#!/usr/bin/env python




##################################################
## 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 xpdeint.Segments.Integrators._Stepper import _Stepper

##################################################
## MODULE CONSTANTS
VFFSL=valueFromFrameOrSearchList
VFSL=valueFromSearchList
VFN=valueForName
currentTime=time.time
__CHEETAH_version__ = '2.4.4'
__CHEETAH_versionTuple__ = (2, 4, 4, 'development', 0)
__CHEETAH_genTime__ = 1413234540.310062
__CHEETAH_genTimestamp__ = 'Tue Oct 14 08:09:00 2014'
__CHEETAH_src__ = '/Users/graham/Library/XMDS/src/xmds2/admin/staging/xmds-2.2.2/xpdeint/Segments/Integrators/RK89Stepper.tmpl'
__CHEETAH_srcLastModified__ = 'Fri Oct 11 15:53:21 2013'
__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 24, 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(u'''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 39, 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(u'''
// 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 198, 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)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 201, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 201, col 1.
        write(u'''
// Step 1

''')
        _v = VFFSL(SL,"copyVectors",False)(VFFSL(SL,"integrationVectors",True), '_akafield') # u"${copyVectors($integrationVectors, '_akafield')}" on line 205, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${copyVectors($integrationVectors, '_akafield')}")) # from line 205, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 1, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 1, parentFunction=function)}" on line 207, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 1, parentFunction=function)}")) # from line 207, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +1, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction=function)}" on line 210, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction=function)}")) # from line 210, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 211, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 211, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 213, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 214, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 214, col 9.
            write(u''' = _akafield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 214, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 214, col 34.
            write(u''';
''')
        write(u'''
// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 218, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 218, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +1, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction=function)}" on line 221, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction=function)}")) # from line 221, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 222, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 222, col 1.
        write(u'''
// Step 2

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 226, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 226, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akbfield_${vector.id}[$index] = _${vector.id}[$index] + _b[1][0]*_akafield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 228, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 232, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 233, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 233, col 9.
            write(u''' = _akbfield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 233, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 233, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 2, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 2, parentFunction=function)}" on line 236, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 2, parentFunction=function)}")) # from line 236, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -2, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -2, parentFunction=function)}" on line 239, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -2, parentFunction=function)}")) # from line 239, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 242, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 242, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +2, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +2, parentFunction=function)}" on line 245, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +2, parentFunction=function)}")) # from line 245, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 246, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 246, col 1.
        write(u'''
// Step 3

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 250, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 250, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 252, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 256, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 257, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 257, col 9.
            write(u''' = _akcfield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 257, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 257, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 3, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 3, parentFunction=function)}" on line 260, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 3, parentFunction=function)}")) # from line 260, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -3, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -3, parentFunction=function)}" on line 263, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -3, parentFunction=function)}")) # from line 263, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 266, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 266, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +3, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +3, parentFunction=function)}" on line 269, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +3, parentFunction=function)}")) # from line 269, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 270, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 270, col 1.
        write(u'''
// Step 4

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 274, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 274, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 276, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 281, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 282, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 282, col 9.
            write(u''' = _akdfield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 282, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 282, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 4, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 4, parentFunction=function)}" on line 285, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 4, parentFunction=function)}")) # from line 285, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -4, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -4, parentFunction=function)}" on line 288, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -4, parentFunction=function)}")) # from line 288, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 291, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 291, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +4, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +4, parentFunction=function)}" on line 294, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +4, parentFunction=function)}")) # from line 294, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 295, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 295, col 1.
        write(u'''
// Step 5

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 299, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 299, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 301, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 306, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 307, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 307, col 9.
            write(u''' = _akefield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 307, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 307, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 5, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 5, parentFunction=function)}" on line 310, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 5, parentFunction=function)}")) # from line 310, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -5, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -5, parentFunction=function)}" on line 313, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -5, parentFunction=function)}")) # from line 313, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 316, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 316, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +5, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +5, parentFunction=function)}" on line 319, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +5, parentFunction=function)}")) # from line 319, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 320, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 320, col 1.
        write(u'''
// Step 6

