.TH "dlatrz.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
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.SH NAME
dlatrz.f \- 
.SH SYNOPSIS
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.SS "Functions/Subroutines"

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.ti -1c
.RI "subroutine \fBdlatrz\fP (M, N, L, A, LDA, TAU, WORK)"
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.RI "\fI\fBDLATRZ\fP factors an upper trapezoidal matrix by means of orthogonal transformations\&. \fP"
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.SH "Function/Subroutine Documentation"
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.SS "subroutine dlatrz (integerM, integerN, integerL, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, double precision, dimension( * )WORK)"

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\fBDLATRZ\fP factors an upper trapezoidal matrix by means of orthogonal transformations\&.  
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\fBPurpose: \fP
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.nf
 DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
 [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+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 M-by-M upper triangular matrices.
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.RE
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\fBParameters:\fP
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\fIM\fP 
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          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
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\fIN\fP 
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          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
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\fIL\fP 
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          L is INTEGER
          The number of columns of the matrix A containing the
          meaningful part of the Householder vectors. N-M >= L >= 0.
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\fIA\fP 
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          A is DOUBLE PRECISION 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
          orthogonal matrix Z as a product of M elementary reflectors.
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\fILDA\fP 
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          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
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\fITAU\fP 
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          TAU is DOUBLE PRECISION array, dimension (M)
          The scalar factors of the elementary reflectors.
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\fIWORK\fP 
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          WORK is DOUBLE PRECISION array, dimension (M)
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.RE
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\fBAuthor:\fP
.RS 4
Univ\&. of Tennessee 
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Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
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NAG Ltd\&. 
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\fBDate:\fP
.RS 4
September 2012 
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\fBContributors: \fP
.RS 4
A\&. Petitet, Computer Science Dept\&., Univ\&. of Tenn\&., Knoxville, USA 
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\fBFurther Details: \fP
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  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 ).
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Definition at line 141 of file dlatrz\&.f\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.