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stpmqrt.f(3) LAPACK stpmqrt.f(3)

NAME

stpmqrt.f -

SYNOPSIS

Functions/Subroutines


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

Function/Subroutine Documentation

subroutine stpmqrt (characterSIDE, characterTRANS, integerM, integerN, integerK, integerL, integerNB, real, dimension( ldv, * )V, integerLDV, real, dimension( ldt, * )T, integerLDT, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( * )WORK, integerINFO)

STPMQRT

Purpose:


STPMQRT 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^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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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:

April 2012

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 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='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 216 of file stpmqrt.f.

Author

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Tue Sep 25 2012 Version 3.4.2