sgebrd (l) - Linux Manuals
sgebrd: reduces a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation
NAME
SGEBRD - reduces a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformationSYNOPSIS
- SUBROUTINE SGEBRD(
- M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, INFO )
- INTEGER INFO, LDA, LWORK, M, N
- REAL A( LDA, * ), D( * ), E( * ), TAUP( * ), TAUQ( * ), WORK( * )
PURPOSE
SGEBRD 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.ARGUMENTS
- M (input) INTEGER
- The number of rows in the matrix A. M >= 0.
- N (input) INTEGER
- The number of columns in the matrix A. N >= 0.
- A (input/output) REAL array, dimension (LDA,N)
- 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) INTEGER The leading dimension of the array A. LDA >= max(1,M).
- D (output) REAL array, dimension (min(M,N))
- The diagonal elements of the bidiagonal matrix B: D(i) = A(i,i).
- E (output) REAL array, dimension (min(M,N)-1)
- 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.
- TAUQ (output) REAL array dimension (min(M,N))
- The scalar factors of the elementary reflectors which represent the orthogonal matrix Q. See Further Details. TAUP (output) REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors which represent the orthogonal matrix P. See Further Details. WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
- LWORK (input) INTEGER
- 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) INTEGER
-
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
FURTHER DETAILS
The matrices Q and P are represented as products of elementary reflectors:If m >= n,
Q
H(i)
If m < n,
Q
H(i)
The contents of A on exit are illustrated by the following examples: m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):