Scroll to navigation

dtpqrt2.f(3) LAPACK dtpqrt2.f(3)

NAME

dtpqrt2.f

SYNOPSIS

Functions/Subroutines


subroutine dtpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO)
DTPQRT2 computes a QR factorization of a real or complex 'triangular-pentagonal' matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

Function/Subroutine Documentation

subroutine dtpqrt2 (integer M, integer N, integer L, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldt, * ) T, integer LDT, integer INFO)

DTPQRT2 computes a QR factorization of a real or complex 'triangular-pentagonal' matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

Purpose:


DTPQRT2 computes a QR factorization of a real "triangular-pentagonal"
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 DOUBLE PRECISION array, dimension (LDA,N)
On entry, the upper triangular N-by-N 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 DOUBLE PRECISION array, dimension (LDB,N)
On entry, the pentagonal M-by-N matrix B. The first M-L 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 DOUBLE PRECISION array, dimension (LDT,N)
The N-by-N 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 i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Further Details:


The input matrix C is a (N+M)-by-N matrix
C = [ A ]
[ B ]
where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
upper trapezoidal matrix B2:
B = [ B1 ] <- (M-L)-by-N rectangular
[ B2 ] <- L-by-N upper trapezoidal.
The upper trapezoidal matrix B2 consists of the first L rows of a
N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
B is rectangular M-by-N; if M=L=N, B is upper triangular.
The matrix W stores the elementary reflectors H(i) in the i-th column
below the diagonal (of A) in the (N+M)-by-N input matrix C
C = [ A ] <- upper triangular N-by-N
[ B ] <- M-by-N pentagonal
so that W can be represented as
W = [ I ] <- identity, N-by-N
[ V ] <- M-by-N, 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 ] <- (M-L)-by-N rectangular
[ V2 ] <- L-by-N 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**T
where W^H is the conjugate transpose of W and T is the upper triangular
factor of the block reflector.

Definition at line 175 of file dtpqrt2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Tue Nov 14 2017 Version 3.8.0