zuncsd2by1 (3)  Linux Manuals
NAME
zuncsd2by1.f 
SYNOPSIS
Functions/Subroutines
subroutine zuncsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO)
ZUNCSD2BY1
Function/Subroutine Documentation
subroutine zuncsd2by1 (characterJOBU1, characterJOBU2, characterJOBV1T, integerM, integerP, integerQ, complex*16, dimension(ldx11,*)X11, integerLDX11, complex*16, dimension(ldx21,*)X21, integerLDX21, double precision, dimension(*)THETA, complex*16, dimension(ldu1,*)U1, integerLDU1, complex*16, dimension(ldu2,*)U2, integerLDU2, complex*16, dimension(ldv1t,*)V1T, integerLDV1T, complex*16, dimension(*)WORK, integerLWORK, double precision, dimension(*)RWORK, integerLRWORK, integer, dimension(*)IWORK, integerINFO)
ZUNCSD2BY1 .SH "Purpose:"
ZUNCSD2BY1 computes the CS decomposition of an MbyQ matrix X with orthonormal columns that has been partitioned into a 2by1 block structure: [ I 0 0 ] [ 0 C 0 ] [ X11 ] [ U1  ] [ 0 0 0 ] X = [] = [] [] V1**T . [ X21 ] [  U2 ] [ 0 0 0 ] [ 0 S 0 ] [ 0 0 I ] X11 is PbyQ. The unitary matrices U1, U2, V1, and V2 are PbyP, (MP)by(MP), QbyQ, and (MQ)by(MQ), respectively. C and S are RbyR nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which R = MIN(P,MP,Q,MQ)..fi 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.
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).
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 X21. LDX21 >= MAX(1,MP).
THETA
THETA is COMPLEX*16 array, dimension (R), in which R = MIN(P,MP,Q,MQ). 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 PbyP 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 (MP) If JOBU2 = 'Y', U2 contains the (MP)by(MP) unitary matrix U2.
LDU2
LDU2 is INTEGER The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= MAX(1,MP).
V1T
V1T is COMPLEX*16 array, dimension (Q) If JOBV1T = 'Y', V1T contains the QbyQ 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*16 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(R1) that, together with THETA(1), ..., THETA(R), define the matrix in intermediate bidiagonalblock 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.
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(R1) that, together with THETA(1), ..., THETA(R), define the matrix in intermediate bidiagonalblock 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.
aram[out] IWORK nsion (MMIN(P,MP,Q,MQ))
INFO
INFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value. > 0: ZBBCSD did not converge. See the description of WORK above for details.
References:
 [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):3365, 2009.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 July 2012
Definition at line 259 of file zuncsd2by1.f.
Author
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