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/* eispack/tred1.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 tred1(nm,n,a,d,e,e2) >*/
/* Subroutine */ int tred1_(integer *nm, integer *n, doublereal *a,
doublereal *d__, doublereal *e, doublereal *e2)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal), d_sign(doublereal *, doublereal *);
/* Local variables */
doublereal f, g, h__;
integer i__, j, k, l, ii, jp1;
doublereal scale;
/*< integer i,j,k,l,n,ii,nm,jp1 >*/
/*< double precision a(nm,n),d(n),e(n),e2(n) >*/
/*< double precision f,g,h,scale >*/
/* this subroutine is a translation of the algol procedure tred1, */
/* num. math. 11, 181-195(1968) by martin, reinsch, and wilkinson. */
/* handbook for auto. comp., vol.ii-linear algebra, 212-226(1971). */
/* this subroutine reduces a real symmetric matrix */
/* to a symmetric tridiagonal matrix using */
/* orthogonal similarity transformations. */
/* 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 matrix. */
/* a contains the real symmetric input matrix. only the */
/* lower triangle of the matrix need be supplied. */
/* on output */
/* a contains information about the orthogonal trans- */
/* formations used in the reduction in its strict lower */
/* triangle. the full upper triangle of a is unaltered. */
/* d contains the diagonal elements of the tridiagonal matrix. */
/* e contains the subdiagonal elements of the tridiagonal */
/* matrix in its last n-1 positions. e(1) is set to zero. */
/* e2 contains the squares of the corresponding elements of e. */
/* e2 may coincide with e if the squares are not needed. */
/* questions and comments should be directed to burton s. garbow, */
/* mathematics and computer science div, argonne national laboratory */
/* this version dated august 1983. */
/* ------------------------------------------------------------------ */
/*< do 100 i = 1, n >*/
/* Parameter adjustments */
--e2;
--e;
--d__;
a_dim1 = *nm;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< d(i) = a(n,i) >*/
d__[i__] = a[*n + i__ * a_dim1];
/*< a(n,i) = a(i,i) >*/
a[*n + i__ * a_dim1] = a[i__ + i__ * a_dim1];
/*< 100 continue >*/
/* L100: */
}
/* .......... for i=n step -1 until 1 do -- .......... */
/*< do 300 ii = 1, n >*/
i__1 = *n;
for (ii = 1; ii <= i__1; ++ii) {
/*< i = n + 1 - ii >*/
i__ = *n + 1 - ii;
/*< l = i - 1 >*/
l = i__ - 1;
/*< h = 0.0d0 >*/
h__ = 0.;
/*< scale = 0.0d0 >*/
scale = 0.;
/*< if (l .lt. 1) go to 130 >*/
if (l < 1) {
goto L130;
}
/* .......... scale row (algol tol then not needed) .......... */
/*< do 120 k = 1, l >*/
i__2 = l;
for (k = 1; k <= i__2; ++k) {
/*< 120 scale = scale + dabs(d(k)) >*/
/* L120: */
scale += (d__1 = d__[k], abs(d__1));
}
/*< if (scale .ne. 0.0d0) go to 140 >*/
if (scale != 0.) {
goto L140;
}
/*< do 125 j = 1, l >*/
i__2 = l;
for (j = 1; j <= i__2; ++j) {
