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## cpbtf2()

subroutine cpbtf2 | ( | character | uplo,
|  | integer | n,
|  | integer | kd,
|  | complex, dimension( ldab, * ) | ab,
|  | integer | ldab,
|  | integer | info )

CPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Download CPBTF2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> CPBTF2 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

  [in]

  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
      !>

  [in]

  N

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

  [in]

  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.
      !>

  [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 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.
      !>

  [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 = -k, the k-th argument had an illegal value
      !>          > 0: if INFO = k, the leading principal minor of order k
      !>               is not positive, and the factorization could not be
      !>               completed.
      !>

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 = 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.
      !>