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## cpbstf()

subroutine cpbstf | ( | character | uplo,
|  | integer | n,
|  | integer | kd,
|  | complex, dimension( ldab, * ) | ab,
|  | integer | ldab,
|  | integer | info )

CPBSTF

Download CPBSTF + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> CPBSTF computes a split Cholesky factorization of a complex
      !> Hermitian positive definite band matrix A.
      !>
      !> This routine is designed to be used in conjunction with CHBGST.
      !>
      !> 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

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>          = 'U':  Upper triangle of A is stored;
      !>          = 'L':  Lower triangle of A is stored.
      !>

  [in]

  N

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

  [in]

  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.
      !>

  [in,out]

  AB

      !>          AB is COMPLEX 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.
      !>

  [in]

  LDAB

      !>          LDAB is INTEGER
      !>          The leading dimension of the array AB.  LDAB >= KD+1.
      !>

  [out]

  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.
      !>