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/* linpack/dpoco.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"
/* Table of constant values */
static integer c__1 = 1;
/*< subroutine dpoco(a,lda,n,rcond,z,info) >*/
/* Subroutine */ int dpoco_(doublereal *a, integer *lda, integer *n,
doublereal *rcond, doublereal *z__, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
doublereal d__1, d__2;
/* Builtin functions */
double d_sign(doublereal *, doublereal *);
/* Local variables */
integer i__, j, k;
doublereal s, t;
integer kb;
doublereal ek, sm, wk;
integer jm1, kp1;
doublereal wkm;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *), dpofa_(doublereal *, integer *, integer *, integer *);
extern doublereal dasum_(integer *, doublereal *, integer *);
doublereal anorm;
extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *);
doublereal ynorm;
/*< integer lda,n,info >*/
/*< double precision a(lda,1),z(1) >*/
/*< double precision rcond >*/
/* dpoco factors a double precision symmetric positive definite */
/* matrix and estimates the condition of the matrix. */
/* if rcond is not needed, dpofa is slightly faster. */
/* to solve a*x = b , follow dpoco by dposl. */
/* to compute inverse(a)*c , follow dpoco by dposl. */
/* to compute determinant(a) , follow dpoco by dpodi. */
/* to compute inverse(a) , follow dpoco by dpodi. */
/* on entry */
/* a double precision(lda, n) */
/* the symmetric matrix to be factored. only the */
/* diagonal and upper triangle are used. */
/* lda integer */
/* the leading dimension of the array a . */
/* n integer */
/* the order of the matrix a . */
/* on return */
/* a an upper triangular matrix r so that a = trans(r)*r */
/* where trans(r) is the transpose. */
/* the strict lower triangle is unaltered. */
/* if info .ne. 0 , the factorization is not complete. */
/* rcond double precision */
/* an estimate of the reciprocal condition of a . */
/* for the system a*x = b , relative perturbations */
/* in a and b of size epsilon may cause */
/* relative perturbations in x of size epsilon/rcond . */
/* if rcond is so small that the logical expression */
/* 1.0 + rcond .eq. 1.0 */
/* is true, then a may be singular to working */
/* precision. in particular, rcond is zero if */
/* exact singularity is detected or the estimate */
/* underflows. if info .ne. 0 , rcond is unchanged. */
/* z double precision(n) */
/* a work vector whose contents are usually unimportant. */
/* if a is close to a singular matrix, then z is */
/* an approximate null vector in the sense that */
/* norm(a*z) = rcond*norm(a)*norm(z) . */
/* if info .ne. 0 , z is unchanged. */
/* info integer */
/* = 0 for normal return. */
/* = k signals an error condition. the leading minor */
/* of order k is not positive definite. */
/* linpack. this version dated 08/14/78 . */
/* cleve moler, university of new mexico, argonne national lab. */
/* subroutines and functions */
/* linpack dpofa */
/* blas daxpy,ddot,dscal,dasum */
/* fortran dabs,dmax1,dreal,dsign */
/* internal variables */
/*< double precision ddot,ek,t,wk,wkm >*/
