dorcsd - onal matrix
RECURSIVE SUBROUTINE DORCSD(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, IWORK, INFO) CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, LDX21, LDX22, LWORK, M, P, Q INTEGER IWORK(*) DOUBLE PRECISION THETA(*) DOUBLE PRECISION U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*), WORK(*), X11(LDX11,*), X12(LDX12,*), X21(LDX21,*), X22(LDX22,*) RECURSIVE SUBROUTINE DORCSD_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, IWORK, INFO) CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS INTEGER*8 INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, LDX21, LDX22, LWORK, M, P, Q INTEGER*8 IWORK(*) DOUBLE PRECISION THETA(*) DOUBLE PRECISION U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*), WORK(*), X11(LDX11,*), X12(LDX12,*), X21(LDX21,*), X22(LDX22,*) F95 INTERFACE RECURSIVE SUBROUTINE ORCSD(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, IWORK, INFO) INTEGER :: M, P, Q, LDX11, LDX12, LDX21, LDX22, LDU1, LDU2, LDV1T, LDV2T, LWORK, INFO CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS INTEGER, DIMENSION(:) :: IWORK REAL(8), DIMENSION(:,:) :: X11, X12, X21, X22, U1, U2, V1T, V2T REAL(8), DIMENSION(:) :: THETA, WORK RECURSIVE SUBROUTINE ORCSD_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, IWORK, INFO) INTEGER(8) :: M, P, Q, LDX11, LDX12, LDX21, LDX22, LDU1, LDU2, LDV1T, LDV2T, LWORK, INFO CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS INTEGER(8), DIMENSION(:) :: IWORK REAL(8), DIMENSION(:,:) :: X11, X12, X21, X22, U1, U2, V1T, V2T REAL(8), DIMENSION(:) :: THETA, WORK C INTERFACE #include <sunperf.h> void dorcsd (char jobu1, char jobu2, char jobv1t, char jobv2t, char trans, char signs, int m, int p, int q, double *x11, int ldx11, double *x12, int ldx12, double *x21, int ldx21, double *x22, int ldx22, double *theta, double *u1, int ldu1, double *u2, int ldu2, double *v1t, int ldv1t, double *v2t, int ldv2t, double *work, int lwork, int *iwork, int *info); void dorcsd_64 (char jobu1, char jobu2, char jobv1t, char jobv2t, char trans, char signs, long m, long p, long q, double *x11, long ldx11, double *x12, long ldx12, double *x21, long ldx21, dou- ble *x22, long ldx22, double *theta, double *u1, long ldu1, double *u2, long ldu2, double *v1t, long ldv1t, double *v2t, long ldv2t, double *work, long lwork, long *iwork, long *info);
Oracle Solaris Studio Performance Library dorcsd(3P)
NAME
dorcsd - compute the CS decomposition of an M-by-M partitioned orthog-
onal matrix
SYNOPSIS
RECURSIVE SUBROUTINE DORCSD(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, IWORK, INFO)
CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, LDX21, LDX22,
LWORK, M, P, Q
INTEGER IWORK(*)
DOUBLE PRECISION THETA(*)
DOUBLE PRECISION U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*),
WORK(*), X11(LDX11,*), X12(LDX12,*), X21(LDX21,*),
X22(LDX22,*)
RECURSIVE SUBROUTINE DORCSD_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, IWORK, INFO)
CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
INTEGER*8 INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, LDX21, LDX22,
LWORK, M, P, Q
INTEGER*8 IWORK(*)
DOUBLE PRECISION THETA(*)
DOUBLE PRECISION U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*),
WORK(*), X11(LDX11,*), X12(LDX12,*), X21(LDX21,*),
X22(LDX22,*)
F95 INTERFACE
RECURSIVE SUBROUTINE ORCSD(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, IWORK, INFO)
INTEGER :: M, P, Q, LDX11, LDX12, LDX21, LDX22, LDU1, LDU2, LDV1T,
LDV2T, LWORK, INFO
CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS
INTEGER, DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:,:) :: X11, X12, X21, X22, U1, U2, V1T, V2T
REAL(8), DIMENSION(:) :: THETA, WORK
RECURSIVE SUBROUTINE ORCSD_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, IWORK, INFO)
INTEGER(8) :: M, P, Q, LDX11, LDX12, LDX21, LDX22, LDU1, LDU2, LDV1T,
LDV2T, LWORK, INFO
CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:,:) :: X11, X12, X21, X22, U1, U2, V1T, V2T
REAL(8), DIMENSION(:) :: THETA, WORK
C INTERFACE
#include <sunperf.h>
void dorcsd (char jobu1, char jobu2, char jobv1t, char jobv2t, char
trans, char signs, int m, int p, int q, double *x11, int
ldx11, double *x12, int ldx12, double *x21, int ldx21, double
*x22, int ldx22, double *theta, double *u1, int ldu1, double
*u2, int ldu2, double *v1t, int ldv1t, double *v2t, int
ldv2t, double *work, int lwork, int *iwork, int *info);
void dorcsd_64 (char jobu1, char jobu2, char jobv1t, char jobv2t, char
trans, char signs, long m, long p, long q, double *x11, long
ldx11, double *x12, long ldx12, double *x21, long ldx21, dou-
ble *x22, long ldx22, double *theta, double *u1, long ldu1,
double *u2, long ldu2, double *v1t, long ldv1t, double *v2t,
long ldv2t, double *work, long lwork, long *iwork, long
*info);
PURPOSE
dorcsd computes the CS decomposition of an M-by-M partitioned orthogo-
nal matrix X:
[ I 0 0 | 0 0 0 ]
[ 0 C 0 | 0 -S 0 ]
[ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**T
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 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.
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 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).
X12 (input/output)
X12 is DOUBLE PRECISION array, dimension (LDX12,M-Q)
On entry, part of the orthogonal matrix whose CSD is desired.
LDX12 (input)
LDX12 is INTEGER
The leading dimension of X12.
LDX12 >= 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 X11.
LDX21 >= MAX(1,M-P).
X22 (input/output)
X22 is DOUBLE PRECISION array, dimension (LDX22,M-Q)
On entry, part of the orthogonal 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 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).
V2T (output)
V2T is DOUBLE PRECISION array, dimension (M-Q)
If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal
matrix V2**T.
LDV2T (input)
LDV2T is INTEGER
The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
MAX(1,M-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.
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.
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 dorcsd(3P)