Zuncsd.f -
recursive subroutine zuncsd (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, RWORK, LRWORK, IWORK, INFO)
ZUNCSD
ZUNCSD
Purpose:
ZUNCSD computes the CS decomposition of an M-by-M partitioned
unitary matrix X:
[ I 0 0 | 0 0 0 ]
[ 0 C 0 | 0 -S 0 ]
[ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**H
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 unitary 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
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 COMPLEX*16 array, dimension (LDX11,Q)
On entry, part of the unitary matrix whose CSD is desired.
LDX11
LDX11 is INTEGER
The leading dimension of X11. LDX11 >= MAX(1,P).
X12
X12 is COMPLEX*16 array, dimension (LDX12,M-Q)
On entry, part of the unitary matrix whose CSD is desired.
LDX12
LDX12 is INTEGER
The leading dimension of X12. LDX12 >= MAX(1,P).
X21
X21 is COMPLEX*16 array, dimension (LDX21,Q)
On entry, part of the unitary matrix whose CSD is desired.
LDX21
LDX21 is INTEGER
The leading dimension of X11. LDX21 >= MAX(1,M-P).
X22
X22 is COMPLEX*16 array, dimension (LDX22,M-Q)
On entry, part of the unitary 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 COMPLEX*16 array, dimension (P)
If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.
LDU1
LDU1 is INTEGER
The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
MAX(1,P).
U2
U2 is COMPLEX*16 array, dimension (M-P)
If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
matrix U2.
LDU2
LDU2 is INTEGER
The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
MAX(1,M-P).
V1T
V1T is COMPLEX*16 array, dimension (Q)
If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
matrix V1**H.
LDV1T
LDV1T is INTEGER
The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
MAX(1,Q).
V2T
V2T is COMPLEX*16 array, dimension (M-Q)
If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) unitary
matrix V2**H.
LDV2T
LDV2T is INTEGER
The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
MAX(1,M-Q).
WORK
WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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.
RWORK
RWORK is DOUBLE PRECISION array, dimension MAX(1,LRWORK)
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
If INFO > 0 on exit, RWORK(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.
LRWORK
LRWORK is INTEGER
The dimension of the array RWORK.
If LRWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the RWORK array, returns
this value as the first entry of the work array, and no error
message related to LRWORK 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: ZBBCSD did not converge. See the description of RWORK
above for details.
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 2013
Definition at line 316 of file zuncsd.f.
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