#!/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__ = 1558054969.9872336
__CHEETAH_genTimestamp__ = 'Fri May 17 11:02:49 2019'
__CHEETAH_src__ = '/home/mattias/xmds-2.2.3/admin/staging/xmds-3.0.0/xpdeint/Segments/Integrators/RK89Stepper.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 RK89Stepper(_Stepper):

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


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

        super(RK89Stepper, 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: RK89 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('''RK89''')
        
        ########################################
        ## END - generated method body
        
        return _dummyTrans and trans.response().getvalue() or ""
        

    def localInitialise(self, **KWS):


        """
        Initialise all of the Cash-Karp coefficients, etc.
        """

        ## CHEETAH: generated from @def localInitialise at line 41, 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
        
        # 
        _v = super(RK89Stepper, self).localInitialise()
        if _v is not None: write(_filter(_v))
        # 
        write('''
// Runge Kutta method constants 
real _a_raw[16];
real _a[16];
real _b[16][16];
real _c[16];
real _cs[16];
real _d[16];

for (unsigned long _i0 = 0; _i0 < 16; _i0++) {
  _a_raw[_i0] = _c[_i0] = _d[_i0] = 0.0;
  for (unsigned long _i1 = 0; _i1 < 16; _i1++)
   _b[_i0][_i1] = 0.0;
}

_a_raw[1]  = 0.02173913043478260869565217391304347;
_a_raw[2]  = 0.09629581047800066670113001679819925;
_a_raw[3]  = 0.14444371571700100005169502519729888;
_a_raw[4]  = 0.52205882352941176470588235294117647;
_a_raw[5]  = 0.22842443612863469578031459099794265;
_a_raw[6]  = 0.54360353589933733219171338103002937;
_a_raw[7]  = 0.64335664335664335664335664335664335;
_a_raw[8]  = 0.48251748251748251748251748251748251;
_a_raw[9]  = 0.06818181818181818181818181818181818;
_a_raw[10] = 0.25060827250608272506082725060827250;
_a_raw[11] = 0.66736715965600568968278165443304378;
_a_raw[12] = 0.85507246376811594202898550724637681;
_a_raw[13] = 0.89795918367346938775510204081632653;
_a_raw[14] = 1.0;
_a_raw[15] = 1.0;

_a[0] = 0.0;
for (unsigned long _i0 = 1; _i0 < 16; _i0++)
  _a[_i0] = _a_raw[_i0] - _a_raw[_i0 - 1];

