text: """Kennedy-Carpenter implicit/explicit RK."""
  
  
  from pymbolic import var
  from leap import TwoOrderAdaptiveMethodBuilderMixin
  from leap.rk import ButcherTableauMethodBuilder
  
  
  __copyright__ = """
  Copyright (C) 2010, 2013 Andreas Kloeckner
  Copyright (C) 2014 Matt Wala
  """
  
  __license__ = """
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
  
  The above copyright notice and this permission notice shall be included in
  all copies or substantial portions of the Software.
  
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
  THE SOFTWARE.
  """
  
  
  __doc__ = """
  
  IMEX Method Builders
  --------------------
  
  .. autoclass :: KennedyCarpenterIMEXRungeKuttaMethodBuilderBase
  """
  
  
  class KennedyCarpenterIMEXRungeKuttaMethodBuilderBase(
          TwoOrderAdaptiveMethodBuilderMixin, ButcherTableauMethodBuilder):
      """
      Christopher A. Kennedy, Mark H. Carpenter. Additive Runge-Kutta
      schemes for convection-diffusion-reaction equations.
      Applied Numerical Mathematics
      Volume 44, Issues 1-2, January 2003, Pages 139-181
      http://dx.doi.org/10.1016/S0168-9274(02)00138-1
  
      User-supplied context:
          <state> + component_id: The value that is integrated
          <func>rhs_expl_ + component_id: The explicit right hand side function
          <func>rhs_impl_ + component_id: The implicit right hand side function
  
      .. automethod:: __init__
      .. automethod:: generate
  
      """
  
      @property
      def a_implicit(self):
          raise NotImplementedError
  
      @property
      def high_order_coeffs(self):
          raise NotImplementedError
  
      @property
      def low_order_coeffs(self):
          raise NotImplementedError
  
      def __init__(self, component_id, use_high_order=True, state_filter_name=None,
              use_explicit=True, use_implicit=True,
              atol=0, rtol=0, max_dt_growth=None, min_dt_shrinkage=None,
              implicit_rhs_name=None, explicit_rhs_name=None):
          ButcherTableauMethodBuilder.__init__(
                  self,
                  component_id=component_id,
                  state_filter_name=state_filter_name)
  
          TwoOrderAdaptiveMethodBuilderMixin.__init__(
                  self,
                  atol=atol,
                  rtol=rtol,
                  max_dt_growth=max_dt_growth,
                  min_dt_shrinkage=min_dt_shrinkage)
  
          if explicit_rhs_name is None:
              explicit_rhs_name = "expl_" + component_id
          if implicit_rhs_name is None:
              implicit_rhs_name = "impl_" + component_id
  
          self.explicit_rhs_name = explicit_rhs_name
          self.implicit_rhs_name = implicit_rhs_name
  
          self.use_high_order = use_high_order
          self.use_explicit = use_explicit
          self.use_implicit = use_implicit
  
      def generate(self):
          """
          :returns: :class:`dagrt.language.DAGCode`
          """
  
          if self.use_high_order:
              estimate_names = ("high_order", "low_order")
          else:
              estimate_names = ("low_order", "high_order")
  
          set_names = []
          if self.use_implicit:
              set_names.append("implicit")
          if self.use_explicit:
              set_names.append("explicit")
  
          return self.generate_butcher(
                  stage_coeff_set_names=set_names,
                  stage_coeff_sets={
                      "explicit": self.a_explicit,
                      "implicit": self.a_implicit,
                      },
                  rhs_funcs={
                      "implicit": var("<func>"+self.implicit_rhs_name),
                      "explicit": var("<func>"+self.explicit_rhs_name),
                      },
                  estimate_coeff_set_names=estimate_names,
                  estimate_coeff_sets={
                      "high_order": self.high_order_coeffs,
                      "low_order": self.low_order_coeffs
                      })
  
      def finish(self, cb, estimate_coeff_set_names, estimate_vars):
          if not self.adaptive:
              super().finish(
                      cb, estimate_coeff_set_names, estimate_vars)
          else:
              high_est = estimate_vars[
                      estimate_coeff_set_names.index("high_order")]
              low_est = estimate_vars[
                      estimate_coeff_set_names.index("low_order")]
              self.finish_adaptive(cb, high_est, low_est)
  
      def finish_nonadaptive(self, cb, high_order_estimate, low_order_estimate):
          if self.use_high_order:
              est = high_order_estimate
          else:
              est = low_order_estimate
  
          cb(self.state, est)
          cb.yield_state(self.state, self.component_id, self.t + self.dt, "final")
          cb(self.t, self.t + self.dt)
  
  
  class KennedyCarpenterIMEXARK4MethodBuilder(
          KennedyCarpenterIMEXRungeKuttaMethodBuilderBase):
      gamma = 1./4.
  
      c = [0, 1/2, 83/250, 31/50, 17/20, 1]
      low_order = 3
      high_order = 4
  
      high_order_coeffs = [
              82889/524892,
              0,
              15625/83664,
              69875/102672,
              -2260/8211,
              1/4]
  
      low_order_coeffs = [
              4586570599/29645900160,
              0,
              178811875/945068544,
              814220225/1159782912,
              -3700637/11593932,
              61727/225920
              ]
  
      # ARK4(3)6L[2]SA-ERK (explicit)
      a_explicit = [[],
              [1/2],
              [13861/62500, 6889/62500],
              [-116923316275/2393684061468,
                  -2731218467317/15368042101831,
                  9408046702089/11113171139209],
              [-451086348788/2902428689909,
                  -2682348792572/7519795681897,
                  12662868775082/11960479115383,
                  3355817975965/11060851509271],
              [647845179188/3216320057751,
                  73281519250/8382639484533,
                  552539513391/3454668386233,
                  3354512671639/8306763924573,
                  4040/17871]]
  
      # ARK4(3)6L[2]SA-ESDIRK (implicit)
      a_implicit = [[],
              [1/4, gamma],
              [8611/62500, -1743/31250, gamma],
              [5012029/34652500, -654441/2922500, 174375/388108, gamma],
              [15267082809/155376265600, -71443401/120774400,
                  730878875/902184768, 2285395/8070912, gamma],
              [82889/524892, 0, 15625/83664, 69875/102672,
                  -2260/8211, gamma]]
  
      recycle_last_stage_coeff_set_names = ("implicit",)
  
      assert (len(a_explicit) == len(a_implicit)
              == len(low_order_coeffs)
              == len(high_order_coeffs)
              == len(c))
  