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

NAME

       LAPACK-3  -  reduces  a  real  symmetric  matrix  A  stored  in  packed  form to symmetric
       tridiagonal form T by an orthogonal similarity transformation

SYNOPSIS

       SUBROUTINE DSPTRD( UPLO, N, AP, D, E, TAU, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, N

           DOUBLE         PRECISION AP( * ), D( * ), E( * ), TAU( * )

PURPOSE

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

ARGUMENTS

        UPLO    (input) CHARACTER*1
                = 'U':  Upper triangle of A is stored;
                = 'L':  Lower triangle of A is stored.

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

        AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
                On entry, the upper or lower triangle of the symmetric matrix
                A, packed columnwise in a linear array.  The j-th column of A
                is stored in the array AP as follows:
                if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
                if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
                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.
                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**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 AP,
        overwriting A(1:i-1,i+1), and tau is stored 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 AP,
        overwriting A(i+2:n,i), and tau is stored in TAU(i).

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