NAME¶

SORMR3 - overwrites the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',

SYNOPSIS¶

SUBROUTINE SORMR3(

SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO )

CHARACTER SIDE, TRANS INTEGER INFO, K, L, LDA, LDC, M, N REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

PURPOSE¶

SORMR3 overwrites the general real m by n matrix C with where Q is a real orthogonal matrix defined as the product of k elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by STZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

ARGUMENTS¶

SIDE (input) CHARACTER*1

= 'L': apply Q or Q' from the Left
= 'R': apply Q or Q' from the Right

TRANS (input) CHARACTER*1

= 'N': apply Q (No transpose)
= 'T': apply Q' (Transpose)

M (input) INTEGER

The number of rows of the matrix C. M >= 0.

N (input) INTEGER

The number of columns of the matrix C. N >= 0.

K (input) INTEGER

The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.

L (input) INTEGER

The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.

A (input) REAL array, dimension

(LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by STZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.

LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(1,K).

TAU (input) REAL array, dimension (K)

TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by STZRZF.

C (input/output) REAL array, dimension (LDC,N)

On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.

LDC (input) INTEGER

The leading dimension of the array C. LDC >= max(1,M).

WORK (workspace) REAL array, dimension

(N) if SIDE = 'L', (M) if SIDE = 'R'

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS¶

Based on contributions by
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA