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NAME
     ssytd2 - reduce a real symmetric matrix A to symmetric  tri-
     diagonal form T by an orthogonal similarity transformation

SYNOPSIS
     SUBROUTINE SSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO )

     CHARACTER UPLO

     INTEGER INFO, LDA, N

     REAL A( LDA, * ), D( * ), E( * ), TAU( * )



     #include <sunperf.h>

     void ssytd2(char uplo, int n, float *sa, int lda, float  *d,
               float *e, float *tau, int *info) ;

PURPOSE
     SSYTD2 reduces a real symmetric matrix A to symmetric tridi-
     agonal 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) REAL array, dimension (LDA,N)
               On entry, the symmetric matrix A.  If UPLO =  'U',
               the leading n-by-n upper triangular part of A con-
               tains 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 tri-
               angular 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 super-
               diagonal of A are overwritten by the corresponding
               elements of the tridiagonal matrix T, and the ele-
               ments  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 tri-
               diagonal 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) REAL array, dimension (N)
               The diagonal elements of the tridiagonal matrix T:
               D(i) = A(i,i).

     E         (output) 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       (output) REAL 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 ille-
               gal 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).

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