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.