
dtprfb.f(3) LAPACK dtprfb.f(3)
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 'triangularpentagonal' blocked reflector to a real
or complex matrix, which is composed of two blocks.
Function/Subroutine Documentation
subroutine dtprfb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM,
integerN, integerK, integerL, double precision, dimension( ldv, * )V, integerLDV, double
precision, dimension( ldt, * )T, integerLDT, double precision, dimension( lda, * )A,
integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision,
dimension( ldwork, * )WORK, integerLDWORK)
DTPRFB applies a real or complex 'triangularpentagonal' blocked reflector to a real or
complex matrix, which is composed of two blocks.
Purpose:
DTPRFB applies a real "triangularpentagonal" 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 KbyK 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 KbyN or MbyK 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 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
B is DOUBLE PRECISION array, dimension (LDB,N)
On entry, the MbyN 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:
September 2012
Further Details:
The matrix C is a composite matrix formed from blocks A and B.
The block B is of size MbyN; if SIDE = 'R', A is of size MbyK,
and if SIDE = 'L', A is of size KbyN.
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 KbyK upper triangular)
If DIRECT = 'F' and STOREV = 'R': V = [V1 V2]
 V2 is lower trapezoidal (first L columns of KbyK lower triangular)
If DIRECT = 'B' and STOREV = 'C': V = [V2]
[V1]
 V2 is lower trapezoidal (last L rows of KbyK lower triangular)
If DIRECT = 'B' and STOREV = 'R': V = [V2 V1]
 V2 is upper trapezoidal (last L columns of KbyK upper triangular)
If STOREV = 'C' and SIDE = 'L', V is MbyK with V2 LbyK.
If STOREV = 'C' and SIDE = 'R', V is NbyK with V2 LbyK.
If STOREV = 'R' and SIDE = 'L', V is KbyM with V2 KbyL.
If STOREV = 'R' and SIDE = 'R', V is KbyN with V2 KbyL.
Definition at line 251 of file dtprfb.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 dtprfb.f(3) 
