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.
460 lines
14 KiB
460 lines
14 KiB
#include "clapack.h" |
|
|
|
/* Table of constant values */ |
|
|
|
static doublereal c_b5 = -1.; |
|
static integer c__1 = 1; |
|
static doublereal c_b11 = 1.; |
|
static doublereal c_b13 = 0.; |
|
static integer c__0 = 0; |
|
|
|
/* Subroutine */ int dlals0_(integer *icompq, integer *nl, integer *nr, |
|
integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal |
|
*bx, integer *ldbx, integer *perm, integer *givptr, integer *givcol, |
|
integer *ldgcol, doublereal *givnum, integer *ldgnum, doublereal * |
|
poles, doublereal *difl, doublereal *difr, doublereal *z__, integer * |
|
k, doublereal *c__, doublereal *s, doublereal *work, integer *info) |
|
{ |
|
/* System generated locals */ |
|
integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset, |
|
difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1, |
|
poles_offset, i__1, i__2; |
|
doublereal d__1; |
|
|
|
/* Local variables */ |
|
integer i__, j, m, n; |
|
doublereal dj; |
|
integer nlp1; |
|
doublereal temp; |
|
extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, |
|
doublereal *, integer *, doublereal *, doublereal *); |
|
extern doublereal dnrm2_(integer *, doublereal *, integer *); |
|
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, |
|
integer *); |
|
doublereal diflj, difrj, dsigj; |
|
extern /* Subroutine */ int dgemv_(char *, integer *, integer *, |
|
doublereal *, doublereal *, integer *, doublereal *, integer *, |
|
doublereal *, doublereal *, integer *), dcopy_(integer *, |
|
doublereal *, integer *, doublereal *, integer *); |
|
extern doublereal dlamc3_(doublereal *, doublereal *); |
|
extern /* Subroutine */ int dlascl_(char *, integer *, integer *, |
|
doublereal *, doublereal *, integer *, integer *, doublereal *, |
|
integer *, integer *), dlacpy_(char *, integer *, integer |
|
*, doublereal *, integer *, doublereal *, integer *), |
|
xerbla_(char *, integer *); |
|
doublereal dsigjp; |
|
|
|
|
|
/* -- LAPACK routine (version 3.1) -- */ |
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
|
/* November 2006 */ |
|
|
|
/* .. Scalar Arguments .. */ |
|
/* .. */ |
|
/* .. Array Arguments .. */ |
|
/* .. */ |
|
|
|
/* Purpose */ |
|
/* ======= */ |
|
|
|
/* DLALS0 applies back the multiplying factors of either the left or the */ |
|
/* right singular vector matrix of a diagonal matrix appended by a row */ |
|
/* to the right hand side matrix B in solving the least squares problem */ |
|
/* using the divide-and-conquer SVD approach. */ |
|
|
|
/* For the left singular vector matrix, three types of orthogonal */ |
|
/* matrices are involved: */ |
|
|
|
/* (1L) Givens rotations: the number of such rotations is GIVPTR; the */ |
|
/* pairs of columns/rows they were applied to are stored in GIVCOL; */ |
|
/* and the C- and S-values of these rotations are stored in GIVNUM. */ |
|
|
|
/* (2L) Permutation. The (NL+1)-st row of B is to be moved to the first */ |
|
/* row, and for J=2:N, PERM(J)-th row of B is to be moved to the */ |
|
/* J-th row. */ |
|
|
|
/* (3L) The left singular vector matrix of the remaining matrix. */ |
|
|
|
/* For the right singular vector matrix, four types of orthogonal */ |
|
/* matrices are involved: */ |
|
|
|
/* (1R) The right singular vector matrix of the remaining matrix. */ |
|
|
|
/* (2R) If SQRE = 1, one extra Givens rotation to generate the right */ |
|
/* null space. */ |
|
|
|
/* (3R) The inverse transformation of (2L). */ |
|
