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

.in +1c
.ti -1c
.RI "subroutine \fBztzrqf\fP (m, n, a, lda, tau, info)"
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.RI "\fBZTZRQF\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine ztzrqf (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, integer info)"

.PP
\fBZTZRQF\fP  
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\fBPurpose:\fP
.RS 4

.PP
.nf
 This routine is deprecated and has been replaced by routine ZTZRZF\&.

 ZTZRQF reduces the M-by-N ( 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 N-by-N unitary matrix and R is an M-by-M upper
 triangular matrix\&.
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.PP
 
.RE
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\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
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.PP
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\fIN\fP 
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.nf
          N is INTEGER
          The number of columns of the matrix A\&.  N >= M\&.
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.PP
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\fIA\fP 
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.nf
          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 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\&.
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\fILDA\fP 
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          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.fi
.PP
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\fITAU\fP 
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          TAU is COMPLEX*16 array, dimension (M)
          The scalar factors of the elementary reflectors\&.
.fi
.PP
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\fIINFO\fP 
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          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.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 ), 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 )\&.
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.RE
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.PP
Definition at line \fB137\fP of file \fBztzrqf\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.