ctzrqf-f(3)

ctzrqf.f –

Synopsis

Functions/Subroutines

subroutine ctzrqf (M, N, A, LDA, TAU, INFO)
CTZRQF

Function/Subroutine Documentation

subroutine ctzrqf (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, integerINFO)

CTZRQF

Purpose:

 This routine is deprecated and has been replaced by routine CTZRZF.
 CTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
 to upper triangular form by means of unitary transformations.
 The upper trapezoidal matrix A is factored as
 A = ( R 0 ) * Z,
 where Z is an N-by-N unitary matrix and R is an M-by-M upper
 triangular matrix.

Parameters:

 M is INTEGER
 The number of rows of the matrix A. M >= 0.

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

 A is COMPLEX array, dimension (LDA,N)
 On entry, the leading M-by-N upper trapezoidal part of the
 array A must contain the matrix to be factorized.
 On exit, the leading M-by-M upper triangular part of A
 contains the upper triangular matrix R, and elements M+1 to
 N of the first M rows of A, with the array TAU, represent the
 unitary matrix Z as a product of M elementary reflectors.

LDA

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

TAU

 TAU is COMPLEX array, dimension (M)
 The scalar factors of the elementary reflectors.

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 2011

Further Details:

 The factorization is obtained by Householder's method. The kth
 transformation matrix, Z( k ), whose conjugate transpose is used to
 introduce zeros into the (m - k + 1)th row of A, is given in the form
 Z( k ) = ( I 0 ),
 ( 0 T( k ) )
 where
 T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ),
 ( 0 )
 ( z( k ) )
 tau is a scalar and z( k ) is an ( n - m ) element vector.
 tau and z( k ) are chosen to annihilate the elements of the kth row
 of X.
 The scalar tau is returned in the kth element of TAU and the vector
 u( k ) in the kth row of A, such that the elements of z( k ) are
 in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
 the upper triangular part of A.
 Z is given by
 Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).

Definition at line 139 of file ctzrqf.f.

Author

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