zuncsd.f - Online Linux Manual Page

Section : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEzuncsd.f
SYNOPSIS
Functions/Subroutinesrecursive 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
Function/Subroutine Documentation
recursive subroutine zuncsd (character JOBU1, character JOBU2, character JOBV1T, character JOBV2T, character TRANS, character SIGNS, integer M, integer P, integer Q, complex*16, dimension( ldx11, * ) X11, integer LDX11, complex*16, dimension( ldx12, * ) X12, integer LDX12, complex*16, dimension( ldx21, * ) X21, integer LDX21, complex*16, dimension( ldx22, * ) X22, integer LDX22, double precision, dimension( * ) THETA, complex*16, dimension( ldu1, * ) U1, integer LDU1, complex*16, dimension( ldu2, * ) U2, integer LDU2, complex*16, dimension( ldv1t, * ) V1T, integer LDV1T, complex*16, dimension( ldv2t, * ) V2T, integer LDV2T, complex*16, dimension( * ) WORK, integer LWORK, double precision, dimension( * ) RWORK, integer LRWORK, integer, dimension( * ) IWORK, integer INFO)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 (LDU1,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 (LDU2,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 (LDV1T,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 (LDV2T,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: June 2017 Definition at line 322 of file zuncsd​.f​.
AuthorGenerated automatically by Doxygen for LAPACK from the source code​. 0
Johanes Gumabo
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