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.
367 lines
11 KiB
367 lines
11 KiB
#include "clapack.h" |
|
|
|
/* Table of constant values */ |
|
|
|
static integer c__1 = 1; |
|
|
|
/* Subroutine */ int dlasdq_(char *uplo, integer *sqre, integer *n, integer * |
|
ncvt, integer *nru, integer *ncc, doublereal *d__, doublereal *e, |
|
doublereal *vt, integer *ldvt, doublereal *u, integer *ldu, |
|
doublereal *c__, integer *ldc, doublereal *work, integer *info) |
|
{ |
|
/* System generated locals */ |
|
integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, |
|
i__2; |
|
|
|
/* Local variables */ |
|
integer i__, j; |
|
doublereal r__, cs, sn; |
|
integer np1, isub; |
|
doublereal smin; |
|
integer sqre1; |
|
extern logical lsame_(char *, char *); |
|
extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, |
|
integer *, doublereal *, doublereal *, doublereal *, integer *), dswap_(integer *, doublereal *, integer * |
|
, doublereal *, integer *); |
|
integer iuplo; |
|
extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, |
|
doublereal *, doublereal *, doublereal *), xerbla_(char *, |
|
integer *), dbdsqr_(char *, integer *, integer *, integer |
|
*, integer *, doublereal *, doublereal *, doublereal *, integer *, |
|
doublereal *, integer *, doublereal *, integer *, doublereal *, |
|
integer *); |
|
logical rotate; |
|
|
|
|
|
/* -- LAPACK auxiliary routine (version 3.1) -- */ |
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
|
/* November 2006 */ |
|
|
|
/* .. Scalar Arguments .. */ |
|
/* .. */ |
|
/* .. Array Arguments .. */ |
|
/* .. */ |
|
|
|
/* Purpose */ |
|
/* ======= */ |
|
|
|
/* DLASDQ computes the singular value decomposition (SVD) of a real */ |
|
/* (upper or lower) bidiagonal matrix with diagonal D and offdiagonal */ |
|
/* E, accumulating the transformations if desired. Letting B denote */ |
|
/* the input bidiagonal matrix, the algorithm computes orthogonal */ |
|
/* matrices Q and P such that B = Q * S * P' (P' denotes the transpose */ |
|
/* of P). The singular values S are overwritten on D. */ |
|
|
|
/* The input matrix U is changed to U * Q if desired. */ |
|
/* The input matrix VT is changed to P' * VT if desired. */ |
|
/* The input matrix C is changed to Q' * C if desired. */ |
|
|
|
/* See "Computing Small Singular Values of Bidiagonal Matrices With */ |
|
/* Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, */ |
|
/* LAPACK Working Note #3, for a detailed description of the algorithm. */ |
|
|
|
/* Arguments */ |
|
/* ========= */ |
|
|
|
/* UPLO (input) CHARACTER*1 */ |
|
/* On entry, UPLO specifies whether the input bidiagonal matrix */ |
|
/* is upper or lower bidiagonal, and wether it is square are */ |
|
/* not. */ |
|
/* UPLO = 'U' or 'u' B is upper bidiagonal. */ |
|
/* UPLO = 'L' or 'l' B is lower bidiagonal. */ |
|
|
|
/* SQRE (input) INTEGER */ |
|
/* = 0: then the input matrix is N-by-N. */ |
|
/* = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and */ |
|
/* (N+1)-by-N if UPLU = 'L'. */ |
|
|
|
/* The bidiagonal matrix has */ |
|
/* N = NL + NR + 1 rows and */ |
|
/* M = N + SQRE >= N columns. */ |
|
|
|
/* N (input) INTEGER */ |
|
/* On entry, N specifies the number of rows and columns */ |
|
/* in the matrix. N must be at least 0. */ |
|
|
|
/* NCVT (input) INTEGER */ |
|
/* On entry, NCVT specifies the number of columns of */ |
|
/* the matrix VT. NCVT must be at least 0. */ |
|
|
|
/* NRU (input) INTEGER */ |
|
/* On entry, NRU specifies the number of rows of */ |
|
/* the matrix U. NRU must be at least 0. */ |
|
|
|
/* NCC (input) INTEGER */ |
|
/* On entry, NCC specifies the number of columns of */ |
|
/* the matrix C. NCC must be at least 0. */ |
|
|
|
