cpbtrf.f man page




subroutine cpbtrf (UPLO, N, KD, AB, LDAB, INFO)

Function/Subroutine Documentation

subroutine cpbtrf (character UPLO, integer N, integer KD, complex, dimension( ldab, * ) AB, integer LDAB, integer INFO)



 CPBTRF 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 and L is lower triangular.


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


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


          KD is INTEGER


          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
          as follows:

          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 is INTEGER


          INFO is INTEGER
          = 0:  successful exit
          > 0:  if INFO = i, the leading minor of order i is not
                positive definite, and the factorization could not be

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.


December 2016

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.

Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

Definition at line 144 of file cpbtrf.f.


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Referenced By

The man page cpbtrf(3) is an alias of cpbtrf.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK