dbbcsd.f (3) - Linux Manuals
NAME
dbbcsd.f -
SYNOPSIS
Functions/Subroutines
subroutine dbbcsd (JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, WORK, LWORK, INFO)
DBBCSD
Function/Subroutine Documentation
subroutine dbbcsd (characterJOBU1, characterJOBU2, characterJOBV1T, characterJOBV2T, characterTRANS, integerM, integerP, integerQ, double precision, dimension( * )THETA, double precision, dimension( * )PHI, double precision, dimension( ldu1, * )U1, integerLDU1, double precision, dimension( ldu2, * )U2, integerLDU2, double precision, dimension( ldv1t, * )V1T, integerLDV1T, double precision, dimension( ldv2t, * )V2T, integerLDV2T, double precision, dimension( * )B11D, double precision, dimension( * )B11E, double precision, dimension( * )B12D, double precision, dimension( * )B12E, double precision, dimension( * )B21D, double precision, dimension( * )B21E, double precision, dimension( * )B22D, double precision, dimension( * )B22E, double precision, dimension( * )WORK, integerLWORK, integerINFO)
DBBCSD
Purpose:
-
DBBCSD computes the CS decomposition of an orthogonal matrix in bidiagonal-block form, [ B11 | B12 0 0 ] [ 0 | 0 -I 0 ] X = [----------------] [ B21 | B22 0 0 ] [ 0 | 0 0 I ] [ C | -S 0 0 ] [ U1 | ] [ 0 | 0 -I 0 ] [ V1 | ]**T = [---------] [---------------] [---------] . [ | U2 ] [ S | C 0 0 ] [ | V2 ] [ 0 | 0 0 I ] X is M-by-M, its top-left block is P-by-Q, and Q must be no larger than P, M-P, or M-Q. (If Q is not the smallest index, then X must be transposed and/or permuted. This can be done in constant time using the TRANS and SIGNS options. See DORCSD for details.) The bidiagonal matrices B11, B12, B21, and B22 are represented implicitly by angles THETA(1:Q) and PHI(1:Q-1). The orthogonal matrices U1, U2, V1T, and V2T are input/output. The input matrices are pre- or post-multiplied by the appropriate singular vector matrices.
Parameters:
-
JOBU1
JOBU1 is CHARACTER = 'Y': U1 is updated; otherwise: U1 is not updated.
JOBU2JOBU2 is CHARACTER = 'Y': U2 is updated; otherwise: U2 is not updated.
JOBV1TJOBV1T is CHARACTER = 'Y': V1T is updated; otherwise: V1T is not updated.
JOBV2TJOBV2T is CHARACTER = 'Y': V2T is updated; otherwise: V2T is not updated.
TRANSTRANS is CHARACTER = 'T': X, U1, U2, V1T, and V2T are stored in row-major order; otherwise: X, U1, U2, V1T, and V2T are stored in column- major order.
MM is INTEGER The number of rows and columns in X, the orthogonal matrix in bidiagonal-block form.
PP is INTEGER The number of rows in the top-left block of X. 0 <= P <= M.
QQ is INTEGER The number of columns in the top-left block of X. 0 <= Q <= MIN(P,M-P,M-Q).
THETATHETA is DOUBLE PRECISION array, dimension (Q) On entry, the angles THETA(1),...,THETA(Q) that, along with PHI(1), ...,PHI(Q-1), define the matrix in bidiagonal-block form. On exit, the angles whose cosines and sines define the diagonal blocks in the CS decomposition.
PHIPHI is DOUBLE PRECISION array, dimension (Q-1) The angles PHI(1),...,PHI(Q-1) that, along with THETA(1),..., THETA(Q), define the matrix in bidiagonal-block form.
U1U1 is DOUBLE PRECISION array, dimension (LDU1,P) On entry, an LDU1-by-P matrix. On exit, U1 is postmultiplied by the left singular vector matrix common to [ B11 ; 0 ] and [ B12 0 0 ; 0 -I 0 0 ].
LDU1LDU1 is INTEGER The leading dimension of the array U1.
U2U2 is DOUBLE PRECISION array, dimension (LDU2,M-P) On entry, an LDU2-by-(M-P) matrix. On exit, U2 is postmultiplied by the left singular vector matrix common to [ B21 ; 0 ] and [ B22 0 0 ; 0 0 I ].
LDU2LDU2 is INTEGER The leading dimension of the array U2.
V1TV1T is DOUBLE PRECISION array, dimension (LDV1T,Q) On entry, a LDV1T-by-Q matrix. On exit, V1T is premultiplied by the transpose of the right singular vector matrix common to [ B11 ; 0 ] and [ B21 ; 0 ].
LDV1TLDV1T is INTEGER The leading dimension of the array V1T.
V2TV2T is DOUBLE PRECISION array, dimenison (LDV2T,M-Q) On entry, a LDV2T-by-(M-Q) matrix. On exit, V2T is premultiplied by the transpose of the right singular vector matrix common to [ B12 0 0 ; 0 -I 0 ] and [ B22 0 0 ; 0 0 I ].
LDV2TLDV2T is INTEGER The leading dimension of the array V2T.
B11DB11D is DOUBLE PRECISION array, dimension (Q) When DBBCSD converges, B11D contains the cosines of THETA(1), ..., THETA(Q). If DBBCSD fails to converge, then B11D contains the diagonal of the partially reduced top-left block.
B11EB11E is DOUBLE PRECISION array, dimension (Q-1) When DBBCSD converges, B11E contains zeros. If DBBCSD fails to converge, then B11E contains the superdiagonal of the partially reduced top-left block.
B12DB12D is DOUBLE PRECISION array, dimension (Q) When DBBCSD converges, B12D contains the negative sines of THETA(1), ..., THETA(Q). If DBBCSD fails to converge, then B12D contains the diagonal of the partially reduced top-right block.
B12EB12E is DOUBLE PRECISION array, dimension (Q-1) When DBBCSD converges, B12E contains zeros. If DBBCSD fails to converge, then B12E contains the subdiagonal of the partially reduced top-right block.
B21DB21D is DOUBLE PRECISION array, dimension (Q) When CBBCSD converges, B21D contains the negative sines of THETA(1), ..., THETA(Q). If CBBCSD fails to converge, then B21D contains the diagonal of the partially reduced bottom-left block.
B21EB21E is DOUBLE PRECISION array, dimension (Q-1) When CBBCSD converges, B21E contains zeros. If CBBCSD fails to converge, then B21E contains the subdiagonal of the partially reduced bottom-left block.
B22DB22D is DOUBLE PRECISION array, dimension (Q) When CBBCSD converges, B22D contains the negative sines of THETA(1), ..., THETA(Q). If CBBCSD fails to converge, then B22D contains the diagonal of the partially reduced bottom-right block.
B22EB22E is DOUBLE PRECISION array, dimension (Q-1) When CBBCSD converges, B22E contains zeros. If CBBCSD fails to converge, then B22E contains the subdiagonal of the partially reduced bottom-right block.
WORKWORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORKLWORK is INTEGER The dimension of the array WORK. LWORK >= MAX(1,8*Q). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the work array, and no error message related to LWORK is issued by XERBLA.
INFOINFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if DBBCSD did not converge, INFO specifies the number of nonzero entries in PHI, and B11D, B11E, etc., contain the partially reduced matrix.
Internal Parameters:
-
TOLMUL DOUBLE PRECISION, default = MAX(10,MIN(100,EPS**(-1/8))) TOLMUL controls the convergence criterion of the QR loop. Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they are within TOLMUL*EPS of either bound.
References:
- [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.
Author:
-
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
- November 2011
Definition at line 330 of file dbbcsd.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.