461 lines
14 KiB
C
461 lines
14 KiB
C
#include "clapack.h"
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/* Table of constant values */
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static doublereal c_b5 = -1.;
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static integer c__1 = 1;
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static doublereal c_b11 = 1.;
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static doublereal c_b13 = 0.;
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static integer c__0 = 0;
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/* Subroutine */ int dlals0_(integer *icompq, integer *nl, integer *nr,
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integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal
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*bx, integer *ldbx, integer *perm, integer *givptr, integer *givcol,
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integer *ldgcol, doublereal *givnum, integer *ldgnum, doublereal *
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poles, doublereal *difl, doublereal *difr, doublereal *z__, integer *
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k, doublereal *c__, doublereal *s, doublereal *work, integer *info)
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{
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/* System generated locals */
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integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset,
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difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1,
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poles_offset, i__1, i__2;
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doublereal d__1;
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/* Local variables */
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integer i__, j, m, n;
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doublereal dj;
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integer nlp1;
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doublereal temp;
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extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
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doublereal *, integer *, doublereal *, doublereal *);
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extern doublereal dnrm2_(integer *, doublereal *, integer *);
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extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
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integer *);
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doublereal diflj, difrj, dsigj;
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extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
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doublereal *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *), dcopy_(integer *,
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doublereal *, integer *, doublereal *, integer *);
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extern doublereal dlamc3_(doublereal *, doublereal *);
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extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
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doublereal *, doublereal *, integer *, integer *, doublereal *,
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integer *, integer *), dlacpy_(char *, integer *, integer
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*, doublereal *, integer *, doublereal *, integer *),
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xerbla_(char *, integer *);
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doublereal dsigjp;
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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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/* DLALS0 applies back the multiplying factors of either the left or the */
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/* right singular vector matrix of a diagonal matrix appended by a row */
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/* to the right hand side matrix B in solving the least squares problem */
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/* using the divide-and-conquer SVD approach. */
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/* For the left singular vector matrix, three types of orthogonal */
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/* matrices are involved: */
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/* (1L) Givens rotations: the number of such rotations is GIVPTR; the */
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/* pairs of columns/rows they were applied to are stored in GIVCOL; */
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/* and the C- and S-values of these rotations are stored in GIVNUM. */
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/* (2L) Permutation. The (NL+1)-st row of B is to be moved to the first */
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/* row, and for J=2:N, PERM(J)-th row of B is to be moved to the */
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/* J-th row. */
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/* (3L) The left singular vector matrix of the remaining matrix. */
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/* For the right singular vector matrix, four types of orthogonal */
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/* matrices are involved: */
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/* (1R) The right singular vector matrix of the remaining matrix. */
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/* (2R) If SQRE = 1, one extra Givens rotation to generate the right */
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/* null space. */
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/* (3R) The inverse transformation of (2L). */
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/* (4R) The inverse transformation of (1L). */
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/* Arguments */
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/* ========= */
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/* ICOMPQ (input) INTEGER */
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/* Specifies whether singular vectors are to be computed in */
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/* factored form: */
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/* = 0: Left singular vector matrix. */
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/* = 1: Right singular vector matrix. */
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/* NL (input) INTEGER */
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/* The row dimension of the upper block. NL >= 1. */
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/* NR (input) INTEGER */
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/* The row dimension of the lower block. NR >= 1. */
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/* SQRE (input) INTEGER */
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/* = 0: the lower block is an NR-by-NR square matrix. */
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/* = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */
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/* The bidiagonal matrix has row dimension N = NL + NR + 1, */
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/* and column dimension M = N + SQRE. */
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/* NRHS (input) INTEGER */
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/* The number of columns of B and BX. NRHS must be at least 1. */
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/* B (input/output) DOUBLE PRECISION array, dimension ( LDB, NRHS ) */
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/* On input, B contains the right hand sides of the least */
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/* squares problem in rows 1 through M. On output, B contains */
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/* the solution X in rows 1 through N. */
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/* LDB (input) INTEGER */
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/* The leading dimension of B. LDB must be at least */
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/* max(1,MAX( M, N ) ). */
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/* BX (workspace) DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */
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/* LDBX (input) INTEGER */
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/* The leading dimension of BX. */
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/* PERM (input) INTEGER array, dimension ( N ) */
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/* The permutations (from deflation and sorting) applied */
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/* to the two blocks. */
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/* GIVPTR (input) 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 (input) INTEGER array, dimension ( LDGCOL, 2 ) */
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/* Each pair of numbers indicates a pair of rows/columns */
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/* involved in a Givens rotation. */
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/* LDGCOL (input) INTEGER */
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/* The leading dimension of GIVCOL, must be at least N. */
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/* GIVNUM (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
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/* Each number indicates the C or S value used in the */
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/* corresponding Givens rotation. */
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/* LDGNUM (input) INTEGER */
