cbbcsd - nal-block form
SUBROUTINE CBBCSD(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, RWORK, LRWORK, INFO) CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LRWORK, M, P, Q REAL B11D(*), B11E(*), B12D(*), B12E(*), B21D(*), B21E(*), B22D(*), B22E(*), PHI(*), THETA(*), RWORK(*) COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*) SUBROUTINE CBBCSD_64(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, RWORK, LRWORK, INFO) CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS INTEGER*8 INFO, LDU1, LDU2, LDV1T, LDV2T, LRWORK, M, P, Q REAL B11D(*), B11E(*), B12D(*), B12E(*), B21D(*), B21E(*), B22D(*), B22E(*), PHI(*), THETA(*), RWORK(*) COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*) F95 INTERFACE SUBROUTINE BBCSD(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, RWORK, LRWORK, INFO) INTEGER :: M, P, Q, LDU1, LDU2, LDV1T, LDV2T, LRWORK, INFO CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS REAL, DIMENSION(:) :: THETA, PHI, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, RWORK COMPLEX, DIMENSION(:,:) :: U1, U2, V1T, V2T SUBROUTINE BBCSD_64(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, RWORK, LRWORK, INFO) INTEGER(8) :: M, P, Q, LDU1, LDU2, LDV1T, LDV2T, LRWORK, INFO CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS REAL, DIMENSION(:) :: THETA, PHI, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, RWORK COMPLEX, DIMENSION(:,:) :: U1, U2, V1T, V2T C INTERFACE #include <sunperf.h> void cbbcsd (char jobu1, char jobu2, char jobv1t, char jobv2t, char trans, int m, int p, int q, float *theta, float *phi, float- complex *u1, int ldu1, floatcomplex *u2, int ldu2, floatcom- plex *v1t, int ldv1t, floatcomplex *v2t, int ldv2t, float *b11d, float *b11e, float *b12d, float *b12e, float *b21d, float *b21e, float *b22d, float *b22e, int *info); void cbbcsd_64 (char jobu1, char jobu2, char jobv1t, char jobv2t, char trans, long m, long p, long q, float *theta, float *phi, floatcomplex *u1, long ldu1, floatcomplex *u2, long ldu2, floatcomplex *v1t, long ldv1t, floatcomplex *v2t, long ldv2t, float *b11d, float *b11e, float *b12d, float *b12e, float *b21d, float *b21e, float *b22d, float *b22e, long *info);
Oracle Solaris Studio Performance Library cbbcsd(3P)
NAME
cbbcsd - compute the CS decomposition of a unitary matrix in bidiago-
nal-block form
SYNOPSIS
SUBROUTINE CBBCSD(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA,
PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D, B11E,
B12D, B12E, B21D, B21E, B22D, B22E, RWORK, LRWORK, INFO)
CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS
INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LRWORK, M, P, Q
REAL B11D(*), B11E(*), B12D(*), B12E(*), B21D(*), B21E(*), B22D(*),
B22E(*), PHI(*), THETA(*), RWORK(*)
COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*)
SUBROUTINE CBBCSD_64(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D,
B11E, B12D, B12E, B21D, B21E, B22D, B22E, RWORK, LRWORK,
INFO)
CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS
INTEGER*8 INFO, LDU1, LDU2, LDV1T, LDV2T, LRWORK, M, P, Q
REAL B11D(*), B11E(*), B12D(*), B12E(*), B21D(*), B21E(*), B22D(*),
B22E(*), PHI(*), THETA(*), RWORK(*)
COMPLEX U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*)
F95 INTERFACE
SUBROUTINE BBCSD(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA,
PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D, B11E,
B12D, B12E, B21D, B21E, B22D, B22E, RWORK, LRWORK, INFO)
