Contents
dorgbr - generate one of the real orthogonal matrices Q or
P**T determined by SGEBRD when reducing a real matrix A to
bidiagonal form
SUBROUTINE DORGBR(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CHARACTER * 1 VECT
INTEGER M, N, K, LDA, LWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
SUBROUTINE DORGBR_64(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CHARACTER * 1 VECT
INTEGER*8 M, N, K, LDA, LWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
F95 INTERFACE
SUBROUTINE ORGBR(VECT, M, [N], K, A, [LDA], TAU, [WORK], [LWORK],
[INFO])
CHARACTER(LEN=1) :: VECT
INTEGER :: M, N, K, LDA, LWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE ORGBR_64(VECT, M, [N], K, A, [LDA], TAU, [WORK], [LWORK],
[INFO])
CHARACTER(LEN=1) :: VECT
INTEGER(8) :: M, N, K, LDA, LWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dorgbr(char vect, int m, int n, int k, double *a, int
lda, double *tau, int *info);
void dorgbr_64(char vect, long m, long n, long k, double *a,
long lda, double *tau, long *info);
dorgbr generates one of the real orthogonal matrices Q or
P**T determined by SGEBRD when reducing a real matrix A to
bidiagonal form: A = Q * B * P**T. Q and P**T are defined
as products of elementary reflectors H(i) or G(i) respec-
tively.
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 SORGBR returns the
first n columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as
an M-by-M matrix.
If VECT = 'P', A is assumed to have been a K-by-N matrix,
and P**T is of order N:
if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the
first m rows of P**T, where n >= m >= k;
if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns
P**T as an N-by-N matrix.
VECT (input)
Specifies whether the matrix Q or the matrix P**T
is required, as defined in the transformation
applied by SGEBRD:
= 'Q': generate Q;
= 'P': generate P**T.
M (input) The number of rows of the matrix Q or P**T to be
returned. M >= 0.
N (input) The number of columns of the matrix Q or P**T 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 SGEBRD. If VECT =
'P', the number of rows in the original K-by-N
matrix reduced by SGEBRD. K >= 0.
A (input/output)
On entry, the vectors which define the elementary
reflectors, as returned by SGEBRD. On exit, the
M-by-N matrix Q or P**T.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,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**T, as returned by SGEBRD 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