LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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zlatrz.f File Reference

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

Function/Subroutine Documentation

subroutine zlatrz ( integer  M,
integer  N,
integer  L,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( * )  TAU,
complex*16, dimension( * )  WORK 

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

Download ZLATRZ + dependencies [TGZ] [ZIP] [TXT]
 ZLATRZ 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.
          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 >= 0.
          L is INTEGER
          The number of columns of the matrix A containing the
          meaningful part of the Householder vectors. N-M >= L >= 0.
          A is COMPLEX*16 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 is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
          TAU is COMPLEX*16 array, dimension (M)
          The scalar factors of the elementary reflectors.
          WORK is COMPLEX*16 array, dimension (M)
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
September 2012
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 ) )


     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 zlatrz.f.

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