zunbdb4 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns
SUBROUTINE ZUNBDB4(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO) INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21 DOUBLE PRECISION PHI(*), THETA(*) DOUBLE COMPLEX PHANTOM(*), TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), X11(LDX11,*), X21(LDX21,*) SUBROUTINE ZUNBDB4_64(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO) INTEGER*8 INFO, LWORK, M, P, Q, LDX11, LDX21 DOUBLE PRECISION PHI(*), THETA(*) DOUBLE COMPLEX PHANTOM(*), TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), X11(LDX11,*), X21(LDX21,*) F95 INTERFACE SUBROUTINE UNBDB4(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO) INTEGER :: M, P, Q, LDX11, LDX21, LWORK, INFO COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, PHANTOM, WORK REAL(8), DIMENSION(:) :: THETA, PHI COMPLEX(8), DIMENSION(:,:) :: X11, X21 SUBROUTINE UNBDB4_64(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO) INTEGER(8) :: M, P, Q, LDX11, LDX21, LWORK, INFO COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, PHANTOM, WORK REAL(8), DIMENSION(:) :: THETA, PHI COMPLEX(8), DIMENSION(:,:) :: X11, X21 C INTERFACE #include <sunperf.h> void zunbdb4 (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, doublecomplex *phantom, int *info); void zunbdb4_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, doublecomplex *phantom, long *info);
Oracle Solaris Studio Performance Library zunbdb4(3P)
NAME
zunbdb4 - simultaneously bidiagonalize the blocks of a tall and skinny
matrix with orthonomal columns
SYNOPSIS
SUBROUTINE ZUNBDB4(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1,
TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO)
INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21
DOUBLE PRECISION PHI(*), THETA(*)
DOUBLE COMPLEX PHANTOM(*), TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
X11(LDX11,*), X21(LDX21,*)
SUBROUTINE ZUNBDB4_64(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO)
INTEGER*8 INFO, LWORK, M, P, Q, LDX11, LDX21
DOUBLE PRECISION PHI(*), THETA(*)
DOUBLE COMPLEX PHANTOM(*), TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
X11(LDX11,*), X21(LDX21,*)
F95 INTERFACE
SUBROUTINE UNBDB4(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1,
TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO)
INTEGER :: M, P, Q, LDX11, LDX21, LWORK, INFO
COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, PHANTOM, WORK
REAL(8), DIMENSION(:) :: THETA, PHI
COMPLEX(8), DIMENSION(:,:) :: X11, X21
SUBROUTINE UNBDB4_64(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO)
INTEGER(8) :: M, P, Q, LDX11, LDX21, LWORK, INFO
COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, PHANTOM, WORK
REAL(8), DIMENSION(:) :: THETA, PHI
COMPLEX(8), DIMENSION(:,:) :: X11, X21
C INTERFACE
#include <sunperf.h>
void zunbdb4 (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, doublecomplex *phantom, int *info);
void zunbdb4_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, doublecomplex *phantom, long *info);
PURPOSE
zunbdb4 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. M-Q must be no larger than P,
M-P, or Q. Routines ZUNBDB1, ZUNBDB2, and ZUNBDB3 handle cases in which
M-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 (M-Q)-by-(M-Q) bidiagonal matrices represented implic-
itly 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 <= M and M-Q <=
min(P,M-P,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.
PHANTOM (output)
PHANTOM is COMPLEX*16 array, dimension (M)
The routine computes an M-by-1 column vector Y that is
orthogonal to the columns of [ X11; X21 ]. PHANTOM(1:P) and
PHANTOM(P+1:M) contain Householder vectors for Y(1:P) and
Y(P+1:M), respectively.
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 zunbdb4(3P)