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.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
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.
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