def _evaluate(self,*args,**kwargs): """ NAME: _evaluate PURPOSE: evaluate the actions (jr,lz,jz) INPUT: Either: a) R,vR,vT,z,vz b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well c= True/False; overrides the object's c= keyword to use C or not scipy.integrate.quadrature keywords OUTPUT: (jr,lz,jz) HISTORY: 2012-11-27 - Written - Bovy (IAS) """ if ((self._c and not ('c' in kwargs and not kwargs['c']))\ or (ext_loaded and (('c' in kwargs and kwargs['c'])))) \ and _check_c(self._pot): if len(args) == 5: #R,vR.vT, z, vz R,vR,vT, z, vz= args elif len(args) == 6: #R,vR.vT, z, vz, phi R,vR,vT, z, vz, phi= args else: self._parse_eval_args(*args) R= self._eval_R vR= self._eval_vR vT= self._eval_vT z= self._eval_z vz= self._eval_vz if isinstance(R,float): R= nu.array([R]) vR= nu.array([vR]) vT= nu.array([vT]) z= nu.array([z]) vz= nu.array([vz]) Lz= R*vT if self._useu0: #First calculate u0 if 'u0' in kwargs: u0= nu.asarray(kwargs['u0']) else: E= nu.array([_evaluatePotentials(self._pot,R[ii],z[ii]) +vR[ii]**2./2.+vz[ii]**2./2.+vT[ii]**2./2. for ii in range(len(R))]) u0= actionAngleStaeckel_c.actionAngleStaeckel_calcu0(E,Lz, self._pot, self._delta)[0] kwargs.pop('u0',None) else: u0= None jr, jz, err= actionAngleStaeckel_c.actionAngleStaeckel_c(\ self._pot,self._delta,R,vR,vT,z,vz,u0=u0) if err == 0: return (jr,Lz,jz) else: #pragma: no cover raise RuntimeError("C-code for calculation actions failed; try with c=False") else: if 'c' in kwargs and kwargs['c'] and not self._c: #pragma: no cover warnings.warn("C module not used because potential does not have a C implementation",galpyWarning) kwargs.pop('c',None) if (len(args) == 5 or len(args) == 6) \ and isinstance(args[0],nu.ndarray): ojr= nu.zeros((len(args[0]))) olz= nu.zeros((len(args[0]))) ojz= nu.zeros((len(args[0]))) for ii in range(len(args[0])): if len(args) == 5: targs= (args[0][ii],args[1][ii],args[2][ii], args[3][ii],args[4][ii]) elif len(args) == 6: targs= (args[0][ii],args[1][ii],args[2][ii], args[3][ii],args[4][ii],args[5][ii]) tjr,tlz,tjz= self(*targs,**copy.copy(kwargs)) ojr[ii]= tjr ojz[ii]= tjz olz[ii]= tlz return (ojr,olz,ojz) else: #Set up the actionAngleStaeckelSingle object aASingle= actionAngleStaeckelSingle(*args,pot=self._pot, delta=self._delta) return (aASingle.JR(**copy.copy(kwargs)), aASingle._R*aASingle._vT, aASingle.Jz(**copy.copy(kwargs)))
def _evaluate(self, *args, **kwargs): """ NAME: __call__ (_evaluate) PURPOSE: evaluate the actions (jr,lz,jz) INPUT: Either: a) R,vR,vT,z,vz[,phi]: 1) floats: phase-space value for single object (phi is optional) (each can be a Quantity) 2) numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity) b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well as the second argument delta= (object-wide default) can be used to override the object-wide focal length; can also be an array with length N to allow different delta for different phase-space points u0= (None) if object-wide option useu0 is set, u0 to use (if useu0 and useu0 is None, a good value will be computed) c= (object-wide default, bool) True/False to override the object-wide setting for whether or not to use the C implementation order= (object-wide default, int) number of points to use in the Gauss-Legendre numerical integration of the relevant action integrals When not using C: fixed_quad= (False) if True, use Gaussian quadrature (scipy.integrate.fixed_quad instead of scipy.integrate.quad) scipy.integrate.fixed_quad or .quad keywords OUTPUT: (jr,lz,jz) HISTORY: 2012-11-27 - Written - Bovy (IAS) 2017-12-27 - Allowed individual delta for each point - Bovy (UofT) """ delta = kwargs.pop('delta', self._delta) order = kwargs.get('order', self._order) if ((self._c and not ('c' in kwargs and not kwargs['c']))\ or (ext_loaded and (('c' in kwargs and kwargs['c'])))) \ and _check_c(self._pot): if len(args) == 5: #R,vR.vT, z, vz R, vR, vT, z, vz = args elif len(args) == 6: #R,vR.vT, z, vz, phi R, vR, vT, z, vz, phi = args else: self._parse_eval_args(*args) R = self._eval_R vR = self._eval_vR vT = self._eval_vT z = self._eval_z vz = self._eval_vz if isinstance(R, float): R = nu.array([R]) vR = nu.array([vR]) vT = nu.array([vT]) z = nu.array([z]) vz = nu.array([vz]) Lz = R * vT if self._useu0: #First calculate u0 if 'u0' in kwargs: u0 = nu.asarray(kwargs['u0']) else: E = nu.array([ _evaluatePotentials(self._pot, R[ii], z[ii]) + vR[ii]**2. / 2. + vz[ii]**2. / 2. + vT[ii]**2. / 2. for ii in range(len(R)) ]) u0= actionAngleStaeckel_c.actionAngleStaeckel_calcu0(\ E,Lz,self._pot,delta)[0] kwargs.pop('u0', None) else: u0 = None jr, jz, err= actionAngleStaeckel_c.actionAngleStaeckel_c(\ self._pot,delta,R,vR,vT,z,vz,u0=u0,order=order) if err == 0: return (jr, Lz, jz) else: #pragma: no cover raise RuntimeError( "C-code for calculation actions failed; try with c=False") else: if 'c' in kwargs and kwargs['c'] and not self._c: #pragma: no cover warnings.warn( "C module not used because potential does not have a C implementation", galpyWarning) kwargs.pop('c', None) if (len(args) == 5 or len(args) == 6) \ and isinstance(args[0],nu.ndarray): ojr = nu.zeros((len(args[0]))) olz = nu.zeros((len(args[0]))) ojz = nu.zeros((len(args[0]))) for ii in range(len(args[0])): if len(args) == 5: targs = (args[0][ii], args[1][ii], args[2][ii], args[3][ii], args[4][ii]) elif len(args) == 6: targs = (args[0][ii], args[1][ii], args[2][ii], args[3][ii], args[4][ii], args[5][ii]) tkwargs = copy.copy(kwargs) try: tkwargs['delta'] = delta[ii] except TypeError: tkwargs['delta'] = delta tjr, tlz, tjz = self(*targs, **tkwargs) ojr[ii] = tjr ojz[ii] = tjz olz[ii] = tlz return (ojr, olz, ojz) else: #Set up the actionAngleStaeckelSingle object aASingle = actionAngleStaeckelSingle(*args, pot=self._pot, delta=delta) return (aASingle.JR(**copy.copy(kwargs)), aASingle._R * aASingle._vT, aASingle.Jz(**copy.copy(kwargs)))
def _actionsFreqsAngles(self,*args,**kwargs): """ NAME: _actionsFreqsAngles PURPOSE: evaluate the actions, frequencies, and angles (jr,lz,jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez) INPUT: Either: a) R,vR,vT,z,vz,phi (MUST HAVE PHI) b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well scipy.integrate.quadrature keywords OUTPUT: (jr,lz,jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez) HISTORY: 2013-08-28 - Written - Bovy (IAS) """ if ((self._c and not ('c' in kwargs and not kwargs['c']))\ or (ext_loaded and (('c' in kwargs and kwargs['c'])))) \ and _check_c(self._pot): if len(args) == 5: #R,vR.vT, z, vz pragma: no cover raise IOError("Must specify phi") elif len(args) == 6: #R,vR.vT, z, vz, phi R,vR,vT, z, vz, phi= args else: self._parse_eval_args(*args) R= self._eval_R vR= self._eval_vR vT= self._eval_vT z= self._eval_z vz= self._eval_vz phi= self._eval_phi if isinstance(R,float): R= nu.array([R]) vR= nu.array([vR]) vT= nu.array([vT]) z= nu.array([z]) vz= nu.array([vz]) phi= nu.array([phi]) Lz= R*vT if self._useu0: #First calculate u0 if 'u0' in kwargs: u0= nu.asarray(kwargs['u0']) else: E= nu.array([_evaluatePotentials(self._pot,R[ii],z[ii]) +vR[ii]**2./2.+vz[ii]**2./2.+vT[ii]**2./2. for ii in range(len(R))]) u0= actionAngleStaeckel_c.actionAngleStaeckel_calcu0(E,Lz, self._pot, self._delta)[0] kwargs.pop('u0',None) else: u0= None jr, jz, Omegar, Omegaphi, Omegaz, angler, anglephi,anglez, err= actionAngleStaeckel_c.actionAngleFreqAngleStaeckel_c(\ self._pot,self._delta,R,vR,vT,z,vz,phi,u0=u0) # Adjustements for close-to-circular orbits indx= nu.isnan(Omegar)*(jr < 10.**-3.)+nu.isnan(Omegaz)*(jz < 10.**-3.) #Close-to-circular and close-to-the-plane orbits if nu.sum(indx) > 0: Omegar[indx]= [epifreq(self._pot,r,use_physical=False) for r in R[indx]] Omegaphi[indx]= [omegac(self._pot,r,use_physical=False) for r in R[indx]] Omegaz[indx]= [verticalfreq(self._pot,r,use_physical=False) for r in R[indx]] if err == 0: return (jr,Lz,jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez) else: raise RuntimeError("C-code for calculation actions failed; try with c=False") #pragma: no cover else: #pragma: no cover if 'c' in kwargs and kwargs['c'] and not self._c: #pragma: no cover warnings.warn("C module not used because potential does not have a C implementation",galpyWarning) raise NotImplementedError("actionsFreqs with c=False not implemented")
def _uminumaxvmin(self, *args, **kwargs): """ NAME: _uminumaxvmin PURPOSE: evaluate u_min, u_max, and v_min INPUT: Either: a) R,vR,vT,z,vz b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well c= True/False; overrides the object's c= keyword to use C or not OUTPUT: (umin,umax,vmin) HISTORY: 2017-12-12 - Written - Bovy (UofT) """ delta = kwargs.pop('delta', self._delta) if ((self._c and not ('c' in kwargs and not kwargs['c']))\ or (ext_loaded and (('c' in kwargs and kwargs['c'])))) \ and _check_c(self._pot): if len(args) == 5: #R,vR.vT, z, vz R, vR, vT, z, vz = args elif len(args) == 6: #R,vR.vT, z, vz, phi R, vR, vT, z, vz, phi = args else: self._parse_eval_args(*args) R = self._eval_R vR = self._eval_vR vT = self._eval_vT z = self._eval_z vz = self._eval_vz if isinstance(R, float): R = nu.array([R]) vR = nu.array([vR]) vT = nu.array([vT]) z = nu.array([z]) vz = nu.array([vz]) Lz = R * vT if self._useu0: #First calculate u0 if 'u0' in kwargs: u0 = nu.asarray(kwargs['u0']) else: E = nu.array([ _evaluatePotentials(self._pot, R[ii], z[ii]) + vR[ii]**2. / 2. + vz[ii]**2. / 2. + vT[ii]**2. / 2. for ii in range(len(R)) ]) u0= actionAngleStaeckel_c.actionAngleStaeckel_calcu0(\ E,Lz,self._pot,delta)[0] kwargs.pop('u0', None) else: u0 = None umin, umax, vmin, err= \ actionAngleStaeckel_c.actionAngleUminUmaxVminStaeckel_c(\ self._pot,delta,R,vR,vT,z,vz,u0=u0) if err == 0: return (umin, umax, vmin) else: #pragma: no cover raise RuntimeError( "C-code for calculation actions failed; try with c=False") else: if 'c' in kwargs and kwargs['c'] and not self._c: #pragma: no cover warnings.warn( "C module not used because potential does not have a C implementation", galpyWarning) kwargs.pop('c', None) if (len(args) == 5 or len(args) == 6) \ and isinstance(args[0],nu.ndarray): oumin = nu.zeros((len(args[0]))) oumax = nu.zeros((len(args[0]))) ovmin = nu.zeros((len(args[0]))) for ii in range(len(args[0])): if len(args) == 5: targs = (args[0][ii], args[1][ii], args[2][ii], args[3][ii], args[4][ii]) elif len(args) == 6: targs = (args[0][ii], args[1][ii], args[2][ii], args[3][ii], args[4][ii], args[5][ii]) tkwargs = copy.copy(kwargs) try: tkwargs['delta'] = delta[ii] except TypeError: tkwargs['delta'] = delta tumin,tumax,tvmin= self._uminumaxvmin(\ *targs,**tkwargs) oumin[ii] = tumin oumax[ii] = tumax ovmin[ii] = tvmin return (oumin, oumax, ovmin) else: #Set up the actionAngleStaeckelSingle object aASingle = actionAngleStaeckelSingle(*args, pot=self._pot, delta=delta) umin, umax = aASingle.calcUminUmax() vmin = aASingle.calcVmin() return (umin, umax, vmin)
def _actionsFreqsAngles(self, *args, **kwargs): """ NAME: actionsFreqsAngles (_actionsFreqsAngles) PURPOSE: evaluate the actions, frequencies, and angles (jr,lz,jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez) INPUT: Either: a) R,vR,vT,z,vz[,phi]: 1) floats: phase-space value for single object (phi is optional) (each can be a Quantity) 2) numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity) b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well as the second argument delta= (object-wide default) can be used to override the object-wide focal length; can also be an array with length N to allow different delta for different phase-space points u0= (None) if object-wide option useu0 is set, u0 to use (if useu0 and useu0 is None, a good value will be computed) c= (object-wide default, bool) True/False to override the object-wide setting for whether or not to use the C implementation order= (10) number of points to use in the Gauss-Legendre numerical integration of the relevant action, frequency, and angle integrals When not using C: fixed_quad= (False) if True, use Gaussian quadrature (scipy.integrate.fixed_quad instead of scipy.integrate.quad) scipy.integrate.fixed_quad or .quad keywords OUTPUT: (jr,lz,jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez) HISTORY: 2013-08-28 - Written - Bovy (IAS) """ delta = kwargs.pop('delta', self._delta) order = kwargs.get('order', self._order) if ((self._c and not ('c' in kwargs and not kwargs['c']))\ or (ext_loaded and (('c' in kwargs and kwargs['c'])))) \ and _check_c(self._pot): if len(args) == 5: #R,vR.vT, z, vz pragma: no cover raise IOError("Must specify phi") elif len(args) == 6: #R,vR.vT, z, vz, phi R, vR, vT, z, vz, phi = args else: self._parse_eval_args(*args) R = self._eval_R vR = self._eval_vR vT = self._eval_vT z = self._eval_z vz = self._eval_vz phi = self._eval_phi if isinstance(R, float): R = nu.array([R]) vR = nu.array([vR]) vT = nu.array([vT]) z = nu.array([z]) vz = nu.array([vz]) phi = nu.array([phi]) Lz = R * vT if self._useu0: #First calculate u0 if 'u0' in kwargs: u0 = nu.asarray(kwargs['u0']) else: E = nu.array([ _evaluatePotentials(self._pot, R[ii], z[ii]) + vR[ii]**2. / 2. + vz[ii]**2. / 2. + vT[ii]**2. / 2. for ii in range(len(R)) ]) u0= actionAngleStaeckel_c.actionAngleStaeckel_calcu0(\ E,Lz,self._pot,delta)[0] kwargs.pop('u0', None) else: u0 = None jr, jz, Omegar, Omegaphi, Omegaz, angler, anglephi,anglez, err= actionAngleStaeckel_c.actionAngleFreqAngleStaeckel_c(\ self._pot,delta,R,vR,vT,z,vz,phi,u0=u0,order=order) # Adjustements for close-to-circular orbits indx = nu.isnan(Omegar) * (jr < 10.**-3.) + nu.isnan(Omegaz) * ( jz < 10.**-3. ) #Close-to-circular and close-to-the-plane orbits if nu.sum(indx) > 0: Omegar[indx] = [ epifreq(self._pot, r, use_physical=False) for r in R[indx] ] Omegaphi[indx] = [ omegac(self._pot, r, use_physical=False) for r in R[indx] ] Omegaz[indx] = [ verticalfreq(self._pot, r, use_physical=False) for r in R[indx] ] if err == 0: return (jr, Lz, jz, Omegar, Omegaphi, Omegaz, angler, anglephi, anglez) else: raise RuntimeError( "C-code for calculation actions failed; try with c=False" ) #pragma: no cover else: #pragma: no cover if 'c' in kwargs and kwargs['c'] and not self._c: #pragma: no cover warnings.warn( "C module not used because potential does not have a C implementation", galpyWarning) raise NotImplementedError( "actionsFreqs with c=False not implemented")
def __init__(self,pot=None,delta=None,Rmax=5., nE=25,npsi=25,nLz=30,numcores=1, **kwargs): """ NAME: __init__ PURPOSE: initialize an actionAngleStaeckelGrid object INPUT: pot= potential or list of potentials delta= focus of prolate confocal coordinate system (can be Quantity) Rmax = Rmax for building grids (natural units) nE=, npsi=, nLz= grid size numcores= number of cpus to use to parallellize ro= distance from vantage point to GC (kpc; can be Quantity) vo= circular velocity at ro (km/s; can be Quantity) OUTPUT: instance HISTORY: 2012-11-29 - Written - Bovy (IAS) """ actionAngle.__init__(self, ro=kwargs.get('ro',None),vo=kwargs.get('vo',None)) if pot is None: raise IOError("Must specify pot= for actionAngleStaeckelGrid") self._pot= pot if delta is None: raise IOError("Must specify delta= for actionAngleStaeckelGrid") if ext_loaded and 'c' in kwargs and kwargs['c']: self._c= True else: self._c= False self._delta= delta if _APY_LOADED and isinstance(self._delta,units.Quantity): self._delta= self._delta.to(units.kpc).value/self._ro self._Rmax= Rmax self._Rmin= 0.01 #Set up the actionAngleStaeckel object that we will use to interpolate