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dtpmlqt.f(3) LAPACK dtpmlqt.f(3)

NAME

dtpmlqt.f

SYNOPSIS

Functions/Subroutines


subroutine dtpmlqt (SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
DTPMLQT

Function/Subroutine Documentation

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

DTPMLQT

Purpose:


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

Parameters:

SIDE


SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.

TRANS


TRANS is CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.

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.

MB


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

V


V is DOUBLE PRECISION array, dimension (LDA,K)
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
DTPLQT 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 DOUBLE PRECISION array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by DTPLQT, stored as a MB-by-K matrix.

LDT


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

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
Q*C or Q**T*C or C*Q or C*Q**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
Q*C or Q**T*C or C*Q or C*Q**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. The dimension of WORK is
N*MB if SIDE = 'L', or M*MB 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 lower trapezoidal, consisting of the first L
rows of a K-by-K upper triangular matrix. If L=K, V2 is lower 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 K-by-M.
[B]
If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is K-by-N.
The real 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='T' and SIDE='L', C is on exit replaced with Q**T * C.
If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.

Definition at line 218 of file dtpmlqt.f.

Author

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Tue Nov 14 2017 Version 3.8.0