dbbcsd - agonal-block form
SUBROUTINE DBBCSD(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, WORK, LWORK, INFO) CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LWORK, M, P, Q DOUBLE PRECISION B11D(*), B11E(*), B12D(*), B12E(*), B21D(*), B21E(*), B22D(*),B22E(*), PHI(*), THETA(*), WORK(*) DOUBLE PRECISION U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*) SUBROUTINE DBBCSD_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, WORK, LWORK, INFO) CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS INTEGER*8 INFO, LDU1, LDU2, LDV1T, LDV2T, LWORK, M, P, Q DOUBLE PRECISION B11D(*), B11E(*), B12D(*), B12E(*), B21D(*), B21E(*), B22D(*), B22E(*), PHI(*), THETA(*), WORK(*) DOUBLE PRECISION 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, WORK, LWORK, INFO) INTEGER :: M, P, Q, LDU1, LDU2, LDV1T, LDV2T, LWORK, INFO CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS REAL(8), DIMENSION(:,:) :: U1, U2, V1T, V2T REAL(8), DIMENSION(:) :: THETA, PHI, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, WORK 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, WORK, LWORK, INFO) INTEGER(8) :: M, P, Q, LDU1, LDU2, LDV1T, LDV2T, LWORK, INFO CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS REAL(8), DIMENSION(:,:) :: U1, U2, V1T, V2T REAL(8), DIMENSION(:) :: THETA, PHI, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, WORK C INTERFACE #include <sunperf.h> void dbbcsd (char jobu1, char jobu2, char jobv1t, char jobv2t, char trans, int m, int p, int q, double *theta, double *phi, dou- ble *u1, int ldu1, double *u2, int ldu2, double *v1t, int ldv1t, double *v2t, int ldv2t, double *b11d, double *b11e, double *b12d, double *b12e, double *b21d, double *b21e, dou- ble *b22d, double *b22e, int *info); void dbbcsd_64 (char jobu1, char jobu2, char jobv1t, char jobv2t, char trans, long m, long p, long q, double *theta, double *phi, double *u1, long ldu1, double *u2, long ldu2, double *v1t, long ldv1t, double *v2t, long ldv2t, double *b11d, double *b11e, double *b12d, double *b12e, double *b21d, double *b21e, double *b22d, double *b22e, long *info);
Oracle Solaris Studio Performance Library dbbcsd(3P)
NAME
dbbcsd - compute the CS decomposition of an orthogonal matrix in bidi-
agonal-block form
SYNOPSIS
SUBROUTINE DBBCSD(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, WORK, LWORK, INFO)
CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS
INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LWORK, M, P, Q
DOUBLE PRECISION B11D(*), B11E(*), B12D(*), B12E(*), B21D(*), B21E(*),
B22D(*),B22E(*), PHI(*), THETA(*), WORK(*)
DOUBLE PRECISION U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), V2T(LDV2T,*)
SUBROUTINE DBBCSD_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, WORK, LWORK, INFO)
CHARACTER*1 JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS
INTEGER*8 INFO, LDU1, LDU2, LDV1T, LDV2T, LWORK, M, P, Q
DOUBLE PRECISION B11D(*), B11E(*), B12D(*), B12E(*), B21D(*), B21E(*),
B22D(*), B22E(*), PHI(*), THETA(*), WORK(*)
DOUBLE PRECISION 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, WORK, LWORK, INFO)
INTEGER :: M, P, Q, LDU1, LDU2, LDV1T, LDV2T, LWORK, INFO
CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS
REAL(8), DIMENSION(:,:) :: U1, U2, V1T, V2T
REAL(8), DIMENSION(:) :: THETA, PHI, B11D, B11E, B12D, B12E, B21D,
B21E, B22D, B22E, WORK
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, WORK, LWORK, INFO)
INTEGER(8) :: M, P, Q, LDU1, LDU2, LDV1T, LDV2T, LWORK, INFO
CHARACTER(LEN=1) :: JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS
REAL(8), DIMENSION(:,:) :: U1, U2, V1T, V2T
REAL(8), DIMENSION(:) :: THETA, PHI, B11D, B11E, B12D, B12E, B21D,
B21E, B22D, B22E, WORK
C INTERFACE
#include <sunperf.h>
void dbbcsd (char jobu1, char jobu2, char jobv1t, char jobv2t, char
trans, int m, int p, int q, double *theta, double *phi, dou-
ble *u1, int ldu1, double *u2, int ldu2, double *v1t, int
ldv1t, double *v2t, int ldv2t, double *b11d, double *b11e,
double *b12d, double *b12e, double *b21d, double *b21e, dou-
ble *b22d, double *b22e, int *info);
void dbbcsd_64 (char jobu1, char jobu2, char jobv1t, char jobv2t, char
trans, long m, long p, long q, double *theta, double *phi,
double *u1, long ldu1, double *u2, long ldu2, double *v1t,
long ldv1t, double *v2t, long ldv2t, double *b11d, double
*b11e, double *b12d, double *b12e, double *b21d, double
*b21e, double *b22d, double *b22e, long *info);
PURPOSE
dbbcsd computes the CS decomposition of an orthogonal matrix in bidiag-
onal-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 | ]**T
= [---------] [---------------] [---------] .
