sormrz(3)

NAME

SORMRZ - overwrite the general real M-by-N matrix C with

SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS

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

PURPOSE

SORMRZ overwrites the general real M-by-N matrix C with

SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T':

Q**T * C C * Q**T

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**T from the Left;
= 'R': apply Q or Q**T from the Right.

TRANS (input) CHARACTER*1

= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.

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 re

flector 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 rou

tine 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 ele

mentary 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**H*C or C*Q**H or C*Q.

LDC (input) INTEGER

The leading dimension of the array C. LDC >=

max(1,M).

WORK (workspace/output) REAL array, dimension (LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal

LWORK.

LWORK (input) INTEGER

The dimension of the array WORK. If SIDE = 'L',

LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum

performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if

SIDE = 'R', 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 ille

gal value

FURTHER DETAILS

Based on contributions by

A. Petitet, Computer Science Dept., Univ. of Tenn.,

Knoxville, USA

LAPACK version 3.0 15 June 2000

SORMRZ(3)