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



NAME
       SORMQR

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



PURPOSE
            SORMQR overwrites the general real M-by-N matrix C with

                            SIDE = 'L'     SIDE = 'R'
            TRANS = 'N':      Q * C          C * Q
            TRANS = 'T':      Q**T * C       C * Q**T

            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 SGEQRF. 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':  No transpose, apply Q;
                     = 'T':  Transpose, apply Q**T.

           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.

           A         (input)
                     A is REAL array, dimension (LDA,K)
                     The i-th column must contain the vector which defines the
                     elementary reflector H(i), for i = 1,2,...,k, as returned by
                     SGEQRF in the first k columns of its array argument A.

           LDA       (input)
                     LDA is INTEGER
                     The leading dimension of the array A.
                     If SIDE = 'L', LDA >= max(1,M);
                     if SIDE = 'R', LDA >= max(1,N).

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

           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 (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK     (input)
                     LWORK is INTEGER
                     The dimension of the array WORK.
                     If SIDE = 'L', LWORK >= max(1,N);
                     if SIDE = 'R', LWORK >= max(1,M).
                     For optimum performance LWORK >= N*NB if SIDE = 'L', and
                     LWORK >= M*NB if SIDE = 'R', where NB is the optimal
                     blocksize.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           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                      SORMQR(3)