/*< double precision anorm,s,dasum,sm,ynorm >*/
/*< integer i,j,jm1,k,kb,kp1 >*/
/* find norm of a using only upper half */
/*< do 30 j = 1, n >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--z__;
/* Function Body */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< z(j) = dasum(j,a(1,j),1) >*/
z__[j] = dasum_(&j, &a[j * a_dim1 + 1], &c__1);
/*< jm1 = j - 1 >*/
jm1 = j - 1;
/*< if (jm1 .lt. 1) go to 20 >*/
if (jm1 < 1) {
goto L20;
}
/*< do 10 i = 1, jm1 >*/
i__2 = jm1;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< z(i) = z(i) + dabs(a(i,j)) >*/
z__[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1));
/*< 10 continue >*/
/* L10: */
}
/*< 20 continue >*/
L20:
/*< 30 continue >*/
/* L30: */
;
}
/*< anorm = 0.0d0 >*/
anorm = 0.;
/*< do 40 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< anorm = dmax1(anorm,z(j)) >*/
/* Computing MAX */
d__1 = anorm, d__2 = z__[j];
anorm = max(d__1,d__2);
/*< 40 continue >*/
/* L40: */
}
/* factor */
/*< call dpofa(a,lda,n,info) >*/
dpofa_(&a[a_offset], lda, n, info);
/*< if (info .ne. 0) go to 180 >*/
if (*info != 0) {
goto L180;
}
/* rcond = 1/(norm(a)*(estimate of norm(inverse(a)))) . */
/* estimate = norm(z)/norm(y) where a*z = y and a*y = e . */
/* the components of e are chosen to cause maximum local */
/* growth in the elements of w where trans(r)*w = e . */
/* the vectors are frequently rescaled to avoid overflow. */
/* solve trans(r)*w = e */
/*< ek = 1.0d0 >*/
ek = 1.;
/*< do 50 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< z(j) = 0.0d0 >*/
z__[j] = 0.;
/*< 50 continue >*/
/* L50: */
}
/*< do 110 k = 1, n >*/
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/*< if (z(k) .ne. 0.0d0) ek = dsign(ek,-z(k)) >*/
if (z__[k] != 0.) {
d__1 = -z__[k];
ek = d_sign(&ek, &d__1);
}
/*< if (dabs(ek-z(k)) .le. a(k,k)) go to 60 >*/
if ((d__1 = ek - z__[k], abs(d__1)) <= a[k + k * a_dim1]) {
goto L60;
}
/*< s = a(k,k)/dabs(ek-z(k)) >*/
s = a[k + k * a_dim1] / (d__1 = ek - z__[k], abs(d__1));
/*< call dscal(n,s,z,1) >*/
dscal_(n, &s, &z__[1], &c__1);
/*< ek = s*ek >*/
ek = s * ek;
/*< 60 continue >*/
L60:
/*< wk = ek - z(k) >*/
wk = ek - z__[k];
/*< wkm = -ek - z(k) >*/
wkm = -ek - z__[k];
/*< s = dabs(wk) >*/
s = abs(wk);
/*< sm = dabs(wkm) >*/
sm = abs(wkm);
/*< wk = wk/a(k,k) >*/
wk /= a[k + k * a_dim1];
/*< wkm = wkm/a(k,k) >*/
wkm /= a[k + k * a_dim1];
/*< kp1 = k + 1 >*/
kp1 = k + 1;
/*< if (kp1 .gt. n) go to 100 >*/
if (kp1 > *n) {
goto L100;
}
/*< do 70 j = kp1, n >*/
i__2 = *n;
for (j = kp1; j <= i__2; ++j) {
/*< sm = sm + dabs(z(j)+wkm*a(k,j)) >*/
sm += (d__1 = z__[j] + wkm * a[k + j * a_dim1], abs(d__1));
/*< z(j) = z(j) + wk*a(k,j) >*/
z__[j] += wk * a[k + j * a_dim1];
/*< s = s + dabs(z(j)) >*/
s += (d__1 = z__[j], abs(d__1));
/*< 70 continue >*/
/* L70: */
}
/*< if (s .ge. sm) go to 90 >*/
if (s >= sm) {
goto L90;
}
/*< t = wkm - wk >*/
t = wkm - wk;
/*< wk = wkm >*/
wk = wkm;
/*< do 80 j = kp1, n >*/
i__2 = *n;
for (j = kp1; j <= i__2; ++j) {
/*< z(j) = z(j) + t*a(k,j) >*/
z__[j] += t * a[k + j * a_dim1];