|
|
/* (4R) The inverse transformation of (1L). */ |
|
|
|
/* Arguments */ |
|
/* ========= */ |
|
|
|
/* ICOMPQ (input) INTEGER */ |
|
/* Specifies whether singular vectors are to be computed in */ |
|
/* factored form: */ |
|
/* = 0: Left singular vector matrix. */ |
|
/* = 1: Right singular vector matrix. */ |
|
|
|
/* 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. */ |
|
|
|
/* NRHS (input) INTEGER */ |
|
/* The number of columns of B and BX. NRHS must be at least 1. */ |
|
|
|
/* B (input/output) DOUBLE PRECISION array, dimension ( LDB, NRHS ) */ |
|
/* On input, B contains the right hand sides of the least */ |
|
/* squares problem in rows 1 through M. On output, B contains */ |
|
/* the solution X in rows 1 through N. */ |
|
|
|
/* LDB (input) INTEGER */ |
|
/* The leading dimension of B. LDB must be at least */ |
|
/* max(1,MAX( M, N ) ). */ |
|
|
|
/* BX (workspace) DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */ |
|
|
|
/* LDBX (input) INTEGER */ |
|
/* The leading dimension of BX. */ |
|
|
|
/* PERM (input) INTEGER array, dimension ( N ) */ |
|
/* The permutations (from deflation and sorting) applied */ |
|
/* to the two blocks. */ |
|
|
|
/* GIVPTR (input) INTEGER */ |
|
/* The number of Givens rotations which took place in this */ |
|
/* subproblem. */ |
|
|
|
/* GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 ) */ |
|
/* Each pair of numbers indicates a pair of rows/columns */ |
|
/* involved in a Givens rotation. */ |
|
|
|
/* LDGCOL (input) INTEGER */ |
|
/* The leading dimension of GIVCOL, must be at least N. */ |
|
|
|
/* GIVNUM (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ |
|
/* Each number indicates the C or S value used in the */ |
|
/* corresponding Givens rotation. */ |
|
|
|
/* LDGNUM (input) INTEGER */ |
|
/* The leading dimension of arrays DIFR, POLES and */ |
|
/* GIVNUM, must be at least K. */ |
|
|
|
/* POLES (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ |
|
/* On entry, POLES(1:K, 1) contains the new singular */ |
|
/* values obtained from solving the secular equation, and */ |
|
/* POLES(1:K, 2) is an array containing the poles in the secular */ |
|
/* equation. */ |
|
|
|
/* DIFL (input) DOUBLE PRECISION array, dimension ( K ). */ |
|
/* On entry, DIFL(I) is the distance between I-th updated */ |
|
/* (undeflated) singular value and the I-th (undeflated) old */ |
|
/* singular value. */ |
|
|
|
/* DIFR (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). */ |
|
/* On entry, DIFR(I, 1) contains the distances between I-th */ |
|
/* updated (undeflated) singular value and the I+1-th */ |
|
/* (undeflated) old singular value. And DIFR(I, 2) is the */ |
|
/* normalizing factor for the I-th right singular vector. */ |
|
|
|
/* Z (input) DOUBLE PRECISION array, dimension ( K ) */ |
|
/* Contain the components of the deflation-adjusted updating row */ |
|
/* vector. */ |
|
|
|
/* K (input) INTEGER */ |
|
/* Contains the dimension of the non-deflated matrix, */ |
|
/* This is the order of the related secular equation. 1 <= K <=N. */ |
|
|
|
/* C (input) DOUBLE PRECISION */ |
|
/* C contains garbage if SQRE =0 and the C-value of a Givens */ |
|
/* rotation related to the right null space if SQRE = 1. */ |
|
|
|
/* S (input) DOUBLE PRECISION */ |
|
/* 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) DOUBLE PRECISION array, dimension ( K ) */ |
|
|
|
/* INFO (output) INTEGER */ |
|
/* = 0: successful exit. */ |
|
/* < 0: if INFO = -i, the i-th argument had an illegal value. */ |
