# dormr3.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **dormr3** (SIDE, TRANS, M, **N**, K, L, A, **LDA**, TAU, C, LDC, WORK, INFO)**DORMR3** multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

## Function/Subroutine Documentation

### subroutine dormr3 (character SIDE, character TRANS, integer M, integer N, integer K, integer L, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) WORK, integer INFO)

**DORMR3** multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

**Purpose:**

DORMR3 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 DTZRZF. 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 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*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,K).

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

*C*C is DOUBLE PRECISION 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 DOUBLE PRECISION 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 dormr3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dormr3(3) is an alias of dormr3.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK