zuncsd2by1 - Q matrix with orthonormal columns that has been partitioned into a 2-by-1 block structure
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) CHARACTER*1 JOBU1, JOBU2, JOBV1T INTEGER INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21, M, P, Q INTEGER LRWORK, LRWORKMIN, LRWORKOPT DOUBLE PRECISION RWORK(*), THETA(*) DOUBLE COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*), X11(LDX11,*), X21(LDX21,*) INTEGER IWORK(*) SUBROUTINE ZUNCSD2BY1_64(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO) CHARACTER*1 JOBU1, JOBU2, JOBV1T INTEGER*8 INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21, M, P, Q INTEGER*8 LRWORK, LRWORKMIN, LRWORKOPT DOUBLE PRECISION RWORK(*), THETA(*) DOUBLE COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*), X11(LDX11,*), X21(LDX21,*) INTEGER*8 IWORK(*) F95 INTERFACE SUBROUTINE UNCSD2BY1(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO) INTEGER :: M, P, Q, LDX11, LDX21, LDU1, LDU2, LDV1T, LWORK, LRWORK, INFO CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T INTEGER, DIMENSION(:) :: IWORK COMPLEX(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:) :: THETA, RWORK COMPLEX(8), DIMENSION(:,:) :: X11, X21, U1, U2, V1T SUBROUTINE UNCSD2BY1_64(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO) INTEGER(8) :: M, P, Q, LDX11, LDX21, LDU1, LDU2, LDV1T, LWORK, LRWORK, INFO CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T INTEGER(8), DIMENSION(:) :: IWORK COMPLEX(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:) :: THETA, RWORK COMPLEX(8), DIMENSION(:,:) :: X11, X21, U1, U2, V1T C INTERFACE #include <sunperf.h> void zuncsd2by1 (char jobu1, char jobu2, char jobv1t, int m, int p, int q, doublecomplex *x11, int ldx11, doublecomplex *x21, int ldx21, double *theta, doublecomplex *u1, int ldu1, doublecom- plex *u2, int ldu2, doublecomplex *v1t, int ldv1t, doublecom- plex *work, int lwork, double *rwork, int lrwork, int *iwork, int *info); void zuncsd2by1_64 (char jobu1, char jobu2, char jobv1t, long m, long p, long q, doublecomplex *x11, long ldx11, doublecomplex *x21, long ldx21, double *theta, doublecomplex *u1, long ldu1, doublecomplex *u2, long ldu2, doublecomplex *v1t, long ldv1t, doublecomplex *work, long lwork, double *rwork, long lrwork, long *iwork, long *info);
Oracle Solaris Studio Performance Library zuncsd2by1(3P)
NAME
zuncsd2by1 - compute the CS decomposition of an M-by-Q matrix with
orthonormal columns that has been partitioned into a 2-by-1 block
structure
SYNOPSIS
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)
CHARACTER*1 JOBU1, JOBU2, JOBV1T
INTEGER INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21, M, P, Q
INTEGER LRWORK, LRWORKMIN, LRWORKOPT
DOUBLE PRECISION RWORK(*), THETA(*)
DOUBLE COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*),
X11(LDX11,*), X21(LDX21,*)
INTEGER IWORK(*)
SUBROUTINE ZUNCSD2BY1_64(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK,
LWORK, RWORK, LRWORK, IWORK, INFO)
CHARACTER*1 JOBU1, JOBU2, JOBV1T
INTEGER*8 INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21, M, P, Q
INTEGER*8 LRWORK, LRWORKMIN, LRWORKOPT
DOUBLE PRECISION RWORK(*), THETA(*)
DOUBLE COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*),
X11(LDX11,*), X21(LDX21,*)
INTEGER*8 IWORK(*)
F95 INTERFACE
SUBROUTINE UNCSD2BY1(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21,
LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK,
RWORK, LRWORK, IWORK, INFO)
INTEGER :: M, P, Q, LDX11, LDX21, LDU1, LDU2, LDV1T, LWORK, LRWORK,
INFO
CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T
INTEGER, DIMENSION(:) :: IWORK
COMPLEX(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:) :: THETA, RWORK
COMPLEX(8), DIMENSION(:,:) :: X11, X21, U1, U2, V1T
SUBROUTINE UNCSD2BY1_64(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21,
LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK,
RWORK, LRWORK, IWORK, INFO)
INTEGER(8) :: M, P, Q, LDX11, LDX21, LDU1, LDU2, LDV1T, LWORK, LRWORK,
INFO
CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T
INTEGER(8), DIMENSION(:) :: IWORK
COMPLEX(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:) :: THETA, RWORK
COMPLEX(8), DIMENSION(:,:) :: X11, X21, U1, U2, V1T
C INTERFACE
#include <sunperf.h>
void zuncsd2by1 (char jobu1, char jobu2, char jobv1t, int m, int p, int
q, doublecomplex *x11, int ldx11, doublecomplex *x21, int
ldx21, double *theta, doublecomplex *u1, int ldu1, doublecom-
plex *u2, int ldu2, doublecomplex *v1t, int ldv1t, doublecom-
plex *work, int lwork, double *rwork, int lrwork, int *iwork,
int *info);
void zuncsd2by1_64 (char jobu1, char jobu2, char jobv1t, long m, long
p, long q, doublecomplex *x11, long ldx11, doublecomplex
*x21, long ldx21, double *theta, doublecomplex *u1, long
ldu1, doublecomplex *u2, long ldu2, doublecomplex *v1t, long
ldv1t, doublecomplex *work, long lwork, double *rwork, long
lrwork, long *iwork, long *info);
PURPOSE
zuncsd2by1 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:
[ 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 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.
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).
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 X21. LDX21 >= MAX(1,M-P).
THETA (output)
THETA is COMPLEX*16 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**T.
LDV1T (input)
LDV1T is INTEGER
The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
MAX(1,Q).
WORK (output)
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),
define the matrix in intermediate bidiagonal-block form
remaining after nonconvergence. INFO specifies the number of
nonzero PHI's.
LWORK (input)
LWORK is INTEGER
The dimension of the array WORK.
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 WORK
above for details.
7 Nov 2015 zuncsd2by1(3P)