mirror of https://github.com/opencv/opencv.git
Open Source Computer Vision Library
https://opencv.org/
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
352 lines
12 KiB
352 lines
12 KiB
15 years ago
|
#include "clapack.h"
|
||
|
|
|
||
|
|
/* Table of constant values */
|
||
|
|
|
||
|
|
static integer c__0 = 0;
|
||
|
|
static real c_b7 = 1.f;
|
||
|
|
static integer c__1 = 1;
|
||
|
|
static integer c_n1 = -1;
|
||
|
|
|
||
|
|
/* Subroutine */ int slasd6_(integer *icompq, integer *nl, integer *nr,
|
||
|
|
integer *sqre, real *d__, real *vf, real *vl, real *alpha, real *beta,
|
||
|
|
integer *idxq, integer *perm, integer *givptr, integer *givcol,
|
||
|
|
integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real *
|
||
|
|
difl, real *difr, real *z__, integer *k, real *c__, real *s, real *
|
||
|
|
work, integer *iwork, integer *info)
|
||
|
|
{
|
||
|
|
/* System generated locals */
|
||
|
|
integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset,
|
||
|
|
poles_dim1, poles_offset, i__1;
|
||
|
|
real r__1, r__2;
|
||
|
|
|
||
|
|
/* Local variables */
|
||
|
|
integer i__, m, n, n1, n2, iw, idx, idxc, idxp, ivfw, ivlw;
|
||
|
|
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
|
||
|
|
integer *), slasd7_(integer *, integer *, integer *, integer *,
|
||
|
|
integer *, real *, real *, real *, real *, real *, real *, real *,
|
||
|
|
real *, real *, real *, integer *, integer *, integer *, integer
|
||
|
|
*, integer *, integer *, integer *, real *, integer *, real *,
|
||
|
|
real *, integer *), slasd8_(integer *, integer *, real *, real *,
|
||
|
|
real *, real *, real *, real *, integer *, real *, real *,
|
||
|
|
integer *);
|
||
|
|
integer isigma;
|
||
|
|
extern /* Subroutine */ int xerbla_(char *, integer *), slascl_(
|
||
|
|
char *, integer *, integer *, real *, real *, integer *, integer *
|
||
|
|
, real *, integer *, integer *), slamrg_(integer *,
|
||
|
|
integer *, real *, integer *, integer *, integer *);
|
||
|
|
real orgnrm;
|
||
|
|
|
||
|
|
|
||
|
|
/* -- LAPACK auxiliary routine (version 3.1) -- */
|
||
|
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
|
||
|
|
/* November 2006 */
|
||
|
|
|
||
|
|
/* .. Scalar Arguments .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Array Arguments .. */
|
||
|
|
/* .. */
|
||
|
|
|
||
|
|
/* Purpose */
|
||
|
|
/* ======= */
|
||
|
|
|
||
|
|
/* SLASD6 computes the SVD of an updated upper bidiagonal matrix B */
|
||
|
|
/* obtained by merging two smaller ones by appending a row. This */
|
||
|
|
/* routine is used only for the problem which requires all singular */
|
||
|
|
/* values and optionally singular vector matrices in factored form. */
|
||
|
|
/* B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */
|
||
|
|
/* A related subroutine, SLASD1, handles the case in which all singular */
|
||
|
|
/* values and singular vectors of the bidiagonal matrix are desired. */
|
||
|
|
|
||
|
|
/* SLASD6 computes the SVD as follows: */
|
||
|
|
|
||
|
|
/* ( D1(in) 0 0 0 ) */
|
||
|
|
/* B = U(in) * ( Z1' a Z2' b ) * VT(in) */
|
||
|
|
/* ( 0 0 D2(in) 0 ) */
|
||
|
|
|
||
|
|
/* = U(out) * ( D(out) 0) * VT(out) */
|
||
|
|
|
||
|
|
/* where Z' = (Z1' a Z2' b) = u' VT', and u is a vector of dimension M */
|
||
|
|
/* with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */
|
||
|
|
/* elsewhere; and the entry b is empty if SQRE = 0. */
|
||
|
|
|
||
|
|
/* The singular values of B can be computed using D1, D2, the first */
|
||
|
|
/* components of all the right singular vectors of the lower block, and */
|
||
|
|
/* the last components of all the right singular vectors of the upper */
|
||
|
|
