zunbdb1 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns
SUBROUTINE ZUNBDB1(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21 DOUBLE PRECISION PHI(*), THETA(*) DOUBLE COMPLEX TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), X11(LDX11,*), X21(LDX21,*) SUBROUTINE ZUNBDB1_64(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) INTEGER*8 INFO, LWORK, M, P, Q, LDX11, LDX21 DOUBLE PRECISION PHI(*), THETA(*) DOUBLE COMPLEX TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), X11(LDX11,*), X21(LDX21,*) F95 INTERFACE SUBROUTINE UNBDB1(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) INTEGER :: M, P, Q, LDX11, LDX21 COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, WORK REAL(8), DIMENSION(:) :: THETA, PHI COMPLEX(8), DIMENSION(:,:) :: X11, X21 INTEGER(8) :: LWORK, INFO SUBROUTINE UNBDB1_64(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) INTEGER(8) :: M, P, Q, LDX11, LDX21 COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, WORK REAL(8), DIMENSION(:) :: THETA, PHI COMPLEX(8), DIMENSION(:,:) :: X11, X21 INTEGER(8)(8) :: LWORK, INFO C INTERFACE #include <sunperf.h> void zunbdb1 (int m, int p, int q, doublecomplex *x11, int ldx11, dou- blecomplex *x21, int ldx21, double *theta, double *phi, dou- blecomplex *taup1, doublecomplex *taup2, doublecomplex *tauq1, long long *info); void zunbdb1_64 (long m, long p, long q, doublecomplex *x11, long ldx11, doublecomplex *x21, long ldx21, double *theta, double *phi, doublecomplex *taup1, doublecomplex *taup2, doublecom- plex *tauq1, long long *info);
Oracle Solaris Studio Performance Library zunbdb1(3P)
NAME
zunbdb1 - simultaneously bidiagonalize the blocks of a tall and skinny
matrix with orthonomal columns
SYNOPSIS
SUBROUTINE ZUNBDB1(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1,
TAUP2, TAUQ1, WORK, LWORK, INFO)
INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21
DOUBLE PRECISION PHI(*), THETA(*)
DOUBLE COMPLEX TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), X11(LDX11,*),
X21(LDX21,*)
SUBROUTINE ZUNBDB1_64(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO)
INTEGER*8 INFO, LWORK, M, P, Q, LDX11, LDX21
DOUBLE PRECISION PHI(*), THETA(*)
DOUBLE COMPLEX TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), X11(LDX11,*),
X21(LDX21,*)
F95 INTERFACE
SUBROUTINE UNBDB1(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1,
TAUP2, TAUQ1, WORK, LWORK, INFO)
INTEGER :: M, P, Q, LDX11, LDX21
COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, WORK
REAL(8), DIMENSION(:) :: THETA, PHI
COMPLEX(8), DIMENSION(:,:) :: X11, X21
INTEGER(8) :: LWORK, INFO
SUBROUTINE UNBDB1_64(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO)
INTEGER(8) :: M, P, Q, LDX11, LDX21
COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, WORK
REAL(8), DIMENSION(:) :: THETA, PHI
COMPLEX(8), DIMENSION(:,:) :: X11, X21
INTEGER(8)(8) :: LWORK, INFO
C INTERFACE
#include <sunperf.h>
void zunbdb1 (int m, int p, int q, doublecomplex *x11, int ldx11, dou-
blecomplex *x21, int ldx21, double *theta, double *phi, dou-
blecomplex *taup1, doublecomplex *taup2, doublecomplex
*tauq1, long long *info);
void zunbdb1_64 (long m, long p, long q, doublecomplex *x11, long
ldx11, doublecomplex *x21, long ldx21, double *theta, double
*phi, doublecomplex *taup1, doublecomplex *taup2, doublecom-
plex *tauq1, long long *info);
PURPOSE
zunbdb1 simultaneously bidiagonalizes the blocks of a tall and skinny
matrix X with orthonomal columns:
[ B11 ]
[ X11 ] [ P1 | ] [ 0 ]
[-----] = [---------] [-----] Q1**T .
[ X21 ] [ | P2 ] [ B21 ]
[ 0 ]
X11 is P-by-Q, and X21 is (M-P)-by-Q. Q must be no larger than P,
M-P, or M-Q. Routines ZUNBDB2, ZUNBDB3, and ZUNBDB4 handle cases in
which Q is not the minimum dimension.
The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P), and (M-
Q)-by-(M-Q), respectively. They are represented implicitly by House-
holder vectors.
B11 and B12 are Q-by-Q bidiagonal matrices represented implicitly by
angles THETA, PHI.
ARGUMENTS
M (input)
M is INTEGER
The number of rows X11 plus the number of rows in X21.
P (input)
P is INTEGER
The number of rows in X11. 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 block of the matrix X to be reduced.
On exit, the columns of tril(X11) specify reflectors for P1
and the rows of triu(X11,1) specify reflectors for Q1.
LDX11 (input)
LDX11 is INTEGER
The leading dimension of X11. LDX11 >= P.
X21 (input/output)
X21 is COMPLEX*16 array, dimension (LDX21,Q)
On entry, the bottom block of the matrix X to be reduced.
On exit, the columns of tril(X21) specify reflectors for P2.
LDX21 (input)
LDX21 is INTEGER
The leading dimension of X21. LDX21 >= M-P.
THETA (output)
THETA is DOUBLE PRECISION array, dimension (Q)
The entries of the bidiagonal blocks B11, B21 are defined by
THETA and PHI. See Further Details.
PHI (output)
PHI is DOUBLE PRECISION array, dimension (Q-1)
The entries of the bidiagonal blocks B11, B21 are defined by
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.
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.
FURTHER DETAILS
The upper-bidiagonal blocks B11, B21 are represented implicitly by
angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
in each bidiagonal band is a product of a sine or cosine of a THETA
with a sine or cosine of a PHI. See [1] or ZUNCSD for details.
P1, P2, and Q1 are represented as products of elementary reflectors.
See ZUNCSD2BY1 for details on generating P1, P2, and Q1 using ZUNGQR
and ZUNGLQ.
7 Nov 2015 zunbdb1(3P)