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 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 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**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 (MAX(1,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 illegal value

FURTHER DETAILS

Based on contributions by

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