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



NAME
       DORMTR

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



PURPOSE
            DORMTR 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 of order nq, with nq = m if
            SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
            nq-1 elementary reflectors, as returned by DSYTRD:

            if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

            if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).




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.

           UPLO      (input)
                     UPLO is CHARACTER*1
                     = 'U': Upper triangle of A contains elementary reflectors
                            from DSYTRD;
                     = 'L': Lower triangle of A contains elementary reflectors
                            from DSYTRD.

           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.

           A         (input)
                     A is DOUBLE PRECISION array, dimension
                                          (LDA,M) if SIDE = 'L'
                                          (LDA,N) if SIDE = 'R'
                     The vectors which define the elementary reflectors, as
                     returned by DSYTRD.

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

           TAU       (input)
                     TAU is DOUBLE PRECISION array, dimension
                                          (M-1) if SIDE = 'L'
                                          (N-1) if SIDE = 'R'
                     TAU(i) must contain the scalar factor of the elementary
                     reflector H(i), as returned by DSYTRD.

           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 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 DOUBLE PRECISION 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                      DORMTR(3)