zunbdb - tioned unitary matrix
SUBROUTINE ZUNBDB(TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO) CHARACTER*1 SIGNS, TRANS INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P, Q DOUBLE PRECISION PHI(*), THETA(*) DOUBLE COMPLEX TAUP1(*), TAUP2(*), TAUQ1(*), TAUQ2(*), WORK(*), X11(LDX11,*), X12(LDX12,*), X21(LDX21,*), X22(LDX22,*) SUBROUTINE ZUNBDB_64(TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO) CHARACTER*1 SIGNS, TRANS INTEGER*8 INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P, Q DOUBLE PRECISION PHI(*), THETA(*) DOUBLE COMPLEX TAUP1(*), TAUP2(*), TAUQ1(*), TAUQ2(*), WORK(*), X11(LDX11,*), X12(LDX12,*), X21(LDX21,*), X22(LDX22,*) F95 INTERFACE SUBROUTINE UNBDB(TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO) INTEGER :: M, P, Q, LDX11, LDX12, LDX21, LDX22, LWORK, INFO CHARACTER(LEN=1) :: TRANS, SIGNS COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, TAUQ2, WORK REAL(8), DIMENSION(:) :: THETA, PHI COMPLEX(8), DIMENSION(:,:) :: X11, X12, X21, X22 SUBROUTINE UNBDB_64(TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO) INTEGER(8) :: M, P, Q, LDX11, LDX12, LDX21, LDX22, LWORK, INFO CHARACTER(LEN=1) :: TRANS, SIGNS COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, TAUQ2, WORK REAL(8), DIMENSION(:) :: THETA, PHI COMPLEX(8), DIMENSION(:,:) :: X11, X12, X21, X22 C INTERFACE #include <sunperf.h> void zunbdb (char trans, char signs, int m, int p, int q, doublecomplex *x11, int ldx11, doublecomplex *x12, int ldx12, doublecomplex *x21, int ldx21, doublecomplex *x22, int ldx22, double *theta, double *phi, doublecomplex *taup1, doublecomplex *taup2, doublecomplex *tauq1, doublecomplex *tauq2, int *info); void zunbdb_64 (char trans, char signs, long m, long p, long q, double- complex *x11, long ldx11, doublecomplex *x12, long ldx12, doublecomplex *x21, long ldx21, doublecomplex *x22, long ldx22, double *theta, double *phi, doublecomplex *taup1, dou- blecomplex *taup2, doublecomplex *tauq1, doublecomplex *tauq2, long *info);
Oracle Solaris Studio Performance Library zunbdb(3P)
NAME
zunbdb - simultaneously bidiagonalize the blocks of an M-by-M parti-
tioned unitary matrix
SYNOPSIS
SUBROUTINE ZUNBDB(TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21,
LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2,
WORK, LWORK, INFO)
CHARACTER*1 SIGNS, TRANS
INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P, Q
DOUBLE PRECISION PHI(*), THETA(*)
DOUBLE COMPLEX TAUP1(*), TAUP2(*), TAUQ1(*), TAUQ2(*), WORK(*),
X11(LDX11,*), X12(LDX12,*), X21(LDX21,*), X22(LDX22,*)
SUBROUTINE ZUNBDB_64(TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1,
TAUQ2, WORK, LWORK, INFO)
CHARACTER*1 SIGNS, TRANS
INTEGER*8 INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P, Q
DOUBLE PRECISION PHI(*), THETA(*)
DOUBLE COMPLEX TAUP1(*), TAUP2(*), TAUQ1(*), TAUQ2(*), WORK(*),
X11(LDX11,*), X12(LDX12,*), X21(LDX21,*), X22(LDX22,*)
F95 INTERFACE
SUBROUTINE UNBDB(TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21,
LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2,
WORK, LWORK, INFO)
INTEGER :: M, P, Q, LDX11, LDX12, LDX21, LDX22, LWORK, INFO
CHARACTER(LEN=1) :: TRANS, SIGNS
COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, TAUQ2, WORK
REAL(8), DIMENSION(:) :: THETA, PHI
COMPLEX(8), DIMENSION(:,:) :: X11, X12, X21, X22
SUBROUTINE UNBDB_64(TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21,
LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2,
WORK, LWORK, INFO)
INTEGER(8) :: M, P, Q, LDX11, LDX12, LDX21, LDX22, LWORK, INFO
CHARACTER(LEN=1) :: TRANS, SIGNS
COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, TAUQ2, WORK
REAL(8), DIMENSION(:) :: THETA, PHI
COMPLEX(8), DIMENSION(:,:) :: X11, X12, X21, X22
C INTERFACE
#include <sunperf.h>
void zunbdb (char trans, char signs, int m, int p, int q, doublecomplex
*x11, int ldx11, doublecomplex *x12, int ldx12, doublecomplex
*x21, int ldx21, doublecomplex *x22, int ldx22, double
*theta, double *phi, doublecomplex *taup1, doublecomplex
*taup2, doublecomplex *tauq1, doublecomplex *tauq2, int
*info);
void zunbdb_64 (char trans, char signs, long m, long p, long q, double-
complex *x11, long ldx11, doublecomplex *x12, long ldx12,
doublecomplex *x21, long ldx21, doublecomplex *x22, long
ldx22, double *theta, double *phi, doublecomplex *taup1, dou-
blecomplex *taup2, doublecomplex *tauq1, doublecomplex
*tauq2, long *info);
PURPOSE
zunbdb simultaneously bidiagonalizes the blocks of an M-by-M parti-
tioned unitary matrix X:
[ B11 | B12 0 0 ]
[ X11 | X12 ] [ P1 | ] [ 0 | 0 -I 0 ] [ Q1 | ]**H
X = [-----------] = [---------] [----------------] [---------] .
