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



NAME
       DGEMQRT

SYNOPSIS
       SUBROUTINE DGEMQRT (SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC,
           WORK, INFO)



PURPOSE
            DGEMQRT 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) = I - V T V**T

            generated using the compact WY representation as returned by DGEQRT.

            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;
                     = 'C':  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.

           NB        (input)
                     NB is INTEGER
                     The block size used for the storage of T.  K >= NB >= 1.
                     This must be the same value of NB used to generate T
                     in CGEQRT.

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

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

           T         (input)
                     T is DOUBLE PRECISION array, dimension (LDT,K)
                     The upper triangular factors of the block reflectors
                     as returned by CGEQRT, stored as a NB-by-N matrix.

           LDT       (input)
                     LDT is INTEGER
                     The leading dimension of the array T.  LDT >= NB.

           C         (input/output)
                     C is DOUBLE PRECISION array, dimension (LDC,N)
                     On entry, the M-by-N matrix C.
                     On exit, C is overwritten by Q C, Q**T C, 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 DOUBLE PRECISION array. The dimension of
                     WORK is N*NB if SIDE = 'L', or  M*NB 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                     DGEMQRT(3)