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ctpmqrt.f(3) LAPACK ctpmqrt.f(3)

NAME

ctpmqrt.f

SYNOPSIS

Functions/Subroutines


subroutine ctpmqrt (SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
CTPMQRT

Function/Subroutine Documentation

subroutine ctpmqrt (character SIDE, character TRANS, integer M, integer N, integer K, integer L, integer NB, complex, dimension( ldv, * ) V, integer LDV, complex, dimension( ldt, * ) T, integer LDT, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( * ) WORK, integer INFO)

CTPMQRT

Purpose:


CTPMQRT applies a complex orthogonal matrix Q obtained from a
"triangular-pentagonal" complex block reflector H to a general
complex matrix C, which consists of two blocks A and B.

Parameters:

SIDE


SIDE is CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.

TRANS


TRANS is CHARACTER*1
= 'N': No transpose, apply Q;
= 'C': Transpose, apply Q**H.

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 number of elementary reflectors whose product defines
the matrix Q.

L


L is INTEGER
The order of the trapezoidal part of V.
K >= L >= 0. See Further Details.

NB


NB is INTEGER
The block size used for the storage of T. K >= NB >= 1.
This must be the same value of NB used to generate T
in CTPQRT.

V


V is COMPLEX array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CTPQRT in B. See Further Details.

LDV


LDV is INTEGER
The leading dimension of the array V.
If SIDE = 'L', LDV >= max(1,M);
if SIDE = 'R', LDV >= max(1,N).

T


T is COMPLEX array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by CTPQRT, stored as a NB-by-K matrix.

LDT


LDT is INTEGER
The leading dimension of the array T. LDT >= NB.

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
Q*C or Q**H*C or C*Q or C*Q**H. 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 COMPLEX array, dimension (LDB,N)
On entry, the M-by-N matrix B.
On exit, B is overwritten by the corresponding block of
Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.

LDB


LDB is INTEGER
The leading dimension of the array B.
LDB >= max(1,M).

WORK


WORK is COMPLEX array. The dimension of WORK is
N*NB if SIDE = 'L', or M*NB if SIDE = 'R'.

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2017

Further Details:


The columns of the pentagonal matrix V contain the elementary reflectors
H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
trapezoidal block V2:
V = [V1]
[V2].
The size of the trapezoidal block V2 is determined by the parameter L,
where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L
rows of a K-by-K upper triangular matrix. If L=K, V2 is upper triangular;
if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is M-by-K.
[B]
If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is N-by-K.
The complex orthogonal matrix Q is formed from V and T.
If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.
If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.

Definition at line 218 of file ctpmqrt.f.

Author

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Tue Nov 14 2017 Version 3.8.0