ctprfb(3)

NAME

ctprfb.f –

SYNOPSIS

Functions/Subroutines

subroutine ctprfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
CTPRFB 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 ctprfb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, integerL, complex, dimension( ldv, * )V, integerLDV, complex, dimension( ldt, * )T, integerLDT, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldwork, * )WORK, integerLDWORK)

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

Purpose:

 CTPRFB applies a complex "triangular-pentagonal" block reflector H or its 
 conjugate transpose H**H to a complex 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 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 order of the matrix T, i.e. the number of elementary
          reflectors whose product defines the block reflector.  
          K >= 0.

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

          V is COMPLEX 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 is COMPLEX 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 is COMPLEX 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 Futher 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 COMPLEX 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 COMPLEX 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:

: September 2012

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 251 of file ctprfb.f.

Author