.TH "SRC/zhetd2.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
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.SH NAME
SRC/zhetd2.f
.SH SYNOPSIS
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.SS "Functions/Subroutines"

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.ti -1c
.RI "subroutine \fBzhetd2\fP (uplo, n, a, lda, d, e, tau, info)"
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.RI "\fBZHETD2\fP reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity transformation (unblocked algorithm)\&. "
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.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zhetd2 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( * ) tau, integer info)"

.PP
\fBZHETD2\fP reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity transformation (unblocked algorithm)\&.  
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\fBPurpose:\fP
.RS 4

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.nf
!>
!> ZHETD2 reduces a complex Hermitian matrix A to real symmetric
!> tridiagonal form T by a unitary similarity transformation:
!> Q**H * A * Q = T\&.
!> 
.fi
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.RE
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\fBParameters\fP
.RS 4
\fIUPLO\fP 
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.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          Hermitian matrix A is stored:
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!> 
.fi
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\fIN\fP 
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!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
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\fIA\fP 
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!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the Hermitian matrix A\&.  If UPLO = 'U', the leading
!>          n-by-n upper triangular part of A contains the upper
!>          triangular part of the matrix A, and the strictly lower
!>          triangular part of A is not referenced\&.  If UPLO = 'L', the
!>          leading n-by-n lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced\&.
!>          On exit, if UPLO = 'U', the diagonal and first superdiagonal
!>          of A are overwritten by the corresponding elements of the
!>          tridiagonal matrix T, and the elements above the first
!>          superdiagonal, with the array TAU, represent the unitary
!>          matrix Q as a product of elementary reflectors; if UPLO
!>          = 'L', the diagonal and first subdiagonal of A are over-
!>          written by the corresponding elements of the tridiagonal
!>          matrix T, and the elements below the first subdiagonal, with
!>          the array TAU, represent the unitary matrix Q as a product
!>          of elementary reflectors\&. See Further Details\&.
!> 
.fi
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.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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\fID\fP 
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!>          D is DOUBLE PRECISION array, dimension (N)
!>          The diagonal elements of the tridiagonal matrix T:
!>          D(i) = A(i,i)\&.
!> 
.fi
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\fIE\fP 
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.nf
!>          E is DOUBLE PRECISION array, dimension (N-1)
!>          The off-diagonal elements of the tridiagonal matrix T:
!>          E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'\&.
!> 
.fi
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.br
\fITAU\fP 
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.nf
!>          TAU is COMPLEX*16 array, dimension (N-1)
!>          The scalar factors of the elementary reflectors (see Further
!>          Details)\&.
!> 
.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
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.RE
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\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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!>
!>  If UPLO = 'U', the matrix Q is represented as a product of elementary
!>  reflectors
!>
!>     Q = H(n-1) \&. \&. \&. H(2) H(1)\&.
!>
!>  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(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
!>  A(1:i-1,i+1), and tau in TAU(i)\&.
!>
!>  If UPLO = 'L', the matrix Q is represented as a product of elementary
!>  reflectors
!>
!>     Q = H(1) H(2) \&. \&. \&. H(n-1)\&.
!>
!>  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) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
!>  and tau in TAU(i)\&.
!>
!>  The contents of A on exit are illustrated by the following examples
!>  with n = 5:
!>
!>  if UPLO = 'U':                       if UPLO = 'L':
!>
!>    (  d   e   v2  v3  v4 )              (  d                  )
!>    (      d   e   v3  v4 )              (  e   d              )
!>    (          d   e   v4 )              (  v1  e   d          )
!>    (              d   e  )              (  v1  v2  e   d      )
!>    (                  d  )              (  v1  v2  v3  e   d  )
!>
!>  where d and e denote diagonal and off-diagonal elements of T, and vi
!>  denotes an element of the vector defining H(i)\&.
!> 
.fi
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Definition at line \fB174\fP of file \fBzhetd2\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.