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



NAME
       DTPMQRT

SYNOPSIS
       SUBROUTINE DTPMQRT (SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A,
           LDA, B, LDB, WORK, INFO)



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.




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 B. M >= 0.

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

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

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

           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 CTPQRT.

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

           A         (input/output)
                     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       (input)
                     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         (input/output)
                     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       (input)
                     LDB is INTEGER
                     The leading dimension of the array B.
                     LDB >= 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






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.



LAPACK routine                  31 October 2017                     DTPMQRT(3)