NAME

       dtpmqrt.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dtpmqrt (SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK,
           INFO)
           DTPMQRT

Function/Subroutine Documentation

   subroutine dtpmqrt (characterSIDE, characterTRANS, integerM, integerN, integerK, integerL,
       integerNB, double precision, dimension( ldv, * )V, integerLDV, double precision,
       dimension( ldt, * )T, integerLDT, double precision, dimension( lda, * )A, integerLDA,
       double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( * )WORK,
       integerINFO)
       DTPMQRT

       Purpose:

            DTPMQRT applies a real orthogonal matrix Q obtained from a
            "triangular-pentagonal" real block reflector H to a general
            real matrix C, which consists of two blocks A and B.

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

           M

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

           N

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

           K

                     K is INTEGER
                     The number of elementary reflectors whose product defines
                     the matrix Q.

           L

                     L is INTEGER
                     The order of the trapezoidal part of V.
                     K >= L >= 0.  See Further Details.

           NB

                     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 CTPQRT.

           V

                     V is DOUBLE PRECISION 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
                     CTPQRT in B.  See Further Details.

           LDV

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

           T

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

           LDT

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

           A

                     A is DOUBLE PRECISION array, dimension
                     (LDA,N) if SIDE = 'L' or
                     (LDA,K) if SIDE = 'R'
                     On entry, the K-by-N or M-by-K matrix A.
                     On exit, A is overwritten by the corresponding block of
                     Q*C or Q**T*C or C*Q or C*Q**T.  See Further Details.

           LDA

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

           B

                     B is DOUBLE PRECISION array, dimension (LDB,N)
                     On entry, the M-by-N matrix B.
                     On exit, B is overwritten by the corresponding block of
                     Q*C or Q**T*C or C*Q or C*Q**T.  See Further Details.

           LDB

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

           WORK

                     WORK is DOUBLE PRECISION array. The dimension of WORK is
                      N*NB if SIDE = 'L', or  M*NB 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:
           November 2013

       Further Details:

             The columns of the pentagonal matrix V contain the elementary reflectors
             H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
             trapezoidal block V2:

                   V = [V1]
                       [V2].

             The size of the trapezoidal block V2 is determined by the parameter L,
             where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L
             rows of a K-by-K upper triangular matrix.  If L=K, V2 is upper triangular;
             if L=0, there is no trapezoidal block, hence V = V1 is rectangular.

             If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is M-by-K.
                                 [B]

             If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is N-by-K.

             The real orthogonal matrix Q is formed from V and T.

             If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.

             If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C.

             If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.

             If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.

       Definition at line 216 of file dtpmqrt.f.

Author

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