--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* Subroutine */ int slaed9_(integer *k, integer *kstart, integer *kstop,
+ integer *n, real *d__, real *q, integer *ldq, real *rho, real *dlamda,
+ real *w, real *s, integer *lds, integer *info)
+{
+ /* System generated locals */
+ integer q_dim1, q_offset, s_dim1, s_offset, i__1, i__2;
+ real r__1;
+
+ /* Builtin functions */
+ double sqrt(doublereal), r_sign(real *, real *);
+
+ /* Local variables */
+ integer i__, j;
+ real temp;
+ extern doublereal snrm2_(integer *, real *, integer *);
+ extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
+ integer *), slaed4_(integer *, integer *, real *, real *, real *,
+ real *, real *, integer *);
+ extern doublereal slamc3_(real *, real *);
+ extern /* Subroutine */ int xerbla_(char *, integer *);
+
+
+/* -- LAPACK routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLAED9 finds the roots of the secular equation, as defined by the */
+/* values in D, Z, and RHO, between KSTART and KSTOP. It makes the */
+/* appropriate calls to SLAED4 and then stores the new matrix of */
+/* eigenvectors for use in calculating the next level of Z vectors. */
+
+/* Arguments */
+/* ========= */
+
+/* K (input) INTEGER */
+/* The number of terms in the rational function to be solved by */
+/* SLAED4. K >= 0. */
+
+/* KSTART (input) INTEGER */
+/* KSTOP (input) INTEGER */
+/* The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP */
+/* are to be computed. 1 <= KSTART <= KSTOP <= K. */
+
+/* N (input) INTEGER */
+/* The number of rows and columns in the Q matrix. */
+/* N >= K (delation may result in N > K). */
+
+/* D (output) REAL array, dimension (N) */
+/* D(I) contains the updated eigenvalues */
+/* for KSTART <= I <= KSTOP. */
+
+/* Q (workspace) REAL array, dimension (LDQ,N) */
+
+/* LDQ (input) INTEGER */
+/* The leading dimension of the array Q. LDQ >= max( 1, N ). */
+
+/* RHO (input) REAL */
+/* The value of the parameter in the rank one update equation. */
+/* RHO >= 0 required. */
+
+/* DLAMDA (input) REAL array, dimension (K) */
+/* The first K elements of this array contain the old roots */
+/* of the deflated updating problem. These are the poles */
+/* of the secular equation. */
+
+/* W (input) REAL array, dimension (K) */
+/* The first K elements of this array contain the components */
+/* of the deflation-adjusted updating vector. */
+
+/* S (output) REAL array, dimension (LDS, K) */
+/* Will contain the eigenvectors of the repaired matrix which */
+/* will be stored for subsequent Z vector calculation and */
+/* multiplied by the previously accumulated eigenvectors */
+/* to update the system. */
+
+/* LDS (input) INTEGER */
+/* The leading dimension of S. LDS >= max( 1, K ). */
+
+/* INFO (output) INTEGER */
+/* = 0: successful exit. */
+/* < 0: if INFO = -i, the i-th argument had an illegal value. */
+/* > 0: if INFO = 1, an eigenvalue did not converge */
+
+/* Further Details */
+/* =============== */
+
+/* Based on contributions by */
+/* Jeff Rutter, Computer Science Division, University of California */
+/* at Berkeley, USA */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ --d__;
+ q_dim1 = *ldq;
+ q_offset = 1 + q_dim1;
+ q -= q_offset;
+ --dlamda;
+ --w;
+ s_dim1 = *lds;
+ s_offset = 1 + s_dim1;
+ s -= s_offset;
+
+ /* Function Body */
+ *info = 0;
+
+ if (*k < 0) {
+ *info = -1;
+ } else if (*kstart < 1 || *kstart > max(1,*k)) {
+ *info = -2;
+ } else if (max(1,*kstop) < *kstart || *kstop > max(1,*k)) {
+ *info = -3;
+ } else if (*n < *k) {
+ *info = -4;
+ } else if (*ldq < max(1,*k)) {
+ *info = -7;
+ } else if (*lds < max(1,*k)) {
+ *info = -12;
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("SLAED9", &i__1);
+ return 0;
+ }
+
+/* Quick return if possible */
+
+ if (*k == 0) {
+ return 0;
+ }
+
+/* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */
+/* be computed with high relative accuracy (barring over/underflow). */
+/* This is a problem on machines without a guard digit in */
+/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */
+/* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */
+/* which on any of these machines zeros out the bottommost */
+/* bit of DLAMDA(I) if it is 1; this makes the subsequent */
+/* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */
+/* occurs. On binary machines with a guard digit (almost all */
+/* machines) it does not change DLAMDA(I) at all. On hexadecimal */
+/* and decimal machines with a guard digit, it slightly */
+/* changes the bottommost bits of DLAMDA(I). It does not account */
+/* for hexadecimal or decimal machines without guard digits */
+/* (we know of none). We use a subroutine call to compute */
+/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */
+/* this code. */
+
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ dlamda[i__] = slamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__];
+/* L10: */
+ }
+
+ i__1 = *kstop;
+ for (j = *kstart; j <= i__1; ++j) {
+ slaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j],
+ info);
+
+/* If the zero finder fails, the computation is terminated. */
+
+ if (*info != 0) {
+ goto L120;
+ }
+/* L20: */
+ }
+
+ if (*k == 1 || *k == 2) {
+ i__1 = *k;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = *k;
+ for (j = 1; j <= i__2; ++j) {
+ s[j + i__ * s_dim1] = q[j + i__ * q_dim1];
+/* L30: */
+ }
+/* L40: */
+ }
+ goto L120;
+ }
+
+/* Compute updated W. */
+
+ scopy_(k, &w[1], &c__1, &s[s_offset], &c__1);
+
+/* Initialize W(I) = Q(I,I) */
+
+ i__1 = *ldq + 1;
+ scopy_(k, &q[q_offset], &i__1, &w[1], &c__1);
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = j - 1;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
+/* L50: */
+ }
+ i__2 = *k;
+ for (i__ = j + 1; i__ <= i__2; ++i__) {
+ w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
+/* L60: */
+ }
+/* L70: */
+ }
+ i__1 = *k;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ r__1 = sqrt(-w[i__]);
+ w[i__] = r_sign(&r__1, &s[i__ + s_dim1]);
+/* L80: */
+ }
+
+/* Compute eigenvectors of the modified rank-1 modification. */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = *k;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ q[i__ + j * q_dim1] = w[i__] / q[i__ + j * q_dim1];
+/* L90: */
+ }
+ temp = snrm2_(k, &q[j * q_dim1 + 1], &c__1);
+ i__2 = *k;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ s[i__ + j * s_dim1] = q[i__ + j * q_dim1] / temp;
+/* L100: */
+ }
+/* L110: */
+ }
+
+L120:
+ return 0;
+
+/* End of SLAED9 */
+
+} /* slaed9_ */
projects / opencv / blobdiff