_b[1][0]   = 1.0/46.0;
_b[2][0]   =-0.11698050118114486205818241524969622;
_b[2][1]   = 0.21327631165914552875931243204789548;
_b[3][0]   = 0.03611092892925025001292375629932472;
_b[3][2]   = 0.10833278678775075003877126889797416;
_b[4][0]   = 1.57329743908138605107331820072051125;
_b[4][2]   =-5.98400943754042002888532938159655553;
_b[4][3]   = 4.93277082198844574251789353381722074;
_b[5][0]   = 0.05052046351120380909008334360006234;
_b[5][3]   = 0.17686653884807108146683657390397612;
_b[5][4]   = 0.00103743376935980522339467349390418;
_b[6][0]   = 0.10543148021953768958529340893598138;
_b[6][3]   =-0.16042415162569842979496486916719383;
_b[6][4]   = 0.11643956912829316045688724281285250;
_b[6][5]   = 0.48215663817720491194449759844838932;
_b[7][0]   = 0.07148407148407148407148407148407148;
_b[7][5]   = 0.32971116090443908023196389566296464;
_b[7][6]   = 0.24216141096813279233990867620960722;
_b[8][0]   = 0.07162368881118881118881118881118881;
_b[8][5]   = 0.32859867301674234161492268975519694;
_b[8][6]   = 0.11622213117906185418927311444060725;
_b[8][7]   =-0.03392701048951048951048951048951048;
_b[9][0]   = 0.04861540768024729180628870095388582;
_b[9][5]   = 0.03998502200331629058445317782406268;
_b[9][6]   = 0.10715724786209388876739304914053506;
_b[9][7]   =-0.02177735985419485163815426357369818;
_b[9][8]   =-0.10579849950964443770179884616296721;
_b[10][0]  =-0.02540141041535143673515871979014924;
_b[10][5]  = 1.0/30.0;
_b[10][6]  =-0.16404854760069182073503553020238782;
_b[10][7]  = 0.03410548898794737788891414566528526;
_b[10][8]  = 0.15836825014108792658008718465091487;
_b[10][9]  = 0.21425115805975734472868683695127609;
_b[11][0]  = 0.00584833331460742801095934302256470;
_b[11][5]  =-0.53954170547283522916525526480339109;
_b[11][6]  = 0.20128430845560909506500331018201158;
_b[11][7]  = 0.04347222773254789483240207937678906;
_b[11][8]  =-0.00402998571475307250775349983910179;
_b[11][9]  = 0.16541535721570612771420482097898952;
_b[11][10] = 0.79491862412512344573322086551518180;
_b[12][0]  =-0.39964965968794892497157706711861448;
_b[12][5]  =-3.79096577568393158554742638116249372;
_b[12][6]  =-0.40349325653530103387515807815498044;
_b[12][7]  =-2.82463879530435263378049668286220715;
_b[12][8]  = 1.04226892772185985533374283289821416;
_b[12][9]  = 1.12510956420436603974237036536924078;
_b[12][10] = 3.32746188718986816186934832571938138;
_b[12][11] = 2.77897957186355606325818219255783627;
_b[13][0]  = 0.39545306350085237157098218205756922;
_b[13][5]  = 5.82534730759650564865380791881446903;
_b[13][6]  =-0.36527452339161313311889856846974452;
_b[13][7]  = 1.18860324058346533283780076203192232;
_b[13][8]  = 0.57970467638357921347110271762687972;
_b[13][9]  =-0.86824862589087693262676988867897834;
_b[13][10] =-5.20227677296454721392873650976792184;
_b[13][11] =-0.79895541420753382543211121058675915;
_b[13][12] = 0.14360623206363792632792463778889008;
_b[14][0]  = 8.49173149061346398013352206978380938;
_b[14][5]  = 86.32213734729036800877634194386790750;
_b[14][6]  = 1.02560575501091662034511526187393241;
_b[14][7]  = 85.77427969817339941806831550695235092;
_b[14][8]  =-13.98699305104110611795532466113248067;
_b[14][9]  =-20.71537405501426352265946477613161883;
_b[14][10] =-72.16597156619946800281180102605140463;
_b[14][11] =-76.71211139107806345587696023064419687;
_b[14][12] = 4.22319427707298828839851258893735507;
_b[14][13] =-1.25649850482823521641825667745565428;
_b[15][0]  =-0.42892119881959353241190195318730008;
_b[15][5]  =-9.16865700950084689999297912545025359;
_b[15][6]  = 1.08317616770620939241547721530003920;
_b[15][7]  =-1.23501525358323653198215832293981810;
_b[15][8]  =-1.21438272617593906232943856422371019;
_b[15][9]  = 1.37226168507232166621351243731869914;
_b[15][10] = 9.15723239697162418155377135344394113;
_b[15][11] = 1.30616301842220047563298585480401671;
_b[15][12] =-0.25285618808937955976690569433069974;
_b[15][13] = 0.38099910799663987066763679926508552;

_c[0]  = 0.01490902081978461022483617102382552;
_c[7]  =-0.20408044692054151258349120934134791;
_c[8]  = 0.22901438600570447264772469337066476;
_c[9]  = 0.12800558251147375669208211573729202;
_c[10] = 0.22380626846054143649770066956485937;
_c[11] = 0.39553165293700054420552389156421651;
_c[12] = 0.05416646758806981196568364538360743;
_c[13] = 0.12691439652445903685643385312168037;
_c[14] =-0.00052539244262118876455834655383035;
_c[15] = 1.0/31.0;

_cs[0]  = 0.00653047880643482012034413441159249;
_cs[7]  =-2.31471038197461347517552506241529830;
_cs[8]  = 0.43528227238866280799530900822377013;
_cs[9]  = 0.14907947287101933118545845390618763;
_cs[10] = 0.17905535442235532311850533252768020;
_cs[11] = 2.53400872222767706921176214508820825;
_cs[12] =-0.55430437423209112896721332268159015;
_cs[13] = 0.56924788787870083224213506297615260;
_cs[14] =-0.03644749690427461198884026816573513;
_cs[15] = 1.0/31.0;

_d[0] = 1.0-_b[15][5]/_b[14][5];
_d[1] = _b[15][0]-_b[14][0]*_b[15][5]/_b[14][5];
_d[2] = _b[15][5]/_b[14][5];
_d[3] = _b[15][6]-_b[14][6]*_b[15][5]/_b[14][5];
_d[4] = _b[15][7]-_b[14][7]*_b[15][5]/_b[14][5];
_d[5] = _b[15][8]-_b[14][8]*_b[15][5]/_b[14][5];
_d[6] = _b[15][9]-_b[14][9]*_b[15][5]/_b[14][5];
_d[7] = _b[15][10]-_b[14][10]*_b[15][5]/_b[14][5];
_d[8] = _b[15][11]-_b[14][11]*_b[15][5]/_b[14][5];
_d[9] = _b[15][12]-_b[14][12]*_b[15][5]/_b[14][5];
_d[10] = _b[15][13]-_b[14][13]*_b[15][5]/_b[14][5];
''')
        # 
        
        ########################################
        ## END - generated method body
        
        return _dummyTrans and trans.response().getvalue() or ""
        

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



        ## CHEETAH: generated from @def singleIntegrationStep($function) at line 200, 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'}
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 203, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 203, col 1.
        write('''
// Step 1

''')
        _v = VFFSL(SL,"copyVectors",False)(VFFSL(SL,"integrationVectors",True), '_akafield') # "${copyVectors($integrationVectors, '_akafield')}" on line 207, col 1
        if _v is not None: write(_filter(_v, rawExpr="${copyVectors($integrationVectors, '_akafield')}")) # from line 207, col 1.
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 1, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 1, parentFunction=function)}" on line 209, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 1, parentFunction=function)}")) # from line 209, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +1, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction=function)}" on line 212, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction=function)}")) # from line 212, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 213, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 213, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 215, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 216, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 216, col 9.
            write(''' = _akafield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 216, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 216, col 34.
            write(''';
''')
        write('''
// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 220, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 220, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +1, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction=function)}" on line 223, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction=function)}")) # from line 223, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 224, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 224, col 1.
        write('''
// Step 2

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 228, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 228, col 1.
        write(''' += _a[1] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akbfield_${vector.id}[$index] = _${vector.id}[$index] + _b[1][0]*_akafield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akbfield_${vector.id}[$index] = _${vector.id}[$index] + _b[1][0]*_akafield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 230, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 234, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 235, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 235, col 9.
            write(''' = _akbfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 235, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 235, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 2, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 2, parentFunction=function)}" on line 238, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 2, parentFunction=function)}")) # from line 238, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -2, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -2, parentFunction=function)}" on line 241, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -2, parentFunction=function)}")) # from line 241, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 244, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 244, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +2, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +2, parentFunction=function)}" on line 247, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +2, parentFunction=function)}")) # from line 247, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 248, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 248, col 1.
        write('''
// Step 3

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 252, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 252, col 1.
        write(''' += _a[2] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akcfield_${vector.id}[$index] = _${vector.id}[$index] + _b[2][0]*_akafield_${vector.id}[$index] + _b[2][1]*_akbfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akcfield_${vector.id}[$index] = _${vector.id}[$index] + _b[2][0]*_akafield_${vector.id}[$index] + _b[2][1]*_akbfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 254, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 258, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 259, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 259, col 9.
            write(''' = _akcfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 259, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 259, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 3, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 3, parentFunction=function)}" on line 262, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 3, parentFunction=function)}")) # from line 262, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -3, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -3, parentFunction=function)}" on line 265, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -3, parentFunction=function)}")) # from line 265, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 268, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 268, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +3, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +3, parentFunction=function)}" on line 271, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +3, parentFunction=function)}")) # from line 271, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 272, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 272, col 1.
        write('''
// Step 4

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 276, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 276, col 1.
        write(''' += _a[3] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akdfield_${vector.id}[$index] = _${vector.id}[$index] + _b[3][0]*_akafield_${vector.id}[$index] + _b[3][1]*_akbfield_${vector.id}[$index]
    + _b[3][2]*_akcfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akdfield_${vector.id}[$index] = _${vector.id}[$index] + _b[3][0]*_akafield_${vector.id}[$index] + _b[3][1]*_akbfield_${vector.id}[$index]\n    + _b[3][2]*_akcfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 278, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 283, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 284, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 284, col 9.
            write(''' = _akdfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 284, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 284, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 4, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 4, parentFunction=function)}" on line 287, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 4, parentFunction=function)}")) # from line 287, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -4, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -4, parentFunction=function)}" on line 290, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -4, parentFunction=function)}")) # from line 290, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 293, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 293, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +4, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +4, parentFunction=function)}" on line 296, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +4, parentFunction=function)}")) # from line 296, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 297, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 297, col 1.
        write('''
// Step 5

