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



NAME
       CGEMQRT

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



PURPOSE
            CGEMQRT overwrites the general complex M-by-N matrix C with

                            SIDE = 'L'     SIDE = 'R'
            TRANS = 'N':      Q C            C Q
            TRANS = 'C':    Q**H C            C Q**H

            where Q is a complex orthogonal matrix defined as the product of K
            elementary reflectors:

                  Q = H(1) H(2) . . . H(K) = I - V T V**H

            generated using the compact WY representation as returned by CGEQRT.

            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**H from the Left;
                     = 'R': apply Q or Q**H from the Right.

           TRANS     (input)
                     TRANS is CHARACTER*1
                     = 'N':  No transpose, apply Q;
                     = 'C':  Transpose, apply Q**H.

           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 COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (LDC,N)
                     On entry, the M-by-N matrix C.
                     On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q.

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

           WORK      (output)
                     WORK is COMPLEX 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                     CGEMQRT(3)