Contents
zungbr - generate one of the complex unitary matrices Q or
P**H determined by CGEBRD when reducing a complex matrix A
to bidiagonal form
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, doublecom-
plex *a, long lda, doublecomplex *tau, long
*info);
zungbr generates one of the complex unitary matrices Q or
P**H determined by CGEBRD 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 columns 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.
VECT (input)
Specifies whether the matrix Q or the matrix P**H
is required, as defined in the transformation
applied by CGEBRD:
= '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 origi-
nal M-by-K matrix reduced by CGEBRD. If VECT =
'P', the number of rows in the original K-by-N
matrix reduced by CGEBRD. K >= 0.
A (input/output)
On entry, the vectors which define the elementary
reflectors, as returned by CGEBRD. 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 ele-
mentary reflector H(i) or G(i), which determines Q
or P**H, as returned by CGEBRD in its array argu-
ment 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 ille-
gal value