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475 lines
14 KiB
475 lines
14 KiB
/* slaed8.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 real c_b3 = -1.f; |
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static integer c__1 = 1; |
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/* Subroutine */ int slaed8_(integer *icompq, integer *k, integer *n, integer |
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*qsiz, real *d__, real *q, integer *ldq, integer *indxq, real *rho, |
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integer *cutpnt, real *z__, real *dlamda, real *q2, integer *ldq2, |
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real *w, integer *perm, integer *givptr, integer *givcol, real * |
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givnum, integer *indxp, integer *indx, integer *info) |
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{ |
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/* System generated locals */ |
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integer q_dim1, q_offset, q2_dim1, q2_offset, i__1; |
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real r__1; |
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/* Builtin functions */ |
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double sqrt(doublereal); |
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/* Local variables */ |
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real c__; |
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integer i__, j; |
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real s, t; |
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integer k2, n1, n2, jp, n1p1; |
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real eps, tau, tol; |
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integer jlam, imax, jmax; |
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extern /* Subroutine */ int srot_(integer *, real *, integer *, real *, |
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integer *, real *, real *), sscal_(integer *, real *, real *, |
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integer *), scopy_(integer *, real *, integer *, real *, integer * |
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); |
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extern doublereal slapy2_(real *, real *), slamch_(char *); |
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extern /* Subroutine */ int xerbla_(char *, integer *); |
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extern integer isamax_(integer *, real *, integer *); |
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extern /* Subroutine */ int slamrg_(integer *, integer *, real *, integer |
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*, integer *, integer *), slacpy_(char *, integer *, integer *, |
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real *, integer *, real *, integer *); |
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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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/* SLAED8 merges the two sets of eigenvalues together into a single */ |
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/* sorted set. Then it tries to deflate the size of the problem. */ |
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/* There are two ways in which deflation can occur: when two or more */ |
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/* eigenvalues are close together or if there is a tiny element in the */ |
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/* Z vector. For each such occurrence the order of the related secular */ |
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/* equation problem is reduced by one. */ |
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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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/* K (output) INTEGER */ |
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/* The number of non-deflated eigenvalues, and the order of the */ |
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/* related secular equation. */ |
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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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/* D (input/output) REAL array, dimension (N) */ |
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/* On entry, the eigenvalues of the two submatrices to be */ |
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/* combined. On exit, the trailing (N-K) updated eigenvalues */ |
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/* (those which were deflated) sorted into increasing order. */ |
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/* Q (input/output) REAL array, dimension (LDQ,N) */ |
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/* If ICOMPQ = 0, Q is not referenced. Otherwise, */ |
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/* on entry, Q contains the eigenvectors of the partially solved */ |
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/* system which has been previously updated in matrix */ |
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/* multiplies with other partially solved eigensystems. */ |
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/* On exit, Q contains the trailing (N-K) updated eigenvectors */ |
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/* (those which were deflated) in its last N-K columns. */ |
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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) INTEGER array, dimension (N) */ |
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/* The permutation which separately sorts the two sub-problems */ |
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/* in D into ascending order. Note that elements in the second */ |
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/* half of this permutation must first have CUTPNT added to */ |
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/* their values in order to be accurate. */ |
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/* RHO (input/output) REAL */ |
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/* On entry, the off-diagonal element associated with the rank-1 */ |
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/* cut which originally split the two submatrices which are now */ |
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/* being recombined. */ |
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/* On exit, RHO has been modified to the value required by */ |
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/* SLAED3. */ |
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/* CUTPNT (input) INTEGER */ |
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/* The location of the last eigenvalue in the leading */ |
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/* sub-matrix. min(1,N) <= CUTPNT <= N. */ |
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/* Z (input) REAL array, dimension (N) */ |
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/* On entry, Z contains the updating vector (the last row of */ |
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/* the first sub-eigenvector matrix and the first row of the */ |
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/* second sub-eigenvector matrix). */ |
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/* On exit, the contents of Z are destroyed by the updating */ |
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/* process. */ |
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/* DLAMDA (output) REAL array, dimension (N) */ |
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/* A copy of the first K eigenvalues which will be used by */ |
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/* SLAED3 to form the secular equation. */ |
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/* Q2 (output) REAL array, dimension (LDQ2,N) */ |
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/* If ICOMPQ = 0, Q2 is not referenced. Otherwise, */ |
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/* a copy of the first K eigenvectors which will be used by */ |
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/* SLAED7 in a matrix multiply (SGEMM) to update the new */ |
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/* eigenvectors. */ |
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/* LDQ2 (input) INTEGER */ |
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/* The leading dimension of the array Q2. LDQ2 >= max(1,N). */ |
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/* W (output) REAL array, dimension (N) */ |
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/* The first k values of the final deflation-altered z-vector and */ |
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/* will be passed to SLAED3. */ |
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/* PERM (output) INTEGER array, dimension (N) */ |
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/* The permutations (from deflation and sorting) to be applied */ |
