CPBSV(3)              LAPACK driver routine (version 3.1)             CPBSV(3)



NAME
       CPBSV  -  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  positive  definite  band
       matrix and X and B are N-by-NRHS matrices.

       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 equa-
       tions 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 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).  See below for further 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 illegal 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   *    *

       Array elements marked * are not used by the routine.




 LAPACK driver routine (version 3.N1o)vember 2006                        CPBSV(3)