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sormr3.f(3) LAPACK sormr3.f(3)

NAME

sormr3.f

SYNOPSIS

Functions/Subroutines


subroutine sormr3 (SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO)
SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

Function/Subroutine Documentation

subroutine sormr3 (character SIDE, character TRANS, integer M, integer N, integer K, integer L, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) WORK, integer INFO)

SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

Purpose:


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

Parameters:

SIDE


SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left
= 'R': apply Q or Q**T from the Right

TRANS


TRANS is CHARACTER*1
= 'N': apply Q (No transpose)
= 'T': apply Q**T (Transpose)

M


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

N


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

K


K is 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


L is 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


A is 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


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

TAU


TAU is REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by STZRZF.

C


C is 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


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

WORK


WORK is REAL array, dimension
(N) if SIDE = 'L',
(M) if SIDE = 'R'

INFO


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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Contributors:

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

Further Details:


Definition at line 180 of file sormr3.f.

Author

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Tue Nov 14 2017 Version 3.8.0