/*< d(j) = a(l,j) >*/
d__[j] = a[l + j * a_dim1];
/*< a(l,j) = a(i,j) >*/
a[l + j * a_dim1] = a[i__ + j * a_dim1];
/*< a(i,j) = 0.0d0 >*/
a[i__ + j * a_dim1] = 0.;
/*< 125 continue >*/
/* L125: */
}
/*< 130 e(i) = 0.0d0 >*/
L130:
e[i__] = 0.;
/*< e2(i) = 0.0d0 >*/
e2[i__] = 0.;
/*< go to 300 >*/
goto L300;
/*< 140 do 150 k = 1, l >*/
L140:
i__2 = l;
for (k = 1; k <= i__2; ++k) {
/*< d(k) = d(k) / scale >*/
d__[k] /= scale;
/*< h = h + d(k) * d(k) >*/
h__ += d__[k] * d__[k];
/*< 150 continue >*/
/* L150: */
}
/*< e2(i) = scale * scale * h >*/
e2[i__] = scale * scale * h__;
/*< f = d(l) >*/
f = d__[l];
/*< g = -dsign(dsqrt(h),f) >*/
d__1 = sqrt(h__);
g = -d_sign(&d__1, &f);
/*< e(i) = scale * g >*/
e[i__] = scale * g;
/*< h = h - f * g >*/
h__ -= f * g;
/*< d(l) = f - g >*/
d__[l] = f - g;
/*< if (l .eq. 1) go to 285 >*/
if (l == 1) {
goto L285;
}
/* .......... form a*u .......... */
/*< do 170 j = 1, l >*/
i__2 = l;
for (j = 1; j <= i__2; ++j) {
/*< 170 e(j) = 0.0d0 >*/
/* L170: */
e[j] = 0.;
}
/*< do 240 j = 1, l >*/
i__2 = l;
for (j = 1; j <= i__2; ++j) {
/*< f = d(j) >*/
f = d__[j];
/*< g = e(j) + a(j,j) * f >*/
g = e[j] + a[j + j * a_dim1] * f;
/*< jp1 = j + 1 >*/
jp1 = j + 1;
/*< if (l .lt. jp1) go to 220 >*/
if (l < jp1) {
goto L220;
}
/*< do 200 k = jp1, l >*/
i__3 = l;
for (k = jp1; k <= i__3; ++k) {
/*< g = g + a(k,j) * d(k) >*/
g += a[k + j * a_dim1] * d__[k];
/*< e(k) = e(k) + a(k,j) * f >*/
e[k] += a[k + j * a_dim1] * f;
/*< 200 continue >*/
/* L200: */
}
/*< 220 e(j) = g >*/
L220:
e[j] = g;
/*< 240 continue >*/
/* L240: */
}
/* .......... form p .......... */
/*< f = 0.0d0 >*/
f = 0.;
/*< do 245 j = 1, l >*/
i__2 = l;
for (j = 1; j <= i__2; ++j) {
/*< e(j) = e(j) / h >*/
e[j] /= h__;
/*< f = f + e(j) * d(j) >*/
f += e[j] * d__[j];
/*< 245 continue >*/
/* L245: */
}
/*< h = f / (h + h) >*/
h__ = f / (h__ + h__);
/* .......... form q .......... */
/*< do 250 j = 1, l >*/
i__2 = l;
for (j = 1; j <= i__2; ++j) {
/*< 250 e(j) = e(j) - h * d(j) >*/
/* L250: */
e[j] -= h__ * d__[j];
}
/* .......... form reduced a .......... */
/*< do 280 j = 1, l >*/
i__2 = l;
for (j = 1; j <= i__2; ++j) {
/*< f = d(j) >*/
f = d__[j];
/*< g = e(j) >*/
g = e[j];
/*< do 260 k = j, l >*/
i__3 = l;
for (k = j; k <= i__3; ++k) {
/*< 260 a(k,j) = a(k,j) - f * e(k) - g * d(k) >*/
/* L260: */
a[k + j * a_dim1] = a[k + j * a_dim1] - f * e[k] - g * d__[k];
}
/*< 280 continue >*/
/* L280: */
}
/*< 285 do 290 j = 1, l >*/
L285:
i__2 = l;
for (j = 1; j <= i__2; ++j) {
/*< f = d(j) >*/
f = d__[j];
/*< d(j) = a(l,j) >*/
d__[j] = a[l + j * a_dim1];
/*< a(l,j) = a(i,j) >*/
a[l + j * a_dim1] = a[i__ + j * a_dim1];
/*< a(i,j) = f * scale >*/
a[i__ + j * a_dim1] = f * scale;
/*< 290 continue >*/
/* L290: */
}
/*< 300 continue >*/
L300:
;
}
/*< return >*/
return 0;
/*< end >*/
} /* tred1_ */
#ifdef __cplusplus
}
#endif
|
