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chetrd.f(3)				      LAPACK				      chetrd.f(3)

NAME
       chetrd.f -

SYNOPSIS
   Functions/Subroutines
       subroutine chetrd (UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO)
	   CHETRD

Function/Subroutine Documentation
   subroutine chetrd (characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, real,
       dimension( * )D, real, dimension( * )E, complex, dimension( * )TAU, complex, dimension( *
       )WORK, integerLWORK, integerINFO)
       CHETRD

       Purpose:

	    CHETRD reduces a complex Hermitian matrix A to real symmetric
	    tridiagonal form T by a unitary similarity transformation:
	    Q**H * A * Q = T.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     = 'U':  Upper triangle of A is stored;
		     = 'L':  Lower triangle of A is stored.

	   N

		     N is INTEGER
		     The order of the matrix A.  N >= 0.

	   A

		     A is COMPLEX 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.

	   LDA

		     LDA is INTEGER
		     The leading dimension of the array A.  LDA >= max(1,N).

	   D

		     D is REAL array, dimension (N)
		     The diagonal elements of the tridiagonal matrix T:
		     D(i) = A(i,i).

	   E

		     E is REAL 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'.

	   TAU

		     TAU is COMPLEX array, dimension (N-1)
		     The scalar factors of the elementary reflectors (see Further
		     Details).

	   WORK

		     WORK is COMPLEX array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

		     LWORK is INTEGER
		     The dimension of the array WORK.  LWORK >= 1.
		     For optimum performance LWORK >= N*NB, where NB is the
		     optimal blocksize.

		     If LWORK = -1, then a workspace query is assumed; the routine
		     only calculates the optimal size of the WORK array, returns
		     this value as the first entry of the WORK array, and no error
		     message related to LWORK is issued by XERBLA.

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     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).

       Definition at line 193 of file chetrd.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      chetrd.f(3)
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