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ssytd2.f(3)				      LAPACK				      ssytd2.f(3)

NAME
       ssytd2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine ssytd2 (UPLO, N, A, LDA, D, E, TAU, INFO)
	   SSYTD2 reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal
	   similarity transformation (unblocked algorithm).

Function/Subroutine Documentation
   subroutine ssytd2 (characterUPLO, integerN, real, dimension( lda, * )A, integerLDA, real,
       dimension( * )D, real, dimension( * )E, real, dimension( * )TAU, integerINFO)
       SSYTD2 reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal
       similarity transformation (unblocked algorithm).

       Purpose:

	    SSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal
	    form T by an orthogonal similarity transformation: Q**T * A * Q = T.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     Specifies whether the upper or lower triangular part of the
		     symmetric matrix A is stored:
		     = 'U':  Upper triangular
		     = 'L':  Lower triangular

	   N

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

	   A

		     A is REAL array, dimension (LDA,N)
		     On entry, the symmetric 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 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.

	   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 REAL 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:
	   September 2012

       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
	     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**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 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 174 of file ssytd2.f.

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

Version 3.4.2				 Tue Sep 25 2012			      ssytd2.f(3)
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