.TH "SRC/zlatrz.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
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.SH NAME
SRC/zlatrz.f
.SH SYNOPSIS
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.SS "Functions/Subroutines"

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.ti -1c
.RI "subroutine \fBzlatrz\fP (m, n, l, a, lda, tau, work)"
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.RI "\fBZLATRZ\fP factors an upper trapezoidal matrix by means of unitary transformations\&. "
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.SH "Function/Subroutine Documentation"
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.SS "subroutine zlatrz (integer m, integer n, integer l, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work)"

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\fBZLATRZ\fP factors an upper trapezoidal matrix by means of unitary transformations\&.  
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\fBPurpose:\fP
.RS 4

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.nf
!>
!> ZLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix
!> [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z by means
!> of unitary transformations, where  Z is an (M+L)-by-(M+L) unitary
!> matrix and, R and A1 are M-by-M upper triangular matrices\&.
!> 
.fi
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.RE
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\fBParameters\fP
.RS 4
\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 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 N-L+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\&.
!> 
.fi
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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 COMPLEX*16 array, dimension (M)
!>          The scalar factors of the elementary reflectors\&.
!> 
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\fIWORK\fP 
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!>          WORK is COMPLEX*16 array, dimension (M)
!> 
.fi
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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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\fBContributors:\fP
.RS 4
A\&. Petitet, Computer Science Dept\&., Univ\&. of Tenn\&., Knoxville, USA 
.RE
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\fBFurther Details:\fP
.RS 4

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.nf
!>
!>  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 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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.RE
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Definition at line \fB139\fP of file \fBzlatrz\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.