self._aA= actionAngleStaeckel.actionAngleStaeckel(pot=self._pot,delta=self._delta,c=self._c) #Build grid self._Lzmin= 0.01 self._Lzs= numpy.linspace(self._Lzmin, self._Rmax\ *galpy.potential.vcirc(self._pot, self._Rmax), nLz) self._Lzmax= self._Lzs[-1] self._nLz= nLz #Calculate E_c(R=RL), energy of circular orbit self._RL= numpy.array([galpy.potential.rl(self._pot,l) for l in self._Lzs]) self._RLInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs, self._RL,k=3) self._ERL= _evaluatePotentials(self._pot,self._RL, numpy.zeros(self._nLz))\ +self._Lzs**2./2./self._RL**2. self._ERLmax= numpy.amax(self._ERL)+1. self._ERLInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs, numpy.log(-(self._ERL-self._ERLmax)),k=3) self._Ramax= 200./8. self._ERa= _evaluatePotentials(self._pot,self._Ramax,0.) +self._Lzs**2./2./self._Ramax**2. #self._EEsc= numpy.array([self._ERL[ii]+galpy.potential.vesc(self._pot,self._RL[ii])**2./4. for ii in range(nLz)]) self._ERamax= numpy.amax(self._ERa)+1. self._ERaInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs, numpy.log(-(self._ERa-self._ERamax)),k=3) y= numpy.linspace(0.,1.,nE) self._nE= nE psis= numpy.linspace(0.,1.,npsi)*numpy.pi/2. self._npsi= npsi jr= numpy.zeros((nLz,nE,npsi)) jz= numpy.zeros((nLz,nE,npsi)) u0= numpy.zeros((nLz,nE)) jrLzE= numpy.zeros((nLz)) jzLzE= numpy.zeros((nLz)) #First calculate u0 thisLzs= (numpy.tile(self._Lzs,(nE,1)).T).flatten() thisERL= (numpy.tile(self._ERL,(nE,1)).T).flatten() thisERa= (numpy.tile(self._ERa,(nE,1)).T).flatten() thisy= (numpy.tile(y,(nLz,1))).flatten() thisE= _invEfunc(_Efunc(thisERa,thisERL)+thisy*(_Efunc(thisERL,thisERL)-_Efunc(thisERa,thisERL)),thisERL) if isinstance(self._pot,galpy.potential.interpRZPotential) and hasattr(self._pot,'_origPot'): u0pot= self._pot._origPot else: u0pot= self._pot if self._c: mu0= actionAngleStaeckel_c.actionAngleStaeckel_calcu0(thisE,thisLzs, u0pot, self._delta)[0] else: if numcores > 1: mu0= multi.parallel_map((lambda x: self.calcu0(thisE[x], thisLzs[x])), range(nE*nLz), numcores=numcores) else: mu0= list(map((lambda x: self.calcu0(thisE[x], thisLzs[x])), range(nE*nLz))) u0= numpy.reshape(mu0,(nLz,nE)) thisR= self._delta*numpy.sinh(u0) thisv= numpy.reshape(self.vatu0(thisE.flatten(),thisLzs.flatten(), u0.flatten(), thisR.flatten()),(nLz,nE)) self.thisv= thisv #reshape thisLzs= numpy.reshape(thisLzs,(nLz,nE)) thispsi= numpy.tile(psis,(nLz,nE,1)).flatten() thisLzs= numpy.tile(thisLzs.T,(npsi,1,1)).T.flatten() thisR= numpy.tile(thisR.T,(npsi,1,1)).T.flatten() thisv= numpy.tile(thisv.T,(npsi,1,1)).T.flatten() mjr, mlz, mjz= self._aA(thisR, #R thisv*numpy.cos(thispsi), #vR thisLzs/thisR, #vT numpy.zeros(len(thisR)), #z thisv*numpy.sin(thispsi), #vz fixed_quad=True) if isinstance(self._pot,galpy.potential.interpRZPotential) and hasattr(self._pot,'_origPot'): #Interpolated potentials have problems with extreme orbits indx= (mjr == 9999.99) indx+= (mjz == 9999.99) #Re-calculate these using the original potential, hopefully not too slow tmpaA= actionAngleStaeckel.actionAngleStaeckel(pot=self._pot._origPot,delta=self._delta,c=self._c) mjr[indx], dum, mjz[indx]= tmpaA(thisR[indx], #R thisv[indx]*numpy.cos(thispsi[indx]), #vR thisLzs[indx]/thisR[indx], #vT numpy.zeros(numpy.sum(indx)), #z thisv[indx]*numpy.sin(thispsi[indx]), #vz fixed_quad=True) jr= numpy.reshape(mjr,(nLz,nE,npsi)) jz= numpy.reshape(mjz,(nLz,nE,npsi)) for ii in range(nLz): jrLzE[ii]= numpy.nanmax(jr[ii,(jr[ii,:,:] != 9999.99)])#:,:]) jzLzE[ii]= numpy.nanmax(jz[ii,(jz[ii,:,:] != 9999.99)])#:,:]) jrLzE[(jrLzE == 0.)]