/* block. These components are stored and updated in VF and VL, */
|
||
|
|
/* respectively, in SLASD6. Hence U and VT are not explicitly */
|
||
|
|
/* referenced. */
|
||
|
|
|
||
|
|
/* The singular values are stored in D. The algorithm consists of two */
|
||
|
|
/* stages: */
|
||
|
|
|
||
|
|
/* The first stage consists of deflating the size of the problem */
|
||
|
|
/* when there are multiple singular values or if there is a zero */
|
||
|
|
/* in the Z vector. For each such occurence the dimension of the */
|
||
|
|
/* secular equation problem is reduced by one. This stage is */
|
||
|
|
/* performed by the routine SLASD7. */
|
||
|
|
|
||
|
|
/* The second stage consists of calculating the updated */
|
||
|
|
/* singular values. This is done by finding the roots of the */
|
||
|
|
/* secular equation via the routine SLASD4 (as called by SLASD8). */
|
||
|
|
/* This routine also updates VF and VL and computes the distances */
|
||
|
|
/* between the updated singular values and the old singular */
|
||
|
|
/* values. */
|
||
|
|
|
||
|
|
/* SLASD6 is called from SLASDA. */
|
||
|
|
|
||
|
|
/* Arguments */
|
||
|
|
/* ========= */
|
||
|
|
|
||
|
|
/* ICOMPQ (input) INTEGER */
|
||
|
|
/* Specifies whether singular vectors are to be computed in */
|
||
|
|
/* factored form: */
|
||
|
|
/* = 0: Compute singular values only. */
|
||
|
|
/* = 1: Compute singular vectors in factored form as well. */
|
||
|
|
|
||
|
|
/* NL (input) INTEGER */
|
||
|
|
/* The row dimension of the upper block. NL >= 1. */
|
||
|
|
|
||
|
|
/* NR (input) INTEGER */
|
||
|
|
/* The row dimension of the lower block. NR >= 1. */
|
||
|
|
|
||
|
|
/* SQRE (input) INTEGER */
|
||
|
|
/* = 0: the lower block is an NR-by-NR square matrix. */
|
||
|
|
/* = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */
|
||
|
|
|
||
|
|
/* The bidiagonal matrix has row dimension N = NL + NR + 1, */
|
||
|
|
/* and column dimension M = N + SQRE. */
|
||
|
|
|
||
|
|
/* D (input/output) REAL array, dimension (NL+NR+1). */
|
||
|
|
/* On entry D(1:NL,1:NL) contains the singular values of the */
|
||
|
|
/* upper block, and D(NL+2:N) contains the singular values */
|
||
|
|
/* of the lower block. On exit D(1:N) contains the singular */
|
||
|
|
/* values of the modified matrix. */
|
||
|
|
|
||
|
|
/* VF (input/output) REAL array, dimension (M) */
|
||
|
|
/* On entry, VF(1:NL+1) contains the first components of all */
|
||
|
|
/* right singular vectors of the upper block; and VF(NL+2:M) */
|
||
|
|
/* contains the first components of all right singular vectors */
|
||
|
|
/* of the lower block. On exit, VF contains the first components */
|
||
|
|
/* of all right singular vectors of the bidiagonal matrix. */
|
||
|
|
|
||
|
|
/* VL (input/output) REAL array, dimension (M) */
|
||
|
|
/* On entry, VL(1:NL+1) contains the last components of all */
|
||
|
|
/* right singular vectors of the upper block; and VL(NL+2:M) */
|
||
|
|
/* contains the last components of all right singular vectors of */
|
||
|
|
/* the lower block. On exit, VL contains the last components of */
|
||
|
|
/* all right singular vectors of the bidiagonal matrix. */
|
||
|
|
|
||
|
|
/* ALPHA (input/output) REAL */
|
||
|
|
/* Contains the diagonal element associated with the added row. */
|
||
|
|
|
||
|
|
/* BETA (input/output) REAL */
|
||
|
|
/* Contains the off-diagonal element associated with the added */
|
||
|
|
/* row. */
|
||
|
|
|
||
|
|
/* IDXQ (output) INTEGER array, dimension (N) */
|
||
|
|
/* This contains the permutation which will reintegrate the */
|
||
|
|
/* subproblem just solved back into sorted order, i.e. */
|
||
|
|
/* D( IDXQ( I = 1, N ) ) will be in ascending order. */
