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RedHat 9 (Linux i386) - man page for dsytd2 (redhat section l)

DSYTD2(l)					)					DSYTD2(l)

NAME
       DSYTD2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal
       similarity transformation

SYNOPSIS
       SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDA, N

	   DOUBLE	  PRECISION A( LDA, * ), D( * ), E( * ), TAU( * )

PURPOSE
       DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal form T by an  orthogonal
       similarity transformation: Q' * A * Q = T.

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

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	       On entry, the symmetric matrix A.  If UPLO = 'U', the leading n-by-n upper  trian-
	       gular  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 cor-
	       responding 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     (input) INTEGER The leading dimension of the array A.  LDA >= max(1,N).

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

       E       (output) 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     (output) DOUBLE PRECISION array, dimension (N-1)
	       The scalar factors of the elementary reflectors (see Further Details).

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value.

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'

       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'

       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).

LAPACK version 3.0			   15 June 2000 				DSYTD2(l)


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