INTEGER :: M, P, Q, LDU1, LDU2, LDV1T, LDV2T, LRWORK, INFO
CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS
REAL, DIMENSION(:) :: THETA, PHI, B11D, B11E, B12D, B12E, B21D, B21E,
B22D, B22E, RWORK
COMPLEX, DIMENSION(:,:) :: U1, U2, V1T, V2T
SUBROUTINE BBCSD_64(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D,
B11E, B12D, B12E, B21D, B21E, B22D, B22E, RWORK, LRWORK,
INFO)
INTEGER(8) :: M, P, Q, LDU1, LDU2, LDV1T, LDV2T, LRWORK, INFO
CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS
REAL, DIMENSION(:) :: THETA, PHI, B11D, B11E, B12D, B12E, B21D, B21E,
B22D, B22E, RWORK
COMPLEX, DIMENSION(:,:) :: U1, U2, V1T, V2T
C INTERFACE
#include <sunperf.h>
void cbbcsd (char jobu1, char jobu2, char jobv1t, char jobv2t, char
trans, int m, int p, int q, float *theta, float *phi, float-
complex *u1, int ldu1, floatcomplex *u2, int ldu2, floatcom-
plex *v1t, int ldv1t, floatcomplex *v2t, int ldv2t, float
*b11d, float *b11e, float *b12d, float *b12e, float *b21d,
float *b21e, float *b22d, float *b22e, int *info);
void cbbcsd_64 (char jobu1, char jobu2, char jobv1t, char jobv2t, char
trans, long m, long p, long q, float *theta, float *phi,
floatcomplex *u1, long ldu1, floatcomplex *u2, long ldu2,
floatcomplex *v1t, long ldv1t, floatcomplex *v2t, long ldv2t,
float *b11d, float *b11e, float *b12d, float *b12e, float
*b21d, float *b21e, float *b22d, float *b22e, long *info);
PURPOSE
cbbcsd computes the CS decomposition of a unitary matrix in bidiagonal-
block form,
[ B11 | B12 0 0 ]
[ 0 | 0 -I 0 ]
X = [----------------]
[ B21 | B22 0 0 ]
[ 0 | 0 0 I ]
[ C | -S 0 0 ]
[ U1 | ] [ 0 | 0 -I 0 ] [ V1 | ]**H
= [---------] [---------------] [---------] .
[ | U2 ] [ S | C 0 0 ] [ | V2 ]
[ 0 | 0 0 I ]
X is M-by-M, its top-left block is P-by-Q, and Q must be no larger
than P, M-P, or M-Q. (If Q is not the smallest index, then X must be
transposed and/or permuted. This can be done in constant time using
the TRANS and SIGNS options. See CUNCSD for details.)
The bidiagonal matrices B11, B12, B21, and B22 are represented
implicitly by angles THETA(1:Q) and PHI(1:Q-1).
The unitary matrices U1, U2, V1T, and V2T are input/output.
The input matrices are pre- or post-multiplied by the appropriate
singular vector matrices.
ARGUMENTS
JOBU1 (input)
JOBU1 is CHARACTER
= 'Y': U1 is updated;
otherwise: U1 is not updated.
JOBU2 (input)
JOBU2 is CHARACTER
= 'Y': U2 is updated;
otherwise: U2 is not updated.
JOBV1T (input)
JOBV1T is CHARACTER
= 'Y': V1T is updated;
otherwise: V1T is not updated.
JOBV2T (input)
JOBV2T is CHARACTER
= 'Y': V2T is updated;
otherwise: V2T is not updated.
TRANS (input)
TRANS is CHARACTER
= 'T': X, U1, U2, V1T, and V2T are stored in row-major
order; in row-major order;
otherwise: X, U1, U2, V1T, and V2T are stored in column-
major order.
M (input)
M is INTEGER
The number of rows and columns in X, the unitary matrix in
bidiagonal-block form.
P (input)
P is INTEGER
The number of rows in the top-left block of X.
0 <= P <= M.
Q (input)
Q is INTEGER
The number of columns in the top-left block of X.
0 <= Q <= MIN(P,M-P,M-Q).
THETA (input/output)
THETA is REAL array, dimension (Q)
On entry, the angles THETA(1),...,THETA(Q) that, along with
PHI(1), ...,PHI(Q-1), define the matrix in bidiagonal-block
form. On exit, the angles whose cosines and sines define the
diagonal blocks in the CS decomposition.
PHI (input/output)
PHI is REAL array, dimension (Q-1)
The angles PHI(1),...,PHI(Q-1) that, along with
THETA(1),...,THETA(Q), define the matrix in bidiagonal-block
form.
