NAME

       dpbtrf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dpbtrf (UPLO, N, KD, AB, LDAB, INFO)
           DPBTRF

Function/Subroutine Documentation

   subroutine dpbtrf (characterUPLO, integerN, integerKD, double precision, dimension( ldab, * )AB, integerLDAB,
       integerINFO)
       DPBTRF

       Purpose:

            DPBTRF computes the Cholesky factorization of a real symmetric
            positive definite band matrix A.

            The factorization has the form
               A = U**T * U,  if UPLO = 'U', or
               A = L  * L**T,  if UPLO = 'L',
            where U is an upper triangular matrix and L is lower triangular.

       Parameters:
           UPLO

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

           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           KD

                     KD is INTEGER
                     The number of superdiagonals of the matrix A if UPLO = 'U',
                     or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

           AB

                     AB is DOUBLE PRECISION array, dimension (LDAB,N)
                     On entry, the upper or lower triangle of the symmetric band
                     matrix A, stored in the first KD+1 rows of the array.  The
                     j-th column of A is stored in the j-th column of the array AB
                     as follows:
                     if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
                     if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

                     On exit, if INFO = 0, the triangular factor U or L from the
                     Cholesky factorization A = U**T*U or A = L*L**T of the band
                     matrix A, in the same storage format as A.

           LDAB

                     LDAB is INTEGER
                     The leading dimension of the array AB.  LDAB >= KD+1.

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value
                     > 0:  if INFO = i, the leading minor of order i is not
                           positive definite, and the factorization could not be
                           completed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Further Details:

             The band storage scheme is illustrated by the following example, when
             N = 6, KD = 2, and UPLO = 'U':

             On entry:                       On exit:

                 *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
                 *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
                a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66

             Similarly, if UPLO = 'L' the format of A is as follows:

             On entry:                       On exit:

                a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
                a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
                a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *

             Array elements marked * are not used by the routine.

       Contributors:
           Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

       Definition at line 143 of file dpbtrf.f.

Author

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2                                    Wed Feb 26 2014                                     dpbtrf.f(3)