|
||
|
|
|
||
|
|
/* PERM (output) INTEGER array, dimension ( N ) */
|
||
|
|
/* The permutations (from deflation and sorting) to be applied */
|
||
|
|
/* to each block. Not referenced if ICOMPQ = 0. */
|
||
|
|
|
||
|
|
/* GIVPTR (output) INTEGER */
|
||
|
|
/* The number of Givens rotations which took place in this */
|
||
|
|
/* subproblem. Not referenced if ICOMPQ = 0. */
|
||
|
|
|
||
|
|
/* GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 ) */
|
||
|
|
/* Each pair of numbers indicates a pair of columns to take place */
|
||
|
|
/* in a Givens rotation. Not referenced if ICOMPQ = 0. */
|
||
|
|
|
||
|
|
/* LDGCOL (input) INTEGER */
|
||
|
|
/* leading dimension of GIVCOL, must be at least N. */
|
||
|
|
|
||
|
|
/* GIVNUM (output) REAL array, dimension ( LDGNUM, 2 ) */
|
||
|
|
/* Each number indicates the C or S value to be used in the */
|
||
|
|
/* corresponding Givens rotation. Not referenced if ICOMPQ = 0. */
|
||
|
|
|
||
|
|
/* LDGNUM (input) INTEGER */
|
||
|
|
/* The leading dimension of GIVNUM and POLES, must be at least N. */
|
||
|
|
|
||
|
|
/* POLES (output) REAL array, dimension ( LDGNUM, 2 ) */
|
||
|
|
/* On exit, POLES(1,*) is an array containing the new singular */
|
||
|
|
/* values obtained from solving the secular equation, and */
|
||
|
|
/* POLES(2,*) is an array containing the poles in the secular */
|
||
|
|
/* equation. Not referenced if ICOMPQ = 0. */
|
||
|
|
|
||
|
|
/* DIFL (output) REAL array, dimension ( N ) */
|
||
|
|
/* On exit, DIFL(I) is the distance between I-th updated */
|
||
|
|
/* (undeflated) singular value and the I-th (undeflated) old */
|
||
|
|
/* singular value. */
|
||
|
|
|
||
|
|
/* DIFR (output) REAL array, */
|
||
|
|
/* dimension ( LDGNUM, 2 ) if ICOMPQ = 1 and */
|
||
|
|
/* dimension ( N ) if ICOMPQ = 0. */
|
||
|
|
/* On exit, DIFR(I, 1) is the distance between I-th updated */
|
||
|
|
/* (undeflated) singular value and the I+1-th (undeflated) old */
|
||
|
|
/* singular value. */
|
||
|
|
|
||
|
|
/* If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */
|
||
|
|
/* normalizing factors for the right singular vector matrix. */
|
||
|
|
|
||
|
|
/* See SLASD8 for details on DIFL and DIFR. */
|
||
|
|
|
||
|
|
/* Z (output) REAL array, dimension ( M ) */
|
||
|
|
/* The first elements of this array contain the components */
|
||
|
|
/* of the deflation-adjusted updating row vector. */
|
||
|
|
|
||
|
|
/* K (output) INTEGER */
|
||
|
|
/* Contains the dimension of the non-deflated matrix, */
|
||
|
|
/* This is the order of the related secular equation. 1 <= K <=N. */
|
||
|
|
|
||
|
|
/* C (output) REAL */
|
||
|
|
/* C contains garbage if SQRE =0 and the C-value of a Givens */
|
||
|
|
/* rotation related to the right null space if SQRE = 1. */
|
||
|
|
|
||
|
|
/* S (output) REAL */
|
||
|
|
/* S contains garbage if SQRE =0 and the S-value of a Givens */
|
||
|
|
/* rotation related to the right null space if SQRE = 1. */
|
||
|
|
|
||
|
|
/* WORK (workspace) REAL array, dimension ( 4 * M ) */
|
||
|
|
|
||
|
|
/* IWORK (workspace) INTEGER array, dimension ( 3 * N ) */
|
||
|
|
|
||
|
|
/* INFO (output) INTEGER */
|
||
|
|
/* = 0: successful exit. */
|
||
|
|
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
|
||
|
|
/* > 0: if INFO = 1, an singular value did not converge */
|
||
|
|
|
||
|
|
/* Further Details */
|
||
|
|
/* =============== */
|
||
|
|
|
||
|
|
/* Based on contributions by */
|
||
|
|
/* Ming Gu and Huan Ren, Computer Science Division, University of */
|
||
|
|
/* California at Berkeley, USA */
|
||
|
|
|
||
|
|
/* ===================================================================== */
