sormr3.f man page

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

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page sormr3(3) is an alias of sormr3.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK