stprfb.f man page

stprfb.f

Synopsis

Functions/Subroutines

subroutine stprfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
STPRFB 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 stprfb (character SIDE, character TRANS, character DIRECT, character STOREV, integer M, integer N, integer K, integer L, real, dimension( ldv, * ) V, integer LDV, real, dimension( ldt, * ) T, integer LDT, real, dimension( lda, * ) A, integer LDA, real, dimension( ldb, * ) B, integer LDB, real, dimension( ldwork, * ) WORK, integer LDWORK)

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

Purpose:

 STPRFB applies a real "triangular-pentagonal" block reflector H or its
 conjugate transpose H^H 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^H from the Left
          = 'R': apply H or H^H from the Right

TRANS

          TRANS is CHARACTER*1
          = 'N': apply H (No transpose)
          = 'C': apply H^H (Conjugate 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 REAL 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 REAL 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 REAL 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^H*C or C*H or C*H^H.  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 REAL 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^H*C or C*H or C*H^H.  See Further Details.

LDB

          LDB is INTEGER
          The leading dimension of the array B.
          LDB >= max(1,M).

WORK

          WORK is REAL 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 stprfb.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page stprfb(3) is an alias of stprfb.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK