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

.in +1c
.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 This routine is deprecated and has been replaced by routine ZLAHR2\&.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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.nf
          N is INTEGER
          The order of the matrix A\&.
.fi
.PP
.br
\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
.PP
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\fINB\fP 
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          NB is INTEGER
          The number of columns to be reduced\&.
.fi
.PP
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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
.PP
.br
\fITAU\fP 
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          TAU is COMPLEX*16 array, dimension (NB)
          The scalar factors of the elementary reflectors\&. See Further
          Details\&.
.fi
.PP
.br
\fIT\fP 
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.nf
          T is COMPLEX*16 array, dimension (LDT,NB)
          The upper triangular matrix T\&.
.fi
.PP
.br
\fILDT\fP 
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.nf
          LDT is INTEGER
          The leading dimension of the array T\&.  LDT >= NB\&.
.fi
.PP
.br
\fIY\fP 
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.nf
          Y is COMPLEX*16 array, dimension (LDY,NB)
          The n-by-nb matrix Y\&.
.fi
.PP
.br
\fILDY\fP 
.PP
.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 
.PP
Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
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\fBFurther Details:\fP
.RS 4

.PP
.nf
  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
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.RE
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.PP
Definition at line \fB166\fP of file \fBzlahrd\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.