dtprfb.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index
 

NAME

dtprfb.f  

SYNOPSIS


 

Functions/Subroutines


subroutine dtprfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
DTPRFB applies a real or complex 'triangular-pentagonal' blocked reflector to a real or complex matrix, which is composed of two blocks.  

Function/Subroutine Documentation

 

subroutine dtprfb (character SIDE, character TRANS, character DIRECT, character STOREV, integer M, integer N, integer K, integer L, 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( ldwork, * ) WORK, integer LDWORK)

DTPRFB applies a real or complex 'triangular-pentagonal' blocked reflector to a real or complex matrix, which is composed of two blocks.

Purpose:

 DTPRFB applies a real "triangular-pentagonal" block reflector H or its
 transpose H**T to a real matrix C, which is composed of two
 blocks A and B, either from the left or right.


 

Parameters:

SIDE

          SIDE is CHARACTER*1
          = 'L': apply H or H**T from the Left
          = 'R': apply H or H**T from the Right


TRANS

          TRANS is CHARACTER*1
          = 'N': apply H (No transpose)
          = 'T': apply H**T (Transpose)


DIRECT

          DIRECT is CHARACTER*1
          Indicates how H is formed from a product of elementary
          reflectors
          = 'F': H = H(1) H(2) . . . H(k) (Forward)
          = 'B': H = H(k) . . . H(2) H(1) (Backward)


STOREV

          STOREV is CHARACTER*1
          Indicates how the vectors which define the elementary
          reflectors are stored:
          = 'C': Columns
          = 'R': Rows


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 order of the matrix T, i.e. the number of elementary
          reflectors whose product defines the block reflector.
          K >= 0.


L

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


V

          V is DOUBLE PRECISION array, dimension
                                (LDV,K) if STOREV = 'C'
                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
          The pentagonal matrix V, which contains the elementary reflectors
          H(1), H(2), ..., H(K).  See Further Details.


LDV

          LDV is INTEGER
          The leading dimension of the array V.
          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
          if STOREV = 'R', LDV >= K.


T

          T is DOUBLE PRECISION array, dimension (LDT,K)
          The triangular K-by-K matrix T in the representation of the
          block reflector.


LDT

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


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
          H*C or H**T*C or C*H or C*H**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
          H*C or H**T*C or C*H or C*H**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, dimension
          (LDWORK,N) if SIDE = 'L',
          (LDWORK,K) if SIDE = 'R'.


LDWORK

          LDWORK is INTEGER
          The leading dimension of the array WORK.
          If SIDE = 'L', LDWORK >= K;
          if SIDE = 'R', LDWORK >= M.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Further Details:

  The matrix C is a composite matrix formed from blocks A and B.
  The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K,
  and if SIDE = 'L', A is of size K-by-N.

  If SIDE = 'R' and DIRECT = 'F', C = [A B].

  If SIDE = 'L' and DIRECT = 'F', C = [A]
                                      [B].

  If SIDE = 'R' and DIRECT = 'B', C = [B A].

  If SIDE = 'L' and DIRECT = 'B', C = [B]
                                      [A].

  The pentagonal matrix V is composed of a rectangular block V1 and a
  trapezoidal block V2.  The size of the trapezoidal block is determined by
  the parameter L, where 0<=L<=K.  If L=K, the V2 block of V is triangular;
  if L=0, there is no trapezoidal block, thus V = V1 is rectangular.

  If DIRECT = 'F' and STOREV = 'C':  V = [V1]
                                         [V2]
     - V2 is upper trapezoidal (first L rows of K-by-K upper triangular)

  If DIRECT = 'F' and STOREV = 'R':  V = [V1 V2]

     - V2 is lower trapezoidal (first L columns of K-by-K lower triangular)

  If DIRECT = 'B' and STOREV = 'C':  V = [V2]
                                         [V1]
     - V2 is lower trapezoidal (last L rows of K-by-K lower triangular)

  If DIRECT = 'B' and STOREV = 'R':  V = [V2 V1]

     - V2 is upper trapezoidal (last L columns of K-by-K upper triangular)

  If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K.

  If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K.

  If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.

  If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.


 

Definition at line 253 of file dtprfb.f.  

Author

Generated automatically by Doxygen for LAPACK from the source code.


 

Index

NAME
SYNOPSIS
Functions/Subroutines
Function/Subroutine Documentation
subroutine dtprfb (character SIDE, character TRANS, character DIRECT, character STOREV, integer M, integer N, integer K, integer L, 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( ldwork, * ) WORK, integer LDWORK)
Author
LinuxReviews : manual page archive : man3