├── MANIFEST.in ├── requirements ├── spectrumfitter ├── __init__.py ├── spectralmodel.py └── spectrumfitter.py ├── .gitignore ├── examples ├── README.md ├── example_fit_dielectric_spectrum.py ├── fit_Raman_IR_dielectric.py ├── water_300K_Raman_Castner.dat ├── water_300.RI ├── water_full_Siegelstein.RI └── eps_omega_water_300K_TTM3F.dat ├── setup.py ├── LICENSE └── README.md /MANIFEST.in: -------------------------------------------------------------------------------- 1 | include README.md 2 | include examples/*.RI 3 | include examples/*.dat 4 | include examples/*.md -------------------------------------------------------------------------------- /requirements: -------------------------------------------------------------------------------- 1 | h5py 2 | numpy 3 | pandas 4 | scipy 5 | rdkit 6 | ipywidgets 7 | matplotlib 8 | scikit-learn 9 | fuel 10 | progressbar2 -------------------------------------------------------------------------------- /spectrumfitter/__init__.py: -------------------------------------------------------------------------------- 1 | #! /usr/bin/env python 2 | # 3 | # Copyright (C) 2017 Daniel C. Elton 4 | # License: MIT 5 | 6 | 7 | """ 8 | ## spectrumfitter 9 | """ 10 | 11 | from .spectrumfitter import * 12 | from .spectralmodel import SpectralModel 13 | 14 | __all__ = ['spectrumfitter','spectralmodel'] -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | *.pyc 2 | *.bak 3 | 4 | # Byte-compiled / optimized / DLL files 5 | __pycache__/ 6 | *.py[cod] 7 | 8 | # C extensions 9 | *.so 10 | 11 | # Packaging related 12 | .eggs/ 13 | *.egg-info/ 14 | .installed.cfg 15 | *.egg 16 | 17 | # PyInstaller 18 | # Usually these files are written by a python script from a template 19 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 20 | *.manifest 21 | *.spec 22 | 23 | # Installer logs 24 | pip-log.txt 25 | pip-delete-this-directory.txt 26 | 27 | .ipynb_checkpoints 28 | -------------------------------------------------------------------------------- /examples/README.md: -------------------------------------------------------------------------------- 1 | 2 | `eps_omega_water_300K_TTM3F.dat` contains real and complex parts of the dielectric spectra from a simulation with the TTM3F model performed by Daniel C. Elton. 3 | 4 | `Water_300K_Raman_Castner.dat` is a Raman spectra from Castner, et al. 5 | 6 | `Siegelstein Data` is full water refractive index (.RI) data from [DJ Segelstein - ‎1981 Ph.D. Thesis](https://mospace.umsystem.edu/xmlui/handle/10355/11599) 7 | 8 | `water_300.RI` and `ice_200K.RI` are complex refractive indices of supercooled liquid water and Ice in the infrared region from 460 to 6000 cm-1 from 9 | Zasetsky, A. Y., Khalizov, A. F., Earle, M. E. & Sloan, J. J., Frequency dependent complex refractive indices of supercooled liquid water and ice determined from aerosol extinction spectra. *J. Phys. Chem.* A **109**, 2760 (2005). 10 | -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | from setuptools import setup 2 | from setuptools import find_packages 3 | 4 | __version__ = '0.1.0' 5 | 6 | def readme(): 7 | with open('README.md') as f: 8 | return f.read() 9 | 10 | setup(name='spectrumfitter', 11 | version='0.1.0', 12 | description='basic utility for fitting dielectric spectra', 13 | author='Daniel C Elton', 14 | download_url='https://github.com/delton137/spectrumfitter/archive/master.zip', 15 | url='https://github.com/delton137/spectrumfitter', 16 | include_package_data=True, 17 | classifiers=[ 18 | 'Topic :: Scientific/Engineering :: Physics', 19 | 'License :: OSI Approved :: MIT License', 20 | 'Programming Language :: Python :: 2.7', 21 | 'Intended Audience :: Science/Research' 22 | ], 23 | license='MIT', 24 | install_requires=['numpy', 'matplotlib', 'scipy'], 25 | packages=find_packages(), 26 | zip_safe=False) 27 | 28 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | COPYRIGHT 2 | 3 | All contributions by Daniel C. Elton 4 | Copyright (c) 2015-2017, Daniel C. Elton. 