
ctpqrt2.f(3) LAPACK ctpqrt2.f(3)
NAME
ctpqrt2.f 
SYNOPSIS
Functions/Subroutines
subroutine ctpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO)
CTPQRT2 computes a QR factorization of a real or complex 'triangularpentagonal'
matrix, which is composed of a triangular block and a pentagonal block, using the
compact WY representation for Q.
Function/Subroutine Documentation
subroutine ctpqrt2 (integerM, integerN, integerL, complex, dimension( lda, * )A, integerLDA,
complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldt, * )T, integerLDT,
integerINFO)
CTPQRT2 computes a QR factorization of a real or complex 'triangularpentagonal' matrix,
which is composed of a triangular block and a pentagonal block, using the compact WY
representation for Q.
Purpose:
CTPQRT2 computes a QR factorization of a complex "triangularpentagonal"
matrix C, which is composed of a triangular block A and pentagonal block B,
using the compact WY representation for Q.
Parameters:
M
M is INTEGER
The total number of rows of the matrix B.
M >= 0.
N
N is INTEGER
The number of columns of the matrix B, and the order of
the triangular matrix A.
N >= 0.
L
L is INTEGER
The number of rows of the upper trapezoidal part of B.
MIN(M,N) >= L >= 0. See Further Details.
A
A is COMPLEX array, dimension (LDA,N)
On entry, the upper triangular NbyN matrix A.
On exit, the elements on and above the diagonal of the array
contain the upper triangular matrix R.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B
B is COMPLEX array, dimension (LDB,N)
On entry, the pentagonal MbyN matrix B. The first ML rows
are rectangular, and the last L rows are upper trapezoidal.
On exit, B contains the pentagonal matrix V. See Further Details.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,M).
T
T is COMPLEX array, dimension (LDT,N)
The NbyN upper triangular factor T of the block reflector.
See Further Details.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= max(1,N)
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:
September 2012
Further Details:
The input matrix C is a (N+M)byN matrix
C = [ A ]
[ B ]
where A is an upper triangular NbyN matrix, and B is MbyN pentagonal
matrix consisting of a (ML)byN rectangular matrix B1 on top of a LbyN
upper trapezoidal matrix B2:
B = [ B1 ] < (ML)byN rectangular
[ B2 ] < LbyN upper trapezoidal.
The upper trapezoidal matrix B2 consists of the first L rows of a
NbyN upper triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
B is rectangular MbyN; if M=L=N, B is upper triangular.
The matrix W stores the elementary reflectors H(i) in the ith column
below the diagonal (of A) in the (N+M)byN input matrix C
C = [ A ] < upper triangular NbyN
[ B ] < MbyN pentagonal
so that W can be represented as
W = [ I ] < identity, NbyN
[ V ] < MbyN, same form as B.
Thus, all of information needed for W is contained on exit in B, which
we call V above. Note that V has the same form as B; that is,
V = [ V1 ] < (ML)byN rectangular
[ V2 ] < LbyN upper trapezoidal.
The columns of V represent the vectors which define the H(i)'s.
The (M+N)by(M+N) block reflector H is then given by
H = I  W * T * W**H
where W**H is the conjugate transpose of W and T is the upper triangular
factor of the block reflector.
Definition at line 174 of file ctpqrt2.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 ctpqrt2.f(3) 
