247 lines
7.6 KiB
C
247 lines
7.6 KiB
C
/* slaed1.f -- translated by f2c (version 20061008).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "clapack.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static integer c_n1 = -1;
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/* Subroutine */ int slaed1_(integer *n, real *d__, real *q, integer *ldq,
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integer *indxq, real *rho, integer *cutpnt, real *work, integer *
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iwork, 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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/* Local variables */
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integer i__, k, n1, n2, is, iw, iz, iq2, cpp1, indx, indxc, indxp;
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extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
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integer *), slaed2_(integer *, integer *, integer *, real *, real
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*, integer *, integer *, real *, real *, real *, real *, real *,
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integer *, integer *, integer *, integer *, integer *), slaed3_(
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integer *, integer *, integer *, real *, real *, integer *, real *
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, real *, real *, integer *, integer *, real *, real *, integer *)
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;
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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 3.2) -- */
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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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/* SLAED1 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 eigenvectors of a tridiagonal matrix. SLAED7 handles */
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/* the case in which eigenvalues only or eigenvalues and eigenvectors */
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/* of a full symmetric matrix (which was reduced to tridiagonal form) */
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/* 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 SLAED2. */
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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 SLAED3). */
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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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/* N (input) INTEGER */
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/* The dimension of the symmetric tridiagonal matrix. N >= 0. */
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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 (input/output) INTEGER array, dimension (N) */
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/* On entry, the permutation which separately sorts the two */
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/* subproblems in D into ascending order. */
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/* On exit, the permutation which will reintegrate the */
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/* subproblems back into sorted order, */
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/* i.e. D( INDXQ( I = 1, N ) ) will be in ascending order. */
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/* RHO (input) REAL */
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/* The subdiagonal entry used to create the rank-1 modification. */
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/* CUTPNT (input) INTEGER */
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/* The location of the last eigenvalue in the leading sub-matrix. */
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/* min(1,N) <= CUTPNT <= N/2. */
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/* WORK (workspace) REAL array, dimension (4*N + N**2) */
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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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/* Modified by Francoise Tisseur, University of Tennessee. */
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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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--work;
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--iwork;
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/* Function Body */
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*info = 0;
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if (*n < 0) {
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*info = -1;
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} else if (*ldq < max(1,*n)) {
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*info = -4;
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} else /* if(complicated condition) */ {
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/* Computing MIN */
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i__1 = 1, i__2 = *n / 2;
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if (min(i__1,i__2) > *cutpnt || *n / 2 < *cutpnt) {
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*info = -7;
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}
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("SLAED1", &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 integer pointers which indicate */
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/* the portion of the workspace */
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/* used by a particular array in SLAED2 and SLAED3. */
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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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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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scopy_(cutpnt, &q[*cutpnt + q_dim1], ldq, &work[iz], &c__1);
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cpp1 = *cutpnt + 1;
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i__1 = *n - *cutpnt;
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scopy_(&i__1, &q[cpp1 + cpp1 * q_dim1], ldq, &work[iz + *cutpnt], &c__1);
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/* Deflate eigenvalues. */
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slaed2_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, &indxq[1], rho, &work[
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iz], &work[idlmda], &work[iw], &work[iq2], &iwork[indx], &iwork[
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indxc], &iwork[indxp], &iwork[coltyp], info);
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if (*info != 0) {
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goto L20;
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}
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/* Solve Secular Equation. */
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if (k != 0) {
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is = (iwork[coltyp] + iwork[coltyp + 1]) * *cutpnt + (iwork[coltyp +
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1] + iwork[coltyp + 2]) * (*n - *cutpnt) + iq2;
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slaed3_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, rho, &work[idlmda],
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&work[iq2], &iwork[indxc], &iwork[coltyp], &work[iw], &work[
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is], info);
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if (*info != 0) {
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goto L20;
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}
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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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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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/* L10: */
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}
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}
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L20:
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return 0;
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/* End of SLAED1 */
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} /* slaed1_ */
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