zpbstf.f(3)

NAME
zpbstf.f -

SYNOPSIS

  Functions/Subroutines

subroutine zpbstf (UPLO, N, KD, AB, LDAB, INFO)
ZPBSTF

Function/Subroutine Documentation

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

ZPBSTF

Purpose:

     ZPBSTF computes a split Cholesky factorization of a complex
     Hermitian positive definite band matrix A.

     This routine is designed to be used in conjunction with ZHBGST.

     The factorization has the form  A = S**H*S  where S is a band matrix
     of the same bandwidth as A and the following structure:

       S = ( U    )
           ( M  L )

     where U is upper triangular of order m = (n+kd)/2, and L is lower
     triangular of order n-m.

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 factor S from the split Cholesky
              factorization A = S**H*S. See Further Details.

    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 factorization could not be completed,
                   because the updated element a(i,i) was negative; the
                   matrix A is not positive definite.

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 = 7, KD = 2:

      S = ( s11  s12  s13                     )
          (      s22  s23  s24                )
          (           s33  s34                )
          (                s44                )
          (           s53  s54  s55           )
          (                s64  s65  s66      )
          (                     s75  s76  s77 )

      If UPLO = 'U', the array AB holds:

      on entry:                          on exit:

       *    *   a13  a24  a35  a46  a57   *    *   s13  s24  s53**H s64**H s75**H
       *   a12  a23  a34  a45  a56  a67   *   s12  s23  s34  s54**H s65**H s76**H
      a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55    s66    s77

      If UPLO = 'L', the array AB holds:

      on entry:                          on exit:

      a11  a22  a33  a44  a55  a66  a77  s11    s22    s33    s44  s55  s66  s77
      a21  a32  a43  a54  a65  a76   *   s12**H s23**H s34**H s54  s65  s76   *
      a31  a42  a53  a64  a64   *    *   s13**H s24**H s53    s64  s75   *    *

      Array elements marked * are not used by the routine; s12**H denotes
      conjg(s12); the diagonal elements of S are real.

Definition at line 154 of file zpbstf.f.

Author

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