--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static doublereal c_b22 = 1.;
+static doublereal c_b23 = 0.;
+
+/* Subroutine */ int dlaed3_(integer *k, integer *n, integer *n1, doublereal *
+ d__, doublereal *q, integer *ldq, doublereal *rho, doublereal *dlamda,
+ doublereal *q2, integer *indx, integer *ctot, doublereal *w,
+ doublereal *s, integer *info)
+{
+ /* System generated locals */
+ integer q_dim1, q_offset, i__1, i__2;
+ doublereal d__1;
+
+ /* Builtin functions */
+ double sqrt(doublereal), d_sign(doublereal *, doublereal *);
+
+ /* Local variables */
+ integer i__, j, n2, n12, ii, n23, iq2;
+ doublereal temp;
+ extern doublereal dnrm2_(integer *, doublereal *, integer *);
+ extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
+ integer *, doublereal *, doublereal *, integer *, doublereal *,
+ integer *, doublereal *, doublereal *, integer *),
+ dcopy_(integer *, doublereal *, integer *, doublereal *, integer
+ *), dlaed4_(integer *, integer *, doublereal *, doublereal *,
+ doublereal *, doublereal *, doublereal *, integer *);
+ extern doublereal dlamc3_(doublereal *, doublereal *);
+ extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
+ doublereal *, integer *, doublereal *, integer *),
+ dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
+ doublereal *, integer *), 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 */
+/* ======= */
+
+/* DLAED3 finds the roots of the secular equation, as defined by the */
+/* values in D, W, and RHO, between 1 and K. It makes the */
+/* appropriate calls to DLAED4 and then updates the eigenvectors by */
+/* multiplying the matrix of eigenvectors of the pair of eigensystems */
+/* being combined by the matrix of eigenvectors of the K-by-K system */
+/* which is solved here. */
+
+/* This code makes very mild assumptions about floating point */
+/* arithmetic. It will work on machines with a guard digit in */
+/* add/subtract, or on those binary machines without guard digits */
+/* which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
+/* It could conceivably fail on hexadecimal or decimal machines */
+/* without guard digits, but we know of none. */
+
+/* Arguments */
+/* ========= */
+
+/* K (input) INTEGER */
+/* The number of terms in the rational function to be solved by */
+/* DLAED4. K >= 0. */
+
+/* N (input) INTEGER */
+/* The number of rows and columns in the Q matrix. */
+/* N >= K (deflation may result in N>K). */
+
+/* N1 (input) INTEGER */
+/* The location of the last eigenvalue in the leading submatrix. */
+/* min(1,N) <= N1 <= N/2. */
+
+/* D (output) DOUBLE PRECISION array, dimension (N) */
+/* D(I) contains the updated eigenvalues for */
+/* 1 <= I <= K. */
+
+/* Q (output) DOUBLE PRECISION array, dimension (LDQ,N) */
+/* Initially the first K columns are used as workspace. */
+/* On output the columns 1 to K contain */
+/* the updated eigenvectors. */
+
+/* LDQ (input) INTEGER */
+/* The leading dimension of the array Q. LDQ >= max(1,N). */
+
+/* RHO (input) DOUBLE PRECISION */
+/* The value of the parameter in the rank one update equation. */
+/* RHO >= 0 required. */
+
+/* DLAMDA (input/output) DOUBLE PRECISION 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. May be changed on output by */
+/* having lowest order bit set to zero on Cray X-MP, Cray Y-MP, */
+/* Cray-2, or Cray C-90, as described above. */
+
+/* Q2 (input) DOUBLE PRECISION array, dimension (LDQ2, N) */
+/* The first K columns of this matrix contain the non-deflated */
+/* eigenvectors for the split problem. */
+
+/* INDX (input) INTEGER array, dimension (N) */
+/* The permutation used to arrange the columns of the deflated */
+/* Q matrix into three groups (see DLAED2). */
+/* The rows of the eigenvectors found by DLAED4 must be likewise */
+/* permuted before the matrix multiply can take place. */
+
+/* CTOT (input) INTEGER array, dimension (4) */
+/* A count of the total number of the various types of columns */
+/* in Q, as described in INDX. The fourth column type is any */
+/* column which has been deflated. */
+
+/* W (input/output) DOUBLE PRECISION array, dimension (K) */
+/* The first K elements of this array contain the components */
+/* of the deflation-adjusted updating vector. Destroyed on */
+/* output. */
+
+/* S (workspace) DOUBLE PRECISION array, dimension (N1 + 1)*K */
+/* Will contain the eigenvectors of the repaired matrix which */
+/* will be 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 */
+/* Modified by Francoise Tisseur, University of Tennessee. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. 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;
+ --q2;
+ --indx;
+ --ctot;
+ --w;
+ --s;
+
+ /* Function Body */
+ *info = 0;
+
+ if (*k < 0) {
+ *info = -1;
+ } else if (*n < *k) {
+ *info = -2;
+ } else if (*ldq < max(1,*n)) {
+ *info = -6;
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("DLAED3", &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 = *k;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__];
+/* L10: */
+ }
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ dlaed4_(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) {
+ goto L110;
+ }
+ if (*k == 2) {
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ w[1] = q[j * q_dim1 + 1];
+ w[2] = q[j * q_dim1 + 2];
+ ii = indx[1];
+ q[j * q_dim1 + 1] = w[ii];
+ ii = indx[2];
+ q[j * q_dim1 + 2] = w[ii];
+/* L30: */
+ }
+ goto L110;
+ }
+
+/* Compute updated W. */
+
+ dcopy_(k, &w[1], &c__1, &s[1], &c__1);
+
+/* Initialize W(I) = Q(I,I) */
+
+ i__1 = *ldq + 1;
+ dcopy_(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]);
+/* L40: */
+ }
+ i__2 = *k;
+ for (i__ = j + 1; i__ <= i__2; ++i__) {
+ w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
+/* L50: */
+ }
+/* L60: */
+ }
+ i__1 = *k;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ d__1 = sqrt(-w[i__]);
+ w[i__] = d_sign(&d__1, &s[i__]);
+/* L70: */
+ }
+
+/* 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__) {
+ s[i__] = w[i__] / q[i__ + j * q_dim1];
+/* L80: */
+ }
+ temp = dnrm2_(k, &s[1], &c__1);
+ i__2 = *k;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ ii = indx[i__];
+ q[i__ + j * q_dim1] = s[ii] / temp;
+/* L90: */
+ }
+/* L100: */
+ }
+
+/* Compute the updated eigenvectors. */
+
+L110:
+
+ n2 = *n - *n1;
+ n12 = ctot[1] + ctot[2];
+ n23 = ctot[2] + ctot[3];
+
+ dlacpy_("A", &n23, k, &q[ctot[1] + 1 + q_dim1], ldq, &s[1], &n23);
+ iq2 = *n1 * n12 + 1;
+ if (n23 != 0) {
+ dgemm_("N", "N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, &
+ c_b23, &q[*n1 + 1 + q_dim1], ldq);
+ } else {
+ dlaset_("A", &n2, k, &c_b23, &c_b23, &q[*n1 + 1 + q_dim1], ldq);
+ }
+
+ dlacpy_("A", &n12, k, &q[q_offset], ldq, &s[1], &n12);
+ if (n12 != 0) {
+ dgemm_("N", "N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23,
+ &q[q_offset], ldq);
+ } else {
+ dlaset_("A", n1, k, &c_b23, &c_b23, &q[q_dim1 + 1], ldq);
+ }
+
+
+L120:
+ return 0;
+
+/* End of DLAED3 */
+
+} /* dlaed3_ */
projects / opencv / blobdiff