/* D (input/output) DOUBLE PRECISION array, dimension (N) */ |
|
/* On entry, D contains the diagonal entries of the */ |
|
/* bidiagonal matrix whose SVD is desired. On normal exit, */ |
|
/* D contains the singular values in ascending order. */ |
|
|
|
/* E (input/output) DOUBLE PRECISION array. */ |
|
/* dimension is (N-1) if SQRE = 0 and N if SQRE = 1. */ |
|
/* On entry, the entries of E contain the offdiagonal entries */ |
|
/* of the bidiagonal matrix whose SVD is desired. On normal */ |
|
/* exit, E will contain 0. If the algorithm does not converge, */ |
|
/* D and E will contain the diagonal and superdiagonal entries */ |
|
/* of a bidiagonal matrix orthogonally equivalent to the one */ |
|
/* given as input. */ |
|
|
|
/* VT (input/output) DOUBLE PRECISION array, dimension (LDVT, NCVT) */ |
|
/* On entry, contains a matrix which on exit has been */ |
|
/* premultiplied by P', dimension N-by-NCVT if SQRE = 0 */ |
|
/* and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0). */ |
|
|
|
/* LDVT (input) INTEGER */ |
|
/* On entry, LDVT specifies the leading dimension of VT as */ |
|
/* declared in the calling (sub) program. LDVT must be at */ |
|
/* least 1. If NCVT is nonzero LDVT must also be at least N. */ |
|
|
|
/* U (input/output) DOUBLE PRECISION array, dimension (LDU, N) */ |
|
/* On entry, contains a matrix which on exit has been */ |
|
/* postmultiplied by Q, dimension NRU-by-N if SQRE = 0 */ |
|
/* and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). */ |
|
|
|
/* LDU (input) INTEGER */ |
|
/* On entry, LDU specifies the leading dimension of U as */ |
|
/* declared in the calling (sub) program. LDU must be at */ |
|
/* least max( 1, NRU ) . */ |
|
|
|
/* C (input/output) DOUBLE PRECISION array, dimension (LDC, NCC) */ |
|
/* On entry, contains an N-by-NCC matrix which on exit */ |
|
/* has been premultiplied by Q' dimension N-by-NCC if SQRE = 0 */ |
|
/* and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). */ |
|
|
|
/* LDC (input) INTEGER */ |
|
/* On entry, LDC specifies the leading dimension of C as */ |
|
/* declared in the calling (sub) program. LDC must be at */ |
|
/* least 1. If NCC is nonzero, LDC must also be at least N. */ |
|
|
|
/* WORK (workspace) DOUBLE PRECISION array, dimension (4*N) */ |
|
/* Workspace. Only referenced if one of NCVT, NRU, or NCC is */ |
|
/* nonzero, and if N is at least 2. */ |
|
|
|
/* INFO (output) INTEGER */ |
|
/* On exit, a value of 0 indicates a successful exit. */ |
|
/* If INFO < 0, argument number -INFO is illegal. */ |
|
/* If INFO > 0, the algorithm did not converge, and INFO */ |
|
/* specifies how many superdiagonals 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 .. */ |
|
/* .. */ |
|
/* .. External Functions .. */ |
|
/* .. */ |
|
/* .. Intrinsic Functions .. */ |
|
/* .. */ |
|
/* .. Executable Statements .. */ |
|
|
|
/* Test the input parameters. */ |
|
|
|
/* Parameter adjustments */ |
|
--d__; |
|
--e; |
|
vt_dim1 = *ldvt; |
|
vt_offset = 1 + vt_dim1; |
|
vt -= vt_offset; |
|
u_dim1 = *ldu; |
|
u_offset = 1 + u_dim1; |
|
u -= u_offset; |
|
c_dim1 = *ldc; |
|
c_offset = 1 + c_dim1; |
|
c__ -= c_offset; |
|
--work; |
|
|
|
/* Function Body */ |
|
*info = 0; |
|
iuplo = 0; |
|
if (lsame_(uplo, "U")) { |
|
iuplo = 1; |
|
} |
|
if (lsame_(uplo, "L")) { |
|
iuplo = 2; |
|
} |
|
if (iuplo == 0) { |
|
*info = -1; |
|
} else if (*sqre < 0 || *sqre > 1) { |
|
*info = -2; |
|
} else if (*n < 0) { |
|
*info = -3; |
|
} else if (*ncvt < 0) { |
|
*info = -4; |
|
} else if (*nru < 0) { |
|
*info = -5; |
|
} else if (*ncc < 0) { |
|
*info = -6; |
|
} else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1,*n)) { |
|
*info = -10; |
|
} else if (*ldu < max(1,*nru)) { |
|
*info = -12; |
|
