DTPMQRT (3) Linux Manual Page

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

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

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

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

          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 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 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 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 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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