--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static doublereal c_b3 = -1.;
+static integer c__1 = 1;
+
+/* Subroutine */ int dlaed2_(integer *k, integer *n, integer *n1, doublereal *
+ d__, doublereal *q, integer *ldq, integer *indxq, doublereal *rho,
+ doublereal *z__, doublereal *dlamda, doublereal *w, doublereal *q2,
+ integer *indx, integer *indxc, integer *indxp, integer *coltyp,
+ integer *info)
+{
+ /* System generated locals */
+ integer q_dim1, q_offset, i__1, i__2;
+ doublereal d__1, d__2, d__3, d__4;
+
+ /* Builtin functions */
+ double sqrt(doublereal);
+
+ /* Local variables */
+ doublereal c__;
+ integer i__, j;
+ doublereal s, t;
+ integer k2, n2, ct, nj, pj, js, iq1, iq2, n1p1;
+ doublereal eps, tau, tol;
+ integer psm[4], imax, jmax;
+ extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
+ doublereal *, integer *, doublereal *, doublereal *);
+ integer ctot[4];
+ extern /* Subroutine */ int 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 */
+/* ======= */
+
+/* DLAED2 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 entry in the */
+/* Z vector. For each such occurrence the order of the related secular */
+/* equation problem is reduced by one. */
+
+/* Arguments */
+/* ========= */
+
+/* K (output) INTEGER */
+/* The number of non-deflated eigenvalues, and the order of the */
+/* related secular equation. 0 <= K <=N. */
+
+/* N (input) INTEGER */
+/* The dimension of the symmetric tridiagonal matrix. N >= 0. */
+
+/* N1 (input) INTEGER */
+/* The location of the last eigenvalue in the leading sub-matrix. */
+/* min(1,N) <= N1 <= N/2. */
+
+/* D (input/output) DOUBLE PRECISION array, dimension (N) */
+/* On entry, D contains the eigenvalues of the two submatrices to */
+/* be combined. */
+/* On exit, D contains the trailing (N-K) updated eigenvalues */
+/* (those which were deflated) sorted into increasing order. */
+
+/* Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N) */
+/* On entry, Q contains the eigenvectors of two submatrices in */
+/* the two square blocks with corners at (1,1), (N1,N1) */
+/* and (N1+1, N1+1), (N,N). */
+/* 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/output) 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 N1 added to their */
+/* values. Destroyed on exit. */
+
+/* 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. */
+
+/* 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 have been 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. */
+
+/* W (output) DOUBLE PRECISION array, dimension (N) */
+/* The first k values of the final deflation-altered z-vector */
+/* which will be passed to DLAED3. */
+
+/* Q2 (output) DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2) */
+/* A copy of the first K eigenvectors which will be used by */
+/* DLAED3 in a matrix multiply (DGEMM) to solve for the new */
+/* eigenvectors. */
+
+/* INDX (workspace) INTEGER array, dimension (N) */
+/* The permutation used to sort the contents of DLAMDA into */
+/* ascending order. */
+
+/* INDXC (output) INTEGER array, dimension (N) */
+/* The permutation used to arrange the columns of the deflated */
+/* Q matrix into three groups: the first group contains non-zero */
+/* elements only at and above N1, the second contains */
+/* non-zero elements only below N1, and the third is dense. */
+
+/* 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. */
+
+/* COLTYP (workspace/output) INTEGER array, dimension (N) */
+/* During execution, a label which will indicate which of the */
