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

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.ti -1c
.RI "subroutine \fBzlahrd\fP (n, k, nb, a, lda, tau, t, ldt, y, ldy)"
.br
.RI "\fBZLAHRD\fP reduces the first nb columns of a general rectangular matrix A so that elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zlahrd (integer n, integer k, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( nb ) tau, complex*16, dimension( ldt, nb ) t, integer ldt, complex*16, dimension( ldy, nb ) y, integer ldy)"

.PP
\fBZLAHRD\fP reduces the first nb columns of a general rectangular matrix A so that elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> This routine is deprecated and has been replaced by routine ZLAHR2\&.
!>
!> ZLAHRD reduces the first NB columns of a complex general n-by-(n-k+1)
!> matrix A so that elements below the k-th subdiagonal are zero\&. The
!> reduction is performed by a unitary similarity transformation
!> Q**H * A * Q\&. The routine returns the matrices V and T which determine
!> Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
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!>          N is INTEGER
!>          The order of the matrix A\&.
!> 
.fi
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\fIK\fP 
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.nf
!>          K is INTEGER
!>          The offset for the reduction\&. Elements below the k-th
!>          subdiagonal in the first NB columns are reduced to zero\&.
!> 
.fi
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\fINB\fP 
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!>          NB is INTEGER
!>          The number of columns to be reduced\&.
!> 
.fi
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\fIA\fP 
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!>          A is COMPLEX*16 array, dimension (LDA,N-K+1)
!>          On entry, the n-by-(n-k+1) general matrix A\&.
!>          On exit, the elements on and above the k-th subdiagonal in
!>          the first NB columns are overwritten with the corresponding
!>          elements of the reduced matrix; the elements below the k-th
!>          subdiagonal, with the array TAU, represent the matrix Q as a
!>          product of elementary reflectors\&. The other columns of A are
!>          unchanged\&. See Further Details\&.
!> 
.fi
.PP
.br
\fILDA\fP 
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!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
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\fITAU\fP 
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.nf
!>          TAU is COMPLEX*16 array, dimension (NB)
!>          The scalar factors of the elementary reflectors\&. See Further
!>          Details\&.
!> 
.fi
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.br
\fIT\fP 
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!>          T is COMPLEX*16 array, dimension (LDT,NB)
!>          The upper triangular matrix T\&.
!> 
.fi
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\fILDT\fP 
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!>          LDT is INTEGER
!>          The leading dimension of the array T\&.  LDT >= NB\&.
!> 
.fi
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.br
\fIY\fP 
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!>          Y is COMPLEX*16 array, dimension (LDY,NB)
!>          The n-by-nb matrix Y\&.
!> 
.fi
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.br
\fILDY\fP 
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.nf
!>          LDY is INTEGER
!>          The leading dimension of the array Y\&. LDY >= max(1,N)\&.
!> 
.fi
.PP
 
.RE
.PP
\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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\fBFurther Details:\fP
.RS 4

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!>
!>  The matrix Q is represented as a product of nb elementary reflectors
!>
!>     Q = H(1) H(2) \&. \&. \&. H(nb)\&.
!>
!>  Each H(i) has the form
!>
!>     H(i) = I - tau * v * v**H
!>
!>  where tau is a complex scalar, and v is a complex vector with
!>  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
!>  A(i+k+1:n,i), and tau in TAU(i)\&.
!>
!>  The elements of the vectors v together form the (n-k+1)-by-nb matrix
!>  V which is needed, with T and Y, to apply the transformation to the
!>  unreduced part of the matrix, using an update of the form:
!>  A := (I - V*T*V**H) * (A - Y*V**H)\&.
!>
!>  The contents of A on exit are illustrated by the following example
!>  with n = 7, k = 3 and nb = 2:
!>
!>     ( a   h   a   a   a )
!>     ( a   h   a   a   a )
!>     ( a   h   a   a   a )
!>     ( h   h   a   a   a )
!>     ( v1  h   a   a   a )
!>     ( v1  v2  a   a   a )
!>     ( v1  v2  a   a   a )
!>
!>  where a denotes an element of the original matrix A, h denotes a
!>  modified element of the upper Hessenberg matrix H, and vi denotes an
!>  element of the vector defining H(i)\&.
!> 
.fi
.PP
 
.RE
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Definition at line \fB166\fP of file \fBzlahrd\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.