[ | 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 DORCSD for details.)
The bidiagonal matrices B11, B12, B21, and B22 are represented
implicitly by angles THETA(1:Q) and PHI(1:Q-1).
The orthogonal 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;
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 orthogonal 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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
[ B12 0 0 ; 0 -I 0 0 ].
LDU1 (input)
LDU1 is INTEGER
The leading dimension of the array U1.
U2 (input/output)
U2 is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDV1T,Q)
On entry, a LDV1T-by-Q matrix. On exit, V1T is premultiplied
by the 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 DOUBLE PRECISION array, dimenison (LDV2T,M-Q)
On entry, a LDV2T-by-(M-Q) matrix. On exit, V2T is premulti-
plied by the 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 DOUBLE PRECISION array, dimension (Q)
When DBBCSD converges, B11D contains the cosines of THETA(1),
..., THETA(Q). If DBBCSD fails to converge, then B11D con-
tains the diagonal of the partially reduced top-left block.
B11E (output)
B11E is DOUBLE PRECISION array, dimension (Q-1)
When DBBCSD converges, B11E contains zeros. If DBBCSD fails
to converge, then B11E contains the superdiagonal of the par-
tially reduced top-left block.
B12D (output)
B12D is DOUBLE PRECISION array, dimension (Q)
When DBBCSD converges, B12D contains the negative sines of
THETA(1), ..., THETA(Q). If DBBCSD fails to converge, then
B12D contains the diagonal of the partially reduced top-right
block.
B12E (output)
B12E is DOUBLE PRECISION array, dimension (Q-1)
When DBBCSD converges, B12E contains zeros. If DBBCSD fails
to converge, then B12E contains the subdiagonal of the par-
tially reduced top-right block.
B21D (output)
B21D is DOUBLE PRECISION array, dimension (Q)
When DBBCSD converges, B21D contains the negative sines of
THETA(1), ..., THETA(Q). If DBBCSD fails to converge, then
B21D contains the diagonal of the partially reduced bottom-
left block.
B21E (output)
B21E is DOUBLE PRECISION array, dimension (Q-1)
When DBBCSD converges, B21E contains zeros. If DBBCSD fails
to converge, then B21E contains the subdiagonal of the par-
tially reduced bottom-left block.
B22D (output)
B22D is DOUBLE PRECISION array, dimension (Q)
When DBBCSD converges, B22D contains the negative sines of
THETA(1), ..., THETA(Q). If DBBCSD fails to converge, then
B22D contains the diagonal of the partially reduced bottom-
right block.
B22E (output)
B22E is DOUBLE PRECISION array, dimension (Q-1)
When DBBCSD converges, B22E contains zeros. If DBBCSD fails
to converge, then B22E contains the subdiagonal of the par-
tially reduced bottom-right block.
WORK (output)
WORK is DOUBLE PRECISION 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.
LWORK >= MAX(1,8*Q).
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.
INFO (output)
INFO is INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal value;
> 0: if DBBCSD did not converge, INFO specifies the number
of nonzero entries in PHI, and B11D, B11E, etc., contain the
partially reduced matrix.
7 Nov 2015 dbbcsd(3P)