--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static doublereal c_b3 = -1.;
+static integer c__1 = 1;
+
+/* Subroutine */ int dlaed8_(integer *icompq, integer *k, integer *n, integer
+ *qsiz, doublereal *d__, doublereal *q, integer *ldq, integer *indxq,
+ doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda,
+ doublereal *q2, integer *ldq2, doublereal *w, integer *perm, integer
+ *givptr, integer *givcol, doublereal *givnum, integer *indxp, integer
+ *indx, integer *info)
+{
+ /* System generated locals */
+ integer q_dim1, q_offset, q2_dim1, q2_offset, i__1;
+ doublereal d__1;
+
+ /* Builtin functions */
+ double sqrt(doublereal);
+
+ /* Local variables */
+ doublereal c__;
+ integer i__, j;
+ doublereal s, t;
+ integer k2, n1, n2, jp, n1p1;
+ doublereal eps, tau, tol;
+ integer jlam, imax, jmax;
+ extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
+ doublereal *, integer *, doublereal *, doublereal *), dscal_(
+ integer *, doublereal *, doublereal *, integer *), dcopy_(integer
+ *, doublereal *, integer *, doublereal *, integer *);
+ extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *);
+ extern integer idamax_(integer *, doublereal *, integer *);
+ extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *,
+ integer *, integer *, integer *), dlacpy_(char *, integer *,
+ integer *, doublereal *, integer *, 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 */
+/* ======= */
+
+/* DLAED8 merges the two sets of eigenvalues together into a single */
+/* sorted set. Then it tries to deflate the size of the problem. */
+/* There are two ways in which deflation can occur: when two or more */
+/* eigenvalues are close together or if there is a tiny element in the */
+/* Z vector. For each such occurrence the order of the related secular */
+/* equation problem is reduced by one. */
+
+/* Arguments */
+/* ========= */
+
+/* ICOMPQ (input) INTEGER */
+/* = 0: Compute eigenvalues only. */
+/* = 1: Compute eigenvectors of original dense symmetric matrix */
+/* also. On entry, Q contains the orthogonal matrix used */
+/* to reduce the original matrix to tridiagonal form. */
+
+/* K (output) INTEGER */
+/* The number of non-deflated eigenvalues, and the order of the */
+/* related secular equation. */
+
+/* N (input) INTEGER */
+/* The dimension of the symmetric tridiagonal matrix. N >= 0. */
+
+/* QSIZ (input) INTEGER */
+/* The dimension of the orthogonal matrix used to reduce */
+/* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */
+
+/* D (input/output) DOUBLE PRECISION array, dimension (N) */
+/* On entry, the eigenvalues of the two submatrices to be */
+/* combined. On exit, the trailing (N-K) updated eigenvalues */
+/* (those which were deflated) sorted into increasing order. */
+
+/* Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N) */
+/* If ICOMPQ = 0, Q is not referenced. Otherwise, */
+/* on entry, Q contains the eigenvectors of the partially solved */
+/* system which has been previously updated in matrix */
+/* multiplies with other partially solved eigensystems. */
+/* On exit, Q contains the trailing (N-K) updated eigenvectors */
+/* (those which were deflated) in its last N-K columns. */
+
+/* LDQ (input) INTEGER */
+/* The leading dimension of the array Q. LDQ >= max(1,N). */
+
+/* INDXQ (input) INTEGER array, dimension (N) */
+/* The permutation which separately sorts the two sub-problems */
+/* in D into ascending order. Note that elements in the second */
+/* half of this permutation must first have CUTPNT added to */
+/* their values in order to be accurate. */
+
+/* RHO (input/output) DOUBLE PRECISION */
+/* On entry, the off-diagonal element associated with the rank-1 */
+/* cut which originally split the two submatrices which are now */
+/* being recombined. */
+/* On exit, RHO has been modified to the value required by */
+/* DLAED3. */
+
+/* CUTPNT (input) INTEGER */
+/* The location of the last eigenvalue in the leading */
+/* sub-matrix. min(1,N) <= CUTPNT <= N. */
+
+/* Z (input) DOUBLE PRECISION array, dimension (N) */
