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  4. sgelqt3(3)

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sgelqt3.f(3) LAPACK sgelqt3.f(3)

NAME

sgelqt3.f

SYNOPSIS

Functions/Subroutines


recursive subroutine sgelqt3 (M, N, A, LDA, T, LDT, INFO)

Function/Subroutine Documentation

recursive subroutine sgelqt3 (integer M, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( ldt, * ) T, integer LDT, integer INFO)

Purpose:

DGELQT3 recursively computes a LQ factorization of a real M-by-N matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

Parameters:

M 



          M is INTEGER


          The number of rows of the matrix A.  M =< N.

N



          N is INTEGER


          The number of columns of the matrix A.  N >= 0.

A



          A is REAL array, dimension (LDA,N)


          On entry, the real M-by-N matrix A.  On exit, the elements on and


          below the diagonal contain the N-by-N lower triangular matrix L; the


          elements above the diagonal are the rows of V.  See below for


          further details.

LDA



          LDA is INTEGER


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

T



          T is REAL array, dimension (LDT,N)


          The N-by-N upper triangular factor of the block reflector.


          The elements on and above the diagonal contain the block


          reflector T; the elements below the diagonal are not used.


          See below for 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:

November 2017

Further Details:

The matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is

V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 v3 v3 )

where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by

H = I - V * T * V**T

where V**T is the transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 116 of file sgelqt3.f.

Author

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Tue Nov 14 2017 Version 3.8.0