NAME

       zpbtrf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zpbtrf (UPLO, N, KD, AB, LDAB, INFO)
           ZPBTRF

Function/Subroutine Documentation

   subroutine zpbtrf (character UPLO, integer N, integer KD, complex*16, dimension( ldab, * ) AB,
       integer LDAB, integer INFO)
       ZPBTRF

       Purpose:

            ZPBTRF computes the Cholesky factorization of a complex Hermitian
            positive definite band matrix A.

            The factorization has the form
               A = U**H * U,  if UPLO = 'U', or
               A = L  * L**H,  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 COMPLEX*16 array, dimension (LDAB,N)
                     On entry, the upper or lower triangle of the Hermitian 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**H*U or A = L*L**H 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

Author

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