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 301, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 301, col 1.
        write(''' += _a[4] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akefield_${vector.id}[$index] = _${vector.id}[$index] + _b[4][0]*_akafield_${vector.id}[$index] + _b[4][1]*_akbfield_${vector.id}[$index]
    + _b[4][2]*_akcfield_${vector.id}[$index] + _b[4][3]*_akdfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akefield_${vector.id}[$index] = _${vector.id}[$index] + _b[4][0]*_akafield_${vector.id}[$index] + _b[4][1]*_akbfield_${vector.id}[$index]\n    + _b[4][2]*_akcfield_${vector.id}[$index] + _b[4][3]*_akdfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 303, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 308, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 309, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 309, col 9.
            write(''' = _akefield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 309, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 309, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 5, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 5, parentFunction=function)}" on line 312, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 5, parentFunction=function)}")) # from line 312, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -5, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -5, parentFunction=function)}" on line 315, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -5, parentFunction=function)}")) # from line 315, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 318, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 318, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +5, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +5, parentFunction=function)}" on line 321, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +5, parentFunction=function)}")) # from line 321, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 322, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 322, col 1.
        write('''
// Step 6

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 326, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 326, col 1.
        write(''' += _a[5] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akifield_${vector.id}[$index] = _${vector.id}[$index] + _b[5][0]*_akafield_${vector.id}[$index] + _b[5][3]*_akdfield_${vector.id}[$index]
    + _b[5][4]*_akefield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akifield_${vector.id}[$index] = _${vector.id}[$index] + _b[5][0]*_akafield_${vector.id}[$index] + _b[5][3]*_akdfield_${vector.id}[$index]\n    + _b[5][4]*_akefield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 328, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 333, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 334, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 334, col 9.
            write(''' = _akifield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 334, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 334, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 6, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 6, parentFunction=function)}" on line 337, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 6, parentFunction=function)}")) # from line 337, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -6, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -6, parentFunction=function)}" on line 340, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -6, parentFunction=function)}")) # from line 340, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 343, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 343, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +6, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +6, parentFunction=function)}" on line 346, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +6, parentFunction=function)}")) # from line 346, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 347, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 347, col 1.
        write('''
// Step 7

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 351, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 351, col 1.
        write(''' += _a[6] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akjfield_${vector.id}[$index] = _${vector.id}[$index] + _b[6][0]*_akafield_${vector.id}[$index] + _b[6][3]*_akdfield_${vector.id}[$index]
    + _b[6][4]*_akefield_${vector.id}[$index] + _b[6][5]*_akifield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akjfield_${vector.id}[$index] = _${vector.id}[$index] + _b[6][0]*_akafield_${vector.id}[$index] + _b[6][3]*_akdfield_${vector.id}[$index]\n    + _b[6][4]*_akefield_${vector.id}[$index] + _b[6][5]*_akifield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 353, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 358, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 359, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 359, col 9.
            write(''' = _akjfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 359, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 359, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 7, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 7, parentFunction=function)}" on line 362, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 7, parentFunction=function)}")) # from line 362, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -7, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -7, parentFunction=function)}" on line 365, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -7, parentFunction=function)}")) # from line 365, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 368, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 368, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +7, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +7, parentFunction=function)}" on line 371, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +7, parentFunction=function)}")) # from line 371, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 372, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 372, col 1.
        write('''
// Step 8

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 376, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 376, col 1.
        write(''' += _a[7] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akbfield_${vector.id}[$index] = _${vector.id}[$index] + _b[7][0]*_akafield_${vector.id}[$index] + _b[7][5]*_akifield_${vector.id}[$index]
    + _b[7][6]*_akjfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akbfield_${vector.id}[$index] = _${vector.id}[$index] + _b[7][0]*_akafield_${vector.id}[$index] + _b[7][5]*_akifield_${vector.id}[$index]\n    + _b[7][6]*_akjfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 378, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 383, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 384, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 384, col 9.
            write(''' = _akbfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 384, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 384, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 8, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 8, parentFunction=function)}" on line 387, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 8, parentFunction=function)}")) # from line 387, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -8, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -8, parentFunction=function)}" on line 390, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -8, parentFunction=function)}")) # from line 390, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 393, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 393, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +8, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +8, parentFunction=function)}" on line 396, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +8, parentFunction=function)}")) # from line 396, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 397, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 397, col 1.
        write('''
// Step 9

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 401, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 401, col 1.
        write(''' += _a[8] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akcfield_${vector.id}[$index] = _${vector.id}[$index] + _b[8][0]*_akafield_${vector.id}[$index] + _b[8][5]*_akifield_${vector.id}[$index]
    + _b[8][6]*_akjfield_${vector.id}[$index]+ _b[8][7]*_akbfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akcfield_${vector.id}[$index] = _${vector.id}[$index] + _b[8][0]*_akafield_${vector.id}[$index] + _b[8][5]*_akifield_${vector.id}[$index]\n    + _b[8][6]*_akjfield_${vector.id}[$index]+ _b[8][7]*_akbfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 403, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 408, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 409, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 409, col 9.
            write(''' = _akcfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 409, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 409, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 9, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 9, parentFunction=function)}" on line 412, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 9, parentFunction=function)}")) # from line 412, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -9, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -9, parentFunction=function)}" on line 415, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -9, parentFunction=function)}")) # from line 415, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 418, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 418, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +9, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +9, parentFunction=function)}" on line 421, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +9, parentFunction=function)}")) # from line 421, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 422, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 422, col 1.
        write('''
// Step 10

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 426, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 426, col 1.
        write(''' += _a[9] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akdfield_${vector.id}[$index] = _${vector.id}[$index] + _b[9][0]*_akafield_${vector.id}[$index] + _b[9][5]*_akifield_${vector.id}[$index]
    + _b[9][6]*_akjfield_${vector.id}[$index]+ _b[9][7]*_akbfield_${vector.id}[$index]+ _b[9][8]*_akcfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akdfield_${vector.id}[$index] = _${vector.id}[$index] + _b[9][0]*_akafield_${vector.id}[$index] + _b[9][5]*_akifield_${vector.id}[$index]\n    + _b[9][6]*_akjfield_${vector.id}[$index]+ _b[9][7]*_akbfield_${vector.id}[$index]+ _b[9][8]*_akcfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 428, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 433, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 434, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 434, col 9.
            write(''' = _akdfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 434, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 434, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 10, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 10, parentFunction=function)}" on line 437, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 10, parentFunction=function)}")) # from line 437, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -10, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -10, parentFunction=function)}" on line 440, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -10, parentFunction=function)}")) # from line 440, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 443, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 443, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +10, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +10, parentFunction=function)}" on line 446, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +10, parentFunction=function)}")) # from line 446, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 447, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 447, col 1.
        write('''
// Step 11

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 451, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 451, col 1.
        write(''' += _a[10] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akefield_${vector.id}[$index] = _${vector.id}[$index] + _b[10][0]*_akafield_${vector.id}[$index] + _b[10][5]*_akifield_${vector.id}[$index]
    + _b[10][6]*_akjfield_${vector.id}[$index]+ _b[10][7]*_akbfield_${vector.id}[$index] + _b[10][8]*_akcfield_${vector.id}[$index]
    + _b[10][9]*_akdfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akefield_${vector.id}[$index] = _${vector.id}[$index] + _b[10][0]*_akafield_${vector.id}[$index] + _b[10][5]*_akifield_${vector.id}[$index]\n    + _b[10][6]*_akjfield_${vector.id}[$index]+ _b[10][7]*_akbfield_${vector.id}[$index] + _b[10][8]*_akcfield_${vector.id}[$index]\n    + _b[10][9]*_akdfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 453, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 459, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 460, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 460, col 9.
            write(''' = _akefield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 460, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 460, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 11, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 11, parentFunction=function)}" on line 463, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 11, parentFunction=function)}")) # from line 463, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -11, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -11, parentFunction=function)}" on line 466, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -11, parentFunction=function)}")) # from line 466, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 469, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 469, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +11, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +11, parentFunction=function)}" on line 472, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +11, parentFunction=function)}")) # from line 472, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 473, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 473, col 1.
        write('''
// Step 12

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 477, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 477, col 1.
        write(''' += _a[11] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akffield_${vector.id}[$index] = _${vector.id}[$index] + _b[11][0]*_akafield_${vector.id}[$index] + _b[11][5]*_akifield_${vector.id}[$index]
    + _b[11][6]*_akjfield_${vector.id}[$index] + _b[11][7]*_akbfield_${vector.id}[$index] + _b[11][8]*_akcfield_${vector.id}[$index]
    + _b[11][9]*_akdfield_${vector.id}[$index] + _b[11][10]*_akefield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akffield_${vector.id}[$index] = _${vector.id}[$index] + _b[11][0]*_akafield_${vector.id}[$index] + _b[11][5]*_akifield_${vector.id}[$index]\n    + _b[11][6]*_akjfield_${vector.id}[$index] + _b[11][7]*_akbfield_${vector.id}[$index] + _b[11][8]*_akcfield_${vector.id}[$index]\n    + _b[11][9]*_akdfield_${vector.id}[$index] + _b[11][10]*_akefield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 479, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 485, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 486, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 486, col 9.
            write(''' = _akffield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 486, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 486, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 12, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 12, parentFunction=function)}" on line 489, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 12, parentFunction=function)}")) # from line 489, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -12, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -12, parentFunction=function)}" on line 492, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -12, parentFunction=function)}")) # from line 492, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 495, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 495, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +12, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +12, parentFunction=function)}" on line 498, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +12, parentFunction=function)}")) # from line 498, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 499, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 499, col 1.
        write('''
// Step 13

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 503, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 503, col 1.
        write(''' += _a[12] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akgfield_${vector.id}[$index] = _${vector.id}[$index] + _b[12][0]*_akafield_${vector.id}[$index] + _b[12][5]*_akifield_${vector.id}[$index]
    + _b[12][6]*_akjfield_${vector.id}[$index]+ _b[12][7]*_akbfield_${vector.id}[$index] + _b[12][8]*_akcfield_${vector.id}[$index]
    + _b[12][9]*_akdfield_${vector.id}[$index] + _b[12][10]*_akefield_${vector.id}[$index] + _b[12][11]*_akffield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akgfield_${vector.id}[$index] = _${vector.id}[$index] + _b[12][0]*_akafield_${vector.id}[$index] + _b[12][5]*_akifield_${vector.id}[$index]\n    + _b[12][6]*_akjfield_${vector.id}[$index]+ _b[12][7]*_akbfield_${vector.id}[$index] + _b[12][8]*_akcfield_${vector.id}[$index]\n    + _b[12][9]*_akdfield_${vector.id}[$index] + _b[12][10]*_akefield_${vector.id}[$index] + _b[12][11]*_akffield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 505, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 511, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 512, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 512, col 9.
            write(''' = _akgfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 512, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 512, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 13, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 13, parentFunction=function)}" on line 515, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 13, parentFunction=function)}")) # from line 515, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -13, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -13, parentFunction=function)}" on line 518, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -13, parentFunction=function)}")) # from line 518, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 521, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 521, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +13, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +13, parentFunction=function)}" on line 524, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +13, parentFunction=function)}")) # from line 524, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 525, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 525, col 1.
        write('''
// Step 14

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 529, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 529, col 1.
        write(''' += _a[13] * _step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akhfield_${vector.id}[$index] = _${vector.id}[$index] + _b[13][0]*_akafield_${vector.id}[$index] + _b[13][5]*_akifield_${vector.id}[$index]
    + _b[13][6]*_akjfield_${vector.id}[$index]+ _b[13][7]*_akbfield_${vector.id}[$index] + _b[13][8]*_akcfield_${vector.id}[$index]
    + _b[13][9]*_akdfield_${vector.id}[$index] + _b[13][10]*_akefield_${vector.id}[$index] + _b[13][11]*_akffield_${vector.id}[$index]
    + _b[13][12]*_akgfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akhfield_${vector.id}[$index] = _${vector.id}[$index] + _b[13][0]*_akafield_${vector.id}[$index] + _b[13][5]*_akifield_${vector.id}[$index]\n    + _b[13][6]*_akjfield_${vector.id}[$index]+ _b[13][7]*_akbfield_${vector.id}[$index] + _b[13][8]*_akcfield_${vector.id}[$index]\n    + _b[13][9]*_akdfield_${vector.id}[$index] + _b[13][10]*_akefield_${vector.id}[$index] + _b[13][11]*_akffield_${vector.id}[$index]\n    + _b[13][12]*_akgfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 531, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 538, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 539, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 539, col 9.
            write(''' = _akhfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 539, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 539, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 14, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 14, parentFunction=function)}" on line 542, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 14, parentFunction=function)}")) # from line 542, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -14, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -14, parentFunction=function)}" on line 545, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -14, parentFunction=function)}")) # from line 545, col 1.
        write('''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 548, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 548, col 1.
        write('''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +14, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +14, parentFunction=function)}" on line 551, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +14, parentFunction=function)}")) # from line 551, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 552, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 552, col 1.
        write('''
// Step 15 and 16 combined to reduce memory use 

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akifield_${vector.id}[$index] = _${vector.id}[$index] + _b[14][0]*_akafield_${vector.id}[$index] + _b[14][5]*_akifield_${vector.id}[$index]
    + _b[14][6]*_akjfield_${vector.id}[$index]+ _b[14][7]*_akbfield_${vector.id}[$index] + _b[14][8]*_akcfield_${vector.id}[$index]
    + _b[14][9]*_akdfield_${vector.id}[$index] + _b[14][10]*_akefield_${vector.id}[$index] + _b[14][11]*_akffield_${vector.id}[$index]
    + _b[14][12]*_akgfield_${vector.id}[$index] + _b[14][13]*_akhfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akifield_${vector.id}[$index] = _${vector.id}[$index] + _b[14][0]*_akafield_${vector.id}[$index] + _b[14][5]*_akifield_${vector.id}[$index]\n    + _b[14][6]*_akjfield_${vector.id}[$index]+ _b[14][7]*_akbfield_${vector.id}[$index] + _b[14][8]*_akcfield_${vector.id}[$index]\n    + _b[14][9]*_akdfield_${vector.id}[$index] + _b[14][10]*_akefield_${vector.id}[$index] + _b[14][11]*_akffield_${vector.id}[$index]\n    + _b[14][12]*_akgfield_${vector.id}[$index] + _b[14][13]*_akhfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 556, col 1.
        write('''
''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akjfield_${vector.id}[$index] = _d[0]*_${vector.id}[$index]
      + _d[1]*_akafield_${vector.id}[$index]
      + _d[2]*_akifield_${vector.id}[$index]
      + _d[3]*_akjfield_${vector.id}[$index]
      + _d[4]*_akbfield_${vector.id}[$index]
      + _d[5]*_akcfield_${vector.id}[$index]
      + _d[6]*_akdfield_${vector.id}[$index]
      + _d[7]*_akefield_${vector.id}[$index]
      + _d[8]*_akffield_${vector.id}[$index]
      + _d[9]*_akgfield_${vector.id}[$index]
      + _d[10]*_akhfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akjfield_${vector.id}[$index] = _d[0]*_${vector.id}[$index]\n      + _d[1]*_akafield_${vector.id}[$index]\n      + _d[2]*_akifield_${vector.id}[$index]\n      + _d[3]*_akjfield_${vector.id}[$index]\n      + _d[4]*_akbfield_${vector.id}[$index]\n      + _d[5]*_akcfield_${vector.id}[$index]\n      + _d[6]*_akdfield_${vector.id}[$index]\n      + _d[7]*_akefield_${vector.id}[$index]\n      + _d[8]*_akffield_${vector.id}[$index]\n      + _d[9]*_akgfield_${vector.id}[$index]\n      + _d[10]*_akhfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 563, col 1.
        write('''
''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 577, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 577, col 1.
        write(''' += _a[14] * _step;

''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 579, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 580, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 580, col 9.
            write(''' = _akifield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 580, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 580, col 34.
            write(''';
''')
        write('''
// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 584, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 584, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 585, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 585, col 1.
        write('''
''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 587, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 587, col 1.
        write(''' += _a[15] * _step;

''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 589, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 590, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 590, col 9.
            write(''' = _akjfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 590, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 590, col 34.
            write(''';
''')
        write('''
// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 594, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 594, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 595, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 595, col 1.
        write('''
// Take full step