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/* to each eigenblock. */ |
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/* GIVPTR (output) INTEGER */ |
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/* The number of Givens rotations which took place in this */ |
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/* subproblem. */ |
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/* GIVCOL (output) INTEGER array, dimension (2, 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 (output) REAL array, dimension (2, 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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/* INDXP (workspace) INTEGER array, dimension (N) */ |
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/* The permutation used to place deflated values of D at the end */ |
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/* of the array. INDXP(1:K) points to the nondeflated D-values */ |
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/* and INDXP(K+1:N) points to the deflated eigenvalues. */ |
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/* INDX (workspace) INTEGER array, dimension (N) */ |
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/* The permutation used to sort the contents of D into ascending */ |
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/* order. */ |
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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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/* 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 Functions .. */ |
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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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--z__; |
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--dlamda; |
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q2_dim1 = *ldq2; |
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q2_offset = 1 + q2_dim1; |
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q2 -= q2_offset; |
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--w; |
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--perm; |
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givcol -= 3; |
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givnum -= 3; |
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--indxp; |
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--indx; |
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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 = -3; |
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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 = -7; |
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} else if (*cutpnt < min(1,*n) || *cutpnt > *n) { |
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*info = -10; |
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} else if (*ldq2 < max(1,*n)) { |
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*info = -14; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("SLAED8", &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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n1 = *cutpnt; |
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n2 = *n - n1; |
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n1p1 = n1 + 1; |
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if (*rho < 0.f) { |
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sscal_(&n2, &c_b3, &z__[n1p1], &c__1); |
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} |
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/* Normalize z so that norm(z) = 1 */ |
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t = 1.f / sqrt(2.f); |
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i__1 = *n; |
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for (j = 1; j <= i__1; ++j) { |
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indx[j] = j; |
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/* L10: */ |
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} |
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sscal_(n, &t, &z__[1], &c__1); |
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*rho = (r__1 = *rho * 2.f, dabs(r__1)); |
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/* Sort the eigenvalues into increasing order */ |
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i__1 = *n; |
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for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) { |
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indxq[i__] += *cutpnt; |
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/* L20: */ |
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} |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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dlamda[i__] = d__[indxq[i__]]; |
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w[i__] = z__[indxq[i__]]; |
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/* L30: */ |
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} |
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i__ = 1; |
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j = *cutpnt + 1; |
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slamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]); |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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d__[i__] = dlamda[indx[i__]]; |
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z__[i__] = w[indx[i__]]; |
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/* L40: */ |
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} |
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/* Calculate the allowable deflation tolerence */ |
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imax = isamax_(n, &z__[1], &c__1); |
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jmax = isamax_(n, &d__[1], &c__1); |
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eps = slamch_("Epsilon"); |
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tol = eps * 8.f * (r__1 = d__[jmax], dabs(r__1)); |
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/* If the rank-1 modifier is small enough, no more needs to be done */ |
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/* except to reorganize Q so that its columns correspond with the */ |
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/* elements in D. */ |
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if (*rho * (r__1 = z__[imax], dabs(r__1)) <= tol) { |
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*k = 0; |
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if (*icompq == 0) { |
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i__1 = *n; |
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for (j = 1; j <= i__1; ++j) { |
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perm[j] = indxq[indx[j]]; |
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/* L50: */ |
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} |
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} else { |
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i__1 = *n; |
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for (j = 1; j <= i__1; ++j) { |
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perm[j] = indxq[indx[j]]; |
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scopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 |
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+ 1], &c__1); |
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/* L60: */ |
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} |
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slacpy_("A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq); |
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} |
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return 0; |
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} |
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/* If there are multiple eigenvalues then the problem deflates. Here */ |
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/* the number of equal eigenvalues are found. As each equal */ |
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/* eigenvalue is found, an elementary reflector is computed to rotate */ |
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/* the corresponding eigensubspace so that the corresponding */ |
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/* components of Z are zero in this new basis. */ |
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*k = 0; |
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*givptr = 0; |
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k2 = *n + 1; |
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i__1 = *n; |
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for (j = 1; j <= i__1; ++j) { |
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if (*rho * (r__1 = z__[j], dabs(r__1)) <= tol) { |
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/* Deflate due to small z component. */ |
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--k2; |
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indxp[k2] = j; |
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if (j == *n) { |
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goto L110; |
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} |
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} else { |
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jlam = j; |
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goto L80; |
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} |
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/* L70: */ |
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} |
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L80: |
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++j; |
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if (j > *n) { |
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goto L100; |
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} |
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if (*rho * (r__1 = z__[j], dabs(r__1)) <= tol) { |
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/* Deflate due to small z component. */ |
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--k2; |
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indxp[k2] = j; |
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} else { |
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/* Check if eigenvalues are close enough to allow deflation. */ |
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s = z__[jlam]; |
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c__ = z__[j]; |
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/* Find sqrt(a**2+b**2) without overflow or */ |
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/* destructive underflow. */ |
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tau = slapy2_(&c__, &s); |
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t = d__[j] - d__[jlam]; |
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c__ /= tau; |
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s = -s / tau; |
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if ((r__1 = t * c__ * s, dabs(r__1)) <= tol) { |
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/* Deflation is possible. */ |
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z__[j] = tau; |
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z__[jlam] = 0.f; |
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/* Record the appropriate Givens rotation */ |
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++(*givptr); |
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givcol[(*givptr << 1) + 1] = indxq[indx[jlam]]; |
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givcol[(*givptr << 1) + 2] = indxq[indx[j]]; |
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givnum[(*givptr << 1) + 1] = c__; |
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givnum[(*givptr << 1) + 2] = s; |
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if (*icompq == 1) { |
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srot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[ |
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indxq[indx[j]] * q_dim1 + 1], &c__1, &c__, &s); |
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} |
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t = d__[jlam] * c__ * c__ + d__[j] * s * s; |
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d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__; |
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d__[jlam] = t; |
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--k2; |
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i__ = 1; |
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L90: |
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if (k2 + i__ <= *n) { |
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if (d__[jlam] < d__[indxp[k2 + i__]]) { |
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indxp[k2 + i__ - 1] = indxp[k2 + i__]; |
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indxp[k2 + i__] = jlam; |
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++i__; |
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goto L90; |
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} else { |
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indxp[k2 + i__ - 1] = jlam; |
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} |
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} else { |
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indxp[k2 + i__ - 1] = jlam; |
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} |
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jlam = j; |
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} else { |
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++(*k); |
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w[*k] = z__[jlam]; |
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dlamda[*k] = d__[jlam]; |
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indxp[*k] = jlam; |
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jlam = j; |
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} |
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} |
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goto L80; |
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L100: |
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/* Record the last eigenvalue. */ |
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++(*k); |
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w[*k] = z__[jlam]; |
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dlamda[*k] = d__[jlam]; |
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indxp[*k] = jlam; |
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L110: |
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/* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */ |
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/* and Q2 respectively. The eigenvalues/vectors which were not */ |
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/* deflated go into the first K slots of DLAMDA and Q2 respectively, */ |
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/* while those which were deflated go into the last N - K slots. */ |
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if (*icompq == 0) { |
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i__1 = *n; |
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for (j = 1; j <= i__1; ++j) { |
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jp = indxp[j]; |
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dlamda[j] = d__[jp]; |
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perm[j] = indxq[indx[jp]]; |
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/* L120: */ |
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} |
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} else { |
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i__1 = *n; |
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for (j = 1; j <= i__1; ++j) { |
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jp = indxp[j]; |
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dlamda[j] = d__[jp]; |
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perm[j] = indxq[indx[jp]]; |
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scopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1] |
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, &c__1); |
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/* L130: */ |
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} |
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} |
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/* The deflated eigenvalues and their corresponding vectors go back */ |
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/* into the last N - K slots of D and Q respectively. */ |
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if (*k < *n) { |
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if (*icompq == 0) { |
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i__1 = *n - *k; |
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scopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); |
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} else { |
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i__1 = *n - *k; |
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scopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); |
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i__1 = *n - *k; |
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slacpy_("A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(* |
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k + 1) * q_dim1 + 1], ldq); |
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} |
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} |
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return 0; |
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/* End of SLAED8 */ |
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} /* slaed8_ */
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