SRC/zpbstf.f(3)

NAME
SRC/zpbstf.f

SYNOPSIS

  Functions/Subroutines
subroutine zpbstf (uplo, n, kd, ab, ldab, info)
ZPBSTF

Function/Subroutine Documentation

  subroutine zpbstf (character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, integer info)

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.

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 152 of file zpbstf.f.

Author

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