--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__2 = 2;
+static integer c__1 = 1;
+static doublereal c_b10 = 1.;
+static doublereal c_b11 = 0.;
+static integer c_n1 = -1;
+
+/* Subroutine */ int dlaed7_(integer *icompq, integer *n, integer *qsiz,
+ integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__,
+ doublereal *q, integer *ldq, integer *indxq, doublereal *rho, integer
+ *cutpnt, doublereal *qstore, integer *qptr, integer *prmptr, integer *
+ perm, integer *givptr, integer *givcol, doublereal *givnum,
+ doublereal *work, integer *iwork, integer *info)
+{
+ /* System generated locals */
+ integer q_dim1, q_offset, i__1, i__2;
+
+ /* Builtin functions */
+ integer pow_ii(integer *, integer *);
+
+ /* Local variables */
+ integer i__, k, n1, n2, is, iw, iz, iq2, ptr, ldq2, indx, curr;
+ extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
+ integer *, doublereal *, doublereal *, integer *, doublereal *,
+ integer *, doublereal *, doublereal *, integer *);
+ integer indxc, indxp;
+ extern /* Subroutine */ int dlaed8_(integer *, integer *, integer *,
+ integer *, doublereal *, doublereal *, integer *, integer *,
+ doublereal *, integer *, doublereal *, doublereal *, doublereal *,
+ integer *, doublereal *, integer *, integer *, integer *,
+ doublereal *, integer *, integer *, integer *), dlaed9_(integer *,
+ integer *, integer *, integer *, doublereal *, doublereal *,
+ integer *, doublereal *, doublereal *, doublereal *, doublereal *,
+ integer *, integer *), dlaeda_(integer *, integer *, integer *,
+ integer *, integer *, integer *, integer *, integer *, doublereal
+ *, doublereal *, integer *, doublereal *, doublereal *, integer *)
+ ;
+ integer idlmda;
+ extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *,
+ integer *, integer *, integer *), xerbla_(char *, integer *);
+ integer coltyp;
+
+
+/* -- LAPACK routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLAED7 computes the updated eigensystem of a diagonal */
+/* matrix after modification by a rank-one symmetric matrix. This */
+/* routine is used only for the eigenproblem which requires all */
+/* eigenvalues and optionally eigenvectors of a dense symmetric matrix */
+/* that has been reduced to tridiagonal form. DLAED1 handles */
+/* the case in which all eigenvalues and eigenvectors of a symmetric */
+/* tridiagonal matrix are desired. */
+
+/* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) */
+
+/* where Z = Q'u, u is a vector of length N with ones in the */
+/* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */
+
+/* The eigenvectors of the original matrix are stored in Q, and the */
+/* eigenvalues are in D. The algorithm consists of three stages: */
+
+/* The first stage consists of deflating the size of the problem */
+/* when there are multiple eigenvalues or if there is a zero in */
+/* the Z vector. For each such occurence the dimension of the */
+/* secular equation problem is reduced by one. This stage is */
+/* performed by the routine DLAED8. */
+
+/* The second stage consists of calculating the updated */
+/* eigenvalues. This is done by finding the roots of the secular */
+/* equation via the routine DLAED4 (as called by DLAED9). */
+/* This routine also calculates the eigenvectors of the current */
+/* problem. */
+
+/* The final stage consists of computing the updated eigenvectors */
+/* directly using the updated eigenvalues. The eigenvectors for */
+/* the current problem are multiplied with the eigenvectors from */
+/* the overall problem. */
+
+/* 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. */
+
+/* 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. */
+
+/* TLVLS (input) INTEGER */
+/* The total number of merging levels in the overall divide and */
+/* conquer tree. */
+
+/* CURLVL (input) INTEGER */
+/* The current level in the overall merge routine, */
+/* 0 <= CURLVL <= TLVLS. */
+
+/* CURPBM (input) INTEGER */
+/* The current problem in the current level in the overall */
+/* merge routine (counting from upper left to lower right). */
+
+/* D (input/output) DOUBLE PRECISION array, dimension (N) */
+/* On entry, the eigenvalues of the rank-1-perturbed matrix. */
+/* On exit, the eigenvalues of the repaired matrix. */
+
+/* Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N) */
+/* On entry, the eigenvectors of the rank-1-perturbed matrix. */
+/* On exit, the eigenvectors of the repaired tridiagonal matrix. */
+
+/* LDQ (input) INTEGER */
+/* The leading dimension of the array Q. LDQ >= max(1,N). */
+
+/* INDXQ (output) INTEGER array, dimension (N) */
+/* The permutation which will reintegrate the subproblem just */
+/* solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) */
+/* will be in ascending order. */
+
+/* RHO (input) DOUBLE PRECISION */
+/* The subdiagonal element used to create the rank-1 */
+/* modification. */
+
