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

.in +1c
.ti -1c
.RI "subroutine \fBztzrqf\fP (M, N, A, LDA, TAU, INFO)"
.br
.RI "\fI\fBZTZRQF\fP \fP"
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine ztzrqf (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, integerINFO)"

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

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.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 This routine is deprecated and has been replaced by routine ZTZRZF.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.
.fi
.PP
 
.RE
.PP
\fBParameters:\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
.fi
.PP
.br
\fIN\fP 
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.nf
          N is INTEGER
          The number of columns of the matrix A.  N >= M.
.fi
.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.
.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).
.fi
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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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.nf
          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 
.PP
Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.RE
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\fBDate:\fP
.RS 4
November 2011 
.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 ).
.fi
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.RE
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Definition at line 139 of file ztzrqf\&.f\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.