stpmqrt (3)  Linux Manuals
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.
TRANSTRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Transpose, apply Q^H.
MM is INTEGER The number of rows of the matrix B. M >= 0.
NN is INTEGER The number of columns of the matrix B. N >= 0.
KK is INTEGER The number of elementary reflectors whose product defines the matrix Q.
LL is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details.
NBNB 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.
VV 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.
LDVLDV is INTEGER The leading dimension of the array V. If SIDE = 'L', LDV >= max(1,M); if SIDE = 'R', LDV >= max(1,N).
TT is REAL array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by CTPQRT, stored as a NBbyK matrix.
LDTLDT is INTEGER The leading dimension of the array T. LDT >= NB.
AA 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.
LDALDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDC >= max(1,K); If SIDE = 'R', LDC >= max(1,M).
BB 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.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).
WORKWORK is REAL array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'.
INFOINFO 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:
 November 2013
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
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