zpbtf2.f(3)

NAME
zpbtf2.f -

SYNOPSIS

  Functions/Subroutines

subroutine zpbtf2 (UPLO, N, KD, AB, LDAB, INFO)
ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Function/Subroutine Documentation

  subroutine zpbtf2 (characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, integerINFO)

ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Purpose:

     ZPBTF2 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, U**H is the conjugate transpose
     of U, and L is lower triangular.

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

Parameters:
    UPLO

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

    N

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

    KD

              KD is 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

              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 = -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.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

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.

Definition at line 143 of file zpbtf2.f.

Author

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