} else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1,*n)) { |
|
*info = -14; |
|
} |
|
if (*info != 0) { |
|
i__1 = -(*info); |
|
xerbla_("DLASDQ", &i__1); |
|
return 0; |
|
} |
|
if (*n == 0) { |
|
return 0; |
|
} |
|
|
|
/* ROTATE is true if any singular vectors desired, false otherwise */ |
|
|
|
rotate = *ncvt > 0 || *nru > 0 || *ncc > 0; |
|
np1 = *n + 1; |
|
sqre1 = *sqre; |
|
|
|
/* If matrix non-square upper bidiagonal, rotate to be lower */ |
|
/* bidiagonal. The rotations are on the right. */ |
|
|
|
if (iuplo == 1 && sqre1 == 1) { |
|
i__1 = *n - 1; |
|
for (i__ = 1; i__ <= i__1; ++i__) { |
|
dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); |
|
d__[i__] = r__; |
|
e[i__] = sn * d__[i__ + 1]; |
|
d__[i__ + 1] = cs * d__[i__ + 1]; |
|
if (rotate) { |
|
work[i__] = cs; |
|
work[*n + i__] = sn; |
|
} |
|
/* L10: */ |
|
} |
|
dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__); |
|
d__[*n] = r__; |
|
e[*n] = 0.; |
|
if (rotate) { |
|
work[*n] = cs; |
|
work[*n + *n] = sn; |
|
} |
|
iuplo = 2; |
|
sqre1 = 0; |
|
|
|
/* Update singular vectors if desired. */ |
|
|
|
if (*ncvt > 0) { |
|
dlasr_("L", "V", "F", &np1, ncvt, &work[1], &work[np1], &vt[ |
|
vt_offset], ldvt); |
|
} |
|
} |
|
|
|
/* If matrix lower bidiagonal, rotate to be upper bidiagonal */ |
|
/* by applying Givens rotations on the left. */ |
|
|
|
if (iuplo == 2) { |
|
i__1 = *n - 1; |
|
for (i__ = 1; i__ <= i__1; ++i__) { |
|
dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); |
|
d__[i__] = r__; |
|
e[i__] = sn * d__[i__ + 1]; |
|
d__[i__ + 1] = cs * d__[i__ + 1]; |
|
if (rotate) { |
|
work[i__] = cs; |
|
work[*n + i__] = sn; |
|
} |
|
/* L20: */ |
|
} |
|
|
|
/* If matrix (N+1)-by-N lower bidiagonal, one additional */ |
|
/* rotation is needed. */ |
|
|
|
if (sqre1 == 1) { |
|
dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__); |
|
d__[*n] = r__; |
|
if (rotate) { |
|
work[*n] = cs; |
|
work[*n + *n] = sn; |
|
} |
|
} |
|
|
|
/* Update singular vectors if desired. */ |
|
|
|
if (*nru > 0) { |
|
if (sqre1 == 0) { |
|
dlasr_("R", "V", "F", nru, n, &work[1], &work[np1], &u[ |
|
u_offset], ldu); |
|
} else { |
|
dlasr_("R", "V", "F", nru, &np1, &work[1], &work[np1], &u[ |
|
u_offset], ldu); |
|
} |
|
} |
|
if (*ncc > 0) { |
|
if (sqre1 == 0) { |
|
dlasr_("L", "V", "F", n, ncc, &work[1], &work[np1], &c__[ |
|
c_offset], ldc); |
|
} else { |
|
dlasr_("L", "V", "F", &np1, ncc, &work[1], &work[np1], &c__[ |
|
c_offset], ldc); |
|
} |
|
} |
|
} |
|
|
|
/* Call DBDSQR to compute the SVD of the reduced real */ |
|
/* N-by-N upper bidiagonal matrix. */ |
|
|
|
dbdsqr_("U", n, ncvt, nru, ncc, &d__[1], &e[1], &vt[vt_offset], ldvt, &u[ |
|
u_offset], ldu, &c__[c_offset], ldc, &work[1], info); |
|
|
|
/* Sort the singular values into ascending order (insertion sort on */ |
|
/* singular values, but only one transposition per singular vector) */ |
|
|
|
i__1 = *n; |
|
for (i__ = 1; i__ <= i__1; ++i__) { |
|
|
|
/* Scan for smallest D(I). */ |
|
|
|
isub = i__; |
|
smin = d__[i__]; |
|
i__2 = *n; |
|
for (j = i__ + 1; j <= i__2; ++j) { |
|
if (d__[j] < smin) { |
|
isub = j; |
|
smin = d__[j]; |
|
} |
|
/* L30: */ |
|
} |
|
if (isub != i__) { |
|
|
|
/* Swap singular values and vectors. */ |
|
|
|
d__[isub] = d__[i__]; |
|
d__[i__] = smin; |
|
if (*ncvt > 0) { |
|
dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[i__ + vt_dim1], |
|
ldvt); |
|
} |
|
if (*nru > 0) { |
|
dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[i__ * u_dim1 + 1] |
|
, &c__1); |
|
} |
|
if (*ncc > 0) { |
|
dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[i__ + c_dim1], ldc) |
|
; |
|
} |
|
} |
|
/* L40: */ |
|
} |
|
|
|
return 0; |
|
|
|
/* End of DLASDQ */ |
|
|
|
} /* dlasdq_ */
|
|
|