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ctprfb-f(3)

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

 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 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

 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

 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

 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

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