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454 lines
14 KiB
454 lines
14 KiB
/* slalsa.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_b7 = 1.f; |
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static real c_b8 = 0.f; |
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static integer c__2 = 2; |
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/* Subroutine */ int slalsa_(integer *icompq, integer *smlsiz, integer *n, |
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integer *nrhs, real *b, integer *ldb, real *bx, integer *ldbx, real * |
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u, integer *ldu, real *vt, integer *k, real *difl, real *difr, real * |
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z__, real *poles, integer *givptr, integer *givcol, integer *ldgcol, |
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integer *perm, real *givnum, real *c__, real *s, 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 givcol_dim1, givcol_offset, perm_dim1, perm_offset, b_dim1, |
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b_offset, bx_dim1, bx_offset, difl_dim1, difl_offset, difr_dim1, |
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difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset, |
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u_dim1, u_offset, vt_dim1, vt_offset, z_dim1, z_offset, i__1, |
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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__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl, ndb1, |
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nlp1, lvl2, nrp1, nlvl, sqre, inode, ndiml; |
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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 ndimr; |
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extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, |
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integer *), slals0_(integer *, integer *, integer *, integer *, |
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integer *, real *, integer *, real *, integer *, integer *, |
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integer *, integer *, integer *, real *, integer *, real *, real * |
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, real *, real *, integer *, real *, real *, real *, integer *), |
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xerbla_(char *, integer *), slasdt_(integer *, integer *, |
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integer *, integer *, integer *, integer *, 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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/* SLALSA is an itermediate step in solving the least squares problem */ |
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/* by computing the SVD of the coefficient matrix in compact form (The */ |
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/* singular vectors are computed as products of simple orthorgonal */ |
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/* matrices.). */ |
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/* If ICOMPQ = 0, SLALSA applies the inverse of the left singular vector */ |
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/* matrix of an upper bidiagonal matrix to the right hand side; and if */ |
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/* ICOMPQ = 1, SLALSA applies the right singular vector matrix to the */ |
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/* right hand side. The singular vector matrices were generated in */ |
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/* compact form by SLALSA. */ |
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/* Arguments */ |
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/* ========= */ |
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/* ICOMPQ (input) INTEGER */ |
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/* Specifies whether the left or the right singular vector */ |
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/* matrix is involved. */ |
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/* = 0: Left singular vector matrix */ |
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/* = 1: Right singular vector matrix */ |
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/* SMLSIZ (input) INTEGER */ |
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/* The maximum size of the subproblems at the bottom of the */ |
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/* computation tree. */ |
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/* N (input) INTEGER */ |
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/* The row and column dimensions of the upper bidiagonal matrix. */ |
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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) REAL 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. */ |
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/* On output, B contains the solution X in rows 1 through N. */ |
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/* LDB (input) INTEGER */ |
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/* The leading dimension of B in the calling subprogram. */ |
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/* LDB must be at least max(1,MAX( M, N ) ). */ |
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/* BX (output) REAL array, dimension ( LDBX, NRHS ) */ |
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/* On exit, the result of applying the left or right singular */ |
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/* vector matrix to B. */ |
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/* LDBX (input) INTEGER */ |
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/* The leading dimension of BX. */ |
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/* U (input) REAL array, dimension ( LDU, SMLSIZ ). */ |
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/* On entry, U contains the left singular vector matrices of all */ |
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/* subproblems at the bottom level. */ |
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/* LDU (input) INTEGER, LDU = > N. */ |
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/* The leading dimension of arrays U, VT, DIFL, DIFR, */ |
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/* POLES, GIVNUM, and Z. */ |
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/* VT (input) REAL array, dimension ( LDU, SMLSIZ+1 ). */ |
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/* On entry, VT' contains the right singular vector matrices of */ |
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/* all subproblems at the bottom level. */ |
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/* K (input) INTEGER array, dimension ( N ). */ |
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/* DIFL (input) REAL array, dimension ( LDU, NLVL ). */ |
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/* where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. */ |
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/* DIFR (input) REAL array, dimension ( LDU, 2 * NLVL ). */ |
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/* On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record */ |
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/* distances between singular values on the I-th level and */ |
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/* singular values on the (I -1)-th level, and DIFR(*, 2 * I) */ |
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/* record the normalizing factors of the right singular vectors */ |
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/* matrices of subproblems on I-th level. */ |
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/* Z (input) REAL array, dimension ( LDU, NLVL ). */ |
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/* On entry, Z(1, I) contains the components of the deflation- */ |
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/* adjusted updating row vector for subproblems on the I-th */ |
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/* level. */ |
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/* POLES (input) REAL array, dimension ( LDU, 2 * NLVL ). */ |
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/* On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old */ |
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/* singular values involved in the secular equations on the I-th */ |
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/* level. */ |
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/* GIVPTR (input) INTEGER array, dimension ( N ). */ |
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/* On entry, GIVPTR( I ) records the number of Givens */ |
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/* rotations performed on the I-th problem on the computation */ |
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/* tree. */ |
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/* GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ). */ |
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/* On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the */ |
