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.

Download DTPRFB + dependencies [TGZ] [ZIP] [TXT]

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:

[in]	SIDE	SIDE is CHARACTER1 = 'L': apply H or HT from the Left = 'R': apply H or H*T from the Right
[in]	TRANS	TRANS is CHARACTER1 = 'N': apply H (No transpose) = 'T': apply H*T (Transpose)
[in]	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)
[in]	STOREV	STOREV is CHARACTER*1 Indicates how the vectors which define the elementary reflectors are stored: = 'C': Columns = 'R': Rows
[in]	M	M is INTEGER The number of rows of the matrix B. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix B. N >= 0.
[in]	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.
[in]	L	L is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details.
[in]	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.
[in]	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.
[in]	T	T is DOUBLE PRECISION array, dimension (LDT,K) The triangular K-by-K matrix T in the representation of the block reflector.
[in]	LDT	LDT is INTEGER The leading dimension of the array T. LDT >= K.
[in,out]	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 HC or HTC or CH or CH**T. See Futher Details.
[in]	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).
[in,out]	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 HC or HTC or CH or CH**T. See Further Details.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LDWORK,N) if SIDE = 'L', (LDWORK,K) if SIDE = 'R'.
[in]	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 dtprfb.f.

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Function/Subroutine Documentation