+/* On entry, Z contains the updating vector (the last row of */
+/* the first sub-eigenvector matrix and the first row of the */
+/* second sub-eigenvector matrix). */
+/* On exit, the contents of Z are destroyed by the updating */
+/* process. */
+
+/* DLAMDA (output) DOUBLE PRECISION array, dimension (N) */
+/* A copy of the first K eigenvalues which will be used by */
+/* DLAED3 to form the secular equation. */
+
+/* Q2 (output) DOUBLE PRECISION array, dimension (LDQ2,N) */
+/* If ICOMPQ = 0, Q2 is not referenced. Otherwise, */
+/* a copy of the first K eigenvectors which will be used by */
+/* DLAED7 in a matrix multiply (DGEMM) to update the new */
+/* eigenvectors. */
+
+/* LDQ2 (input) INTEGER */
+/* The leading dimension of the array Q2. LDQ2 >= max(1,N). */
+
+/* W (output) DOUBLE PRECISION array, dimension (N) */
+/* The first k values of the final deflation-altered z-vector and */
+/* will be passed to DLAED3. */
+
+/* PERM (output) INTEGER array, dimension (N) */
+/* The permutations (from deflation and sorting) to be applied */
+/* to each eigenblock. */
+
+/* GIVPTR (output) INTEGER */
+/* The number of Givens rotations which took place in this */
+/* subproblem. */
+
+/* GIVCOL (output) INTEGER array, dimension (2, N) */
+/* Each pair of numbers indicates a pair of columns to take place */
+/* in a Givens rotation. */
+
+/* GIVNUM (output) DOUBLE PRECISION array, dimension (2, N) */
+/* Each number indicates the S value to be used in the */
+/* corresponding Givens rotation. */
+
+/* INDXP (workspace) INTEGER array, dimension (N) */
+/* The permutation used to place deflated values of D at the end */
+/* of the array. INDXP(1:K) points to the nondeflated D-values */
+/* and INDXP(K+1:N) points to the deflated eigenvalues. */
+
+/* INDX (workspace) INTEGER array, dimension (N) */
+/* The permutation used to sort the contents of D into ascending */
+/* order. */
+
+/* INFO (output) INTEGER */
+/* = 0: successful exit. */
+/* < 0: if INFO = -i, the i-th argument had an illegal value. */
+
+/* Further Details */
+/* =============== */
+
+/* Based on contributions by */
+/* Jeff Rutter, Computer Science Division, University of California */
+/* at Berkeley, USA */
+
+/* ===================================================================== */
+
+/* .. 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;
+ --indxq;
+ --z__;
+ --dlamda;
+ q2_dim1 = *ldq2;
+ q2_offset = 1 + q2_dim1;
+ q2 -= q2_offset;
+ --w;
+ --perm;
+ givcol -= 3;
+ givnum -= 3;
+ --indxp;
+ --indx;
+
+ /* Function Body */
+ *info = 0;
+
+ if (*icompq < 0 || *icompq > 1) {
+ *info = -1;
+ } else if (*n < 0) {
+ *info = -3;
+ } else if (*icompq == 1 && *qsiz < *n) {
+ *info = -4;
+ } else if (*ldq < max(1,*n)) {
+ *info = -7;
+ } else if (*cutpnt < min(1,*n) || *cutpnt > *n) {
+ *info = -10;
+ } else if (*ldq2 < max(1,*n)) {
+ *info = -14;
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("DLAED8", &i__1);
+ return 0;
+ }
+
+/* Quick return if possible */
+
+ if (*n == 0) {
+ return 0;
+ }
+
+ n1 = *cutpnt;
+ n2 = *n - n1;
+ n1p1 = n1 + 1;
+
+ if (*rho < 0.) {
+ dscal_(&n2, &c_b3, &z__[n1p1], &c__1);
+ }
+
+/* Normalize z so that norm(z) = 1 */
+
+ t = 1. / sqrt(2.);
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ indx[j] = j;
+/* L10: */
+ }
+ dscal_(n, &t, &z__[1], &c__1);
+ *rho = (d__1 = *rho * 2., abs(d__1));
+
+/* Sort the eigenvalues into increasing order */
+
+ i__1 = *n;
+ for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) {
+ indxq[i__] += *cutpnt;
+/* L20: */
+ }
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ dlamda[i__] = d__[indxq[i__]];
+ w[i__] = z__[indxq[i__]];
+/* L30: */
+ }
+ i__ = 1;
+ j = *cutpnt + 1;
+ dlamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]);
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ d__[i__] = dlamda[indx[i__]];
+ z__[i__] = w[indx[i__]];
+/* L40: */
+ }
+
+/* Calculate the allowable deflation tolerence */
+
+ imax = idamax_(n, &z__[1], &c__1);
+ jmax = idamax_(n, &d__[1], &c__1);
+ eps = dlamch_("Epsilon");
+ tol = eps * 8. * (d__1 = d__[jmax], abs(d__1));
+
+/* If the rank-1 modifier is small enough, no more needs to be done */
+/* except to reorganize Q so that its columns correspond with the */
+/* elements in D. */
+
+ if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) {
+ *k = 0;
+ if (*icompq == 0) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ perm[j] = indxq[indx[j]];
+/* L50: */
+ }
+ } else {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ perm[j] = indxq[indx[j]];
+ dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1
+ + 1], &c__1);
+/* L60: */
+ }
+ dlacpy_("A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq);
+ }
+ return 0;
+ }
+
+/* If there are multiple eigenvalues then the problem deflates. Here */
+/* the number of equal eigenvalues are found. As each equal */
+/* eigenvalue is found, an elementary reflector is computed to rotate */
+/* the corresponding eigensubspace so that the corresponding */
+/* components of Z are zero in this new basis. */
+
+ *k = 0;
+ *givptr = 0;
+ k2 = *n + 1;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) {
+
+/* Deflate due to small z component. */
+
+ --k2;
+ indxp[k2] = j;
+ if (j == *n) {
+ goto L110;
+ }
+ } else {
+ jlam = j;
+ goto L80;
+ }
+/* L70: */
+ }
+L80:
+ ++j;
+ if (j > *n) {
+ goto L100;
+ }
+ if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) {
+
+/* Deflate due to small z component. */
+
+ --k2;
+ indxp[k2] = j;
+ } else {
+
+/* Check if eigenvalues are close enough to allow deflation. */
+
+ s = z__[jlam];
+ c__ = z__[j];
+
+/* Find sqrt(a**2+b**2) without overflow or */
+/* destructive underflow. */
+
+ tau = dlapy2_(&c__, &s);
+ t = d__[j] - d__[jlam];
+ c__ /= tau;
+ s = -s / tau;
+ if ((d__1 = t * c__ * s, abs(d__1)) <= tol) {
+
+/* Deflation is possible. */
+
+ z__[j] = tau;
+ z__[jlam] = 0.;
+
+/* Record the appropriate Givens rotation */
+
+ ++(*givptr);
+ givcol[(*givptr << 1) + 1] = indxq[indx[jlam]];
+ givcol[(*givptr << 1) + 2] = indxq[indx[j]];
+ givnum[(*givptr << 1) + 1] = c__;
+ givnum[(*givptr << 1) + 2] = s;
+ if (*icompq == 1) {
+ drot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[
+ indxq[indx[j]] * q_dim1 + 1], &c__1, &c__, &s);
+ }
+ t = d__[jlam] * c__ * c__ + d__[j] * s * s;
+ d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__;
+ d__[jlam] = t;
+ --k2;
+ i__ = 1;
+L90:
+ if (k2 + i__ <= *n) {
+ if (d__[jlam] < d__[indxp[k2 + i__]]) {
+ indxp[k2 + i__ - 1] = indxp[k2 + i__];
+ indxp[k2 + i__] = jlam;
+ ++i__;
+ goto L90;
+ } else {
+ indxp[k2 + i__ - 1] = jlam;
+ }
+ } else {
+ indxp[k2 + i__ - 1] = jlam;
+ }
+ jlam = j;
+ } else {
+ ++(*k);
+ w[*k] = z__[jlam];
+ dlamda[*k] = d__[jlam];
+ indxp[*k] = jlam;
+ jlam = j;
+ }
+ }
+ goto L80;
+L100:
+
+/* Record the last eigenvalue. */
+
+ ++(*k);
+ w[*k] = z__[jlam];
+ dlamda[*k] = d__[jlam];
+ indxp[*k] = jlam;
+
+L110:
+
+/* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */
+/* and Q2 respectively. The eigenvalues/vectors which were not */
+/* deflated go into the first K slots of DLAMDA and Q2 respectively, */
+/* while those which were deflated go into the last N - K slots. */
+
+ if (*icompq == 0) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ jp = indxp[j];
+ dlamda[j] = d__[jp];
+ perm[j] = indxq[indx[jp]];
+/* L120: */
+ }
+ } else {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ jp = indxp[j];
+ dlamda[j] = d__[jp];
+ perm[j] = indxq[indx[jp]];
+ dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1]
+, &c__1);
+/* L130: */
+ }
+ }
+
+/* The deflated eigenvalues and their corresponding vectors go back */
+/* into the last N - K slots of D and Q respectively. */
+
+ if (*k < *n) {
+ if (*icompq == 0) {
+ i__1 = *n - *k;
+ dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
+ } else {
+ i__1 = *n - *k;
+ dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
+ i__1 = *n - *k;
+ dlacpy_("A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*
+ k + 1) * q_dim1 + 1], ldq);
+ }
+ }
+
+ return 0;
+
+/* End of DLAED8 */
+
+} /* dlaed8_ */
projects / opencv / blobdiff