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/* locations of Givens rotations performed on the I-th level on */ |
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/* the computation tree. */ |
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/* LDGCOL (input) INTEGER, LDGCOL = > N. */ |
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/* The leading dimension of arrays GIVCOL and PERM. */ |
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/* PERM (input) INTEGER array, dimension ( LDGCOL, NLVL ). */ |
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/* On entry, PERM(*, I) records permutations done on the I-th */ |
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/* level of the computation tree. */ |
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/* GIVNUM (input) REAL array, dimension ( LDU, 2 * NLVL ). */ |
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/* On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S- */ |
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/* values of Givens rotations performed on the I-th level on the */ |
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/* computation tree. */ |
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/* C (input) REAL array, dimension ( N ). */ |
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/* On entry, if the I-th subproblem is not square, */ |
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/* C( I ) contains the C-value of a Givens rotation related to */ |
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/* the right null space of the I-th subproblem. */ |
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/* S (input) REAL array, dimension ( N ). */ |
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/* On entry, if the I-th subproblem is not square, */ |
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/* S( I ) contains the S-value of a Givens rotation related to */ |
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/* the right null space of the I-th subproblem. */ |
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/* WORK (workspace) REAL array. */ |
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/* The dimension must be at least N. */ |
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/* IWORK (workspace) INTEGER array. */ |
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/* The dimension must be at least 3 * 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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/* 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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/* .. 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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givnum_dim1 = *ldu; |
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givnum_offset = 1 + givnum_dim1; |
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givnum -= givnum_offset; |
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poles_dim1 = *ldu; |
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poles_offset = 1 + poles_dim1; |
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poles -= poles_offset; |
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z_dim1 = *ldu; |
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z_offset = 1 + z_dim1; |
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z__ -= z_offset; |
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difr_dim1 = *ldu; |
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difr_offset = 1 + difr_dim1; |
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difr -= difr_offset; |
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difl_dim1 = *ldu; |
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difl_offset = 1 + difl_dim1; |
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difl -= difl_offset; |
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vt_dim1 = *ldu; |
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vt_offset = 1 + vt_dim1; |
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vt -= vt_offset; |
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u_dim1 = *ldu; |
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u_offset = 1 + u_dim1; |
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u -= u_offset; |
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--k; |
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--givptr; |
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perm_dim1 = *ldgcol; |
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perm_offset = 1 + perm_dim1; |
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perm -= perm_offset; |
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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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--c__; |
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--s; |
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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 (*smlsiz < 3) { |
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*info = -2; |
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} else if (*n < *smlsiz) { |
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*info = -3; |
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} else if (*nrhs < 1) { |
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*info = -4; |
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} else if (*ldb < *n) { |
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*info = -6; |
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} else if (*ldbx < *n) { |
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*info = -8; |
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} else if (*ldu < *n) { |
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*info = -10; |
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} else if (*ldgcol < *n) { |
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*info = -19; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("SLALSA", &i__1); |
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return 0; |
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} |
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/* Book-keeping and setting up the computation tree. */ |
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inode = 1; |
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ndiml = inode + *n; |
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ndimr = ndiml + *n; |
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slasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], |
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smlsiz); |
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/* The following code applies back the left singular vector factors. */ |
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/* For applying back the right singular vector factors, go to 50. */ |
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if (*icompq == 1) { |
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goto L50; |
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} |
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/* The nodes on the bottom level of the tree were solved */ |
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/* by SLASDQ. The corresponding left and right singular vector */ |
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/* matrices are in explicit form. First apply back the left */ |
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/* singular vector matrices. */ |
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ndb1 = (nd + 1) / 2; |
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i__1 = nd; |
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for (i__ = ndb1; i__ <= i__1; ++i__) { |
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/* IC : center row of each node */ |
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/* NL : number of rows of left subproblem */ |
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/* NR : number of rows of right subproblem */ |
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/* NLF: starting row of the left subproblem */ |
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/* NRF: starting row of the right subproblem */ |
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i1 = i__ - 1; |
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ic = iwork[inode + i1]; |
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nl = iwork[ndiml + i1]; |
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nr = iwork[ndimr + i1]; |
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nlf = ic - nl; |
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nrf = ic + 1; |
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sgemm_("T", "N", &nl, nrhs, &nl, &c_b7, &u[nlf + u_dim1], ldu, &b[nlf |
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+ b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx); |
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sgemm_("T", "N", &nr, nrhs, &nr, &c_b7, &u[nrf + u_dim1], ldu, &b[nrf |
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+ b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx); |
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/* L10: */ |
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} |
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/* Next copy the rows of B that correspond to unchanged rows */ |
