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

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.ti -1c
.RI "subroutine \fBstzrqf\fP (m, n, a, lda, tau, info)"
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.RI "\fBSTZRQF\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine stzrqf (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, integer info)"

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

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.nf
!>
!> This routine is deprecated and has been replaced by routine STZRZF\&.
!>
!> STZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
!> to upper triangular form by means of orthogonal transformations\&.
!>
!> The upper trapezoidal matrix A is factored as
!>
!>    A = ( R  0 ) * Z,
!>
!> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
!> triangular matrix\&.
!> 
.fi
.PP
 
.RE
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\fBParameters\fP
.RS 4
\fIM\fP 
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.nf
!>          M is INTEGER
!>          The number of rows of the matrix A\&.  M >= 0\&.
!> 
.fi
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.br
\fIN\fP 
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.nf
!>          N is INTEGER
!>          The number of columns of the matrix A\&.  N >= M\&.
!> 
.fi
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.br
\fIA\fP 
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.nf
!>          A is REAL 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
!>          orthogonal matrix Z as a product of M elementary reflectors\&.
!> 
.fi
.PP
.br
\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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.br
\fITAU\fP 
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.nf
!>          TAU is REAL array, dimension (M)
!>          The scalar factors of the elementary reflectors\&.
!> 
.fi
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.br
\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
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\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

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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 )**T,   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 \fB137\fP of file \fBstzrqf\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.