+/* following types a column in the Q2 matrix is: */
+/* 1 : non-zero in the upper half only; */
+/* 2 : dense; */
+/* 3 : non-zero in the lower half only; */
+/* 4 : deflated. */
+/* On exit, COLTYP(i) is the number of columns of type i, */
+/* for i=1 to 4 only. */
+
+/* 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 */
+/* Modified by Francoise Tisseur, University of Tennessee. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Arrays .. */
+/* .. */
+/* .. 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;
+ --w;
+ --q2;
+ --indx;
+ --indxc;
+ --indxp;
+ --coltyp;
+
+ /* Function Body */
+ *info = 0;
+
+ if (*n < 0) {
+ *info = -2;
+ } else if (*ldq < max(1,*n)) {
+ *info = -6;
+ } else /* if(complicated condition) */ {
+/* Computing MIN */
+ i__1 = 1, i__2 = *n / 2;
+ if (min(i__1,i__2) > *n1 || *n / 2 < *n1) {
+ *info = -3;
+ }
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("DLAED2", &i__1);
+ return 0;
+ }
+
+/* Quick return if possible */
+
+ if (*n == 0) {
+ return 0;
+ }
+
+ n2 = *n - *n1;
+ n1p1 = *n1 + 1;
+
+ if (*rho < 0.) {
+ dscal_(&n2, &c_b3, &z__[n1p1], &c__1);
+ }
+
+/* Normalize z so that norm(z) = 1. Since z is the concatenation of */
+/* two normalized vectors, norm2(z) = sqrt(2). */
+
+ t = 1. / sqrt(2.);
+ dscal_(n, &t, &z__[1], &c__1);
+
+/* RHO = ABS( norm(z)**2 * RHO ) */
+
+ *rho = (d__1 = *rho * 2., abs(d__1));
+
+/* Sort the eigenvalues into increasing order */
+
+ i__1 = *n;
+ for (i__ = n1p1; i__ <= i__1; ++i__) {
+ indxq[i__] += *n1;
+/* L10: */
+ }
+
+/* re-integrate the deflated parts from the last pass */
+
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ dlamda[i__] = d__[indxq[i__]];
+/* L20: */
+ }
+ dlamrg_(n1, &n2, &dlamda[1], &c__1, &c__1, &indxc[1]);
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ indx[i__] = indxq[indxc[i__]];
+/* L30: */
+ }
+
+/* Calculate the allowable deflation tolerance */
+
+ imax = idamax_(n, &z__[1], &c__1);
+ jmax = idamax_(n, &d__[1], &c__1);
+ eps = dlamch_("Epsilon");
+/* Computing MAX */
+ d__3 = (d__1 = d__[jmax], abs(d__1)), d__4 = (d__2 = z__[imax], abs(d__2))
+ ;
+ tol = eps * 8. * max(d__3,d__4);
+
+/* 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;
+ iq2 = 1;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__ = indx[j];
+ dcopy_(n, &q[i__ * q_dim1 + 1], &c__1, &q2[iq2], &c__1);
+ dlamda[j] = d__[i__];
+ iq2 += *n;
+/* L40: */
+ }
+ dlacpy_("A", n, n, &q2[1], n, &q[q_offset], ldq);
+ dcopy_(n, &dlamda[1], &c__1, &d__[1], &c__1);
+ goto L190;
+ }
+
+/* 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. */
+
+ i__1 = *n1;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ coltyp[i__] = 1;
+/* L50: */
+ }
+ i__1 = *n;
+ for (i__ = n1p1; i__ <= i__1; ++i__) {
+ coltyp[i__] = 3;
+/* L60: */
+ }
+
+
+ *k = 0;
+ k2 = *n + 1;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ nj = indx[j];
+ if (*rho * (d__1 = z__[nj], abs(d__1)) <= tol) {
+
+/* Deflate due to small z component. */
+
+ --k2;
+ coltyp[nj] = 4;
+ indxp[k2] = nj;
+ if (j == *n) {
+ goto L100;
+ }
+ } else {
+ pj = nj;
+ goto L80;
+ }
+/* L70: */
+ }
+L80:
+ ++j;
+ nj = indx[j];
+ if (j > *n) {
+ goto L100;
+ }
+ if (*rho * (d__1 = z__[nj], abs(d__1)) <= tol) {
+
+/* Deflate due to small z component. */
+
+ --k2;
+ coltyp[nj] = 4;
+ indxp[k2] = nj;
+ } else {
+
+/* Check if eigenvalues are close enough to allow deflation. */
+
+ s = z__[pj];
+ c__ = z__[nj];
+
+/* Find sqrt(a**2+b**2) without overflow or */
+/* destructive underflow. */
+
+ tau = dlapy2_(&c__, &s);
+ t = d__[nj] - d__[pj];
+ c__ /= tau;
