dtpmqrt.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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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 (character SIDE, character TRANS, integer M, integer N, integer K, integer L, integer NB, 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)

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;
          = '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.


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 2017

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 218 of file dtpmqrt.f.  

Author

Generated automatically by Doxygen for LAPACK from the source code.


 

Index

NAME
SYNOPSIS
Functions/Subroutines
Function/Subroutine Documentation
subroutine dtpmqrt (character SIDE, character TRANS, integer M, integer N, integer K, integer L, integer NB, 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)
Author
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