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

NAME

       LAPACK-3 - computes the factorization of a real symmetric matrix A stored in packed format
       using the Bunch-Kaufman diagonal pivoting method

SYNOPSIS

       SUBROUTINE SSPTRF( UPLO, N, AP, IPIV, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, N

           INTEGER        IPIV( * )

           REAL           AP( * )

PURPOSE

       SSPTRF computes the factorization of a real symmetric matrix A  stored  in  packed  format
       using the Bunch-Kaufman diagonal pivoting method:
           A = U*D*U**T  or  A = L*D*L**T
        where U (or L) is a product of permutation and unit upper (lower)
        triangular matrices, and D is symmetric and block diagonal with
        1-by-1 and 2-by-2 diagonal blocks.

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) REAL 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)*(2n-j)/2) = A(i,j) for j<=i<=n.
                On exit, the block diagonal matrix D and the multipliers used
                to obtain the factor U or L, stored as a packed triangular
                matrix overwriting A (see below for further details).

        IPIV    (output) INTEGER array, dimension (N)
                Details of the interchanges and the block structure of D.
                If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                interchanged and D(k,k) is a 1-by-1 diagonal block.
                If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
                columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
                is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
                IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
                interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

        INFO    (output) INTEGER
                = 0: successful exit
                < 0: if INFO = -i, the i-th argument had an illegal value
                > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
                has been completed, but the block diagonal matrix D is
                exactly singular, and division by zero will occur if it
                is used to solve a system of equations.

FURTHER DETAILS

        5-96 - Based on modifications by J. Lewis, Boeing Computer Services
               Company
        If UPLO = 'U', then A = U*D*U**T, where
           U = P(n)*U(n)* ... *P(k)U(k)* ...,
        i.e., U is a product of terms P(k)*U(k), where k decreases from n to
        1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
        and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
        defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
        that if the diagonal block D(k) is of order s (s = 1 or 2), then
                   (   I    v    0   )   k-s
           U(k) =  (   0    I    0   )   s
                   (   0    0    I   )   n-k
                      k-s   s   n-k
        If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
        If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
        and A(k,k), and v overwrites A(1:k-2,k-1:k).
        If UPLO = 'L', then A = L*D*L**T, where
           L = P(1)*L(1)* ... *P(k)*L(k)* ...,
        i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
        n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
        and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
        defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
        that if the diagonal block D(k) is of order s (s = 1 or 2), then
                   (   I    0     0   )  k-1
           L(k) =  (   0    I     0   )  s
                   (   0    v     I   )  n-k-s+1
                      k-1   s  n-k-s+1
        If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
        If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
        and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

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