zuncsd - M partitioned unitary matrix
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) CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, LDX21, LDX22, LRWORK, LWORK, M, P, Q INTEGER IWORK(*) DOUBLE PRECISION THETA(*), RWORK(*) DOUBLE COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*), WORK(*), X11(LDX11,*), X12(LDX12,*), X21(LDX21,*), X22(LDX22,*) RECURSIVE SUBROUTINE ZUNCSD_64(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) CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS INTEGER*8 INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, LDX21, LDX22, LRWORK, LWORK, M, P, Q INTEGER*8 IWORK(*) DOUBLE PRECISION THETA(*), RWORK(*) DOUBLE COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*), WORK(*), X11(LDX11,*), X12(LDX12,*), X21(LDX21,*), X22(LDX22, *) F95 INTERFACE RECURSIVE SUBROUTINE UNCSD(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) INTEGER :: M, P, Q, LDX11, LDX12, LDX21, LDX22, LDU1, LDU2, LDV1T, LDV2T, LWORK, LRWORK, INFO CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS INTEGER, DIMENSION(:) :: IWORK COMPLEX(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:) :: THETA, RWORK COMPLEX(8), DIMENSION(:,:) :: X11, X12, X21, X22, U1, U2, V1T, V2T RECURSIVE SUBROUTINE UNCSD_64(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) INTEGER(8) :: M, P, Q, LDX11, LDX12, LDX21, LDX22, LDU1, LDU2, LDV1T, LDV2T, LWORK, LRWORK, INFO CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS INTEGER(8), DIMENSION(:) :: IWORK COMPLEX(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:) :: THETA, RWORK COMPLEX(8), DIMENSION(:,:) :: X11, X12, X21, X22, U1, U2, V1T, V2T C INTERFACE #include <sunperf.h> void zuncsd (char jobu1, char jobu2, char jobv1t, char jobv2t, char trans, char signs, int m, int p, int q, doublecomplex *x11, int ldx11, doublecomplex *x12, int ldx12, doublecomplex *x21, int ldx21, doublecomplex *x22, int ldx22, double *theta, dou- blecomplex *u1, int ldu1, doublecomplex *u2, int ldu2, dou- blecomplex *v1t, int ldv1t, doublecomplex *v2t, int ldv2t, double *rwork, int lrwork, int *iwork, int *info); void zuncsd_64 (char jobu1, char jobu2, char jobv1t, char jobv2t, char trans, char signs, long m, long p, long q, doublecomplex *x11, long ldx11, doublecomplex *x12, long ldx12, doublecom- plex *x21, long ldx21, doublecomplex *x22, long ldx22, double *theta, doublecomplex *u1, long ldu1, doublecomplex *u2, long ldu2, doublecomplex *v1t, long ldv1t, doublecomplex *v2t, long ldv2t, double *rwork, long lrwork, long *iwork, long *info);
Oracle Solaris Studio Performance Library zuncsd(3P)
NAME
zuncsd - compute the CS decomposition of an M-by-M partitioned unitary
matrix
SYNOPSIS
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)
CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, LDX21, LDX22,
LRWORK, LWORK, M, P, Q
INTEGER IWORK(*)
DOUBLE PRECISION THETA(*), RWORK(*)
DOUBLE COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*),
WORK(*), X11(LDX11,*), X12(LDX12,*), X21(LDX21,*),
X22(LDX22,*)
RECURSIVE SUBROUTINE ZUNCSD_64(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)
CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
INTEGER*8 INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, LDX21, LDX22,
LRWORK, LWORK, M, P, Q
INTEGER*8 IWORK(*)
DOUBLE PRECISION THETA(*), RWORK(*)
DOUBLE COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*),
WORK(*), X11(LDX11,*), X12(LDX12,*), X21(LDX21,*), X22(LDX22,
*)
F95 INTERFACE
RECURSIVE SUBROUTINE UNCSD(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)
INTEGER :: M, P, Q, LDX11, LDX12, LDX21, LDX22, LDU1, LDU2, LDV1T,
LDV2T, LWORK, LRWORK, INFO
CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS
INTEGER, DIMENSION(:) :: IWORK
COMPLEX(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:) :: THETA, RWORK
COMPLEX(8), DIMENSION(:,:) :: X11, X12, X21, X22, U1, U2, V1T, V2T
RECURSIVE SUBROUTINE UNCSD_64(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)
INTEGER(8) :: M, P, Q, LDX11, LDX12, LDX21, LDX22, LDU1, LDU2, LDV1T,
LDV2T, LWORK, LRWORK, INFO
CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS
INTEGER(8), DIMENSION(:) :: IWORK