|
|
|
/* Further Details */ |
|
/* =============== */ |
|
|
|
/* Based on contributions by */ |
|
/* Ming Gu and Ren-Cang Li, Computer Science Division, University of */ |
|
/* California at Berkeley, USA */ |
|
/* Osni Marques, LBNL/NERSC, USA */ |
|
|
|
/* ===================================================================== */ |
|
|
|
/* .. Parameters .. */ |
|
/* .. */ |
|
/* .. Local Scalars .. */ |
|
/* .. */ |
|
/* .. External Subroutines .. */ |
|
/* .. */ |
|
/* .. External Functions .. */ |
|
/* .. */ |
|
/* .. Intrinsic Functions .. */ |
|
/* .. */ |
|
/* .. Executable Statements .. */ |
|
|
|
/* Test the input parameters. */ |
|
|
|
/* Parameter adjustments */ |
|
b_dim1 = *ldb; |
|
b_offset = 1 + b_dim1; |
|
b -= b_offset; |
|
bx_dim1 = *ldbx; |
|
bx_offset = 1 + bx_dim1; |
|
bx -= bx_offset; |
|
--perm; |
|
givcol_dim1 = *ldgcol; |
|
givcol_offset = 1 + givcol_dim1; |
|
givcol -= givcol_offset; |
|
difr_dim1 = *ldgnum; |
|
difr_offset = 1 + difr_dim1; |
|
difr -= difr_offset; |
|
poles_dim1 = *ldgnum; |
|
poles_offset = 1 + poles_dim1; |
|
poles -= poles_offset; |
|
givnum_dim1 = *ldgnum; |
|
givnum_offset = 1 + givnum_dim1; |
|
givnum -= givnum_offset; |
|
--difl; |
|
--z__; |
|
--work; |
|
|
|
/* Function Body */ |
|
*info = 0; |
|
|
|
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; |
|
} |
|
|
|
n = *nl + *nr + 1; |
|
|
|
if (*nrhs < 1) { |
|
*info = -5; |
|
} else if (*ldb < n) { |
|
*info = -7; |
|
} else if (*ldbx < n) { |
|
*info = -9; |
|
} else if (*givptr < 0) { |
|
*info = -11; |
|
} else if (*ldgcol < n) { |
|
*info = -13; |
|
} else if (*ldgnum < n) { |
|
*info = -15; |
|
} else if (*k < 1) { |
|
*info = -20; |
|
} |
|
if (*info != 0) { |
|
i__1 = -(*info); |
|
xerbla_("DLALS0", &i__1); |
|
return 0; |
|
} |
|
|
|
m = n + *sqre; |
|
nlp1 = *nl + 1; |
|
|
|
if (*icompq == 0) { |
|
|
|
/* Apply back orthogonal transformations from the left. */ |
|
|
|
/* Step (1L): apply back the Givens rotations performed. */ |
|
|
|
i__1 = *givptr; |
|
for (i__ = 1; i__ <= i__1; ++i__) { |
|
drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, & |
|
b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + |
|
(givnum_dim1 << 1)], &givnum[i__ + givnum_dim1]); |
|
/* L10: */ |
|
} |
|
|
|
/* Step (2L): permute rows of B. */ |
|
|
|
dcopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx); |
|
i__1 = n; |
|
for (i__ = 2; i__ <= i__1; ++i__) { |
|
dcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1], |
|
ldbx); |
|
/* L20: */ |
|
} |
|
|
|
/* Step (3L): apply the inverse of the left singular vector */ |
|
/* matrix to BX. */ |
|
|
|
if (*k == 1) { |
|
dcopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb); |
|
if (z__[1] < 0.) { |
|
dscal_(nrhs, &c_b5, &b[b_offset], ldb); |
|
} |
|
} else { |
|
i__1 = *k; |
|
for (j = 1; j <= i__1; ++j) { |
|
diflj = difl[j]; |
|
dj = poles[j + poles_dim1]; |
|
dsigj = -poles[j + (poles_dim1 << 1)]; |
|
if (j < *k) { |
|
difrj = -difr[j + difr_dim1]; |
|
dsigjp = -poles[j + 1 + (poles_dim1 << 1)]; |
|
} |
|
if (z__[j] == 0. || poles[j + (poles_dim1 << 1)] == 0.) { |
|
work[j] = 0.; |
|
} else { |
|
work[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj / |
|
(poles[j + (poles_dim1 << 1)] + dj); |
|
} |
|
i__2 = j - 1; |
|
for (i__ = 1; i__ <= i__2; ++i__) { |
|
if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == |
|
0.) { |
|
work[i__] = 0.; |
|
} else { |
|
work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] |
|
/ (dlamc3_(&poles[i__ + (poles_dim1 << 1)], & |
