"atomic bomb" commit. Reorganized OpenCV directory structure
This commit is contained in:
Vadim Pisarevsky
475
3rdparty/lapack/dlasda.c
vendored
Normal file
475
3rdparty/lapack/dlasda.c
vendored
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@@ -0,0 +1,475 @@
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#include "clapack.h"
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/* Table of constant values */
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static integer c__0 = 0;
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static doublereal c_b11 = 0.;
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static doublereal c_b12 = 1.;
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static integer c__1 = 1;
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static integer c__2 = 2;
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/* Subroutine */ int dlasda_(integer *icompq, integer *smlsiz, integer *n,
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integer *sqre, doublereal *d__, doublereal *e, doublereal *u, integer
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*ldu, doublereal *vt, integer *k, doublereal *difl, doublereal *difr,
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doublereal *z__, doublereal *poles, integer *givptr, integer *givcol,
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integer *ldgcol, integer *perm, doublereal *givnum, doublereal *c__,
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doublereal *s, doublereal *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, difl_dim1,
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difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset,
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poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset,
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z_dim1, z_offset, i__1, 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, m, i1, ic, lf, nd, ll, nl, vf, nr, vl, im1, ncc, nlf, nrf,
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vfi, iwk, vli, lvl, nru, ndb1, nlp1, lvl2, nrp1;
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doublereal beta;
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integer idxq, nlvl;
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doublereal alpha;
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integer inode, ndiml, ndimr, idxqi, itemp;
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extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
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doublereal *, integer *);
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integer sqrei;
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extern /* Subroutine */ int dlasd6_(integer *, integer *, integer *,
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integer *, doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *, integer *, integer *, integer *, integer *,
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integer *, doublereal *, integer *, doublereal *, doublereal *,
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doublereal *, doublereal *, integer *, doublereal *, doublereal *,
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doublereal *, integer *, integer *);
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integer nwork1, nwork2;
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extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer
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*, integer *, integer *, doublereal *, doublereal *, doublereal *,
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integer *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, integer *), dlasdt_(integer *, integer *,
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integer *, integer *, integer *, integer *, integer *), dlaset_(
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char *, integer *, integer *, doublereal *, doublereal *,
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doublereal *, integer *), xerbla_(char *, integer *);
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integer smlszp;
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/* -- LAPACK auxiliary 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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/* Using a divide and conquer approach, DLASDA computes the singular */
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/* value decomposition (SVD) of a real upper bidiagonal N-by-M matrix */
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/* B with diagonal D and offdiagonal E, where M = N + SQRE. The */
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/* algorithm computes the singular values in the SVD B = U * S * VT. */
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/* The orthogonal matrices U and VT are optionally computed in */
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/* compact form. */
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/* A related subroutine, DLASD0, computes the singular values and */
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/* the singular vectors in explicit form. */
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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 */
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/* in compact form, as follows */
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/* = 0: Compute singular values only. */
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/* = 1: Compute singular vectors of upper bidiagonal */
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/* matrix in compact form. */
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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 dimension of the upper bidiagonal matrix. This is */
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/* also the dimension of the main diagonal array D. */
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/* SQRE (input) INTEGER */
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/* Specifies the column dimension of the bidiagonal matrix. */
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/* = 0: The bidiagonal matrix has column dimension M = N; */
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/* = 1: The bidiagonal matrix has column dimension M = N + 1. */
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/* D (input/output) DOUBLE PRECISION array, dimension ( N ) */
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/* On entry D contains the main diagonal of the bidiagonal */
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/* matrix. On exit D, if INFO = 0, contains its singular values. */
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/* E (input) DOUBLE PRECISION array, dimension ( M-1 ) */
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/* Contains the subdiagonal entries of the bidiagonal matrix. */
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/* On exit, E has been destroyed. */
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/* U (output) DOUBLE PRECISION array, */
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/* dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced */
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/* if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left */
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/* singular vector matrices of all subproblems at the bottom */
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/* level. */
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/* LDU (input) INTEGER, LDU = > N. */
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/* The leading dimension of arrays U, VT, DIFL, DIFR, POLES, */
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/* GIVNUM, and Z. */
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/* VT (output) DOUBLE PRECISION array, */
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/* dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced */
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/* if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT' contains the right */
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/* singular vector matrices of all subproblems at the bottom */
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/* level. */
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/* K (output) INTEGER array, */
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/* dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. */
