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

.in +1c
.ti -1c
.RI "subroutine \fBclatrz\fP (m, n, l, a, lda, tau, work)"
.br
.RI "\fBCLATRZ\fP factors an upper trapezoidal matrix by means of unitary transformations\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine clatrz (integer m, integer n, integer l, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work)"

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

.PP
.nf
 CLATRZ 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\&.
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.RE
.PP
\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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.PP
.br
\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\&.
.fi
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\fIA\fP 
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.nf
          A is COMPLEX 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\&.
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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 array, dimension (M)
          The scalar factors of the elementary reflectors\&.
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.PP
.br
\fIWORK\fP 
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.nf
          WORK is COMPLEX array, dimension (M)
.fi
.PP
 
.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\&. 
.RE
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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

.PP
.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 )\&.
.fi
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.RE
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Definition at line \fB139\fP of file \fBclatrz\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.