+/* CUTPNT (input) INTEGER */
+/* Contains the location of the last eigenvalue in the leading */
+/* sub-matrix. min(1,N) <= CUTPNT <= N. */
+
+/* QSTORE (input/output) DOUBLE PRECISION array, dimension (N**2+1) */
+/* Stores eigenvectors of submatrices encountered during */
+/* divide and conquer, packed together. QPTR points to */
+/* beginning of the submatrices. */
+
+/* QPTR (input/output) INTEGER array, dimension (N+2) */
+/* List of indices pointing to beginning of submatrices stored */
+/* in QSTORE. The submatrices are numbered starting at the */
+/* bottom left of the divide and conquer tree, from left to */
+/* right and bottom to top. */
+
+/* PRMPTR (input) INTEGER array, dimension (N lg N) */
+/* Contains a list of pointers which indicate where in PERM a */
+/* level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */
+/* indicates the size of the permutation and also the size of */
+/* the full, non-deflated problem. */
+
+/* PERM (input) INTEGER array, dimension (N lg N) */
+/* Contains the permutations (from deflation and sorting) to be */
+/* applied to each eigenblock. */
+
+/* GIVPTR (input) INTEGER array, dimension (N lg N) */
+/* Contains a list of pointers which indicate where in GIVCOL a */
+/* level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */
+/* indicates the number of Givens rotations. */
+
+/* GIVCOL (input) INTEGER array, dimension (2, N lg N) */
+/* Each pair of numbers indicates a pair of columns to take place */
+/* in a Givens rotation. */
+
+/* GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N) */
+/* Each number indicates the S value to be used in the */
+/* corresponding Givens rotation. */
+
+/* WORK (workspace) DOUBLE PRECISION array, dimension (3*N+QSIZ*N) */
+
+/* IWORK (workspace) INTEGER array, dimension (4*N) */
+
+/* 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 */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. 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;
+ --qstore;
+ --qptr;
+ --prmptr;
+ --perm;
+ --givptr;
+ givcol -= 3;
+ givnum -= 3;
+ --work;
+ --iwork;
+
+ /* Function Body */
+ *info = 0;
+
+ if (*icompq < 0 || *icompq > 1) {
+ *info = -1;
+ } else if (*n < 0) {
+ *info = -2;
+ } else if (*icompq == 1 && *qsiz < *n) {
+ *info = -4;
+ } else if (*ldq < max(1,*n)) {
+ *info = -9;
+ } else if (min(1,*n) > *cutpnt || *n < *cutpnt) {
+ *info = -12;
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("DLAED7", &i__1);
+ return 0;
+ }
+
+/* Quick return if possible */
+
+ if (*n == 0) {
+ return 0;
+ }
+
+/* The following values are for bookkeeping purposes only. They are */
+/* integer pointers which indicate the portion of the workspace */
+/* used by a particular array in DLAED8 and DLAED9. */
+
+ if (*icompq == 1) {
+ ldq2 = *qsiz;
+ } else {
+ ldq2 = *n;
+ }
+
+ iz = 1;
+ idlmda = iz + *n;
+ iw = idlmda + *n;
+ iq2 = iw + *n;
+ is = iq2 + *n * ldq2;
+
+ indx = 1;
+ indxc = indx + *n;
+ coltyp = indxc + *n;
+ indxp = coltyp + *n;
+
+/* Form the z-vector which consists of the last row of Q_1 and the */
+/* first row of Q_2. */
+
+ ptr = pow_ii(&c__2, tlvls) + 1;
+ i__1 = *curlvl - 1;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = *tlvls - i__;
+ ptr += pow_ii(&c__2, &i__2);
+/* L10: */
+ }
+ curr = ptr + *curpbm;
+ dlaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], &
+ givcol[3], &givnum[3], &qstore[1], &qptr[1], &work[iz], &work[iz
+ + *n], info);
+
+/* When solving the final problem, we no longer need the stored data, */
+/* so we will overwrite the data from this level onto the previously */
+/* used storage space. */
+
+ if (*curlvl == *tlvls) {
+ qptr[curr] = 1;
+ prmptr[curr] = 1;
+ givptr[curr] = 1;
+ }
+
+/* Sort and Deflate eigenvalues. */
+
+ dlaed8_(icompq, &k, n, qsiz, &d__[1], &q[q_offset], ldq, &indxq[1], rho,
+ cutpnt, &work[iz], &work[idlmda], &work[iq2], &ldq2, &work[iw], &
+ perm[prmptr[curr]], &givptr[curr + 1], &givcol[(givptr[curr] << 1)
+ + 1], &givnum[(givptr[curr] << 1) + 1], &iwork[indxp], &iwork[
+ indx], info);
+ prmptr[curr + 1] = prmptr[curr] + *n;
+ givptr[curr + 1] += givptr[curr];
+
+/* Solve Secular Equation. */
+
+ if (k != 0) {
+ dlaed9_(&k, &c__1, &k, n, &d__[1], &work[is], &k, rho, &work[idlmda],
+ &work[iw], &qstore[qptr[curr]], &k, info);
+ if (*info != 0) {
+ goto L30;
+ }
+ if (*icompq == 1) {
+ dgemm_("N", "N", qsiz, &k, &k, &c_b10, &work[iq2], &ldq2, &qstore[
+ qptr[curr]], &k, &c_b11, &q[q_offset], ldq);
+ }
+/* Computing 2nd power */
+ i__1 = k;
+ qptr[curr + 1] = qptr[curr] + i__1 * i__1;
+
+/* Prepare the INDXQ sorting permutation. */
+
+ n1 = k;
+ n2 = *n - k;
+ dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]);
+ } else {
+ qptr[curr + 1] = qptr[curr];
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ indxq[i__] = i__;
+/* L20: */
+ }
+ }
+
+L30:
+ return 0;
+
+/* End of DLAED7 */
+
+} /* dlaed7_ */
projects / opencv / blobdiff