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/* eispack/reduc.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"
/*< subroutine reduc(nm,n,a,b,dl,ierr) >*/
/* Subroutine */ int reduc_(integer *nm, integer *n, doublereal *a,
doublereal *b, doublereal *dl, integer *ierr)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k;
doublereal x, y=0;
integer i1, j1, nn;
/*< integer i,j,k,n,i1,j1,nm,nn,ierr >*/
/*< double precision a(nm,n),b(nm,n),dl(n) >*/
/*< double precision x,y >*/
/* this subroutine is a translation of the algol procedure reduc1, */
/* num. math. 11, 99-110(1968) by martin and wilkinson. */
/* handbook for auto. comp., vol.ii-linear algebra, 303-314(1971). */
/* this subroutine reduces the generalized symmetric eigenproblem */
/* ax=(lambda)bx, where b is positive definite, to the standard */
/* symmetric eigenproblem using the cholesky factorization of b. */
/* on input */
/* nm must be set to the row dimension of two-dimensional */
/* array parameters as declared in the calling program */
/* dimension statement. */
/* n is the order of the matrices a and b. if the cholesky */
/* factor l of b is already available, n should be prefixed */
/* with a minus sign. */
/* a and b contain the real symmetric input matrices. only the */
/* full upper triangles of the matrices need be supplied. if */
/* n is negative, the strict lower triangle of b contains, */
/* instead, the strict lower triangle of its cholesky factor l. */
/* dl contains, if n is negative, the diagonal elements of l. */
/* on output */
/* a contains in its full lower triangle the full lower triangle */
/* of the symmetric matrix derived from the reduction to the */
/* standard form. the strict upper triangle of a is unaltered. */
/* b contains in its strict lower triangle the strict lower */
/* triangle of its cholesky factor l. the full upper */
/* triangle of b is unaltered. */
/* dl contains the diagonal elements of l. */
/* ierr is set to */
/* zero for normal return, */
/* 7*n+1 if b is not positive definite. */
/* questions and comments should be directed to burton s. garbow, */
/* mathematics and computer science div, argonne national laboratory */
/* this version dated august 1983. */
/* ------------------------------------------------------------------ */
/*< ierr = 0 >*/
/* Parameter adjustments */
--dl;
b_dim1 = *nm;
b_offset = 1 + b_dim1;
b -= b_offset;
a_dim1 = *nm;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
*ierr = 0;
/*< nn = iabs(n) >*/
nn = abs(*n);
/*< if (n .lt. 0) go to 100 >*/
if (*n < 0) {
goto L100;
}
/* .......... form l in the arrays b and dl .......... */
/*< do 80 i = 1, n >*/
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< i1 = i - 1 >*/
i1 = i__ - 1;
/*< do 80 j = i, n >*/
i__2 = *n;
for (j = i__; j <= i__2; ++j) {
/*< x = b(i,j) >*/
x = b[i__ + j * b_dim1];
/*< if (i .eq. 1) go to 40 >*/
if (i__ == 1) {
goto L40;
}
/*< do 20 k = 1, i1 >*/
i__3 = i1;
for (k = 1; k <= i__3; ++k) {
/*< 20 x = x - b(i,k) * b(j,k) >*/
/* L20: */
x -= b[i__ + k * b_dim1] * b[j + k * b_dim1];
}
/*< 40 if (j .ne. i) go to 60 >*/
L40:
if (j != i__) {
goto L60;
}
/*< if (x .le. 0.0d0) go to 1000 >*/
if (x <= 0.) {
goto L1000;
}
/*< y = dsqrt(x) >*/
y = sqrt(x);
/*< dl(i) = y >*/
dl[i__] = y;
/*< go to 80 >*/
goto L80;
/*< 60 b(j,i) = x / y >*/
L60:
b[j + i__ * b_dim1] = x / y;
/*< 80 continue >*/
L80:
;
}
}
/* .......... form the transpose of the upper triangle of inv(l)*a */
/* in the lower triangle of the array a .......... */
/*< 100 do 200 i = 1, nn >*/
L100:
i__2 = nn;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< i1 = i - 1 >*/
i1 = i__ - 1;
/*< y = dl(i) >*/
y = dl[i__];
/*< do 200 j = i, nn >*/
i__1 = nn;
for (j = i__; j <= i__1; ++j) {
/*< x = a(i,j) >*/
x = a[i__ + j * a_dim1];
/*< if (i .eq. 1) go to 180 >*/
if (i__ == 1) {
goto L180;
}
/*< do 160 k = 1, i1 >*/
i__3 = i1;
for (k = 1; k <= i__3; ++k) {
/*< 160 x = x - b(i,k) * a(j,k) >*/
/* L160: */
x -= b[i__ + k * b_dim1] * a[j + k * a_dim1];
}
/*< 180 a(j,i) = x / y >*/
L180:
a[j + i__ * a_dim1] = x / y;
/*< 200 continue >*/
/* L200: */
}
}
/* .......... pre-multiply by inv(l) and overwrite .......... */
/*< do 300 j = 1, nn >*/
i__1 = nn;
for (j = 1; j <= i__1; ++j) {
/*< j1 = j - 1 >*/
j1 = j - 1;
/*< do 300 i = j, nn >*/
i__2 = nn;
for (i__ = j; i__ <= i__2; ++i__) {
/*< x = a(i,j) >*/
x = a[i__ + j * a_dim1];
/*< if (i .eq. j) go to 240 >*/
if (i__ == j) {
goto L240;
}
/*< i1 = i - 1 >*/
i1 = i__ - 1;
/*< do 220 k = j, i1 >*/
i__3 = i1;
for (k = j; k <= i__3; ++k) {
/*< 220 x = x - a(k,j) * b(i,k) >*/
/* L220: */
x -= a[k + j * a_dim1] * b[i__ + k * b_dim1];
}
/*< 240 if (j .eq. 1) go to 280 >*/
L240:
if (j == 1) {
goto L280;
}
/*< do 260 k = 1, j1 >*/
i__3 = j1;
for (k = 1; k <= i__3; ++k) {
/*< 260 x = x - a(j,k) * b(i,k) >*/
/* L260: */
x -= a[j + k * a_dim1] * b[i__ + k * b_dim1];
}
/*< 280 a(i,j) = x / dl(i) >*/
L280:
a[i__ + j * a_dim1] = x / dl[i__];
/*< 300 continue >*/
/* L300: */
}
}
/*< go to 1001 >*/
goto L1001;
/* .......... set error -- b is not positive definite .......... */
/*< 1000 ierr = 7 * n + 1 >*/
L1000:
*ierr = *n * 7 + 1;
/*< 1001 return >*/
L1001:
return 0;
/*< end >*/
} /* reduc_ */
#ifdef __cplusplus
}
#endif
|
