sormtr(3)

NAME

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

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

SYNOPSIS

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

PURPOSE

SORMTR 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 of order nq, with nq =

m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the

product of nq-1 elementary reflectors, as returned by SSYTRD:

if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

ARGUMENTS

SIDE (input) CHARACTER*1

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

UPLO (input) CHARACTER*1

= 'U': Upper triangle of A contains elementary re

flectors from SSYTRD; = 'L': Lower triangle of A contains elemen

tary reflectors from SSYTRD.

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.

A (input) REAL array, dimension

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

vectors which define the elementary reflectors, as returned by

SSYTRD.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.

TAU (input) REAL array, dimension

(M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i)

must contain the scalar factor of the elementary reflector H(i),

as returned by SSYTRD.

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

LAPACK version 3.0 15 June 2000

SORMTR(3)