Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  reduces  a  real  symmetric  matrix  A  to symmetric tridiagonal 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( * )

PURPOSE

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

 LAPACK routine (version 3.3.1)             April 2011                            SSYTD2(3lapack)