# slabrd (l) - Linux Manuals

## slabrd: reduces the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Qaq * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A

## NAME

SLABRD - reduces the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Qaq * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A## SYNOPSIS

- SUBROUTINE SLABRD(
- M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, LDY )

- INTEGER LDA, LDX, LDY, M, N, NB

- REAL A( LDA, * ), D( * ), E( * ), TAUP( * ), TAUQ( * ), X( LDX, * ), Y( LDY, * )

## PURPOSE

SLABRD reduces the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Qaq * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A. If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower bidiagonal form.This is an auxiliary routine called by SGEBRD

## ARGUMENTS

- M (input) INTEGER
- The number of rows in the matrix A.
- N (input) INTEGER
- The number of columns in the matrix A.
- NB (input) INTEGER
- The number of leading rows and columns of A to be reduced.
- A (input/output) REAL array, dimension (LDA,N)
- On entry, the m by n general matrix to be reduced. On exit, the first NB rows and columns of the matrix are overwritten; the rest of the array is unchanged. If m >= n, elements on and below the diagonal in the first NB columns, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors; and elements above the diagonal in the first NB rows, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors. If m < n, elements below the diagonal in the first NB columns, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and elements on and above the diagonal in the first NB rows, 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 (NB)
- The diagonal elements of the first NB rows and columns of the reduced matrix. D(i) = A(i,i).
- E (output) REAL array, dimension (NB)
- The off-diagonal elements of the first NB rows and columns of the reduced matrix.
- TAUQ (output) REAL array dimension (NB)
- The scalar factors of the elementary reflectors which represent the orthogonal matrix Q. See Further Details. TAUP (output) REAL array, dimension (NB) The scalar factors of the elementary reflectors which represent the orthogonal matrix P. See Further Details. X (output) REAL array, dimension (LDX,NB) The m-by-nb matrix X required to update the unreduced part of A.
- LDX (input) INTEGER
- The leading dimension of the array X. LDX >= M.
- Y (output) REAL array, dimension (LDY,NB)
- The n-by-nb matrix Y required to update the unreduced part of A.
- LDY (input) INTEGER
- The leading dimension of the array Y. LDY >= N.

## FURTHER DETAILS

The matrices Q and P are represented as products of elementary reflectors:Q

H(i)

The contents of A on exit are illustrated by the following examples with nb = 2:

m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):