Loading src/yapsut/blackbody_mks.py 0 → 100644 +335 −0 Original line number Diff line number Diff line __DESCRIPTION__=""" MKS = an object returning the CGS units and constants See: import blackbody_mks help(blackbody.MKS) The package manages numpy.array(). Version 1.0 - 2011 Set 1 - 2012 Apr 5 - M.Maris """ import numpy as np from yapsut import MKS class _CnPlanck : def __call__(self,n,x) : return self.bx(n,x) def Norm(self,n) : """normalization constant of x^n/(exp(x)-1) integrated between 0 and 1""" from scipy.special import gamma, zeta if n==0 : return 1 elif n==1 : return np.pi**2/12 elif n==2 : # gamma(3)*zeta(3) return 2*zeta(3) elif n==3 : # gamma(4)*zeta(4) return np.pi**4/15 else : # gamma(n+1)*zeta(n+1) return gamma(n+1)*zeta(n+1) def bx(self,n,x) : return x**n/(np.exp(x)-1) def Tcumulant(self,n,xmax,nsteps) : x=np.linspace(0.,xmax,nsteps) dx=xmax/float(nsteps) bx=np.zeros(nsteps) bx[1:]=self.bx(n,x[1:]) if n == 0 : bx[0]=+np.infty elif n==1 : bx[0]=1. #else : # bx[0]=0 out=np.zeros(nsteps) out[1:]=(bx[1:]+bx[:-1]).cumsum() out*=dx/2/self.Norm(n) return x,out def Scumulant(self,n,xmax=708,nsteps=300000) : """ returns a spline interpolating the cumulant of the planck function """ class scumspline : """ spline interpolation for cumulants of x^n/(exp(2)-1) with 300000 points typical accuracy some 10^-6 with 3000000 points typical accuracy some 10^-7 produced through Scumulant of AdimPlanckFunction """ @property def n(self) : return self._n @property def norm(self) : return self._norm @property def tck(self) : return self._tck @property def xmax(self) : return self._xmax @property def max(self) : return self._max @property def cumulant_accuracy(self) : return 1-self._max def __init__(self,x,y,norm,n) : from scipy.interpolate import splrep self._n=n self._nsamp=len(x) self._tck,self._fp,self._ierr,self._msg=splrep(x,y,full_output=True) self._xmax=x.max() self._norm=norm self._max=self(self.xmax) def __call__(self,x) : """ is x > xmax or x < 0 a nan is produced x : either a number or a numpy array """ from scipy.interpolate import splev _x=np.array(x) out=splev(_x,self._tck) out[(_x>self.xmax)+(_x<0)]=np.nan return out def __len__(self) : return self._nsamp def copy(self) : import copy return copy.deepcopy(self) def pdf(self,x) : """ computes the pdf(n) = x^n/(np.exp(x)-1)/norm """ return x**self._n/(np.exp(x)-1)/self._norm def __repr__(self) : return "<"+"n = "+str(self.n)+"; xmax = "+str(self.xmax)+"; nsmp = "+str(len(self))+"; ierr = "+str(self._ierr)+"; accuracy = "+str(self.cumulant_accuracy)+">" # x,y=self.Tcumulant(n,xmax,nsteps) return scumspline(x,y,self.Norm(n),n) def cumulant(self,n,xmax,nsteps=1000) : x=np.linspace(0,xmax,nsteps) dx=x[1]-x[0] bx=np.zeros(nsteps) bx[1:]=self.bx(n,x[1:]) if n == 0 : b[0]=+np.infty elif n==1 : b[0]=1. return dx*bx.sum()/self.Norm(n) @property def xwien(self) : return 4.965114231744276303 @property def nu_wien(self) : return MKS.kB/MKS.h*self.xwien @property def lambda_wien(self) : return MKS.kB/(MKS.c*MKS.h)*self.xwien Wien_x = 4.965114231744276303 Wien_nu = MKS.kB/MKS.h*Wien_x Wien_lambda = MKS.kB/(MKS.c*MKS.h)*Wien_x def MeanPhotonEnergy(T) : """ returns the mean photon energy in J for a bb at temperature T """ #return 3.7294e-23*T return MKS.meanBBPhotEn*T # Wien #Wien_x=4.965114231744276303 #Wien_nu=MKS.kB/MKS.h*Wien_x #Wien_lambda=(MKS.c*MKS.h)/(MKS.kB*Wien_x) PlanckCn=_CnPlanck() #PlanckC2=PlanckCn.Scumulant(2) #PlanckC3=PlanckCn.Scumulant(3) #PlanckC4=PlanckCn.Scumulant(4) #PlanckC5=PlanckCn.Scumulant(5) class _black_body_mks() : def __init__(self,Type) : if Type == 'bbn' : self.A=2*MKS.h/MKS.c**2 self.NA=2/MKS.c**2/MKS.Navo self.B=MKS.h/MKS.kB elif Type == 'sedn' : self.A=2*MKS.h/MKS.c**2*MKS.rad2sed self.NA=2/MKS.c**2/MKS.Navo*MKS.rad2sed self.B=MKS.h/MKS.kB elif Type == 'bbl' : self.A=2*MKS.h*MKS.c**2 self.NA=2*MKS.c/MKS.Navo self.B=MKS.h*MKS.c/MKS.kB elif Type == 'sedl' : self.A=2*MKS.h*MKS.c**2*MKS.rad2sed self.NA=2*MKS.c/MKS.Navo*MKS.rad2sed self.B=MKS.h*MKS.c/MKS.kB else : raise Exception("Black Body Type %s is not valid"%Type,"") def valid(self,FreqTHz,T) : return (FreqTHz >= 0.) * (T >= 0.) class _bbl_mks(_black_body_mks) : """ ! ! BB(lambda,T) thermal radiance function mks ! ! lambda in m ! ! bbl_mks = J/(m2 s m sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'bbl') def __call__(self,Lambda,T) : FT = self.A/Lambda**5 ET = np.exp( self.B/(Lambda*T) )-1; return FT / ET bbl_mks=_bbl_mks() class _pi_bbl_mks(_black_body_mks) : """ ! ! pi*BB(lambda,T) thermal radiance function mks ! ! lambda in m ! ! bbl_mks = J/(m2 s m sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'bbl') def __call__(self,Lambda,T) : FT = np.pi*self.A/Lambda**5 ET = np.exp( self.B/(Lambda*T) )-1; return FT / ET pbbl_mks=_pi_bbl_mks() class _bbl_sed_mks(_black_body_mks) : """ ! ! BB(lambda,T) thermal sed function mks ! ! lambda in m ! ! bbl_mks = J/(m2 s m sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'sedl') def __call__(self,Lambda,T) : FT = self.A/Lambda**5 ET = np.exp( self.B/(Lambda*T) )-1; return FT / ET bbl_sed_mks=_bbl_sed_mks() class _Npbbl_mks(_black_body_mks) : """ ! ! NpBB(lambda,T) thermal photons function mks ! ! lambda in m ! ! Nbbl_mks = photons/(m2 s m) ! """ def __init__(self): _black_body_mks.__init__(self,'bbl') def __call__(self,Lambda,T) : FT = np.pi*self.NA/Lambda**4 ET = np.exp( self.B/(Lambda*T) )-1; return FT / ET Npbbl_mks=_Npbbl_mks() class _Nbbl_sed_mks(_black_body_mks) : """ ! ! NBB(lambda,T) thermal radiance function mks ! ! lambda in m ! ! Nbbl_mks = photons/(m2 s m sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'sedl') def __call__(self,Lambda,T) : FT = self.NA/Lambda**4 ET = np.exp( self.B/(Lambda*T) )-1; return FT / ET Nbbl_sed_mks=_Nbbl_sed_mks() class _bbn_mks(_black_body_mks) : """ ! ! BB(nu,T) thermal radiance function mks ! ! nu in Hz ! ! bbn_mks = J/(m2 s Hz sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'bbn') def __call__(self,nu,T) : FT = self.A*nu**3 ET = np.exp(self.B*nu/T)-1 return FT / ET bbn_mks=_bbn_mks() class _bbn_sed_mks(_black_body_mks) : """ ! ! BB(nu,T) thermal sed function mks ! ! nu in Hz ! ! bbn_mks = J/(m2 s Hz sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'sedn') def __call__(self,nu,T) : FT = self.A*nu**3 ET = np.exp(self.B*nu/T)-1 return FT / ET bbn_sed_mks=_bbn_sed_mks() class _Nbbn_mks(_black_body_mks) : """ ! ! NBB(nu,T) photons radiance mks = bbn_mks / h nu ! ! nu in Hz ! ! Nbbn_mks = photons/(m2 s Hz sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'bbn') def __call__(self,nu,T) : FT = self.NA*nu**2 ET = np.exp(self.B*nu/T)-1 return FT / ET Nbbn_mks=_bbn_mks() class _Nbbn_sed_mks(_black_body_mks) : """ ! ! NBB(nu,T) photons sed mks = bbn_mks / h nu ! ! nu in Hz ! ! Nbbn_mks = photons/(m2 s Hz sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'sedn') def __call__(self,nu,T) : FT = self.NA*nu**2 ET = np.exp(self.B*nu/T)-1 return FT / ET Nbbn_sed_mks=_Nbbn_sed_mks() Loading