= numpy.nanmin(jrLzE[(jrLzE > 0.)]) jzLzE[(jzLzE == 0.)]= numpy.nanmin(jzLzE[(jzLzE > 0.)]) for ii in range(nLz): jr[ii,:,:]/= jrLzE[ii] jz[ii,:,:]/= jzLzE[ii] #Deal w/ 9999.99 jr[(jr > 1.)]= 1. jz[(jz > 1.)]= 1. #Deal w/ NaN jr[numpy.isnan(jr)]= 0. jz[numpy.isnan(jz)]= 0. #First interpolate the maxima self._jr= jr self._jz= jz self._u0= u0 self._jrLzE= jrLzE self._jzLzE= jzLzE self._jrLzInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs, numpy.log(jrLzE+10.**-5.),k=3) self._jzLzInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs, numpy.log(jzLzE+10.**-5.),k=3) #Interpolate u0 self._logu0Interp= interpolate.RectBivariateSpline(self._Lzs, y, numpy.log(u0), kx=3,ky=3,s=0.) #spline filter jr and jz, such that they can be used with ndimage.map_coordinates self._jrFiltered= ndimage.spline_filter(numpy.log(self._jr+10.**-10.),order=3) self._jzFiltered= ndimage.spline_filter(numpy.log(self._jz+10.**-10.),order=3) # Check the units self._check_consistent_units() return None
def __call__(self, *args, **kwargs): """ NAME: __call__ PURPOSE: evaluate the actions (jr,lz,jz) INPUT: Either: a) R,vR,vT,z,vz b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well c= True/False; overrides the object's c= keyword to use C or not scipy.integrate.quadrature keywords OUTPUT: (jr,lz,jz) HISTORY: 2012-11-27 - Written - Bovy (IAS) """ if ((self._c and not ('c' in kwargs and not kwargs['c']))\ or (ext_loaded and (('c' in kwargs and kwargs['c'])))) \ and _check_c(self._pot): if len(args) == 5: #R,vR.vT, z, vz R, vR, vT, z, vz = args elif len(args) == 6: #R,vR.vT, z, vz, phi R, vR, vT, z, vz, phi = args else: meta = actionAngle(*args) R = meta._R vR = meta._vR vT = meta._vT z = meta._z vz = meta._vz if isinstance(R, float): R = nu.array([R]) vR = nu.array([vR]) vT = nu.array([vT]) z = nu.array([z]) vz = nu.array([vz]) Lz = R * vT if self._useu0: #First calculate u0 if 'u0' in kwargs: u0 = nu.asarray(kwargs['u0']) else: E = nu.array([ evaluatePotentials(R[ii], z[ii], self._pot) + vR[ii]**2. / 2. + vz[ii]**2. / 2. + vT[ii]**2. / 2. for ii in range(len(R)) ]) u0 = actionAngleStaeckel_c.actionAngleStaeckel_calcu0( E, Lz, self._pot, self._delta)[0] kwargs.pop('u0', None) else: u0 = None jr, jz, err= actionAngleStaeckel_c.actionAngleStaeckel_c(\ self._pot,self._delta,R,vR,vT,z,vz,u0=u0) if err == 0: return (jr, Lz, jz) else: #pragma: no cover raise RuntimeError( "C-code for calculation actions failed; try with c=False") else: if 'c' in kwargs and kwargs['c'] and not self._c: #pragma: no cover warnings.warn( "C module not used because potential does not have a C implementation", galpyWarning) kwargs.pop('c', None) if (len(args) == 5 or len(args) == 