LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  dlatrz (M, N, L, A, LDA, TAU, WORK) 
DLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations. 
subroutine dlatrz  (  integer  M, 
integer  N,  
integer  L,  
double precision, dimension( lda, * )  A,  
integer  LDA,  
double precision, dimension( * )  TAU,  
double precision, dimension( * )  WORK  
) 
DLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.
Download DLATRZ + dependencies [TGZ] [ZIP] [TXT]DLATRZ factors the Mby(M+L) real upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,NL+1:N) ] as ( R 0 ) * Z, by means of orthogonal transformations. Z is an (M+L)by(M+L) orthogonal matrix and, R and A1 are MbyM upper triangular matrices.
[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 >= 0. 
[in]  L  L is INTEGER The number of columns of the matrix A containing the meaningful part of the Householder vectors. NM >= L >= 0. 
[in,out]  A  A is DOUBLE PRECISION 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 NL+1 to N of the first M rows of A, with the array TAU, represent the orthogonal 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 DOUBLE PRECISION array, dimension (M) The scalar factors of the elementary reflectors. 
[out]  WORK  WORK is DOUBLE PRECISION array, dimension (M) 
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 )**T, 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 dlatrz.f.