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Open Source Computer Vision Library
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444 lines
14 KiB
444 lines
14 KiB
15 years ago
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#include "clapack.h"
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/* Table of constant values */
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static doublereal c_b7 = 1.;
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static doublereal c_b8 = 0.;
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static integer c__2 = 2;
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/* Subroutine */ int dlalsa_(integer *icompq, integer *smlsiz, integer *n,
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integer *nrhs, doublereal *b, integer *ldb, doublereal *bx, integer *
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ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *k,
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doublereal *difl, doublereal *difr, doublereal *z__, doublereal *
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poles, integer *givptr, integer *givcol, integer *ldgcol, integer *
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perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal *
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work, integer *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;
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extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
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integer *, doublereal *, doublereal *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, integer *);
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integer inode, ndiml, ndimr;
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extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
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doublereal *, integer *), dlals0_(integer *, integer *, integer *,
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integer *, integer *, doublereal *, integer *, doublereal *,
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integer *, integer *, integer *, integer *, integer *, doublereal
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*, integer *, doublereal *, doublereal *, doublereal *,
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doublereal *, integer *, doublereal *, doublereal *, doublereal *,
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integer *), dlasdt_(integer *, integer *, integer *, integer *,
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integer *, integer *, integer *), xerbla_(char *, integer *);
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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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/* DLALSA 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, DLALSA 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, DLALSA 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 DLALSA. */
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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) 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. */
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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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension ( LDU, NLVL ). */
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/* where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. */
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/* DIFR (input) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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_("DLALSA", &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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dlasdt_(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 DLASDQ. 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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dgemm_("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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dgemm_("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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dcopy_(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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dlals0_(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;
|
||
|
} else {
|
||
|
sqre = 1;
|
||
|
}
|
||
|
++j;
|
||
|
dlals0_(icompq, &nl, &nr, &sqre, nrhs, &b[nlf + b_dim1], ldb, &bx[
|
||
|
nlf + bx_dim1], ldbx, &perm[nlf + lvl * perm_dim1], &
|
||
|
givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, &
|
||
|
givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 *
|
||
|
poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf +
|
||
|
lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[
|
||
|
j], &s[j], &work[1], info);
|
||
|
/* L60: */
|
||
|
}
|
||
|
/* L70: */
|
||
|
}
|
||
|
|
||
|
/* The nodes on the bottom level of the tree were solved */
|
||
|
/* by DLASDQ. The corresponding right singular vector */
|
||
|
/* matrices are in explicit form. Apply them back. */
|
||
|
|
||
|
ndb1 = (nd + 1) / 2;
|
||
|
i__1 = nd;
|
||
|
for (i__ = ndb1; i__ <= i__1; ++i__) {
|
||
|
i1 = i__ - 1;
|
||
|
ic = iwork[inode + i1];
|
||
|
nl = iwork[ndiml + i1];
|
||
|
nr = iwork[ndimr + i1];
|
||
|
nlp1 = nl + 1;
|
||
|
if (i__ == nd) {
|
||
|
nrp1 = nr;
|
||
|
} else {
|
||
|
nrp1 = nr + 1;
|
||
|
}
|
||
|
nlf = ic - nl;
|
||
|
nrf = ic + 1;
|
||
|
dgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b7, &vt[nlf + vt_dim1], ldu, &
|
||
|
b[nlf + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx);
|
||
|
dgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b7, &vt[nrf + vt_dim1], ldu, &
|
||
|
b[nrf + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx);
|
||
|
/* L80: */
|
||
|
}
|
||
|
|
||
|
L90:
|
||
|
|
||
|
return 0;
|
||
|
|
||
|
/* End of DLALSA */
|
||
|
|
||
|
} /* dlalsa_ */
|