LAPACK  3.4.0
LAPACK: Linear Algebra PACKage
Functions/Subroutines
ztzrzf.f File Reference

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Functions/Subroutines

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

Function/Subroutine Documentation

subroutine ZTZRZF ( INTEGER  M,
INTEGER  N,
COMPLEX*16, dimension( lda, * )  A,
INTEGER  LDA,
COMPLEX*16, dimension( * )  TAU,
COMPLEX*16, dimension( * )  WORK,
INTEGER  LWORK,
INTEGER  INFO 
)

ZTZRZF

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Purpose: 

 ZTZRZF 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:
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= M.
[in,out]A
          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 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.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[out]TAU
          TAU is COMPLEX*16 array, dimension (M)
          The scalar factors of the elementary reflectors.
[out]WORK
          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]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.
[out]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
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 ( 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 161 of file ztzrzf.f.

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