|
||
|
|
|
||
|
|
/* .. Parameters .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Local Scalars .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. External Subroutines .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Intrinsic Functions .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Executable Statements .. */
|
||
|
|
|
||
|
|
/* Test the input parameters. */
|
||
|
|
|
||
|
|
/* Parameter adjustments */
|
||
|
|
--d__;
|
||
|
|
--vf;
|
||
|
|
--vl;
|
||
|
|
--idxq;
|
||
|
|
--perm;
|
||
|
|
givcol_dim1 = *ldgcol;
|
||
|
|
givcol_offset = 1 + givcol_dim1;
|
||
|
|
givcol -= givcol_offset;
|
||
|
|
poles_dim1 = *ldgnum;
|
||
|
|
poles_offset = 1 + poles_dim1;
|
||
|
|
poles -= poles_offset;
|
||
|
|
givnum_dim1 = *ldgnum;
|
||
|
|
givnum_offset = 1 + givnum_dim1;
|
||
|
|
givnum -= givnum_offset;
|
||
|
|
--difl;
|
||
|
|
--difr;
|
||
|
|
--z__;
|
||
|
|
--work;
|
||
|
|
--iwork;
|
||
|
|
|
||
|
|
/* Function Body */
|
||
|
|
*info = 0;
|
||
|
|
n = *nl + *nr + 1;
|
||
|
|
m = n + *sqre;
|
||
|
|
|
||
|
|
if (*icompq < 0 || *icompq > 1) {
|
||
|
|
*info = -1;
|
||
|
|
} else if (*nl < 1) {
|
||
|
|
*info = -2;
|
||
|
|
} else if (*nr < 1) {
|
||
|
|
*info = -3;
|
||
|
|
} else if (*sqre < 0 || *sqre > 1) {
|
||
|
|
*info = -4;
|
||
|
|
} else if (*ldgcol < n) {
|
||
|
|
*info = -14;
|
||
|
|
} else if (*ldgnum < n) {
|
||
|
|
*info = -16;
|
||
|
|
}
|
||
|
|
if (*info != 0) {
|
||
|
|
i__1 = -(*info);
|
||
|
|
xerbla_("SLASD6", &i__1);
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* The following values are for bookkeeping purposes only. They are */
|
||
|
|
/* integer pointers which indicate the portion of the workspace */
|
||
|
|
/* used by a particular array in SLASD7 and SLASD8. */
|
||
|
|
|
||
|
|
isigma = 1;
|
||
|
|
iw = isigma + n;
|
||
|
|
ivfw = iw + m;
|
||
|
|
ivlw = ivfw + m;
|
||
|
|
|
||
|
|
idx = 1;
|
||
|
|
idxc = idx + n;
|
||
|
|
idxp = idxc + n;
|
||
|
|
|
||
|
|
/* Scale. */
|
||
|
|
|
||
|
|
/* Computing MAX */
|
||
|
|
r__1 = dabs(*alpha), r__2 = dabs(*beta);
|
||
|
|
orgnrm = dmax(r__1,r__2);
|
||
|
|
d__[*nl + 1] = 0.f;
|
||
|
|
i__1 = n;
|
||
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
||
|
|
if ((r__1 = d__[i__], dabs(r__1)) > orgnrm) {
|
||
|
|
orgnrm = (r__1 = d__[i__], dabs(r__1));
|
||
|
|
}
|
||
|
|
/* L10: */
|
||
|
|
}
|
||
|
|
slascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info);
|
||
|
|
*alpha /= orgnrm;
|
||
|
|
*beta /= orgnrm;
|
||
|
|
|
||
|
|
/* Sort and Deflate singular values. */
|
||
|
|
|
||
|
|
slasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], &
|
||
|
|
work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], &
|
||
|
|
iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[
|
||
|
|
givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s,
|
||
|
|
info);
|
||
|
|
|
||
|
|
/* Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */
|
||
|
|
|
||
|
|
slasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1],
|
||
|
|
ldgnum, &work[isigma], &work[iw], info);
|
||
|
|
|
||
|
|
/* Save the poles if ICOMPQ = 1. */
|
||
|
|
|
||
|
|
if (*icompq == 1) {
|
||
|
|
scopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1);
|
||
|
|
scopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Unscale. */
|
||
|
|
|
||
|
|
slascl_("G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info);
|
||
|
|
|
||
|
|
/* Prepare the IDXQ sorting permutation. */
|
||
|
|
|
||
|
|
n1 = *k;
|
||
|
|
n2 = n - *k;
|
||
|
|
slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]);
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
|
||
|
|
/* End of SLASD6 */
|
||
|
|
|
||
|
|
} /* slasd6_ */
|