SRC/dtpmlqt.f(3)

NAME
SRC/dtpmlqt.f

SYNOPSIS

  Functions/Subroutines
subroutine dtpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
DTPMLQT

Function/Subroutine Documentation

  subroutine dtpmlqt (character side, character trans, integer m, integer n, integer k, integer l, integer mb, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer info)

DTPMLQT

Purpose:

    !>
    !> DTPMQRT applies a real orthogonal matrix Q obtained from a
    !>  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;
    !>          = 'T':  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.
    !>

    MB

    !>          MB is INTEGER
    !>          The block size used for the storage of T.  K >= MB >= 1.
    !>          This must be the same value of MB used to generate T
    !>          in DTPLQT.
    !>

    V

    !>          V is DOUBLE PRECISION array, dimension (LDV,K)
    !>          The i-th row must contain the vector which defines the
    !>          elementary reflector H(i), for i = 1,2,...,k, as returned by
    !>          DTPLQT in B.  See Further Details.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array V. LDV >= K.
    !>

    T

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

    LDT

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

    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', LDA >= max(1,K);
    !>          If SIDE = 'R', LDA >= 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*MB if SIDE = 'L', or  M*MB 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.

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 lower trapezoidal, consisting of the first L
    !>  rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower 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 K-by-M.
    !>                      [B]
    !>
    !>  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.
    !>
    !>  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 212 of file dtpmlqt.f.

Author

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