ctzrzf-f(3)

ctzrzf.f –

Synopsis

Functions/Subroutines

subroutine ctzrzf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
CTZRZF

Function/Subroutine Documentation

subroutine ctzrzf (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK, integerLWORK, integerINFO)

CTZRZF

Purpose:

 CTZRZF 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.

WORK

 WORK is COMPLEX array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

 LWORK is INTEGER
 The dimension of the array WORK. LWORK >= max(1,M).
 For optimum performance LWORK >= M*NB, where NB is
 the optimal blocksize.
 If LWORK = -1, then a workspace query is assumed; the routine
 only calculates the optimal size of the WORK array, returns
 this value as the first entry of the WORK array, and no error
 message related to LWORK is issued by XERBLA.

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:

April 2012

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

 The N-by-N matrix Z can be computed by
 Z = Z(1)*Z(2)* ... *Z(M)
 where each N-by-N Z(k) is given by
 Z(k) = I - tau(k)*v(k)*v(k)**H
 with v(k) is the kth row vector of the M-by-N matrix
 V = ( I A(:,M+1:N) )
 I is the M-by-M identity matrix, A(:,M+1:N) 
 is the output stored in A on exit from DTZRZF,
 and tau(k) is the kth element of the array TAU.

Definition at line 152 of file ctzrzf.f.

Author

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