ZPBTRS (3lapack)

solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF

SYNOPSIS

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

      CHARACTER      UPLO

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

      COMPLEX*16     AB( LDAB, * ), B( LDB, * )

PURPOSE

  ZPBTRS solves a system of linear equations A*X = B with a Hermitian
  positive definite band matrix A using the Cholesky factorization A = U**H*U
  or A = L*L**H computed by ZPBTRF.

ARGUMENTS

  UPLO    (input) CHARACTER*1
          = 'U':  Upper triangular factor stored in AB;
          = 'L':  Lower triangular factor stored in AB.

  N       (input) INTEGER
          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) COMPLEX*16 array, dimension (LDAB,N)
          The triangular factor U or L from the Cholesky factorization A =
          U**H*U or A = L*L**H of the band matrix A, stored in the first KD+1
          rows of the array.  The j-th column of U or L is stored in the j-th
          column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) =
          U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j)    = L(i,j)
          for j<=i<=min(n,j+kd).

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

  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B.  On exit, the 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