// ai = a
''')
        _v = VFFSL(SL,"copyVectors",False)(VFFSL(SL,"integrationVectors",True), '_initial') # "${copyVectors($integrationVectors, '_initial')}" on line 600, col 1
        if _v is not None: write(_filter(_v, rawExpr="${copyVectors($integrationVectors, '_initial')}")) # from line 600, col 1.
        write('''
// a = a + etc
''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_${vector.id}[$index] += _c[0]*_akafield_${vector.id}[$index] + _c[7]*_akbfield_${vector.id}[$index] + _c[8]*_akcfield_${vector.id}[$index]
    + _c[9]*_akdfield_${vector.id}[$index] + _c[10]*_akefield_${vector.id}[$index] + _c[11]*_akffield_${vector.id}[$index]
    + _c[12]*_akgfield_${vector.id}[$index] + _c[13]*_akhfield_${vector.id}[$index] + _c[14]*_akifield_${vector.id}[$index]
    + _c[15]*_akjfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_${vector.id}[$index] += _c[0]*_akafield_${vector.id}[$index] + _c[7]*_akbfield_${vector.id}[$index] + _c[8]*_akcfield_${vector.id}[$index]\n    + _c[9]*_akdfield_${vector.id}[$index] + _c[10]*_akefield_${vector.id}[$index] + _c[11]*_akffield_${vector.id}[$index]\n    + _c[12]*_akgfield_${vector.id}[$index] + _c[13]*_akhfield_${vector.id}[$index] + _c[14]*_akifield_${vector.id}[$index]\n    + _c[15]*_akjfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 603, col 1.
        write('''
// a* = a + etc
''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akafield_${vector.id}[$index] = _initial_${vector.id}[$index] + _cs[0]*_akafield_${vector.id}[$index] + _cs[7]*_akbfield_${vector.id}[$index]
    + _cs[8]*_akcfield_${vector.id}[$index] + _cs[9]*_akdfield_${vector.id}[$index] + _cs[10]*_akefield_${vector.id}[$index]
    + _cs[11]*_akffield_${vector.id}[$index] + _cs[12]*_akgfield_${vector.id}[$index] + _cs[13]*_akhfield_${vector.id}[$index]
    + _cs[14]*_akifield_${vector.id}[$index] + _cs[15]*_akjfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akafield_${vector.id}[$index] = _initial_${vector.id}[$index] + _cs[0]*_akafield_${vector.id}[$index] + _cs[7]*_akbfield_${vector.id}[$index]\n    + _cs[8]*_akcfield_${vector.id}[$index] + _cs[9]*_akdfield_${vector.id}[$index] + _cs[10]*_akefield_${vector.id}[$index]\n    + _cs[11]*_akffield_${vector.id}[$index] + _cs[12]*_akgfield_${vector.id}[$index] + _cs[13]*_akhfield_${vector.id}[$index]\n    + _cs[14]*_akifield_${vector.id}[$index] + _cs[15]*_akjfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 611, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 618, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 619, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 619, col 9.
            write(''' = _''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 619, col 25
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 619, col 25.
            write(''';
''')
        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('''
''')
        # 
        # RK89Stepper.tmpl
        # 
        # Created by Graham Dennis on 2008-02-11.
        # 
        # Copyright (c) 2008-2012, 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 (ARK89)
        
        ########################################
        ## 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 =   [ '1.000000000000000', '0.978260869565217', '0.903704189521999', '0.855556284282999',    '0.477941176470588', '0.771575563871365', '0.456396464100663', '0.356643356643357',    '0.517482517482518', '0.931818181818182', '0.749391727493917', '0.332632840343994',    '0.144927536231884', '0.102040816326531' ]

    extraIntegrationArrayNames =   [ 'akafield', 'akbfield', 'akcfield', 'akdfield', 'akefield', 'akffield', 'akgfield',    'akhfield', 'akifield', 'akjfield', 'initial']

    errorFieldName = 'akafield'

    resetFieldName = 'initial'

    integrationOrder = 9.0

    _mainCheetahMethod_for_RK89Stepper = 'writeBody'

## END CLASS DEFINITION

if not hasattr(RK89Stepper, '_initCheetahAttributes'):
    templateAPIClass = getattr(RK89Stepper,
                               '_CHEETAH_templateClass',
                               Template)
    templateAPIClass._addCheetahPlumbingCodeToClass(RK89Stepper)


# 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=RK89Stepper()).run()