SORMR3(3)      LAPACK routine of NEC Numeric Library Collection      SORMR3(3)



NAME
       SORMR3

SYNOPSIS
       SUBROUTINE SORMR3 (SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK,
           INFO)



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'.




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

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

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

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

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

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

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

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

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



LAPACK routine                  31 October 2017                      SORMR3(3)