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/* The leading dimension of arrays DIFR, POLES and */
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/* GIVNUM, must be at least K. */
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/* POLES (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
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/* On entry, POLES(1:K, 1) contains the new singular */
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/* values obtained from solving the secular equation, and */
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/* POLES(1:K, 2) is an array containing the poles in the secular */
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/* equation. */
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/* DIFL (input) DOUBLE PRECISION array, dimension ( K ). */
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/* On entry, DIFL(I) is the distance between I-th updated */
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/* (undeflated) singular value and the I-th (undeflated) old */
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/* singular value. */
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/* DIFR (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). */
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/* On entry, DIFR(I, 1) contains the distances between I-th */
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/* updated (undeflated) singular value and the I+1-th */
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/* (undeflated) old singular value. And DIFR(I, 2) is the */
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/* normalizing factor for the I-th right singular vector. */
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/* Z (input) DOUBLE PRECISION array, dimension ( K ) */
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/* Contain the components of the deflation-adjusted updating row */
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/* vector. */
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/* K (input) INTEGER */
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/* Contains the dimension of the non-deflated matrix, */
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/* This is the order of the related secular equation. 1 <= K <=N. */
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/* C (input) DOUBLE PRECISION */
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/* C contains garbage if SQRE =0 and the C-value of a Givens */
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/* rotation related to the right null space if SQRE = 1. */
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/* S (input) DOUBLE PRECISION */
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/* S contains garbage if SQRE =0 and the S-value of a Givens */
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/* rotation related to the right null space if SQRE = 1. */
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/* WORK (workspace) DOUBLE PRECISION array, dimension ( K ) */
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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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/* Ming Gu and Ren-Cang Li, Computer Science Division, University of */
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/* California at Berkeley, USA */
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/* Osni Marques, LBNL/NERSC, 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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/* .. External Functions .. */
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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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b_dim1 = *ldb;
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b_offset = 1 + b_dim1;
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b -= b_offset;
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bx_dim1 = *ldbx;
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bx_offset = 1 + bx_dim1;
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bx -= bx_offset;
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--perm;
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givcol_dim1 = *ldgcol;
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givcol_offset = 1 + givcol_dim1;
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givcol -= givcol_offset;
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difr_dim1 = *ldgnum;
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difr_offset = 1 + difr_dim1;
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difr -= difr_offset;
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poles_dim1 = *ldgnum;
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poles_offset = 1 + poles_dim1;
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poles -= poles_offset;
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givnum_dim1 = *ldgnum;
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givnum_offset = 1 + givnum_dim1;
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givnum -= givnum_offset;
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--difl;
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--z__;
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--work;
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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 (*nl < 1) {
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*info = -2;
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} else if (*nr < 1) {
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*info = -3;
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} else if (*sqre < 0 || *sqre > 1) {
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*info = -4;
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}
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n = *nl + *nr + 1;
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if (*nrhs < 1) {
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*info = -5;
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} else if (*ldb < n) {
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*info = -7;
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} else if (*ldbx < n) {
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*info = -9;
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} else if (*givptr < 0) {
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*info = -11;
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} else if (*ldgcol < n) {
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*info = -13;
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} else if (*ldgnum < n) {
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*info = -15;
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} else if (*k < 1) {
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*info = -20;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DLALS0", &i__1);
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return 0;
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}
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m = n + *sqre;
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nlp1 = *nl + 1;
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if (*icompq == 0) {
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/* Apply back orthogonal transformations from the left. */
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/* Step (1L): apply back the Givens rotations performed. */
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i__1 = *givptr;
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for (i__ = 1; i__ <= i__1; ++i__) {
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drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, &
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b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ +
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(givnum_dim1 << 1)], &givnum[i__ + givnum_dim1]);
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/* L10: */
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}
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/* Step (2L): permute rows of B. */
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dcopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx);
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i__1 = n;
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for (i__ = 2; i__ <= i__1; ++i__) {
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dcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1],
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ldbx);
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/* L20: */
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}
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/* Step (3L): apply the inverse of the left singular vector */
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/* matrix to BX. */
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if (*k == 1) {
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dcopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb);
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if (z__[1] < 0.) {
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dscal_(nrhs, &c_b5, &b[b_offset], ldb);
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}
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} else {
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i__1 = *k;
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for (j = 1; j <= i__1; ++j) {
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diflj = difl[j];
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dj = poles[j + poles_dim1];
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dsigj = -poles[j + (poles_dim1 << 1)];
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if (j < *k) {
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difrj = -difr[j + difr_dim1];
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dsigjp = -poles[j + 1 + (poles_dim1 << 1)];
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}
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if (z__[j] == 0. || poles[j + (poles_dim1 << 1)] == 0.) {
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work[j] = 0.;
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} else {
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work[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj /
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(poles[j + (poles_dim1 << 1)] + dj);
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}
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i__2 = j - 1;
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for (i__ = 1; i__ <= i__2; ++i__) {
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if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] ==
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0.) {
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work[i__] = 0.;
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} else {
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work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__]
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/ (dlamc3_(&poles[i__ + (poles_dim1 << 1)], &
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dsigj) - diflj) / (poles[i__ + (poles_dim1 <<
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1)] + dj);
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}
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/* L30: */
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}
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i__2 = *k;
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for (i__ = j + 1; i__ <= i__2; ++i__) {
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if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] ==
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0.) {
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work[i__] = 0.;
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} else {
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work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__]
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/ (dlamc3_(&poles[i__ + (poles_dim1 << 1)], &
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dsigjp) + difrj) / (poles[i__ + (poles_dim1 <<
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1)] + dj);
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}
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/* L40: */
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}
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work[1] = -1.;
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temp = dnrm2_(k, &work[1], &c__1);
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dgemv_("T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], &
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c__1, &c_b13, &b[j + b_dim1], ldb);
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dlascl_("G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j +
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b_dim1], ldb, info);
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/* L50: */
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}
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}
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/* Move the deflated rows of BX to B also. */
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if (*k < max(m,n)) {
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i__1 = n - *k;
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dlacpy_("A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1
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+ b_dim1], ldb);
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}
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} else {
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/* Apply back the right orthogonal transformations. */
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/* Step (1R): apply back the new right singular vector matrix */
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/* to B. */
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if (*k == 1) {
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dcopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx);
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} else {
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i__1 = *k;
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for (j = 1; j <= i__1; ++j) {
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dsigj = poles[j + (poles_dim1 << 1)];
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if (z__[j] == 0.) {
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work[j] = 0.;
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} else {
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work[j] = -z__[j] / difl[j] / (dsigj + poles[j +
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poles_dim1]) / difr[j + (difr_dim1 << 1)];
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}
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i__2 = j - 1;
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for (i__ = 1; i__ <= i__2; ++i__) {
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if (z__[j] == 0.) {
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work[i__] = 0.;
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} else {
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d__1 = -poles[i__ + 1 + (poles_dim1 << 1)];
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work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[
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i__ + difr_dim1]) / (dsigj + poles[i__ +
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poles_dim1]) / difr[i__ + (difr_dim1 << 1)];
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}
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/* L60: */
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}
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i__2 = *k;
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for (i__ = j + 1; i__ <= i__2; ++i__) {
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if (z__[j] == 0.) {
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work[i__] = 0.;
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} else {
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d__1 = -poles[i__ + (poles_dim1 << 1)];
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work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[
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i__]) / (dsigj + poles[i__ + poles_dim1]) /
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difr[i__ + (difr_dim1 << 1)];
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}
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/* L70: */
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}
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dgemv_("T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], &
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c__1, &c_b13, &bx[j + bx_dim1], ldbx);
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/* L80: */
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}
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}
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/* Step (2R): if SQRE = 1, apply back the rotation that is */
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/* related to the right null space of the subproblem. */
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if (*sqre == 1) {
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dcopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx);
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drot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__,
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s);
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}
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if (*k < max(m,n)) {
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i__1 = n - *k;
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dlacpy_("A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 +
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bx_dim1], ldbx);
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}
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/* Step (3R): permute rows of B. */
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dcopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb);
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if (*sqre == 1) {
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dcopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb);
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}
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i__1 = n;
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for (i__ = 2; i__ <= i__1; ++i__) {
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dcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1],
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ldb);
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/* L90: */
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}
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/* Step (4R): apply back the Givens rotations performed. */
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for (i__ = *givptr; i__ >= 1; --i__) {
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d__1 = -givnum[i__ + givnum_dim1];
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drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, &
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b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ +
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(givnum_dim1 << 1)], &d__1);
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/* L100: */
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}
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}
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return 0;
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/* End of DLALS0 */
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} /* dlals0_ */
|