/*< 80 continue >*/
/* L80: */
}
/*< 90 continue >*/
L90:
/*< 100 continue >*/
L100:
/*< z(k) = wk >*/
z__[k] = wk;
/*< 110 continue >*/
/* L110: */
}
/*< s = 1.0d0/dasum(n,z,1) >*/
s = 1. / dasum_(n, &z__[1], &c__1);
/*< call dscal(n,s,z,1) >*/
dscal_(n, &s, &z__[1], &c__1);
/* solve r*y = w */
/*< do 130 kb = 1, n >*/
i__1 = *n;
for (kb = 1; kb <= i__1; ++kb) {
/*< k = n + 1 - kb >*/
k = *n + 1 - kb;
/*< if (dabs(z(k)) .le. a(k,k)) go to 120 >*/
if ((d__1 = z__[k], abs(d__1)) <= a[k + k * a_dim1]) {
goto L120;
}
/*< s = a(k,k)/dabs(z(k)) >*/
s = a[k + k * a_dim1] / (d__1 = z__[k], abs(d__1));
/*< call dscal(n,s,z,1) >*/
dscal_(n, &s, &z__[1], &c__1);
/*< 120 continue >*/
L120:
/*< z(k) = z(k)/a(k,k) >*/
z__[k] /= a[k + k * a_dim1];
/*< t = -z(k) >*/
t = -z__[k];
/*< call daxpy(k-1,t,a(1,k),1,z(1),1) >*/
i__2 = k - 1;
daxpy_(&i__2, &t, &a[k * a_dim1 + 1], &c__1, &z__[1], &c__1);
/*< 130 continue >*/
/* L130: */
}
/*< s = 1.0d0/dasum(n,z,1) >*/
s = 1. / dasum_(n, &z__[1], &c__1);
/*< call dscal(n,s,z,1) >*/
dscal_(n, &s, &z__[1], &c__1);
/*< ynorm = 1.0d0 >*/
ynorm = 1.;
/* solve trans(r)*v = y */
/*< do 150 k = 1, n >*/
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/*< z(k) = z(k) - ddot(k-1,a(1,k),1,z(1),1) >*/
i__2 = k - 1;
z__[k] -= ddot_(&i__2, &a[k * a_dim1 + 1], &c__1, &z__[1], &c__1);
/*< if (dabs(z(k)) .le. a(k,k)) go to 140 >*/
if ((d__1 = z__[k], abs(d__1)) <= a[k + k * a_dim1]) {
goto L140;
}
/*< s = a(k,k)/dabs(z(k)) >*/
s = a[k + k * a_dim1] / (d__1 = z__[k], abs(d__1));
/*< call dscal(n,s,z,1) >*/
dscal_(n, &s, &z__[1], &c__1);
/*< ynorm = s*ynorm >*/
ynorm = s * ynorm;
/*< 140 continue >*/
L140:
/*< z(k) = z(k)/a(k,k) >*/
z__[k] /= a[k + k * a_dim1];
/*< 150 continue >*/
/* L150: */
}
/*< s = 1.0d0/dasum(n,z,1) >*/
s = 1. / dasum_(n, &z__[1], &c__1);
/*< call dscal(n,s,z,1) >*/
dscal_(n, &s, &z__[1], &c__1);
/*< ynorm = s*ynorm >*/
ynorm = s * ynorm;
/* solve r*z = v */
/*< do 170 kb = 1, n >*/
i__1 = *n;
for (kb = 1; kb <= i__1; ++kb) {
/*< k = n + 1 - kb >*/
k = *n + 1 - kb;
/*< if (dabs(z(k)) .le. a(k,k)) go to 160 >*/
if ((d__1 = z__[k], abs(d__1)) <= a[k + k * a_dim1]) {
goto L160;
}
/*< s = a(k,k)/dabs(z(k)) >*/
s = a[k + k * a_dim1] / (d__1 = z__[k], abs(d__1));
/*< call dscal(n,s,z,1) >*/
dscal_(n, &s, &z__[1], &c__1);
/*< ynorm = s*ynorm >*/
ynorm = s * ynorm;
/*< 160 continue >*/
L160:
/*< z(k) = z(k)/a(k,k) >*/
z__[k] /= a[k + k * a_dim1];
/*< t = -z(k) >*/
t = -z__[k];
/*< call daxpy(k-1,t,a(1,k),1,z(1),1) >*/
i__2 = k - 1;
daxpy_(&i__2, &t, &a[k * a_dim1 + 1], &c__1, &z__[1], &c__1);
/*< 170 continue >*/
/* L170: */
}
/* make znorm = 1.0 */
/*< s = 1.0d0/dasum(n,z,1) >*/
s = 1. / dasum_(n, &z__[1], &c__1);
/*< call dscal(n,s,z,1) >*/
dscal_(n, &s, &z__[1], &c__1);
/*< ynorm = s*ynorm >*/
ynorm = s * ynorm;
/*< if (anorm .ne. 0.0d0) rcond = ynorm/anorm >*/
if (anorm != 0.) {
*rcond = ynorm / anorm;
}
/*< if (anorm .eq. 0.0d0) rcond = 0.0d0 >*/
if (anorm == 0.) {
*rcond = 0.;
}
/*< 180 continue >*/
L180:
/*< return >*/
return 0;
/*< end >*/
} /* dpoco_ */
#ifdef __cplusplus
}
#endif
|