COMPLEX(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:) :: THETA, RWORK
COMPLEX(8), DIMENSION(:,:) :: X11, X12, X21, X22, U1, U2, V1T, V2T
C INTERFACE
#include <sunperf.h>
void zuncsd (char jobu1, char jobu2, char jobv1t, char jobv2t, char
trans, char signs, int m, int p, int q, doublecomplex *x11,
int ldx11, doublecomplex *x12, int ldx12, doublecomplex *x21,
int ldx21, doublecomplex *x22, int ldx22, double *theta, dou-
blecomplex *u1, int ldu1, doublecomplex *u2, int ldu2, dou-
blecomplex *v1t, int ldv1t, doublecomplex *v2t, int ldv2t,
double *rwork, int lrwork, int *iwork, int *info);
void zuncsd_64 (char jobu1, char jobu2, char jobv1t, char jobv2t, char
trans, char signs, long m, long p, long q, doublecomplex
*x11, long ldx11, doublecomplex *x12, long ldx12, doublecom-
plex *x21, long ldx21, doublecomplex *x22, long ldx22, double
*theta, doublecomplex *u1, long ldu1, doublecomplex *u2, long
ldu2, doublecomplex *v1t, long ldv1t, doublecomplex *v2t,
long ldv2t, double *rwork, long lrwork, long *iwork, long
*info);
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).
ARGUMENTS
JOBU1 (input)
JOBU1 is CHARACTER
= 'Y': U1 is computed;
otherwise: U1 is not computed.
JOBU2 (input)
JOBU2 is CHARACTER
= 'Y': U2 is computed;
otherwise: U2 is not computed.
JOBV1T (input)
JOBV1T is CHARACTER
= 'Y': V1T is computed;
otherwise: V1T is not computed.
JOBV2T (input)
JOBV2T is CHARACTER
= 'Y': V2T is computed;
otherwise: V2T is not computed.
TRANS (input)
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 (input)
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 (input)
M is INTEGER
The number of rows and columns in X.
P (input)
P is INTEGER
The number of rows in X11 and X12. 0 <= P <= M.
Q (input)
Q is INTEGER
The number of columns in X11 and X21. 0 <= Q <= M.
X11 (input/output)
X11 is COMPLEX*16 array, dimension (LDX11,Q)
On entry, part of the unitary matrix whose CSD is desired.
LDX11 (input)
LDX11 is INTEGER
The leading dimension of X11. LDX11 >= MAX(1,P).
X12 (input/output)
X12 is COMPLEX*16 array, dimension (LDX12,M-Q)
On entry, part of the unitary matrix whose CSD is desired.
LDX12 (input)
LDX12 is INTEGER
The leading dimension of X12. LDX12 >= MAX(1,P).
X21 (input/output)
X21 is COMPLEX*16 array, dimension (LDX21,Q)
On entry, part of the unitary matrix whose CSD is desired.
LDX21 (input)
LDX21 is INTEGER
The leading dimension of X11. LDX21 >= MAX(1,M-P).
X22 (input/output)
X22 is COMPLEX*16 array, dimension (LDX22,M-Q)
On entry, part of the unitary matrix whose CSD is desired.
LDX22 (input)
LDX22 is INTEGER
The leading dimension of X11. LDX22 >= MAX(1,M-P).
THETA (output)
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 (output)
U1 is COMPLEX*16 array, dimension (P)
If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.
LDU1 (input)
LDU1 is INTEGER
The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
MAX(1,P).
U2 (output)
U2 is COMPLEX*16 array, dimension (M-P)
If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary matrix
U2.
LDU2 (input)
LDU2 is INTEGER
The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= MAX(1,M-
P).
V1T (output)
V1T is COMPLEX*16 array, dimension (Q)
If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
matrix V1**H.
LDV1T (input)
LDV1T is INTEGER
The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
MAX(1,Q).
V2T (output)
V2T is COMPLEX*16 array, dimension (M-Q)
If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) unitary
matrix V2**H.
LDV2T (input)
LDV2T is INTEGER
The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
MAX(1,M-Q).
WORK (output)
WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
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 (output)
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),
define the matrix in intermediate bidiagonal-block form
remaining after nonconvergence. INFO specifies the number of
nonzero PHI's.
LRWORK (input)
LRWORK is INTEGER
The dimension of the array RWORK.
If LRWORK = -1, then a workspace query is assumed; the rou-
tine 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 (output)
IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
INFO (output)
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.
7 Nov 2015 zuncsd(3P)