subroutine cuncsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO)
CUNCSD2BY1
CUNCSD2BY1
Purpose:
CUNCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with orthonormal columns that has been partitioned into a 2-by-1 block structure: [ I1 0 0 ] [ 0 C 0 ] [ X11 ] [ U1 | ] [ 0 0 0 ] X = [-----] = [---------] [----------] V1**T . [ X21 ] [ | U2 ] [ 0 0 0 ] [ 0 S 0 ] [ 0 0 I2] X11 is P-by-Q. The unitary matrices U1, U2, and V1 are P-by-P, (M-P)-by-(M-P), and Q-by-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). I1 is a K1-by-K1 identity matrix and I2 is a K2-by-K2 identity matrix, where K1 = MAX(Q+P-M,0), K2 = MAX(Q-P,0).
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.
M
M is INTEGER The number of rows in X.
P
P is INTEGER The number of rows in X11. 0 <= P <= M.
Q
Q is INTEGER The number of columns in X11 and X21. 0 <= Q <= M.
X11
X11 is COMPLEX 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).
X21
X21 is COMPLEX array, dimension (LDX21,Q) On entry, part of the unitary matrix whose CSD is desired.
LDX21
LDX21 is INTEGER The leading dimension of X21. LDX21 >= MAX(1,M-P).
THETA
THETA is REAL 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 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 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 array, dimension (Q) If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary matrix V1**T.
LDV1T
LDV1T is INTEGER The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= MAX(1,Q).
WORK
WORK is COMPLEX 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 REAL 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: CBBCSD 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 257 of file cuncsd2by1.f.
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