debian man page for zhptrd

zhptrd.f(3)							      LAPACK							       zhptrd.f(3)

NAME
       zhptrd.f -

SYNOPSIS
   Functions/Subroutines
       subroutine zhptrd (UPLO, N, AP, D, E, TAU, INFO)
	   ZHPTRD

Function/Subroutine Documentation
   subroutine zhptrd (characterUPLO, integerN, complex*16, dimension( * )AP, double precision, dimension( * )D, double precision, dimension( * )E,
       complex*16, dimension( * )TAU, integerINFO)
       ZHPTRD

       Purpose:

	    ZHPTRD 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*16 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 DOUBLE PRECISION array, dimension (N)
		     The diagonal elements of the tridiagonal matrix T:
		     D(i) = A(i,i).

	   E

		     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'.

	   TAU

		     TAU is COMPLEX*16 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 zhptrd.f.

Author
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Version 3.4.1							  Sun May 26 2013						       zhptrd.f(3)