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# ctprfb.f

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

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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