sgebd2 (l) - Linux Manuals
sgebd2: reduces a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation
NAME
SGEBD2 - reduces a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformationSYNOPSIS
- SUBROUTINE SGEBD2(
- M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )
- INTEGER INFO, LDA, M, N
- REAL A( LDA, * ), D( * ), E( * ), TAUP( * ), TAUQ( * ), WORK( * )
PURPOSE
SGEBD2 reduces a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Qaq * 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) REAL array, dimension (max(M,N))
- 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):