340 lines
11 KiB
C
340 lines
11 KiB
C
#include "clapack.h"
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/* Table of constant values */
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static integer c__2 = 2;
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static integer c__1 = 1;
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static real c_b10 = 1.f;
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static real c_b11 = 0.f;
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static integer c_n1 = -1;
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/* Subroutine */ int slaed7_(integer *icompq, integer *n, integer *qsiz,
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integer *tlvls, integer *curlvl, integer *curpbm, real *d__, real *q,
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integer *ldq, integer *indxq, real *rho, integer *cutpnt, real *
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qstore, integer *qptr, integer *prmptr, integer *perm, integer *
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givptr, integer *givcol, real *givnum, real *work, integer *iwork,
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integer *info)
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{
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/* System generated locals */
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integer q_dim1, q_offset, i__1, i__2;
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/* Builtin functions */
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integer pow_ii(integer *, integer *);
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/* Local variables */
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integer i__, k, n1, n2, is, iw, iz, iq2, ptr, ldq2, indx, curr, indxc;
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extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
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integer *, real *, real *, integer *, real *, integer *, real *,
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real *, integer *);
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integer indxp;
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extern /* Subroutine */ int slaed8_(integer *, integer *, integer *,
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integer *, real *, real *, integer *, integer *, real *, integer *
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, real *, real *, real *, integer *, real *, integer *, integer *,
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integer *, real *, integer *, integer *, integer *), slaed9_(
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integer *, integer *, integer *, integer *, real *, real *,
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integer *, real *, real *, real *, real *, integer *, integer *),
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slaeda_(integer *, integer *, integer *, integer *, integer *,
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integer *, integer *, integer *, real *, real *, integer *, real *
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, real *, integer *);
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integer idlmda;
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extern /* Subroutine */ int xerbla_(char *, integer *), slamrg_(
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integer *, integer *, real *, integer *, integer *, integer *);
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integer coltyp;
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/* -- LAPACK routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* SLAED7 computes the updated eigensystem of a diagonal */
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/* matrix after modification by a rank-one symmetric matrix. This */
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/* routine is used only for the eigenproblem which requires all */
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/* eigenvalues and optionally eigenvectors of a dense symmetric matrix */
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/* that has been reduced to tridiagonal form. SLAED1 handles */
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/* the case in which all eigenvalues and eigenvectors of a symmetric */
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/* tridiagonal matrix are desired. */
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/* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) */
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/* where Z = Q'u, u is a vector of length N with ones in the */
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/* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */
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/* The eigenvectors of the original matrix are stored in Q, and the */
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/* eigenvalues are in D. The algorithm consists of three stages: */
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/* The first stage consists of deflating the size of the problem */
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/* when there are multiple eigenvalues or if there is a zero in */
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/* the Z vector. For each such occurence the dimension of the */
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/* secular equation problem is reduced by one. This stage is */
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/* performed by the routine SLAED8. */
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/* The second stage consists of calculating the updated */
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/* eigenvalues. This is done by finding the roots of the secular */
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/* equation via the routine SLAED4 (as called by SLAED9). */
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/* This routine also calculates the eigenvectors of the current */
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/* problem. */
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/* The final stage consists of computing the updated eigenvectors */
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/* directly using the updated eigenvalues. The eigenvectors for */
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/* the current problem are multiplied with the eigenvectors from */
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/* the overall problem. */
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/* Arguments */
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/* ========= */
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/* ICOMPQ (input) INTEGER */
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/* = 0: Compute eigenvalues only. */
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/* = 1: Compute eigenvectors of original dense symmetric matrix */
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/* also. On entry, Q contains the orthogonal matrix used */
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/* to reduce the original matrix to tridiagonal form. */
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/* N (input) INTEGER */
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/* The dimension of the symmetric tridiagonal matrix. N >= 0. */
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/* QSIZ (input) INTEGER */
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/* The dimension of the orthogonal matrix used to reduce */
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/* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */
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/* TLVLS (input) INTEGER */
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/* The total number of merging levels in the overall divide and */
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/* conquer tree. */
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/* CURLVL (input) INTEGER */
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/* The current level in the overall merge routine, */
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/* 0 <= CURLVL <= TLVLS. */
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/* CURPBM (input) INTEGER */
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/* The current problem in the current level in the overall */
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/* merge routine (counting from upper left to lower right). */
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/* D (input/output) REAL array, dimension (N) */
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/* On entry, the eigenvalues of the rank-1-perturbed matrix. */
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/* On exit, the eigenvalues of the repaired matrix. */
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/* Q (input/output) REAL array, dimension (LDQ, N) */
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/* On entry, the eigenvectors of the rank-1-perturbed matrix. */
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/* On exit, the eigenvectors of the repaired tridiagonal matrix. */
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/* LDQ (input) INTEGER */
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/* The leading dimension of the array Q. LDQ >= max(1,N). */
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/* INDXQ (output) INTEGER array, dimension (N) */
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/* The permutation which will reintegrate the subproblem just */
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/* solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) */
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/* will be in ascending order. */
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/* RHO (input) REAL */
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/* The subdiagonal element used to create the rank-1 */
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/* modification. */
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/* CUTPNT (input) INTEGER */
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/* Contains the location of the last eigenvalue in the leading */
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/* sub-matrix. min(1,N) <= CUTPNT <= N. */
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/* QSTORE (input/output) REAL array, dimension (N**2+1) */
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/* Stores eigenvectors of submatrices encountered during */
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/* divide and conquer, packed together. QPTR points to */
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/* beginning of the submatrices. */
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/* QPTR (input/output) INTEGER array, dimension (N+2) */
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/* List of indices pointing to beginning of submatrices stored */
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/* in QSTORE. The submatrices are numbered starting at the */
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/* bottom left of the divide and conquer tree, from left to */
