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.

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

  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.