(P, 9) = Err >*/
srmat[*p + 909] = err;
/*< ELSE >*/
} else {
/*< DO J=(M + 1),P,-1 >*/
i__1 = *p;
for (j = *m + 1; j >= i__1; --j) {
/*< DO K=1,11 >*/
for (k = 1; k <= 11; ++k) {
/*< SRmat(J, K) = SRmat(J - 1, K) >*/
srmat[j + k * 101] = srmat[j - 1 + k * 101];
/*< ENDDO >*/
}
/*< ENDDO >*/
}
/*< M = M + 1 >*/
++(*m);
/*< DO K=1,11 >*/
for (k = 1; k <= 11; ++k) {
/*< SRmat(P, K) = SR1vec(K) >*/
srmat[*p + k * 101] = sr1vec[k - 1];
/*< ENDDO >*/
}
/*< DO K=1,11 >*/
for (k = 1; k <= 11; ++k) {
/*< SRmat(P + 1, K) = SR2vec(K) >*/
srmat[*p + 1 + k * 101] = sr2vec[k - 1];
/*< ENDDO >*/
}
/*< State = Iterating >*/
*state = iterating;
/*< ENDIF >*/
}
/*< RETURN >*/
return 0;
/*< END >*/
} /* refine_ */
/*< SUBROUTINE Srule(F,A,B,Tol0,SRvec) >*/
/* Subroutine */ int srule_(
v3p_netlib_doublereal (*f)(v3p_netlib_doublereal*),
doublereal *a, doublereal *b, doublereal * tol0, doublereal *srvec)
{
doublereal c__, h__, s, s2, fa, fb, fc, err, tol1, check;
/*< DOUBLE PRECISION A,B,Tol0,SRvec >*/
/*< DOUBLE PRECISION C,H,Fa,Fb,Fc,S,S2,Tol1,Err,Check >*/
/*< DIMENSION SRvec(1:11) >*/
/*< EXTERNAL F >*/
/*< H = (B - A) / 2 >*/
/* Parameter adjustments */
--srvec;
/* Function Body */
h__ = (*b - *a) / 2;
/*< C = (A + B) / 2 >*/
c__ = (*a + *b) / 2;
/*< Fa = F(A) >*/
fa = (*f)(a);
/*< Fc = F(C) >*/
fc = (*f)(&c__);
/*< Fb = F(B) >*/
fb = (*f)(b);
/*< S = H * (F(A) + 4 * F(C) + F(B)) / 3 >*/
s = h__ * ((*f)(a) + (*f)(&c__) * 4 + (*f)(b)) / 3;
/*< S2 = S >*/
s2 = s;
/*< Tol1 = Tol0 >*/
tol1 = *tol0;
/*< Err = Tol0 >*/
err = *tol0;
/*< Check = 0 >*/
check = 0.;
/*< SRvec(1) = A >*/
srvec[1] = *a;
/*< SRvec(2) = C >*/
srvec[2] = c__;
/*< SRvec(3) = B >*/
srvec[3] = *b;
/*< SRvec(4) = Fa >*/
srvec[4] = fa;
/*< SRvec(5) = Fc >*/
srvec[5] = fc;
/*< SRvec(6) = Fb >*/
srvec[6] = fb;
/*< SRvec(7) = S >*/
srvec[7] = s;
/*< SRvec(8) = S2 >*/
srvec[8] = s2;
/*< SRvec(9) = Err >*/
srvec[9] = err;
/*< SRvec(10) = Tol1 >*/
srvec[10] = tol1;
/*< SRvec(11) = Check >*/
srvec[11] = check;
/*< RETURN >*/
return 0;
/*< END >*/
} /* srule_ */
#ifdef __cplusplus
}
#endif
|
