DGEQRT3 (3) Linux Manual Page

dgeqrt3.f –

Synopsis

Functions/Subroutines

recursive subroutine dgeqrt3 (M, N, A, LDA, T, LDT, INFO)
DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Function/Subroutine Documentation

recursive subroutine dgeqrt3 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldt, * )T, integerLDT, integerINFO)

DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

 DGEQRT3 recursively computes a QR 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 DOUBLE PRECISION array, dimension (LDA,N)

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

 above the diagonal contain the N-by-N upper triangular matrix R; the

 elements below the diagonal are the columns 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 DOUBLE PRECISION 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:

September 2012

Further Details:

 The matrix V stores the elementary reflectors H(i) in the i-th column

 below the diagonal. For example, if M=5 and N=3, the matrix V is

 V = ( 1 )

 ( v1 1 )

 ( v1 v2 1 )

 ( v1 v2 v3 )

 ( v1 v2 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 133 of file dgeqrt3.f.

Author

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