zungbr(3P) Sun Performance Library zungbr(3P)NAMEzungbr - generate one of the complex unitary matrices Q or P**H deter‐
mined by ZGEBRD when reducing a complex matrix A to bidiagonal form
SYNOPSIS
SUBROUTINE ZUNGBR(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CHARACTER * 1 VECT
DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER M, N, K, LDA, LWORK, INFO
SUBROUTINE ZUNGBR_64(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CHARACTER * 1 VECT
DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER*8 M, N, K, LDA, LWORK, INFO
F95 INTERFACE
SUBROUTINE UNGBR(VECT, M, [N], K, A, [LDA], TAU, [WORK], [LWORK],
[INFO])
CHARACTER(LEN=1) :: VECT
COMPLEX(8), DIMENSION(:) :: TAU, WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: M, N, K, LDA, LWORK, INFO
SUBROUTINE UNGBR_64(VECT, M, [N], K, A, [LDA], TAU, [WORK], [LWORK],
[INFO])
CHARACTER(LEN=1) :: VECT
COMPLEX(8), DIMENSION(:) :: TAU, WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: M, N, K, LDA, LWORK, INFO
C INTERFACE
#include <sunperf.h>
void zungbr(char vect, int m, int n, int k, doublecomplex *a, int lda,
doublecomplex *tau, int *info);
void zungbr_64(char vect, long m, long n, long k, doublecomplex *a,
long lda, doublecomplex *tau, long *info);
PURPOSEzungbr generates one of the complex unitary matrices Q or P**H deter‐
mined by ZGEBRD when reducing a complex matrix A to bidiagonal form: A
= Q * B * P**H. Q and P**H are defined as products of elementary
reflectors H(i) or G(i) respectively.
If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q is of
order M:
if m >= k, Q = H(1)H(2) . . . H(k) and ZUNGBR returns the first n col‐
umns of Q, where m >= n >= k;
if m < k, Q = H(1)H(2) . . . H(m-1) and ZUNGBR returns Q as an M-by-M
matrix.
If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H is
of order N:
if k < n, P**H = G(k) . . . G(2)G(1) and ZUNGBR returns the first m
rows of P**H, where n >= m >= k;
if k >= n, P**H = G(n-1) . . . G(2)G(1) and ZUNGBR returns P**H as an
N-by-N matrix.
ARGUMENTS
VECT (input)
Specifies whether the matrix Q or the matrix P**H is
required, as defined in the transformation applied by ZGEBRD:
= 'Q': generate Q;
= 'P': generate P**H.
M (input) The number of rows of the matrix Q or P**H to be returned. M
>= 0.
N (input) The number of columns of the matrix Q or P**H to be returned.
N >= 0. If VECT = 'Q', M >= N >= min(M,K); if VECT = 'P', N
>= M >= min(N,K).
K (input) If VECT = 'Q', the number of columns in the original M-by-K
matrix reduced by ZGEBRD. If VECT = 'P', the number of rows
in the original K-by-N matrix reduced by ZGEBRD. K >= 0.
A (input/output)
On entry, the vectors which define the elementary reflectors,
as returned by ZGEBRD. On exit, the M-by-N matrix Q or P**H.
LDA (input)
The leading dimension of the array A. LDA >= M.
TAU (input)
(min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P' TAU(i) must
contain the scalar factor of the elementary reflector H(i) or
G(i), which determines Q or P**H, as returned by ZGEBRD in
its array argument TAUQ or TAUP.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension of the array WORK. LWORK >= max(1,min(M,N)).
For optimum performance LWORK >= min(M,N)*NB, where NB is the
optimal blocksize.
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)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 zungbr(3P)