|
dsigj) - diflj) / (poles[i__ + (poles_dim1 << |
|
1)] + dj); |
|
} |
|
/* L30: */ |
|
} |
|
i__2 = *k; |
|
for (i__ = j + 1; i__ <= i__2; ++i__) { |
|
if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == |
|
0.) { |
|
work[i__] = 0.; |
|
} else { |
|
work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] |
|
/ (dlamc3_(&poles[i__ + (poles_dim1 << 1)], & |
|
dsigjp) + difrj) / (poles[i__ + (poles_dim1 << |
|
1)] + dj); |
|
} |
|
/* L40: */ |
|
} |
|
work[1] = -1.; |
|
temp = dnrm2_(k, &work[1], &c__1); |
|
dgemv_("T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], & |
|
c__1, &c_b13, &b[j + b_dim1], ldb); |
|
dlascl_("G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j + |
|
b_dim1], ldb, info); |
|
/* L50: */ |
|
} |
|
} |
|
|
|
/* Move the deflated rows of BX to B also. */ |
|
|
|
if (*k < max(m,n)) { |
|
i__1 = n - *k; |
|
dlacpy_("A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1 |
|
+ b_dim1], ldb); |
|
} |
|
} else { |
|
|
|
/* Apply back the right orthogonal transformations. */ |
|
|
|
/* Step (1R): apply back the new right singular vector matrix */ |
|
/* to B. */ |
|
|
|
if (*k == 1) { |
|
dcopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx); |
|
} else { |
|
i__1 = *k; |
|
for (j = 1; j <= i__1; ++j) { |
|
dsigj = poles[j + (poles_dim1 << 1)]; |
|
if (z__[j] == 0.) { |
|
work[j] = 0.; |
|
} else { |
|
work[j] = -z__[j] / difl[j] / (dsigj + poles[j + |
|
poles_dim1]) / difr[j + (difr_dim1 << 1)]; |
|
} |
|
i__2 = j - 1; |
|
for (i__ = 1; i__ <= i__2; ++i__) { |
|
if (z__[j] == 0.) { |
|
work[i__] = 0.; |
|
} else { |
|
d__1 = -poles[i__ + 1 + (poles_dim1 << 1)]; |
|
work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[ |
|
i__ + difr_dim1]) / (dsigj + poles[i__ + |
|
poles_dim1]) / difr[i__ + (difr_dim1 << 1)]; |
|
} |
|
/* L60: */ |
|
} |
|
i__2 = *k; |
|
for (i__ = j + 1; i__ <= i__2; ++i__) { |
|
if (z__[j] == 0.) { |
|
work[i__] = 0.; |
|
} else { |
|
d__1 = -poles[i__ + (poles_dim1 << 1)]; |
|
work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[ |
|
i__]) / (dsigj + poles[i__ + poles_dim1]) / |
|
difr[i__ + (difr_dim1 << 1)]; |
|
} |
|
/* L70: */ |
|
} |
|
dgemv_("T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], & |
|
c__1, &c_b13, &bx[j + bx_dim1], ldbx); |
|
/* L80: */ |
|
} |
|
} |
|
|
|
/* Step (2R): if SQRE = 1, apply back the rotation that is */ |
|
/* related to the right null space of the subproblem. */ |
|
|
|
if (*sqre == 1) { |
|
dcopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx); |
|
drot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__, |
|
s); |
|
} |
|
if (*k < max(m,n)) { |
|
i__1 = n - *k; |
|
dlacpy_("A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 + |
|
bx_dim1], ldbx); |
|
} |
|
|
|
/* Step (3R): permute rows of B. */ |
|
|
|
dcopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb); |
|
if (*sqre == 1) { |
|
dcopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb); |
|
} |
|
i__1 = n; |
|
for (i__ = 2; i__ <= i__1; ++i__) { |
|
dcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1], |
|
ldb); |
|
/* L90: */ |
|
} |
|
|
|
/* Step (4R): apply back the Givens rotations performed. */ |
|
|
|
for (i__ = *givptr; i__ >= 1; --i__) { |
|
d__1 = -givnum[i__ + givnum_dim1]; |
|
drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, & |
|
b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + |
|
(givnum_dim1 << 1)], &d__1); |
|
/* L100: */ |
|
} |
|
} |
|
|
|
return 0; |
|
|
|
/* End of DLALS0 */ |
|
|
|
} /* dlals0_ */
|
|
|