recursive subroutine dorcsd (JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, WORK, LWORK, IWORK, INFO)
DORCSD
DORCSD
Purpose:
DORCSD computes the CS decomposition of an M-by-M partitioned orthogonal matrix X: [ I 0 0 | 0 0 0 ] [ 0 C 0 | 0 -S 0 ] [ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**T X = [-----------] = [---------] [---------------------] [---------] . [ X21 | X22 ] [ | U2 ] [ 0 0 0 | I 0 0 ] [ | V2 ] [ 0 S 0 | 0 C 0 ] [ 0 0 I | 0 0 0 ] X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P, (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which R = MIN(P,M-P,Q,M-Q).
Parameters:
JOBU1 is CHARACTER = 'Y': U1 is computed; otherwise: U1 is not computed.
JOBU2
JOBU2 is CHARACTER = 'Y': U2 is computed; otherwise: U2 is not computed.
JOBV1T
JOBV1T is CHARACTER = 'Y': V1T is computed; otherwise: V1T is not computed.
JOBV2T
JOBV2T is CHARACTER = 'Y': V2T is computed; otherwise: V2T is not computed.
TRANS
TRANS 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.
SIGNS
SIGNS is CHARACTER = 'O': The lower-left block is made nonpositive (the "other" convention); otherwise: The upper-right block is made nonpositive (the "default" convention).
M
M is INTEGER The number of rows and columns in X.
P
P is INTEGER The number of rows in X11 and X12. 0 <= P <= M.
Q
Q is INTEGER The number of columns in X11 and X21. 0 <= Q <= M.
X11
X11 is DOUBLE PRECISION array, dimension (LDX11,Q) On entry, part of the orthogonal matrix whose CSD is desired.
LDX11
LDX11 is INTEGER The leading dimension of X11. LDX11 >= MAX(1,P).
X12
X12 is DOUBLE PRECISION array, dimension (LDX12,M-Q) On entry, part of the orthogonal matrix whose CSD is desired.
LDX12
LDX12 is INTEGER The leading dimension of X12. LDX12 >= MAX(1,P).
X21
X21 is DOUBLE PRECISION array, dimension (LDX21,Q) On entry, part of the orthogonal matrix whose CSD is desired.
LDX21
LDX21 is INTEGER The leading dimension of X11. LDX21 >= MAX(1,M-P).
X22
X22 is DOUBLE PRECISION array, dimension (LDX22,M-Q) On entry, part of the orthogonal matrix whose CSD is desired.
LDX22
LDX22 is INTEGER The leading dimension of X11. LDX22 >= MAX(1,M-P).
THETA
THETA is DOUBLE PRECISION array, dimension (R), in which R = MIN(P,M-P,Q,M-Q). C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
U1
U1 is DOUBLE PRECISION array, dimension (LDU1,P) If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.
LDU1
LDU1 is INTEGER The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= MAX(1,P).
U2
U2 is DOUBLE PRECISION array, dimension (LDU2,M-P) If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal matrix U2.
LDU2
LDU2 is INTEGER The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= MAX(1,M-P).
V1T
V1T is DOUBLE PRECISION array, dimension (LDV1T,Q) If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal matrix V1**T.
LDV1T
LDV1T is INTEGER The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= MAX(1,Q).
V2T
V2T is DOUBLE PRECISION array, dimension (LDV2T,M-Q) If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal matrix V2**T.
LDV2T
LDV2T is INTEGER The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >= MAX(1,M-Q).
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. If INFO > 0 on exit, WORK(2:R) contains the values PHI(1), ..., PHI(R-1) that, together with THETA(1), ..., THETA(R), define the matrix in intermediate bidiagonal-block form remaining after nonconvergence. INFO specifies the number of nonzero PHI's.
LWORK
LWORK is INTEGER The dimension of the array WORK. 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.
IWORK
IWORK is INTEGER array, dimension (M-MIN(P, M-P, Q, M-Q))
INFO
INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: DBBCSD did not converge. See the description of WORK above for details.
References:
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 302 of file dorcsd.f.
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