+ s = -s / tau;
+ if ((d__1 = t * c__ * s, abs(d__1)) <= tol) {
+
+/* Deflation is possible. */
+
+ z__[nj] = tau;
+ z__[pj] = 0.;
+ if (coltyp[nj] != coltyp[pj]) {
+ coltyp[nj] = 2;
+ }
+ coltyp[pj] = 4;
+ drot_(n, &q[pj * q_dim1 + 1], &c__1, &q[nj * q_dim1 + 1], &c__1, &
+ c__, &s);
+/* Computing 2nd power */
+ d__1 = c__;
+/* Computing 2nd power */
+ d__2 = s;
+ t = d__[pj] * (d__1 * d__1) + d__[nj] * (d__2 * d__2);
+/* Computing 2nd power */
+ d__1 = s;
+/* Computing 2nd power */
+ d__2 = c__;
+ d__[nj] = d__[pj] * (d__1 * d__1) + d__[nj] * (d__2 * d__2);
+ d__[pj] = t;
+ --k2;
+ i__ = 1;
+L90:
+ if (k2 + i__ <= *n) {
+ if (d__[pj] < d__[indxp[k2 + i__]]) {
+ indxp[k2 + i__ - 1] = indxp[k2 + i__];
+ indxp[k2 + i__] = pj;
+ ++i__;
+ goto L90;
+ } else {
+ indxp[k2 + i__ - 1] = pj;
+ }
+ } else {
+ indxp[k2 + i__ - 1] = pj;
+ }
+ pj = nj;
+ } else {
+ ++(*k);
+ dlamda[*k] = d__[pj];
+ w[*k] = z__[pj];
+ indxp[*k] = pj;
+ pj = nj;
+ }
+ }
+ goto L80;
+L100:
+
+/* Record the last eigenvalue. */
+
+ ++(*k);
+ dlamda[*k] = d__[pj];
+ w[*k] = z__[pj];
+ indxp[*k] = pj;
+
+/* Count up the total number of the various types of columns, then */
+/* form a permutation which positions the four column types into */
+/* four uniform groups (although one or more of these groups may be */
+/* empty). */
+
+ for (j = 1; j <= 4; ++j) {
+ ctot[j - 1] = 0;
+/* L110: */
+ }
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ ct = coltyp[j];
+ ++ctot[ct - 1];
+/* L120: */
+ }
+
+/* PSM(*) = Position in SubMatrix (of types 1 through 4) */
+
+ psm[0] = 1;
+ psm[1] = ctot[0] + 1;
+ psm[2] = psm[1] + ctot[1];
+ psm[3] = psm[2] + ctot[2];
+ *k = *n - ctot[3];
+
+/* Fill out the INDXC array so that the permutation which it induces */
+/* will place all type-1 columns first, all type-2 columns next, */
+/* then all type-3's, and finally all type-4's. */
+
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ js = indxp[j];
+ ct = coltyp[js];
+ indx[psm[ct - 1]] = js;
+ indxc[psm[ct - 1]] = j;
+ ++psm[ct - 1];
+/* L130: */
+ }
+
+/* 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. */
+
+ i__ = 1;
+ iq1 = 1;
+ iq2 = (ctot[0] + ctot[1]) * *n1 + 1;
+ i__1 = ctot[0];
+ for (j = 1; j <= i__1; ++j) {
+ js = indx[i__];
+ dcopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1);
+ z__[i__] = d__[js];
+ ++i__;
+ iq1 += *n1;
+/* L140: */
+ }
+
+ i__1 = ctot[1];
+ for (j = 1; j <= i__1; ++j) {
+ js = indx[i__];
+ dcopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1);
+ dcopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1);
+ z__[i__] = d__[js];
+ ++i__;
+ iq1 += *n1;
+ iq2 += n2;
+/* L150: */
+ }
+
+ i__1 = ctot[2];
+ for (j = 1; j <= i__1; ++j) {
+ js = indx[i__];
+ dcopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1);
+ z__[i__] = d__[js];
+ ++i__;
+ iq2 += n2;
+/* L160: */
+ }
+
+ iq1 = iq2;
+ i__1 = ctot[3];
+ for (j = 1; j <= i__1; ++j) {
+ js = indx[i__];
+ dcopy_(n, &q[js * q_dim1 + 1], &c__1, &q2[iq2], &c__1);
+ iq2 += *n;
+ z__[i__] = d__[js];
+ ++i__;
+/* L170: */
+ }
+
+/* The deflated eigenvalues and their corresponding vectors go back */
+/* into the last N - K slots of D and Q respectively. */
+
+ dlacpy_("A", n, &ctot[3], &q2[iq1], n, &q[(*k + 1) * q_dim1 + 1], ldq);
+ i__1 = *n - *k;
+ dcopy_(&i__1, &z__[*k + 1], &c__1, &d__[*k + 1], &c__1);
+
+/* Copy CTOT into COLTYP for referencing in DLAED3. */
+
+ for (j = 1; j <= 4; ++j) {
+ coltyp[j] = ctot[j - 1];
+/* L180: */
+ }
+
+L190:
+ return 0;
+
+/* End of DLAED2 */
+
+} /* dlaed2_ */
projects / opencv / blobdiff