# sorml2.f - Man Page

SRC/sorml2.f

## Synopsis

### Functions/Subroutines

subroutine **sorml2** (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)**SORML2** multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm).

## Function/Subroutine Documentation

### subroutine sorml2 (character side, character trans, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)

**SORML2** multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm).

**Purpose:**

SORML2 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 = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'T', where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by SGELQF. 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.

*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 SGELQF in the first 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 SGELQF.

*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.

Definition at line **157** of file **sorml2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sorml2(3) is an alias of sorml2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK