LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  ztzrqf (M, N, A, LDA, TAU, INFO) 
ZTZRQF 
subroutine ztzrqf  (  integer  M, 
integer  N,  
complex*16, dimension( lda, * )  A,  
integer  LDA,  
complex*16, dimension( * )  TAU,  
integer  INFO  
) 
ZTZRQF
Download ZTZRQF + dependencies [TGZ] [ZIP] [TXT]This routine is deprecated and has been replaced by routine ZTZRZF. ZTZRQF reduces the MbyN ( 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 NbyN unitary matrix and R is an MbyM upper triangular matrix.
[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 MbyN upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading MbyM 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]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value 
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.