dgebrd
dgebrd - reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation
SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
* INFO)
INTEGER M, N, LDA, LWORK, INFO
DOUBLE PRECISION A(LDA,*), D(*), E(*), TAUQ(*), TAUP(*), WORK(*)
SUBROUTINE DGEBRD_64( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
* INFO)
INTEGER*8 M, N, LDA, LWORK, INFO
DOUBLE PRECISION A(LDA,*), D(*), E(*), TAUQ(*), TAUP(*), WORK(*)
SUBROUTINE GEBRD( [M], [N], A, [LDA], D, E, TAUQ, TAUP, [WORK],
* [LWORK], [INFO])
INTEGER :: M, N, LDA, LWORK, INFO
REAL(8), DIMENSION(:) :: D, E, TAUQ, TAUP, WORK
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE GEBRD_64( [M], [N], A, [LDA], D, E, TAUQ, TAUP, [WORK],
* [LWORK], [INFO])
INTEGER(8) :: M, N, LDA, LWORK, INFO
REAL(8), DIMENSION(:) :: D, E, TAUQ, TAUP, WORK
REAL(8), DIMENSION(:,:) :: A
#include <sunperf.h>
void dgebrd(int m, int n, double *a, int lda, double *d, double *e, double *tauq, double *taup, int *info);
void dgebrd_64(long m, long n, double *a, long lda, double *d, double *e, double *tauq, double *taup, long *info);
dgebrd reduces a general real M-by-N matrix A to upper or lower
bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
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* M (input)
-
The number of rows in the matrix A. M >= 0.
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* N (input)
-
The number of columns in the matrix A. N >= 0.
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* A (input/output)
-
On entry, the M-by-N general matrix to be reduced.
On exit,
if m >= n, the diagonal and the first superdiagonal are
overwritten with the upper bidiagonal matrix B; the
elements below the diagonal, with the array TAUQ, represent
the orthogonal matrix Q as a product of elementary
reflectors, and the elements above the first superdiagonal,
with the array TAUP, represent the orthogonal matrix P as
a product of elementary reflectors;
if m < n, the diagonal and the first subdiagonal are
overwritten with the lower bidiagonal matrix B; the
elements below the first subdiagonal, with the array TAUQ,
represent the orthogonal matrix Q as a product of
elementary reflectors, and the elements above the diagonal,
with the array TAUP, represent the orthogonal matrix P as
a product of elementary reflectors.
See Further Details.
-
* LDA (input)
-
The leading dimension of the array A. LDA >= max(1,M).
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* D (output)
-
The diagonal elements of the bidiagonal matrix B:
D(i) = A(i,i).
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* E (output)
-
The off-diagonal elements of the bidiagonal matrix B:
if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
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* TAUQ (output)
-
The scalar factors of the elementary reflectors which
represent the orthogonal matrix Q. See Further Details.
-
* TAUP (output)
-
The scalar factors of the elementary reflectors which
represent the orthogonal matrix P. See Further Details.
-
* WORK (workspace)
-
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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* LWORK (input)
-
The length of the array WORK. LWORK >= max(1,M,N).
For optimum performance LWORK >= (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)
-