6) \ and isinstance(args[0],nu.ndarray): ojr = nu.zeros((len(args[0]))) olz = nu.zeros((len(args[0]))) ojz = nu.zeros((len(args[0]))) for ii in range(len(args[0])): if len(args) == 5: targs = (args[0][ii], args[1][ii], args[2][ii], args[3][ii], args[4][ii]) elif len(args) == 6: targs = (args[0][ii], args[1][ii], args[2][ii], args[3][ii], args[4][ii], args[5][ii]) tjr, tlz, tjz = self(*targs, **copy.copy(kwargs)) ojr[ii] = tjr ojz[ii] = tjz olz[ii] = tlz return (ojr, olz, ojz) else: #Set up the actionAngleStaeckelSingle object aASingle = actionAngleStaeckelSingle(*args, pot=self._pot, delta=self._delta) return (aASingle.JR(**copy.copy(kwargs)), aASingle._R * aASingle._vT, aASingle.Jz(**copy.copy(kwargs)))
def actionsFreqsAngles(self, *args, **kwargs): """ NAME: actionsFreqsAngles PURPOSE: evaluate the actions, frequencies, and angles (jr,lz,jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez) INPUT: Either: a) R,vR,vT,z,vz,phi (MUST HAVE PHI) b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well scipy.integrate.quadrature keywords OUTPUT: (jr,lz,jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez) HISTORY: 2013-08-28 - Written - Bovy (IAS) """ if ((self._c and not ('c' in kwargs and not kwargs['c']))\ or (ext_loaded and (('c' in kwargs and kwargs['c'])))) \ and _check_c(self._pot): if len(args) == 5: #R,vR.vT, z, vz pragma: no cover raise IOError("Must specify phi") elif len(args) == 6: #R,vR.vT, z, vz, phi R, vR, vT, z, vz, phi = args else: meta = actionAngle(*args) R = meta._R vR = meta._vR vT = meta._vT z = meta._z vz = meta._vz phi = meta._phi if isinstance(R, float): R = nu.array([R]) vR = nu.array([vR]) vT = nu.array([vT]) z = nu.array([z]) vz = nu.array([vz]) phi = nu.array([phi]) Lz = R * vT if self._useu0: #First calculate u0 if 'u0' in kwargs: u0 = nu.asarray(kwargs['u0']) else: E = nu.array([ evaluatePotentials(R[ii], z[ii], self._pot) + vR[ii]**2. / 2. + vz[ii]**2. / 2. + vT[ii]**2. / 2. for ii in range(len(R)) ]) u0 = actionAngleStaeckel_c.actionAngleStaeckel_calcu0( E, Lz, self._pot, self._delta)[0] kwargs.pop('u0', None) else: u0 = None jr, jz, Omegar, Omegaphi, Omegaz, angler, anglephi,anglez, err= actionAngleStaeckel_c.actionAngleFreqAngleStaeckel_c(\ self._pot,self._delta,R,vR,vT,z,vz,phi,u0=u0) # Adjustements for close-to-circular orbits indx = nu.isnan(Omegar) * (jr < 10.**-3.) + nu.isnan(Omegaz) * ( jz < 10.**-3. ) #Close-to-circular and close-to-the-plane orbits if nu.sum(indx) > 0: Omegar[indx] = [epifreq(self._pot, r) for r in R[indx]] Omegaphi[indx] = [omegac(self._pot, r) for r in R[indx]] Omegaz[indx] = [verticalfreq(self._pot, r) for r in R[indx]] if err == 0: return (jr, Lz, jz, Omegar, Omegaphi, Omegaz, angler, anglephi, anglez) else: raise RuntimeError( "C-code for calculation actions failed; try with c=False" ) #pragma: no cover else: #pragma: no cover if 'c' in kwargs and kwargs['c'] and not self._c: #pragma: no cover warnings.warn( "C module not used because potential does not have a C implementation", galpyWarning) raise NotImplementedError( "actionsFreqs with c=False not implemented")