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/* right and bottom to top. */
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/* PRMPTR (input) INTEGER array, dimension (N lg N) */
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/* Contains a list of pointers which indicate where in PERM a */
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/* level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */
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/* indicates the size of the permutation and also the size of */
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/* the full, non-deflated problem. */
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/* PERM (input) INTEGER array, dimension (N lg N) */
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/* Contains the permutations (from deflation and sorting) to be */
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/* applied to each eigenblock. */
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/* GIVPTR (input) INTEGER array, dimension (N lg N) */
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/* Contains a list of pointers which indicate where in GIVCOL a */
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/* level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */
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/* indicates the number of Givens rotations. */
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/* GIVCOL (input) INTEGER array, dimension (2, N lg N) */
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/* Each pair of numbers indicates a pair of columns to take place */
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/* in a Givens rotation. */
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/* GIVNUM (input) REAL array, dimension (2, N lg N) */
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/* Each number indicates the S value to be used in the */
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/* corresponding Givens rotation. */
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/* WORK (workspace) REAL array, dimension (3*N+QSIZ*N) */
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/* IWORK (workspace) INTEGER array, dimension (4*N) */
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/* INFO (output) INTEGER */
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/* = 0: successful exit. */
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/* < 0: if INFO = -i, the i-th argument had an illegal value. */
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/* > 0: if INFO = 1, an eigenvalue did not converge */
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/* Further Details */
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/* =============== */
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/* Based on contributions by */
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/* Jeff Rutter, Computer Science Division, University of California */
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/* at Berkeley, USA */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters. */
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/* Parameter adjustments */
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--d__;
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q_dim1 = *ldq;
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q_offset = 1 + q_dim1;
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q -= q_offset;
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--indxq;
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--qstore;
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--qptr;
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--prmptr;
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--perm;
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--givptr;
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givcol -= 3;
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givnum -= 3;
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--work;
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--iwork;
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/* Function Body */
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*info = 0;
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if (*icompq < 0 || *icompq > 1) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*icompq == 1 && *qsiz < *n) {
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*info = -4;
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} else if (*ldq < max(1,*n)) {
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*info = -9;
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} else if (min(1,*n) > *cutpnt || *n < *cutpnt) {
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*info = -12;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("SLAED7", &i__1);
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return 0;
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}
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/* Quick return if possible */
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if (*n == 0) {
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return 0;
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}
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/* The following values are for bookkeeping purposes only. They are */
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/* integer pointers which indicate the portion of the workspace */
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/* used by a particular array in SLAED8 and SLAED9. */
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if (*icompq == 1) {
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ldq2 = *qsiz;
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} else {
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ldq2 = *n;
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}
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iz = 1;
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idlmda = iz + *n;
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iw = idlmda + *n;
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iq2 = iw + *n;
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is = iq2 + *n * ldq2;
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indx = 1;
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indxc = indx + *n;
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coltyp = indxc + *n;
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indxp = coltyp + *n;
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/* Form the z-vector which consists of the last row of Q_1 and the */
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/* first row of Q_2. */
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ptr = pow_ii(&c__2, tlvls) + 1;
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i__1 = *curlvl - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = *tlvls - i__;
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ptr += pow_ii(&c__2, &i__2);
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/* L10: */
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}
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curr = ptr + *curpbm;
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slaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], &
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givcol[3], &givnum[3], &qstore[1], &qptr[1], &work[iz], &work[iz
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+ *n], info);
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/* When solving the final problem, we no longer need the stored data, */
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/* so we will overwrite the data from this level onto the previously */
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/* used storage space. */
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if (*curlvl == *tlvls) {
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qptr[curr] = 1;
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prmptr[curr] = 1;
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givptr[curr] = 1;
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}
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/* Sort and Deflate eigenvalues. */
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slaed8_(icompq, &k, n, qsiz, &d__[1], &q[q_offset], ldq, &indxq[1], rho,
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cutpnt, &work[iz], &work[idlmda], &work[iq2], &ldq2, &work[iw], &
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perm[prmptr[curr]], &givptr[curr + 1], &givcol[(givptr[curr] << 1)
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+ 1], &givnum[(givptr[curr] << 1) + 1], &iwork[indxp], &iwork[
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indx], info);
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prmptr[curr + 1] = prmptr[curr] + *n;
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givptr[curr + 1] += givptr[curr];
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/* Solve Secular Equation. */
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if (k != 0) {
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slaed9_(&k, &c__1, &k, n, &d__[1], &work[is], &k, rho, &work[idlmda],
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&work[iw], &qstore[qptr[curr]], &k, info);
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if (*info != 0) {
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goto L30;
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}
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if (*icompq == 1) {
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sgemm_("N", "N", qsiz, &k, &k, &c_b10, &work[iq2], &ldq2, &qstore[
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qptr[curr]], &k, &c_b11, &q[q_offset], ldq);
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}
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/* Computing 2nd power */
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i__1 = k;
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qptr[curr + 1] = qptr[curr] + i__1 * i__1;
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/* Prepare the INDXQ sorting permutation. */
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n1 = k;
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n2 = *n - k;
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slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]);
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} else {
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qptr[curr + 1] = qptr[curr];
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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indxq[i__] = i__;
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/* L20: */
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}
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}
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L30:
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return 0;
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/* End of SLAED7 */
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} /* slaed7_ */
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