DORMRZ(3f)

NAME
DORMRZ - the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS

SUBROUTINE DORMRZ(
    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

DOUBLE
    PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

PURPOSE
DORMRZ 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 DTZRZF. 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) DOUBLE PRECISION 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 DTZRZF 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) DOUBLE PRECISION array, dimension (K)
    TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DTZRZF.

C       (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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