CPBSV - compute the solution to a complex system of linear
       equations A * X = B,


SYNOPSIS

       SUBROUTINE CPBSV( UPLO, N, KD, NRHS,  AB,  LDAB,  B,  LDB,
                         INFO )

           CHARACTER     UPLO

           INTEGER       INFO, KD, LDAB, LDB, N, NRHS

           COMPLEX       AB( LDAB, * ), B( LDB, * )


PURPOSE

       CPBSV  computes the solution to a complex system of linear
       equations A * X = B, where A is an N-by-N Hermitian  posi­
       tive definite band matrix and X and B are N-by-NRHS matri­
       ces.

       The Cholesky decomposition is used to factor A as
          A = U**H * U,  if UPLO = 'U', or
          A = L * L**H,  if UPLO = 'L',
       where U is an upper triangular band matrix,  and  L  is  a
       lower  triangular  band  matrix,  with  the same number of
       superdiagonals or subdiagonals as A.  The factored form of
       A is then used to solve the system of equations A * X = B.


ARGUMENTS

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

       N       (input) INTEGER
               The number of linear equations, i.e., the order of
               the matrix A.  N >= 0.

       KD      (input) INTEGER
               The  number  of  superdiagonals of the matrix A if
               UPLO = 'U', or the number of subdiagonals if  UPLO
               = 'L'.  KD >= 0.

       NRHS    (input) INTEGER
               The  number  of right hand sides, i.e., the number
               of columns of the matrix B.  NRHS >= 0.

       AB      (input/output) COMPLEX array, dimension (LDAB,N)
               On entry, the upper or lower triangle of the  Her­
               mitian  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)

               details.

               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    (input) INTEGER
               The leading dimension of the array  AB.   LDAB  >=
               KD+1.

       B       (input/output) COMPLEX array, dimension (LDB,NRHS)
               On entry, the N-by-NRHS right hand side matrix  B.
               On  exit,  if  INFO  =  0,  the N-by-NRHS solution
               matrix X.

       LDB     (input) INTEGER
               The leading dimension of  the  array  B.   LDB  >=
               max(1,N).

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value
               > 0:  if INFO = i, the leading minor of order i of
               A  is  not positive definite, so the factorization
               could not be completed, and the solution  has  not
               been computed.


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   *
       *



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