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zpbtf2

 NAME
      ZPBTF2 - compute the Cholesky factorization of a complex
      Hermitian positive definite band matrix A

 SYNOPSIS
      SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, INFO )

          CHARACTER      UPLO

          INTEGER        INFO, KD, LDAB, N

          COMPLEX*16     AB( LDAB, * )

 PURPOSE
      ZPBTF2 computes the Cholesky factorization of a complex Her-
      mitian positive definite band matrix A.

      The factorization has the form
         A = U' * U ,  if UPLO = 'U', or
         A = L  * L',  if UPLO = 'L',
      where U is an upper triangular matrix, U' is the conjugate
      transpose of U, and L is lower triangular.

      This is the unblocked version of the algorithm, calling
      Level 2 BLAS.

 ARGUMENTS
      UPLO    (input) CHARACTER*1
              Specifies whether the upper or lower triangular part
              of the Hermitian matrix A is stored:
              = 'U':  Upper triangular
              = 'L':  Lower triangular

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

      KD      (input) INTEGER
              The number of super-diagonals of the matrix A if
              UPLO = 'U', or the number of sub-diagonals if UPLO =
              'L'.  KD >= 0.

      AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
              On entry, the upper or lower triangle of the Hermi-
              tian 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'*U or A = L*L'
              of the band matrix A, in the same storage format as
              A.

      LDAB    (input) INTEGER
              The leading dimension of the array AB.  LDAB >=
              KD+1.

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

 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.