
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
"triangularpentagonal" 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 ith 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 NBbyK 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 KbyN or MbyK 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 MbyN 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 ith 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 KbyK 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 KbyN, B is MbyN and V is MbyK.
[B]
If SIDE = 'R': C = [A B] where A is MbyK, B is MbyN and V is NbyK.
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
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 stpmqrt.f(3) 
