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ctplqt.f(3) LAPACK ctplqt.f(3)

NAME

ctplqt.f

SYNOPSIS

Functions/Subroutines


subroutine ctplqt (M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK, INFO)

Function/Subroutine Documentation

subroutine ctplqt (integer M, integer N, integer L, integer MB, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldt, * ) T, integer LDT, complex, dimension( * ) WORK, integer INFO)

Purpose:

CTPLQT computes a blocked LQ factorization of a complex '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 number of rows of the matrix B, and the order of the
triangular matrix A.
M >= 0.

N


N is INTEGER
The number of columns of the matrix B.
N >= 0.

L


L is INTEGER
The number of rows of the lower trapezoidal part of B.
MIN(M,N) >= L >= 0. See Further Details.

MB


MB is INTEGER
The block size to be used in the blocked QR. M >= MB >= 1.

A


A is COMPLEX array, dimension (LDA,M)
On entry, the lower triangular M-by-M matrix A.
On exit, the elements on and below the diagonal of the array
contain the lower triangular matrix L.

LDA


LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).

B


B is COMPLEX array, dimension (LDB,N)
On entry, the pentagonal M-by-N matrix B. The first N-L columns
are rectangular, and the last L columns are lower 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 lower triangular block reflectors stored in compact form
as a sequence of upper triangular blocks. See Further Details.

LDT


LDT is INTEGER
The leading dimension of the array T. LDT >= MB.

WORK


WORK is COMPLEX array, dimension (MB*M)

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:

June 2017

Further Details:

The input matrix C is a M-by-(M+N) matrix

C = [ A ] [ B ]

where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L upper trapezoidal matrix B2: [ B ] = [ B1 ] [ B2 ] [ B1 ] <- M-by-(N-L) rectangular [ B2 ] <- M-by-L lower trapezoidal.

The lower trapezoidal matrix B2 consists of the first L columns of a M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0, B is rectangular M-by-N; if M=L=N, B is lower triangular.

The matrix W stores the elementary reflectors H(i) in the i-th row above the diagonal (of A) in the M-by-(M+N) input matrix C [ C ] = [ A ] [ B ] [ A ] <- lower triangular M-by-M [ B ] <- M-by-N pentagonal

so that W can be represented as [ W ] = [ I ] [ V ] [ I ] <- identity, M-by-M [ 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 ] [ V2 ] [ V1 ] <- M-by-(N-L) rectangular [ V2 ] <- M-by-L lower trapezoidal.

The rows of V represent the vectors which define the H(i)'s.

The number of blocks is B = ceiling(M/MB), where each block is of order MB except for the last block, which is of order IB = M - (M-1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-N matrix T as

T = [T1 T2 ... TB].

Definition at line 174 of file ctplqt.f.

Author

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Tue Nov 14 2017 Version 3.8.0