dtpmqrt.f(3)

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:
    April 2012

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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