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dsptrd.f(3)				      LAPACK				      dsptrd.f(3)

NAME
       dsptrd.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dsptrd (UPLO, N, AP, D, E, TAU, INFO)
	   DSPTRD

Function/Subroutine Documentation
   subroutine dsptrd (characterUPLO, integerN, double precision, dimension( * )AP, double
       precision, dimension( * )D, double precision, dimension( * )E, double precision,
       dimension( * )TAU, integerINFO)
       DSPTRD

       Purpose:

	    DSPTRD reduces a real symmetric matrix A stored in packed form to
	    symmetric tridiagonal form T by an orthogonal similarity
	    transformation: Q**T * 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 DOUBLE PRECISION array, dimension (N*(N+1)/2)
		     On entry, the upper or lower triangle of the symmetric 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 orthogonal
		     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 orthogonal 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 DOUBLE PRECISION 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**T

	     where tau is a real scalar, and v is a real 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**T

	     where tau is a real scalar, and v is a real 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 151 of file dsptrd.f.

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

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