dorcsd2by1 - Q matrix with orthonormal columns that has been partitioned into a 2-by-1 block structure
SUBROUTINE DORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, IWORK, INFO ) CHARACTER*1 JOBU1, JOBU2, JOBV1T INTEGER INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21, M, P, Q DOUBLE PRECISION THETA(*), U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*), X11(LDX11,*), X21(LDX21,*) INTEGER IWORK(*) SUBROUTINE DORCSD2BY1_64(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, IWORK, INFO) CHARACTER*1 JOBU1, JOBU2, JOBV1T INTEGER*8 INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21, M, P, Q DOUBLE PRECISION THETA(*), U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*), X11(LDX11,*), X21(LDX21,*) INTEGER*8 IWORK(*) F95 INTERFACE SUBROUTINE ORCSD2BY1(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, IWORK, INFO) INTEGER :: M, P, Q, LDX11, LDX21, LDU1, LDU2, LDV1T, LWORK, INFO CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T INTEGER, DIMENSION(:) :: IWORK REAL(8), DIMENSION(:,:) :: X11, X21, U1, U2, V1T REAL(8), DIMENSION(:) :: THETA, WORK SUBROUTINE ORCSD2BY1_64(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, IWORK, INFO) INTEGER(8) :: M, P, Q, LDX11, LDX21, LDU1, LDU2, LDV1T, LWORK, INFO CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T INTEGER(8), DIMENSION(:) :: IWORK REAL(8), DIMENSION(:,:) :: X11, X21, U1, U2, V1T REAL(8), DIMENSION(:) :: THETA, WORK C INTERFACE #include <sunperf.h> void dorcsd2by1 (char jobu1, char jobu2, char jobv1t, int m, int p, int q, double *x11, int ldx11, double *x21, int ldx21, double *theta, double *u1, int ldu1, double *u2, int ldu2, double *v1t, int ldv1t, double *work, int lwork, int *iwork, int *info); void dorcsd2by1_64 (char jobu1, char jobu2, char jobv1t, long m, long p, long q, double *x11, long ldx11, double *x21, long ldx21, double *theta, double *u1, long ldu1, double *u2, long ldu2, double *v1t, long ldv1t, double *work, long lwork, long *iwork, long *info);
Oracle Solaris Studio Performance Library dorcsd2by1(3P)
NAME
dorcsd2by1 - 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 DORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21,
LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK,
IWORK, INFO )
CHARACTER*1 JOBU1, JOBU2, JOBV1T
INTEGER INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21, M, P, Q
DOUBLE PRECISION THETA(*), U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*),
WORK(*), X11(LDX11,*), X21(LDX21,*)
INTEGER IWORK(*)
SUBROUTINE DORCSD2BY1_64(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK,
LWORK, IWORK, INFO)
CHARACTER*1 JOBU1, JOBU2, JOBV1T
INTEGER*8 INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21, M, P, Q
DOUBLE PRECISION THETA(*), U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*),
WORK(*), X11(LDX11,*), X21(LDX21,*)
INTEGER*8 IWORK(*)
F95 INTERFACE
SUBROUTINE ORCSD2BY1(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21,
LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK,
IWORK, INFO)
INTEGER :: M, P, Q, LDX11, LDX21, LDU1, LDU2, LDV1T, LWORK, INFO
CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T
INTEGER, DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:,:) :: X11, X21, U1, U2, V1T
REAL(8), DIMENSION(:) :: THETA, WORK
SUBROUTINE ORCSD2BY1_64(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21,
LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK,
IWORK, INFO)
INTEGER(8) :: M, P, Q, LDX11, LDX21, LDU1, LDU2, LDV1T, LWORK, INFO
CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:,:) :: X11, X21, U1, U2, V1T
REAL(8), DIMENSION(:) :: THETA, WORK
C INTERFACE
#include <sunperf.h>
void dorcsd2by1 (char jobu1, char jobu2, char jobv1t, int m, int p, int
q, double *x11, int ldx11, double *x21, int ldx21, double
*theta, double *u1, int ldu1, double *u2, int ldu2, double
*v1t, int ldv1t, double *work, int lwork, int *iwork, int
*info);
void dorcsd2by1_64 (char jobu1, char jobu2, char jobv1t, long m, long
p, long q, double *x11, long ldx11, double *x21, long ldx21,
double *theta, double *u1, long ldu1, double *u2, long ldu2,
double *v1t, long ldv1t, double *work, long lwork, long
*iwork, long *info);
PURPOSE
dorcsd2by1 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 orthogonal 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 DOUBLE PRECISION array, dimension (LDX11,Q)
On entry, part of the orthogonal matrix whose CSD is desired.
LDX11 (input)
LDX11 is INTEGER
The leading dimension of X11. LDX11 >= MAX(1,P).
X21 (input/output)
X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
On entry, part of the orthogonal matrix whose CSD is desired.
LDX21 (input)
LDX21 is INTEGER
The leading dimension of X21. LDX21 >= 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 DOUBLE PRECISION array, dimension (P)
If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.
LDU1 (input)
LDU1 is INTEGER
The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
MAX(1,P).
U2 (output)
U2 is DOUBLE PRECISION array, dimension (M-P)
If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
matrix U2.
LDU2 (input)
LDU2 is INTEGER
The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= MAX(1,M-
P).
V1T (output)
V1T is DOUBLE PRECISION array, dimension (Q)
If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
matrix V1**T.
LDV1T (input)
LDV1T is INTEGER
The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
MAX(1,Q).
WORK (output)
WORK is DOUBLE PRECISION 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.
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: DBBCSD did not converge. See the description of WORK
above for details.
7 Nov 2015 dorcsd2by1(3P)