cgeqrt3-f(3)

cgeqrt3.f –

Synopsis

Functions/Subroutines

recursive subroutine cgeqrt3 (M, N, A, LDA, T, LDT, INFO)
CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Function/Subroutine Documentation

recursive subroutine cgeqrt3 (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldt, * )T, integerLDT, integerINFO)

CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

 CGEQRT3 recursively computes a QR factorization of a complex 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 is INTEGER
 The number of rows of the matrix A. M >= N.

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

 A is COMPLEX array, dimension (LDA,N)
 On entry, the complex 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 is COMPLEX 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**H
 where V**H is the conjugate transpose of V.
 For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 133 of file cgeqrt3.f.

Author

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