clatrz(3)

NAME

clatrz.f –

SYNOPSIS

Functions/Subroutines

subroutine clatrz (M, N, L, A, LDA, TAU, WORK)
CLATRZ factors an upper trapezoidal matrix by means of unitary transformations.

Function/Subroutine Documentation

subroutine clatrz (integerM, integerN, integerL, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK)

CLATRZ factors an upper trapezoidal matrix by means of unitary transformations.

Purpose:

CLATRZ factors the M - by - (M + L) complex upper trapezoidal matrix[A1 A2] = [A(1
                                                                                 : M, 1
                                                                                 : M) A(1
                                                                                        : M, N - L + 1
                                                                                        : N)] as(R 0) *
                                                                              Z by means
                                                                              of unitary transformations,
                                                                        where Z is an(M + L) - by - (M + L) unitary matrix and, R and A1 are M - by - M upper triangular matrices.

 

Parameters:

M

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

N

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

L

          L is INTEGER
          The number of columns of the matrix A containing the
          meaningful part of the Householder vectors. N-M >= L >= 0.

A

          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 N-L+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 (M)

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Contributors:

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

Further Details:

  The factorization is obtained by Householder's method.  The kth
  transformation matrix, Z( k ), which 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 l element vector. tau and z( k )
  are chosen to annihilate the elements of the kth row of A2.
  The scalar tau is returned in the kth element of TAU and the vector
  u( k ) in the kth row of A2, such that the elements of z( k ) are
  in  a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
  the upper triangular part of A1.
  Z is given by
     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).

 

Definition at line 141 of file clatrz.f.

Author

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