src/yapsut/blackbody_mks.py 0 → 100644 +335 −0 Original line number Diff line number Diff line __DESCRIPTION__=""" MKS = an object returning the CGS units and constants See: import blackbody_mks help(blackbody.MKS) The package manages numpy.array(). Version 1.0 - 2011 Set 1 - 2012 Apr 5 - M.Maris """ import numpy as np from yapsut import MKS class _CnPlanck : def __call__(self,n,x) : return self.bx(n,x) def Norm(self,n) : """normalization constant of x^n/(exp(x)-1) integrated between 0 and 1""" from scipy.special import gamma, zeta if n==0 : return 1 elif n==1 : return np.pi**2/12 elif n==2 : # gamma(3)*zeta(3) return 2*zeta(3) elif n==3 : # gamma(4)*zeta(4) return np.pi**4/15 else : # gamma(n+1)*zeta(n+1) return gamma(n+1)*zeta(n+1) def bx(self,n,x) : return x**n/(np.exp(x)-1) def Tcumulant(self,n,xmax,nsteps) : x=np.linspace(0.,xmax,nsteps) dx=xmax/float(nsteps) bx=np.zeros(nsteps) bx[1:]=self.bx(n,x[1:]) if n == 0 : bx[0]=+np.infty elif n==1 : bx[0]=1. #else : # bx[0]=0 out=np.zeros(nsteps) out[1:]=(bx[1:]+bx[:-1]).cumsum() out*=dx/2/self.Norm(n) return x,out def Scumulant(self,n,xmax=708,nsteps=300000) : """ returns a spline interpolating the cumulant of the planck function """ class scumspline : """ spline interpolation for cumulants of x^n/(exp(2)-1) with 300000 points typical accuracy some 10^-6 with 3000000 points typical accuracy some 10^-7 produced through Scumulant of AdimPlanckFunction """ @property def n(self) : return self._n @property def norm(self) : return self._norm @property def tck(self) : return self._tck @property def xmax(self) : return self._xmax @property def max(self) : return self._max @property def cumulant_accuracy(self) : return 1-self._max def __init__(self,x,y,norm,n) : from scipy.interpolate import splrep self._n=n self._nsamp=len(x) self._tck,self._fp,self._ierr,self._msg=splrep(x,y,full_output=True) self._xmax=x.max() self._norm=norm self._max=self(self.xmax) def __call__(self,x) : """ is x > xmax or x < 0 a nan is produced x : either a number or a numpy array """ from scipy.interpolate import splev _x=np.array(x) out=splev(_x,self._tck) out[(_x>self.xmax)+(_x<0)]=np.nan return out def __len__(self) : return self._nsamp def copy(self) : import copy return copy.deepcopy(self) def pdf(self,x) : """ computes the pdf(n) = x^n/(np.exp(x)-1)/norm """ return x**self._n/(np.exp(x)-1)/self._norm def __repr__(self) : return "<"+"n = "+str(self.n)+"; xmax = "+str(self.xmax)+"; nsmp = "+str(len(self))+"; ierr = "+str(self._ierr)+"; accuracy = "+str(self.cumulant_accuracy)+">" # x,y=self.Tcumulant(n,xmax,nsteps) return scumspline(x,y,self.Norm(n),n) def cumulant(self,n,xmax,nsteps=1000) : x=np.linspace(0,xmax,nsteps) dx=x[1]-x[0] bx=np.zeros(nsteps) bx[1:]=self.bx(n,x[1:]) if n == 0 : b[0]=+np.infty elif n==1 : b[0]=1. return dx*bx.sum()/self.Norm(n) @property def xwien(self) : return 4.965114231744276303 @property def nu_wien(self) : return MKS.kB/MKS.h*self.xwien @property def lambda_wien(self) : return MKS.kB/(MKS.c*MKS.h)*self.xwien Wien_x = 4.965114231744276303 Wien_nu = MKS.kB/MKS.h*Wien_x Wien_lambda = MKS.kB/(MKS.c*MKS.h)*Wien_x def MeanPhotonEnergy(T) : """ returns the mean photon energy in J for a bb at temperature T """ #return 3.7294e-23*T return MKS.meanBBPhotEn*T # Wien #Wien_x=4.965114231744276303 #Wien_nu=MKS.kB/MKS.h*Wien_x #Wien_lambda=(MKS.c*MKS.h)/(MKS.kB*Wien_x) PlanckCn=_CnPlanck() #PlanckC2=PlanckCn.Scumulant(2) #PlanckC3=PlanckCn.Scumulant(3) #PlanckC4=PlanckCn.Scumulant(4) #PlanckC5=PlanckCn.Scumulant(5) class _black_body_mks() : def __init__(self,Type) : if Type == 'bbn' : self.A=2*MKS.h/MKS.c**2 self.NA=2/MKS.c**2/MKS.Navo self.B=MKS.h/MKS.kB elif Type == 'sedn' : self.A=2*MKS.h/MKS.c**2*MKS.rad2sed self.NA=2/MKS.c**2/MKS.Navo*MKS.rad2sed self.B=MKS.h/MKS.kB elif Type == 'bbl' : self.A=2*MKS.h*MKS.c**2 self.NA=2*MKS.c/MKS.Navo self.B=MKS.h*MKS.c/MKS.kB elif Type == 'sedl' : self.A=2*MKS.h*MKS.c**2*MKS.rad2sed self.NA=2*MKS.c/MKS.Navo*MKS.rad2sed self.B=MKS.h*MKS.c/MKS.kB else : raise Exception("Black Body Type %s is not valid"%Type,"") def valid(self,FreqTHz,T) : return (FreqTHz >= 0.) * (T >= 0.) class _bbl_mks(_black_body_mks) : """ ! ! BB(lambda,T) thermal radiance function mks ! ! lambda in m ! ! bbl_mks = J/(m2 s m sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'bbl') def __call__(self,Lambda,T) : FT = self.A/Lambda**5 ET = np.exp( self.B/(Lambda*T) )-1; return FT / ET bbl_mks=_bbl_mks() class _pi_bbl_mks(_black_body_mks) : """ ! ! pi*BB(lambda,T) thermal radiance function mks ! ! lambda in m ! ! bbl_mks = J/(m2 s m sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'bbl') def __call__(self,Lambda,T) : FT = np.pi*self.A/Lambda**5 ET = np.exp( self.B/(Lambda*T) )-1; return FT / ET pbbl_mks=_pi_bbl_mks() class _bbl_sed_mks(_black_body_mks) : """ ! ! BB(lambda,T) thermal sed function mks ! ! lambda in m ! ! bbl_mks = J/(m2 s m sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'sedl') def __call__(self,Lambda,T) : FT = self.A/Lambda**5 ET = np.exp( self.B/(Lambda*T) )-1; return FT / ET bbl_sed_mks=_bbl_sed_mks() class _Npbbl_mks(_black_body_mks) : """ ! ! NpBB(lambda,T) thermal photons function mks ! ! lambda in m ! ! Nbbl_mks = photons/(m2 s m) ! """ def __init__(self): _black_body_mks.__init__(self,'bbl') def __call__(self,Lambda,T) : FT = np.pi*self.NA/Lambda**4 ET = np.exp( self.B/(Lambda*T) )-1; return FT / ET Npbbl_mks=_Npbbl_mks() class _Nbbl_sed_mks(_black_body_mks) : """ ! ! NBB(lambda,T) thermal radiance function mks ! ! lambda in m ! ! Nbbl_mks = photons/(m2 s m sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'sedl') def __call__(self,Lambda,T) : FT = self.NA/Lambda**4 ET = np.exp( self.B/(Lambda*T) )-1; return FT / ET Nbbl_sed_mks=_Nbbl_sed_mks() class _bbn_mks(_black_body_mks) : """ ! ! BB(nu,T) thermal radiance function mks ! ! nu in Hz ! ! bbn_mks = J/(m2 s Hz sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'bbn') def __call__(self,nu,T) : FT = self.A*nu**3 ET = np.exp(self.B*nu/T)-1 return FT / ET bbn_mks=_bbn_mks() class _bbn_sed_mks(_black_body_mks) : """ ! ! BB(nu,T) thermal sed function mks ! ! nu in Hz ! ! bbn_mks = J/(m2 s Hz sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'sedn') def __call__(self,nu,T) : FT = self.A*nu**3 ET = np.exp(self.B*nu/T)-1 return FT / ET bbn_sed_mks=_bbn_sed_mks() class _Nbbn_mks(_black_body_mks) : """ ! ! NBB(nu,T) photons radiance mks = bbn_mks / h nu ! ! nu in Hz ! ! Nbbn_mks = photons/(m2 s Hz sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'bbn') def __call__(self,nu,T) : FT = self.NA*nu**2 ET = np.exp(self.B*nu/T)-1 return FT / ET Nbbn_mks=_bbn_mks() class _Nbbn_sed_mks(_black_body_mks) : """ ! ! NBB(nu,T) photons sed mks = bbn_mks / h nu ! ! nu in Hz ! ! Nbbn_mks = photons/(m2 s Hz sterad) ! """ def __init__(self): _black_body_mks.__init__(self,'sedn') def __call__(self,nu,T) : FT = self.NA*nu**2 ET = np.exp(self.B*nu/T)-1 return FT / ET Nbbn_sed_mks=_Nbbn_sed_mks()