[ X21 | X22 ] [ | P2 ] [ B21 | B22 0 0 ] [ | Q2 ]
[ 0 | 0 0 I ]
X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is
not the case, then X must be transposed and/or permuted. This can be
done in constant time using the TRANS and SIGNS options. See ZUNCSD for
details.)
The unitary matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by- (M-P), Q-
by-Q, and (M-Q)-by-(M-Q), respectively. They are represented implicitly
by Householder vectors.
B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
implicitly by angles THETA, PHI.
ARGUMENTS
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 <=
MIN(P,M-P,M-Q).
X11 (input/output)
X11 is COMPLEX*16 array, dimension (LDX11,Q)
On entry, the top-left block of the unitary matrix to be
reduced. On exit, the form depends on TRANS:
If TRANS = 'N', then the columns of tril(X11) specify reflec-
tors for P1, the rows of triu(X11,1) specify reflectors for
Q1;
else TRANS = 'T', and the rows of triu(X11) specify reflec-
tors for P1, the columns of tril(X11,-1) specify reflectors
for Q1.
LDX11 (input)
LDX11 is INTEGER
The leading dimension of X11. If TRANS = 'N', then LDX11 >=
P; else LDX11 >= Q.
X12 (input/output)
X12 is COMPLEX*16 array, dimension (LDX12,M-Q)
On entry, the top-right block of the unitary matrix to be
reduced. On exit, the form depends on TRANS:
If TRANS = 'N', then the rows of triu(X12) specify the first
P reflectors for Q2;
else TRANS = 'T', and the columns of tril(X12) specify the
first P reflectors for Q2.
LDX12 (input)
LDX12 is INTEGER
The leading dimension of X12. If TRANS = 'N', then LDX12 >=
P; else LDX11 >= M-Q.
X21 (input/output)
X21 is COMPLEX*16 array, dimension (LDX21,Q)
On entry, the bottom-left block of the unitary matrix to be
reduced. On exit, the form depends on TRANS:
If TRANS = 'N', then the columns of tril(X21) specify reflec-
tors for P2;
else TRANS = 'T', and the rows of triu(X21) specify reflec-
tors for P2.
LDX21 (input)
LDX21 is INTEGER
The leading dimension of X21. If TRANS = 'N', then LDX21 >=
M-P; else LDX21 >= Q.
X22 (input/output)
X22 is COMPLEX*16 array, dimension (LDX22,M-Q)
On entry, the bottom-right block of the unitary matrix to be
reduced. On exit, the form depends on TRANS:
If TRANS = 'N', then the rows of triu(X22(Q+1:M-P,P+1:M-Q))
specify the last M-P-Q reflectors for Q2,
else TRANS = 'T', and the columns of tril(X22(P+1:M-Q,Q+1:M-
P)) specify the last M-P-Q reflectors for P2.
LDX22 (input)
LDX22 is INTEGER
The leading dimension of X22. If TRANS = 'N', then LDX22 >=
M-P; else LDX22 >= M-Q.
THETA (output)
THETA is DOUBLE PRECISION array, dimension (Q)
The entries of the bidiagonal blocks B11, B12, B21, B22 can
be computed from the angles THETA and PHI. See Further
Details.
PHI (output)
PHI is DOUBLE PRECISION array, dimension (Q-1)
The entries of the bidiagonal blocks B11, B12, B21, B22 can
be computed from the angles THETA and PHI. See Further
Details.
TAUP1 (output)
TAUP1 is COMPLEX*16 array, dimension (P)
The scalar factors of the elementary reflectors that define
P1.
TAUP2 (output)
TAUP2 is COMPLEX*16 array, dimension (M-P)
The scalar factors of the elementary reflectors that define
P2.
TAUQ1 (output)
TAUQ1 is COMPLEX*16 array, dimension (Q)
The scalar factors of the elementary reflectors that define
Q1.
TAUQ2 (output)
TAUQ2 is COMPLEX*16 array, dimension (M-Q)
The scalar factors of the elementary reflectors that define
Q2.
WORK (output)
WORK is COMPLEX*16 array, dimension (LWORK)
LWORK (input)
LWORK is INTEGER
The dimension of the array WORK. LWORK >= M-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.
7 Nov 2015 zunbdb(3P)