#!/usr/bin/env python3




##################################################
## DEPENDENCIES
import sys
import os
import os.path
try:
    import builtins as builtin
except ImportError:
    import __builtin__ as builtin
from os.path import getmtime, exists
import time
import types
from Cheetah.Version import MinCompatibleVersion as RequiredCheetahVersion
from Cheetah.Version import MinCompatibleVersionTuple as RequiredCheetahVersionTuple
from Cheetah.Template import Template
from Cheetah.DummyTransaction import *
from Cheetah.NameMapper import NotFound, valueForName, valueFromSearchList, valueFromFrameOrSearchList
from Cheetah.CacheRegion import CacheRegion
import Cheetah.Filters as Filters
import Cheetah.ErrorCatchers as ErrorCatchers
from Cheetah.compat import unicode
from xpdeint.Segments.Integrators._Stepper import _Stepper

##################################################
## MODULE CONSTANTS
VFFSL=valueFromFrameOrSearchList
VFSL=valueFromSearchList
VFN=valueForName
currentTime=time.time
__CHEETAH_version__ = '3.2.3'
__CHEETAH_versionTuple__ = (3, 2, 3, 'final', 0)
__CHEETAH_genTime__ = 1558054970.6663795
__CHEETAH_genTimestamp__ = 'Fri May 17 11:02:50 2019'
__CHEETAH_src__ = '/home/mattias/xmds-2.2.3/admin/staging/xmds-3.0.0/xpdeint/Segments/Integrators/RK4Stepper.tmpl'
__CHEETAH_srcLastModified__ = 'Thu Apr  4 16:29:24 2019'
__CHEETAH_docstring__ = 'Autogenerated by Cheetah: The Python-Powered Template Engine'

if __CHEETAH_versionTuple__ < RequiredCheetahVersionTuple:
    raise AssertionError(
      'This template was compiled with Cheetah version'
      ' %s. Templates compiled before version %s must be recompiled.'%(
         __CHEETAH_version__, RequiredCheetahVersion))

##################################################
## CLASSES

class RK4Stepper(_Stepper):

    ##################################################
    ## CHEETAH GENERATED METHODS


    def __init__(self, *args, **KWs):

        super(RK4Stepper, self).__init__(*args, **KWs)
        if not self._CHEETAH__instanceInitialized:
            cheetahKWArgs = {}
            allowedKWs = 'searchList namespaces filter filtersLib errorCatcher'.split()
            for k,v in KWs.items():
                if k in allowedKWs: cheetahKWArgs[k] = v
            self._initCheetahInstance(**cheetahKWArgs)
        

    def name(self, **KWS):



        ## Generated from @def name: RK4 at line 26, col 1.
        trans = KWS.get("trans")
        if (not trans and not self._CHEETAH__isBuffering and not callable(self.transaction)):
            trans = self.transaction # is None unless self.awake() was called
        if not trans:
            trans = DummyTransaction()
            _dummyTrans = True
        else: _dummyTrans = False
        write = trans.response().write
        SL = self._CHEETAH__searchList
        _filter = self._CHEETAH__currentFilter
        
        ########################################
        ## START - generated method body
        
        write('''RK4''')
        
        ########################################
        ## END - generated method body
        
        return _dummyTrans and trans.response().getvalue() or ""
        

    def singleIntegrationStep(self, function, **KWS):



        ## CHEETAH: generated from @def singleIntegrationStep($function) at line 38, col 1.
        trans = KWS.get("trans")
        if (not trans and not self._CHEETAH__isBuffering and not callable(self.transaction)):
            trans = self.transaction # is None unless self.awake() was called
        if not trans:
            trans = DummyTransaction()
            _dummyTrans = True
        else: _dummyTrans = False
        write = trans.response().write
        SL = self._CHEETAH__searchList
        _filter = self._CHEETAH__currentFilter
        
        ########################################
        ## START - generated method body
        
        # 
        arguments = {'_step': '_step', VFFSL(SL,"propagationDimension",True): VFFSL(SL,"propagationDimension",True)}
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 41, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 41, col 1.
        write('''
// a_k = a
''')
        _v = VFFSL(SL,"copyVectors",False)(VFFSL(SL,"integrationVectors",True), '_akfield') # "${copyVectors($integrationVectors, '_akfield')}" on line 44, col 1
        if _v is not None: write(_filter(_v, rawExpr="${copyVectors($integrationVectors, '_akfield')}")) # from line 44, col 1.
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 1, parentFunction = function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 1, parentFunction = function)}" on line 46, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 1, parentFunction = function)}")) # from line 46, col 1.
        write('''

// a = D[a]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +1, parentFunction = function) # "${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction = function)}" on line 49, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction = function)}")) # from line 49, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 50, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 50, col 1.
        write('''
// a_i = a
''')
        _v = VFFSL(SL,"copyVectors",False)(VFFSL(SL,"integrationVectors",True), '_aifield') # "${copyVectors($integrationVectors, '_aifield')}" on line 53, col 1
        if _v is not None: write(_filter(_v, rawExpr="${copyVectors($integrationVectors, '_aifield')}")) # from line 53, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 55, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 56, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 56, col 9.
            write(''' = _akfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 56, col 33
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 56, col 33.
            write(''';
''')
        write('''  
// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction = function) # "${callFunction('deltaA', arguments, parentFunction = function)}" on line 60, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction = function)}")) # from line 60, col 1.
        write('''

// a_k = D[a_k]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +1, parentFunction = function) # "${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction = function)}" on line 63, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction = function)}")) # from line 63, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 64, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 64, col 1.
        write('''
''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True), 
"""// a = a + a_k/6
_${vector.id}[$index] += _akfield_${vector.id}[$index]/6.0;
// a_k = a_i + a_k/2
_akfield_${vector.id}[$index] = _aifield_${vector.id}[$index] + 0.5*_akfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors, \n"""// a = a + a_k/6\n_${vector.id}[$index] += _akfield_${vector.id}[$index]/6.0;\n// a_k = a_i + a_k/2\n_akfield_${vector.id}[$index] = _aifield_${vector.id}[$index] + 0.5*_akfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 66, col 1.
        write('''
''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 73, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 73, col 1.
        write(''' += 0.5*_step;
''')
        if VFFSL(SL,"cross",True): # generated from line 74, col 3
            write('''
''')
            _v = VFFSL(SL,"interpolateDependencies",True) # '${interpolateDependencies}' on line 76, col 1
            if _v is not None: write(_filter(_v, rawExpr='${interpolateDependencies}')) # from line 76, col 1.
        write('''
// a_k = G[a_k, t + h/2]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction = function) # "${callFunction('deltaA', arguments, parentFunction = function)}" on line 80, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction = function)}")) # from line 80, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 81, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 81, col 1.
        write('''
''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""// a = a + a_k/3
_${vector.id}[$index] += _akfield_${vector.id}[$index]/3.0;
// a_k = a_i + a_k/2
_akfield_${vector.id}[$index] = _aifield_${vector.id}[$index] + 0.5*_akfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""// a = a + a_k/3\n_${vector.id}[$index] += _akfield_${vector.id}[$index]/3.0;\n// a_k = a_i + a_k/2\n_akfield_${vector.id}[$index] = _aifield_${vector.id}[$index] + 0.5*_akfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 83, col 1.
        write('''
// a_k = G[a_k, t + h/2]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction = function) # "${callFunction('deltaA', arguments, parentFunction = function)}" on line 91, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction = function)}")) # from line 91, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 92, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 92, col 1.
        write('''
''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""// a = a + a_k/3
_${vector.id}[$index] += _akfield_${vector.id}[$index]/3.0;
// a_k = a_i + a_k
_akfield_${vector.id}[$index] = _aifield_${vector.id}[$index] + _akfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""// a = a + a_k/3\n_${vector.id}[$index] += _akfield_${vector.id}[$index]/3.0;\n// a_k = a_i + a_k\n_akfield_${vector.id}[$index] = _aifield_${vector.id}[$index] + _akfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 94, col 1.
        write('''
// a_k = D[a_k]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +1, parentFunction = function) # "${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction = function)}" on line 102, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction = function)}")) # from line 102, col 1.
        write('''

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 104, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 104, col 1.
        write(''' += 0.5*_step;
''')
        if VFFSL(SL,"cross",True): # generated from line 105, col 3
            write('''
''')
            _v = VFFSL(SL,"updateDependenciesForNextStep",True) # '${updateDependenciesForNextStep}' on line 107, col 1
            if _v is not None: write(_filter(_v, rawExpr='${updateDependenciesForNextStep}')) # from line 107, col 1.
        write('''
// a_k = G[a_k, t + h]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction = function) # "${callFunction('deltaA', arguments, parentFunction = function)}" on line 111, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction = function)}")) # from line 111, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 112, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 112, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 114, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 115, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 115, col 9.
            write(''' = _''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 115, col 25
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 115, col 25.
            write(''';
''')
        write('''
// a = D[a]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +1, parentFunction = function) # "${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction = function)}" on line 119, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction = function)}")) # from line 119, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 120, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 120, col 1.
        write('''
''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True), 
"""// a = a + a_k/6
_${vector.id}[$index] += _akfield_${vector.id}[$index]/6.0;
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors, \n"""// a = a + a_k/6\n_${vector.id}[$index] += _akfield_${vector.id}[$index]/6.0;\n""", basis = $homeBasis)}')) # from line 122, col 1.
        # 
        
        ########################################
        ## END - generated method body
        
        return _dummyTrans and trans.response().getvalue() or ""
        

    def interpolateDependencies(self, **KWS):



        ## CHEETAH: generated from @def interpolateDependencies at line 130, col 1.
        trans = KWS.get("trans")
        if (not trans and not self._CHEETAH__isBuffering and not callable(self.transaction)):
            trans = self.transaction # is None unless self.awake() was called
        if not trans:
            trans = DummyTransaction()
            _dummyTrans = True
        else: _dummyTrans = False
        write = trans.response().write
        SL = self._CHEETAH__searchList
        _filter = self._CHEETAH__currentFilter
        
        ########################################
        ## START - generated method body
        
        # 
        #  Insert code to interpolate the dependency vectors onto the half-step point.
        #  
        write('''// Create 4th order midpoint interpolation for dependencies
if (_istep == 0) {
  // We are at the first point
  ''')
        _v = VFFSL(SL,"reducedFieldCopy",False)(VFFSL(SL,"integrator.dependencyMap",True), 
"""
_active_${reducedVector.id}[_${reducedVector.id}_index_pointer + ${componentIndex}] = \\
    1.0/16.0*( 5.0*_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex}]
            + 15.0*_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} + ${skipSize} * _${vector.id}_ncomponents]
            -  5.0*_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} + 2 * ${skipSize} * _${vector.id}_ncomponents]
            +      _active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} + 3 * ${skipSize} * _${vector.id}_ncomponents]);
""")
        if _v is not None: write(_filter(_v, autoIndent=True, rawExpr='${reducedFieldCopy($integrator.dependencyMap, \n"""\n_active_${reducedVector.id}[_${reducedVector.id}_index_pointer + ${componentIndex}] = \\\\\n    1.0/16.0*( 5.0*_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex}]\n            + 15.0*_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} + ${skipSize} * _${vector.id}_ncomponents]\n            -  5.0*_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} + 2 * ${skipSize} * _${vector.id}_ncomponents]\n            +      _active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} + 3 * ${skipSize} * _${vector.id}_ncomponents]);\n"""), autoIndent=True}')) # from line 137, col 3.
        write('''} else if (_istep == (''')
        _v = VFFSL(SL,"integrator.stepCount",True) # '${integrator.stepCount}' on line 145, col 23
        if _v is not None: write(_filter(_v, rawExpr='${integrator.stepCount}')) # from line 145, col 23.
        write(''' - 1)) {
  // We are at the last point
  ''')
        _v = VFFSL(SL,"reducedFieldCopy",False)(VFFSL(SL,"integrator.dependencyMap",True), 
"""
_active_${reducedVector.id}[_${reducedVector.id}_index_pointer + ${componentIndex}] = \\
    1.0/16.0*(15.0*_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex}]
            +  5.0*_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} + ${skipSize} * _${vector.id}_ncomponents]
            -  5.0*_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} - ${skipSize} * _${vector.id}_ncomponents]
            +      _active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} - 2 * ${skipSize} * _${vector.id}_ncomponents]);
""")
        if _v is not None: write(_filter(_v, autoIndent=True, rawExpr='${reducedFieldCopy($integrator.dependencyMap, \n"""\n_active_${reducedVector.id}[_${reducedVector.id}_index_pointer + ${componentIndex}] = \\\\\n    1.0/16.0*(15.0*_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex}]\n            +  5.0*_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} + ${skipSize} * _${vector.id}_ncomponents]\n            -  5.0*_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} - ${skipSize} * _${vector.id}_ncomponents]\n            +      _active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} - 2 * ${skipSize} * _${vector.id}_ncomponents]);\n"""), autoIndent=True}')) # from line 147, col 3.
        write('''} else {
  // We are somewhere in the middle
  ''')
        _v = VFFSL(SL,"reducedFieldCopy",False)(VFFSL(SL,"integrator.dependencyMap",True), 
"""
_active_${reducedVector.id}[_${reducedVector.id}_index_pointer + ${componentIndex}] = \\
    9.0/16.0*(_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex}]
            + _active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} + ${skipSize} * _${vector.id}_ncomponents])
  - 1.0/16.0*(_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} - ${skipSize} * _${vector.id}_ncomponents]
            + _active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} + 2 * ${skipSize} * _${vector.id}_ncomponents]);
""")
        if _v is not None: write(_filter(_v, autoIndent=True, rawExpr='${reducedFieldCopy($integrator.dependencyMap, \n"""\n_active_${reducedVector.id}[_${reducedVector.id}_index_pointer + ${componentIndex}] = \\\\\n    9.0/16.0*(_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex}]\n            + _active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} + ${skipSize} * _${vector.id}_ncomponents])\n  - 1.0/16.0*(_active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} - ${skipSize} * _${vector.id}_ncomponents]\n            + _active_${vector.id}[_${vector.id}_index_pointer + ${componentIndex} + 2 * ${skipSize} * _${vector.id}_ncomponents]);\n"""), autoIndent=True}')) # from line 157, col 3.
        write('''}
''')
        # 
        
        ########################################
        ## END - generated method body
        
        return _dummyTrans and trans.response().getvalue() or ""
        

    def writeBody(self, **KWS):



        ## CHEETAH: main method generated for this template
        trans = KWS.get("trans")
        if (not trans and not self._CHEETAH__isBuffering and not callable(self.transaction)):
            trans = self.transaction # is None unless self.awake() was called
        if not trans:
            trans = DummyTransaction()
            _dummyTrans = True
        else: _dummyTrans = False
        write = trans.response().write
        SL = self._CHEETAH__searchList
        _filter = self._CHEETAH__currentFilter
        
        ########################################
        ## START - generated method body
        
        write('''
''')
        # 
        # RK4Stepper.tmpl
        # 
        # Created by Graham Dennis on 2007-09-23.
        # 
        # Copyright (c) 2007-2012, Graham Dennis
        # 
        # This program is free software: you can redistribute it and/or modify
        # it under the terms of the GNU General Public License as published by
        # the Free Software Foundation, either version 2 of the License, or
        # (at your option) any later version.
        # 
        # This program is distributed in the hope that it will be useful,
        # but WITHOUT ANY WARRANTY; without even the implied warranty of
        # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
        # GNU General Public License for more details.
        # 
        # You should have received a copy of the GNU General Public License
        # along with this program.  If not, see <http://www.gnu.org/licenses/>.
        # 
        write('''



''')
        # 
        #   Single integration step (RK4)
        write('''

''')
        
        ########################################
        ## END - generated method body
        
        return _dummyTrans and trans.response().getvalue() or ""
        
    ##################################################
    ## CHEETAH GENERATED ATTRIBUTES


    _CHEETAH__instanceInitialized = False

    _CHEETAH_version = __CHEETAH_version__

    _CHEETAH_versionTuple = __CHEETAH_versionTuple__

    _CHEETAH_genTime = __CHEETAH_genTime__

    _CHEETAH_genTimestamp = __CHEETAH_genTimestamp__

    _CHEETAH_src = __CHEETAH_src__

    _CHEETAH_srcLastModified = __CHEETAH_srcLastModified__

    ipPropagationStepFractions = ['0.5']

    extraIntegrationArrayNames = ['akfield', 'aifield']

    isCrossCapable = True

    resetFieldName = 'aifield'

    integrationOrder = 4.0

    _mainCheetahMethod_for_RK4Stepper = 'writeBody'

## END CLASS DEFINITION

if not hasattr(RK4Stepper, '_initCheetahAttributes'):
    templateAPIClass = getattr(RK4Stepper,
                               '_CHEETAH_templateClass',
                               Template)
    templateAPIClass._addCheetahPlumbingCodeToClass(RK4Stepper)


# CHEETAH was developed by Tavis Rudd and Mike Orr
# with code, advice and input from many other volunteers.
# For more information visit https://cheetahtemplate.org/

##################################################
## if run from command line:
if __name__ == '__main__':
    from Cheetah.TemplateCmdLineIface import CmdLineIface
    CmdLineIface(templateObj=RK4Stepper()).run()


