NAME

       dormr3.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dormr3 (SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO)
           DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization
           determined by stzrzf (unblocked algorithm).

Function/Subroutine Documentation

   subroutine dormr3 (characterSIDE, characterTRANS, integerM, integerN, integerK, integerL,
       double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU,
       double precision, dimension( ldc, * )C, integerLDC, double precision, dimension( * )WORK,
       integerINFO)
       DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization
       determined by stzrzf (unblocked algorithm).

       Purpose:

            DORMR3 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 DTZRZF. Q is of order m if SIDE = 'L' and of order n
            if SIDE = 'R'.

       Parameters:
           SIDE

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

           TRANS

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

           M

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

           N

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

           K

                     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

                     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

                     A is DOUBLE PRECISION 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
                     DTZRZF in the last k rows of its array argument A.
                     A is modified by the routine but restored on exit.

           LDA

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

           TAU

                     TAU is DOUBLE PRECISION array, dimension (K)
                     TAU(i) must contain the scalar factor of the elementary
                     reflector H(i), as returned by DTZRZF.

           C

                     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

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

           WORK

                     WORK is DOUBLE PRECISION array, dimension
                                              (N) if SIDE = 'L',
                                              (M) if SIDE = 'R'

           INFO

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Contributors:
           A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

       Further Details:

       Definition at line 178 of file dormr3.f.

Author

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