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/* in the bidiagonal matrix to BX. */ |
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i__1 = nd; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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ic = iwork[inode + i__ - 1]; |
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scopy_(nrhs, &b[ic + b_dim1], ldb, &bx[ic + bx_dim1], ldbx); |
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/* L20: */ |
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} |
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/* Finally go through the left singular vector matrices of all */ |
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/* the other subproblems bottom-up on the tree. */ |
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j = pow_ii(&c__2, &nlvl); |
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sqre = 0; |
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for (lvl = nlvl; lvl >= 1; --lvl) { |
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lvl2 = (lvl << 1) - 1; |
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/* find the first node LF and last node LL on */ |
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/* the current level LVL */ |
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if (lvl == 1) { |
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lf = 1; |
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ll = 1; |
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} else { |
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i__1 = lvl - 1; |
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lf = pow_ii(&c__2, &i__1); |
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ll = (lf << 1) - 1; |
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} |
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i__1 = ll; |
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for (i__ = lf; i__ <= i__1; ++i__) { |
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im1 = i__ - 1; |
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ic = iwork[inode + im1]; |
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nl = iwork[ndiml + im1]; |
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nr = iwork[ndimr + im1]; |
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nlf = ic - nl; |
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nrf = ic + 1; |
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--j; |
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slals0_(icompq, &nl, &nr, &sqre, nrhs, &bx[nlf + bx_dim1], ldbx, & |
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b[nlf + b_dim1], ldb, &perm[nlf + lvl * perm_dim1], & |
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givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, & |
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givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * |
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poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + |
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lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[ |
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j], &s[j], &work[1], info); |
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/* L30: */ |
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} |
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/* L40: */ |
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} |
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goto L90; |
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/* ICOMPQ = 1: applying back the right singular vector factors. */ |
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L50: |
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/* First now go through the right singular vector matrices of all */ |
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/* the tree nodes top-down. */ |
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j = 0; |
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i__1 = nlvl; |
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for (lvl = 1; lvl <= i__1; ++lvl) { |
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lvl2 = (lvl << 1) - 1; |
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/* Find the first node LF and last node LL on */ |
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/* the current level LVL. */ |
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if (lvl == 1) { |
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lf = 1; |
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ll = 1; |
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} else { |
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i__2 = lvl - 1; |
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lf = pow_ii(&c__2, &i__2); |
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ll = (lf << 1) - 1; |
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} |
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i__2 = lf; |
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for (i__ = ll; i__ >= i__2; --i__) { |
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im1 = i__ - 1; |
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ic = iwork[inode + im1]; |
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nl = iwork[ndiml + im1]; |
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nr = iwork[ndimr + im1]; |
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nlf = ic - nl; |
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nrf = ic + 1; |
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if (i__ == ll) { |
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sqre = 0; |
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} else { |
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sqre = 1; |
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} |
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++j; |
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slals0_(icompq, &nl, &nr, &sqre, nrhs, &b[nlf + b_dim1], ldb, &bx[ |
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nlf + bx_dim1], ldbx, &perm[nlf + lvl * perm_dim1], & |
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givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, & |
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givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * |
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poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + |
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lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[ |
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j], &s[j], &work[1], info); |
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/* L60: */ |
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} |
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/* L70: */ |
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} |
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/* The nodes on the bottom level of the tree were solved */ |
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/* by SLASDQ. The corresponding right singular vector */ |
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/* matrices are in explicit form. Apply them back. */ |
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ndb1 = (nd + 1) / 2; |
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i__1 = nd; |
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for (i__ = ndb1; i__ <= i__1; ++i__) { |
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i1 = i__ - 1; |
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ic = iwork[inode + i1]; |
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nl = iwork[ndiml + i1]; |
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nr = iwork[ndimr + i1]; |
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nlp1 = nl + 1; |
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if (i__ == nd) { |
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nrp1 = nr; |
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} else { |
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nrp1 = nr + 1; |
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} |
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nlf = ic - nl; |
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nrf = ic + 1; |
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sgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b7, &vt[nlf + vt_dim1], ldu, & |
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b[nlf + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx); |
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sgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b7, &vt[nrf + vt_dim1], ldu, & |
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b[nrf + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx); |
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/* L80: */ |
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} |
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L90: |
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return 0; |
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/* End of SLALSA */ |
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} /* slalsa_ */
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