Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - 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',

**SYNOPSIS**

SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO ) CHARACTER SIDE, TRANS INTEGER INFO, K, L, LDA, LDC, M, N DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

**PURPOSE**

DORMR3 overwrites the general real m by n matrix C with 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': apply Q (No transpose) = 'T': apply Q**T (Transpose) 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**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) DOUBLE PRECISION array, dimension (N) if SIDE = 'L', (M) if SIDE = 'R' 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 LAPACK routine (version 3.3.1) April 2011 DORMR3(3lapack)