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 324, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 324, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 326, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 331, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 332, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 332, col 9.
            write(u''' = _akifield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 332, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 332, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 6, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 6, parentFunction=function)}" on line 335, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 6, parentFunction=function)}")) # from line 335, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -6, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -6, parentFunction=function)}" on line 338, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -6, parentFunction=function)}")) # from line 338, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 341, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 341, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +6, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +6, parentFunction=function)}" on line 344, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +6, parentFunction=function)}")) # from line 344, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 345, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 345, col 1.
        write(u'''
// Step 7

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 349, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 349, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 351, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 356, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 357, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 357, col 9.
            write(u''' = _akjfield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 357, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 357, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 7, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 7, parentFunction=function)}" on line 360, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 7, parentFunction=function)}")) # from line 360, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -7, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -7, parentFunction=function)}" on line 363, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -7, parentFunction=function)}")) # from line 363, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 366, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 366, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +7, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +7, parentFunction=function)}" on line 369, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +7, parentFunction=function)}")) # from line 369, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 370, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 370, col 1.
        write(u'''
// Step 8

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 374, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 374, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 376, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 381, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 382, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 382, col 9.
            write(u''' = _akbfield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 382, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 382, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 8, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 8, parentFunction=function)}" on line 385, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 8, parentFunction=function)}")) # from line 385, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -8, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -8, parentFunction=function)}" on line 388, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -8, parentFunction=function)}")) # from line 388, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 391, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 391, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +8, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +8, parentFunction=function)}" on line 394, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +8, parentFunction=function)}")) # from line 394, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 395, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 395, col 1.
        write(u'''
// Step 9

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 399, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 399, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 401, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 406, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 407, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 407, col 9.
            write(u''' = _akcfield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 407, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 407, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 9, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 9, parentFunction=function)}" on line 410, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 9, parentFunction=function)}")) # from line 410, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -9, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -9, parentFunction=function)}" on line 413, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -9, parentFunction=function)}")) # from line 413, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 416, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 416, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +9, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +9, parentFunction=function)}" on line 419, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +9, parentFunction=function)}")) # from line 419, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 420, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 420, col 1.
        write(u'''
// Step 10

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 424, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 424, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 426, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 431, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 432, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 432, col 9.
            write(u''' = _akdfield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 432, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 432, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 10, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 10, parentFunction=function)}" on line 435, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 10, parentFunction=function)}")) # from line 435, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -10, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -10, parentFunction=function)}" on line 438, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -10, parentFunction=function)}")) # from line 438, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 441, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 441, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +10, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +10, parentFunction=function)}" on line 444, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +10, parentFunction=function)}")) # from line 444, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 445, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 445, col 1.
        write(u'''
// Step 11

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 449, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 449, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 451, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 457, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 458, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 458, col 9.
            write(u''' = _akefield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 458, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 458, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 11, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 11, parentFunction=function)}" on line 461, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 11, parentFunction=function)}")) # from line 461, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -11, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -11, parentFunction=function)}" on line 464, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -11, parentFunction=function)}")) # from line 464, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 467, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 467, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +11, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +11, parentFunction=function)}" on line 470, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +11, parentFunction=function)}")) # from line 470, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 471, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 471, col 1.
        write(u'''
// Step 12

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 475, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 475, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 477, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 483, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 484, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 484, col 9.
            write(u''' = _akffield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 484, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 484, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 12, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 12, parentFunction=function)}" on line 487, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 12, parentFunction=function)}")) # from line 487, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -12, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -12, parentFunction=function)}" on line 490, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -12, parentFunction=function)}")) # from line 490, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 493, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 493, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +12, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +12, parentFunction=function)}" on line 496, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +12, parentFunction=function)}")) # from line 496, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 497, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 497, col 1.
        write(u'''
// Step 13