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/* If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th */
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/* secular equation on the computation tree. */
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/* DIFL (output) DOUBLE PRECISION array, dimension ( LDU, NLVL ), */
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/* where NLVL = floor(log_2 (N/SMLSIZ))). */
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/* DIFR (output) DOUBLE PRECISION array, */
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/* dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and */
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/* dimension ( N ) if ICOMPQ = 0. */
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/* If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) */
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/* record distances between singular values on the I-th */
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/* level and singular values on the (I -1)-th level, and */
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/* DIFR(1:N, 2 * I ) contains the normalizing factors for */
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/* the right singular vector matrix. See DLASD8 for details. */
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/* Z (output) DOUBLE PRECISION array, */
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/* dimension ( LDU, NLVL ) if ICOMPQ = 1 and */
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/* dimension ( N ) if ICOMPQ = 0. */
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/* The first K elements of Z(1, I) contain the components of */
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/* the deflation-adjusted updating row vector for subproblems */
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/* on the I-th level. */
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/* POLES (output) DOUBLE PRECISION array, */
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/* dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced */
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/* if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and */
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/* POLES(1, 2*I) contain the new and old singular values */
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/* involved in the secular equations on the I-th level. */
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/* GIVPTR (output) INTEGER array, */
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/* dimension ( N ) if ICOMPQ = 1, and not referenced if */
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/* ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records */
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/* the number of Givens rotations performed on the I-th */
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/* problem on the computation tree. */
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/* GIVCOL (output) INTEGER array, */
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/* dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not */
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/* referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */
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/* GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations */
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/* of Givens rotations performed on the I-th level on the */
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/* 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 (output) INTEGER array, */
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/* dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced */
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/* if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records */
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/* permutations done on the I-th level of the computation tree. */
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/* GIVNUM (output) DOUBLE PRECISION array, */
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/* dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not */
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/* referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */
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/* GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- */
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/* values of Givens rotations performed on the I-th level on */
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/* the computation tree. */
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/* C (output) DOUBLE PRECISION array, */
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/* dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. */
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/* If ICOMPQ = 1 and the I-th subproblem is not square, on exit, */
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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 (output) DOUBLE PRECISION array, dimension ( N ) if */
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/* ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 */
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/* and the I-th subproblem is not square, on exit, S( I ) */
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/* 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, dimension */
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/* (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). */
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/* IWORK (workspace) INTEGER array. */
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/* Dimension must be at least (7 * N). */
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/* INFO (output) INTEGER */
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/* = 0: successful exit. */
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/* < 0: if INFO = -i, the i-th argument had an illegal value. */
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/* > 0: if INFO = 1, an singular value did not converge */
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/* Further Details */
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/* =============== */
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/* Based on contributions by */
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/* Ming Gu and Huan Ren, Computer Science Division, University of */
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/* California at Berkeley, USA */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External 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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--d__;
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--e;
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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 < 0) {
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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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} else if (*ldu < *n + *sqre) {
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*info = -8;
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} else if (*ldgcol < *n) {
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*info = -17;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DLASDA", &i__1);
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return 0;
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}
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m = *n + *sqre;
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/* If the input matrix is too small, call DLASDQ to find the SVD. */
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if (*n <= *smlsiz) {
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if (*icompq == 0) {
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dlasdq_("U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[
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vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, &
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work[1], info);
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} else {
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dlasdq_("U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset]
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, ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1],
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info);
