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chptrd.f(3)				      LAPACK				      chptrd.f(3)

NAME
       chptrd.f -

SYNOPSIS
   Functions/Subroutines
       subroutine chptrd (UPLO, N, AP, D, E, TAU, INFO)
	   CHPTRD

Function/Subroutine Documentation
   subroutine chptrd (characterUPLO, integerN, complex, dimension( * )AP, real, dimension( * )D,
       real, dimension( * )E, complex, dimension( * )TAU, integerINFO)
       CHPTRD

       Purpose:

	    CHPTRD reduces a complex Hermitian matrix A stored in packed form 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.

	   AP

		     AP is COMPLEX array, dimension (N*(N+1)/2)
		     On entry, the upper or lower triangle of the Hermitian matrix
		     A, packed columnwise in a linear array.  The j-th column of A
		     is stored in the array AP as follows:
		     if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
		     if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
		     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.

	   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).

	   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 AP,
	     overwriting A(1:i-1,i+1), and tau is stored 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 AP,
	     overwriting A(i+2:n,i), and tau is stored in TAU(i).

       Definition at line 152 of file chptrd.f.

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

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