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 501, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 501, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 503, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 509, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 510, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 510, col 9.
            write(u''' = _akgfield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 510, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 510, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 13, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 13, parentFunction=function)}" on line 513, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 13, parentFunction=function)}")) # from line 513, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -13, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -13, parentFunction=function)}" on line 516, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -13, parentFunction=function)}")) # from line 516, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 519, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 519, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +13, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +13, parentFunction=function)}" on line 522, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +13, parentFunction=function)}")) # from line 522, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 523, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 523, col 1.
        write(u'''
// Step 14

''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 527, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 527, col 1.
        write(u''' += _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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 529, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 536, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 537, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 537, col 9.
            write(u''' = _akhfield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 537, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 537, col 34.
            write(u''';
''')
        write(u'''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 14, parentFunction=function) # u"${callFunction('nonconstantIPFields', arguments, _exponent = 14, parentFunction=function)}" on line 540, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('nonconstantIPFields', arguments, _exponent = 14, parentFunction=function)}")) # from line 540, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -14, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = -14, parentFunction=function)}" on line 543, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = -14, parentFunction=function)}")) # from line 543, col 1.
        write(u'''

// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 546, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 546, col 1.
        write(u'''

// a_i=D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +14, parentFunction=function) # u"${callFunction('ipEvolve', arguments, _exponent = +14, parentFunction=function)}" on line 549, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('ipEvolve', arguments, _exponent = +14, parentFunction=function)}")) # from line 549, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 550, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 550, col 1.
        write(u'''
// 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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 554, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akjfield_${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}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr=u'${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 = $homeBasis)}')) # from line 561, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 575, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 575, col 1.
        write(u''' += _a[14] * _step;

''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 577, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 578, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 578, col 9.
            write(u''' = _akifield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 578, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 578, col 34.
            write(u''';
''')
        write(u'''
// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 582, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 582, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 583, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 583, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"propagationDimension",True) # u'${propagationDimension}' on line 585, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${propagationDimension}')) # from line 585, col 1.
        write(u''' += _a[15] * _step;

''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 587, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 588, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 588, col 9.
            write(u''' = _akjfield_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 588, col 34
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 588, col 34.
            write(u''';
''')
        write(u'''
// a_k=G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # u"${callFunction('deltaA', arguments, parentFunction=function)}" on line 592, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 592, col 1.
        write(u'''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # u'${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 593, col 1
        if _v is not None: write(_filter(_v, rawExpr=u'${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 593, col 1.
        write(u'''
// Take full step

// ai = a
''')
        _v = VFFSL(SL,"copyVectors",False)(VFFSL(SL,"integrationVectors",True), '_initial') # u"${copyVectors($integrationVectors, '_initial')}" on line 598, col 1
        if _v is not None: write(_filter(_v, rawExpr=u"${copyVectors($integrationVectors, '_initial')}")) # from line 598, col 1.
        write(u'''
// 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=u'${loopOverVectorsWithInnerContentTemplate($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 = $homeBasis)}')) # from line 601, col 1.
        write(u'''
// a* = a + etc
''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akafield_${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}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr=u'${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 = $homeBasis)}')) # from line 609, col 1.
        write(u'''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 616, col 3
            write(u'''_active_''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 617, col 9
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 617, col 9.
            write(u''' = _''')
            _v = VFFSL(SL,"vector.id",True) # u'${vector.id}' on line 617, col 25
            if _v is not None: write(_filter(_v, rawExpr=u'${vector.id}')) # from line 617, col 25.
            write(u''';
''')
        write(u'''
''')
        # 
        
        ########################################
        ## 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
        
        # 
        # 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(u'''




''')
        # 
        #   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 http://www.CheetahTemplate.org/

##################################################
## if run from command line:
if __name__ == '__main__':
    from Cheetah.TemplateCmdLineIface import CmdLineIface
    CmdLineIface(templateObj=RK89Stepper()).run()