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}
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return 0;
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}
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/* Book-keeping and set 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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idxq = ndimr + *n;
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iwk = idxq + *n;
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ncc = 0;
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nru = 0;
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smlszp = *smlsiz + 1;
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vf = 1;
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vl = vf + m;
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nwork1 = vl + m;
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nwork2 = nwork1 + smlszp * smlszp;
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dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr],
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smlsiz);
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/* for the nodes on bottom level of the tree, solve */
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/* their subproblems by DLASDQ. */
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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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nlp1 = nl + 1;
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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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idxqi = idxq + nlf - 2;
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vfi = vf + nlf - 1;
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vli = vl + nlf - 1;
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sqrei = 1;
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if (*icompq == 0) {
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dlaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp);
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dlasdq_("U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], &
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work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2],
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&nl, &work[nwork2], info);
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itemp = nwork1 + nl * smlszp;
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dcopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1);
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dcopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1);
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} else {
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dlaset_("A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu);
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dlaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1],
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ldu);
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dlasdq_("U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], &
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vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf +
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u_dim1], ldu, &work[nwork1], info);
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dcopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1);
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dcopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1)
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;
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}
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if (*info != 0) {
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return 0;
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}
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i__2 = nl;
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for (j = 1; j <= i__2; ++j) {
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iwork[idxqi + j] = j;
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/* L10: */
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}
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if (i__ == nd && *sqre == 0) {
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sqrei = 0;
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} else {
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sqrei = 1;
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}
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idxqi += nlp1;
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vfi += nlp1;
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vli += nlp1;
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nrp1 = nr + sqrei;
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if (*icompq == 0) {
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dlaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp);
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dlasdq_("U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], &
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work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2],
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&nr, &work[nwork2], info);
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itemp = nwork1 + (nrp1 - 1) * smlszp;
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dcopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1);
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dcopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1);
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} else {
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dlaset_("A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu);
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dlaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1],
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ldu);
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dlasdq_("U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], &
|
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vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf +
|
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u_dim1], ldu, &work[nwork1], info);
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dcopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1);
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dcopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1)
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;
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}
|
||||
if (*info != 0) {
|
||||
return 0;
|
||||
}
|
||||
i__2 = nr;
|
||||
for (j = 1; j <= i__2; ++j) {
|
||||
iwork[idxqi + j] = j;
|
||||
/* L20: */
|
||||
}
|
||||
/* L30: */
|
||||
}
|
||||
|
||||
/* Now conquer each subproblem bottom-up. */
|
||||
|
||||
j = pow_ii(&c__2, &nlvl);
|
||||
for (lvl = nlvl; lvl >= 1; --lvl) {
|
||||
lvl2 = (lvl << 1) - 1;
|
||||
|
||||
/* Find the first node LF and last node LL on */
|
||||
/* the current level LVL. */
|
||||
|
||||
if (lvl == 1) {
|
||||
lf = 1;
|
||||
ll = 1;
|
||||
} else {
|
||||
i__1 = lvl - 1;
|
||||
lf = pow_ii(&c__2, &i__1);
|
||||
ll = (lf << 1) - 1;
|
||||
}
|
||||
i__1 = ll;
|
||||
for (i__ = lf; i__ <= i__1; ++i__) {
|
||||
im1 = i__ - 1;
|
||||
ic = iwork[inode + im1];
|
||||
nl = iwork[ndiml + im1];
|
||||
nr = iwork[ndimr + im1];
|
||||
nlf = ic - nl;
|
||||
nrf = ic + 1;
|
||||
if (i__ == ll) {
|
||||
sqrei = *sqre;
|
||||
} else {
|
||||
sqrei = 1;
|
||||
}
|
||||
vfi = vf + nlf - 1;
|
||||
vli = vl + nlf - 1;
|
||||
idxqi = idxq + nlf - 1;
|
||||
alpha = d__[ic];
|
||||
beta = e[ic];
|
||||
if (*icompq == 0) {
|
||||
dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &
|
||||
work[vli], &alpha, &beta, &iwork[idxqi], &perm[
|
||||
perm_offset], &givptr[1], &givcol[givcol_offset],
|
||||
ldgcol, &givnum[givnum_offset], ldu, &poles[
|
||||
poles_offset], &difl[difl_offset], &difr[difr_offset],
|
||||
&z__[z_offset], &k[1], &c__[1], &s[1], &work[nwork1],
|
||||
&iwork[iwk], info);
|
||||
} else {
|
||||
--j;
|
||||
dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &
|
||||
work[vli], &alpha, &beta, &iwork[idxqi], &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[nwork1], &iwork[iwk], info);
|
||||
}
|
||||
if (*info != 0) {
|
||||
return 0;
|
||||
}
|
||||
/* L40: */
|
||||
}
|
||||
/* L50: */
|
||||
}
|
||||
|
||||
return 0;
|
||||
|
||||
/* End of DLASDA */
|
||||
|
||||
} /* dlasda_ */
|
||||
Reference in New Issue
Block a user