U1 (input/output)
U1 is COMPLEX array, dimension (LDU1,P)
On entry, an LDU1-by-P matrix. On exit, U1 is postmultiplied
by the left singular vector matrix common to [ B11 ; 0 ] and
by the left singular vector matrix common to [ B11 ; 0 ] and
[ B12 0 0 ; 0 -I 0 0 ].
LDU1 (input)
LDU1 is INTEGER
The leading dimension of the array U1.
U2 (input/output)
U2 is COMPLEX array, dimension (LDU2,M-P)
On entry, an LDU2-by-(M-P) matrix. On exit, U2 is postmulti-
plied by the left singular vector matrix common to [ B21 ; 0
] and [ B22 0 0 ; 0 0 I ].
LDU2 (input)
LDU2 is INTEGER
The leading dimension of the array U2.
V1T (input/output)
V1T is COMPLEX array, dimension (LDV1T,Q)
On entry, a LDV1T-by-Q matrix. On exit, V1T is premultiplied
by the conjugate transpose of the right singular vector
matrix common to [ B11 ; 0 ] and [ B21 ; 0 ].
LDV1T (input)
LDV1T is INTEGER
The leading dimension of the array V1T.
V2T (input/output)
V2T is COMPLEX array, dimenison (LDV2T,M-Q)
On entry, a LDV2T-by-(M-Q) matrix. On exit, V2T is premulti-
plied by the conjugate transpose of the right singular vector
matrix common to [ B12 0 0 ; 0 -I 0 ] and [ B22 0 0 ; 0 0 I
].
LDV2T (input)
LDV2T is INTEGER
The leading dimension of the array V2T.
B11D (output)
B11D is REAL array, dimension (Q)
When CBBCSD converges, B11D contains the cosines of
THETA(1),..., THETA(Q). If CBBCSD fails to converge, then
B11D contains the diagonal of the partially reduced top-left
block.
B11E (output)
B11E is REAL array, dimension (Q-1)
When CBBCSD converges, B11E contains zeros. If CBBCSD fails
to converge, then B11E contains the superdiagonal of the par-
tially reduced top-left block.
B12D (output)
B12D is REAL array, dimension (Q)
When CBBCSD converges, B12D contains the negative sines of
THETA(1), ..., THETA(Q). If CBBCSD fails to converge, then
B12D contains the diagonal of the partially reduced top-right
block.
B12E (output)
B12E is REAL array, dimension (Q-1)
When CBBCSD converges, B12E contains zeros. If CBBCSD fails
to converge, then B12E contains the subdiagonal of the par-
tially reduced top-right block.
B21D (output)
B21D is REAL array, dimension (Q)
When CBBCSD converges, B21D contains the negative sines of
THETA(1), ..., THETA(Q). If CBBCSD fails to converge, then
B21D contains the diagonal of the partially reduced bottom-
left block.
B21E (output)
B21E is REAL array, dimension (Q-1)
When CBBCSD converges, B21E contains zeros. If CBBCSD fails
to converge, then B21E contains the subdiagonal of the par-
tially reduced bottom-left block.
B22D (output)
B22D is REAL array, dimension (Q)
When CBBCSD converges, B22D contains the negative sines of
THETA(1), ..., THETA(Q). If CBBCSD fails to converge, then
B22D contains the diagonal of the partially reduced bottom-
right block.
B22E (output)
B22E is REAL array, dimension (Q-1)
When CBBCSD converges, B22E contains zeros. If CBBCSD fails
to converge, then B22E contains the subdiagonal of the par-
tially reduced bottom-right block.
RWORK (output)
RWORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, RWORK(1) returns the optimal LWORK.
LRWORK (input)
LRWORK is INTEGER
The dimension of the array RWORK.
LRWORK >= MAX(1,8*Q).
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.
INFO (output)
INFO is INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal value;
> 0: if CBBCSD did not converge, INFO specifies the number
of nonzero entries in PHI, and B11D, B11E, etc., contain the
partially reduced matrix.
7 Nov 2015 cbbcsd(3P)