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ztzrqf.f(3) LAPACK ztzrqf.f(3)

ztzrqf.f -


subroutine ztzrqf (M, N, A, LDA, TAU, INFO)
 
ZTZRQF

ZTZRQF
Purpose:
 This routine is deprecated and has been replaced by routine ZTZRZF.
ZTZRQF 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
          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 >= M.
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.
LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
TAU
          TAU is COMPLEX*16 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 ztzrqf.f.

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