5 | All rights reserved. 6 | 7 | LICENSE 8 | 9 | The MIT License (MIT) 10 | 11 | Permission is hereby granted, free of charge, to any person obtaining a copy 12 | of this software and associated documentation files (the "Software"), to deal 13 | in the Software without restriction, including without limitation the rights 14 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 15 | copies of the Software, and to permit persons to whom the Software is 16 | furnished to do so, subject to the following conditions: 17 | 18 | The above copyright notice and this permission notice shall be included in 19 | all copies or substantial portions of the Software. 20 | 21 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 22 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 23 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 24 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 25 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 26 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 27 | THE SOFTWARE. 28 | 29 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | [![license](https://img.shields.io/github/license/mashape/apistatus.svg)](https://pypi.python.org/pypi/spectrumfitter) 2 | [![PyPI version](https://badge.fury.io/py/spectrumfitter.svg)](https://badge.fury.io/py/spectrumfitter) 3 | 4 | # spectrumfitter 5 | 6 | The **spectrumfitter** package is an obect-oriented framework for fitting dielectric spectra. 7 | 8 | The following lineshapes are supported (bold text refers to the class name): 9 | * **Debye** - Debye dielectric relxation 10 | * **DHO** - Damped harmonic oscillator 11 | * **Gaussian()** - Gaussian function for imaginary part and corresponding real part. 12 | * **Constant()** - constant function for real part, 0 imaginary part. 13 | * **ColeCole()** - Cole-Cole dielectric relaxation 14 | * **VanVleck()** - Van Vleck & Weisskopf lineshape [*Rev. Mod. Phys.*, **17**:227 236, (1945)] 15 | * **BrendelDHO** - Brendel DHO [Ref: *J. Appl. Phys*. **71**, 1 (1992) ] 16 | * **PowerLawDebye()** - Debye lineshape with truncated power law wing. [*J. Phys. Chem. B* **109** (12), 6031 (2005)] 17 | * **StrExp** - Stretched exponential relaxation lineshape (a non-analytic function). 18 | 19 | 20 | Besides basic fitting it has several advanced features, such as: 21 | * Use the *f*-sum rule as a constraint 22 | * Use the generalized LST (gLST) relation as a constraint 23 | * Fit and plot the longitudinal dielectric function 24 | 25 | Example codes are shown in the `examples` directory. 26 | 27 | 28 | 29 | -------------------------------------------------------------------------------- /examples/example_fit_dielectric_spectrum.py: -------------------------------------------------------------------------------- 1 | __author__ = "Daniel C. Elton" 2 | __maintainer__ = "Daniel C. Elton" 3 | __copyright__ = "Copyright 2015, Daniel C. Elton" 4 | __license__ = "MIT" 5 | __status__ = "Development" 6 | 7 | from scipy import optimize 8 | from numpy import * 9 | from spectrumfitter.spectrumfitter import * 10 | from spectrumfitter.spectralmodel import * 11 | import pickle 12 | 13 | 14 | #---------------------------------------------------------------------------------- 15 | #---------- Load and convert index of refraction data ---------------------------- 16 | #---------------------------------------------------------------------------------- 17 | 18 | data = loadtxt(fname='water_full_Siegelstein.RI') 19 | 20 | max_freq_to_analyze = 1000 21 | 22 | maxw = len(data[data[:,0] < max_freq_to_analyze,0]) 23 | rawomegas = data[0:maxw,0] 24 | min_freq = min(rawomegas) 25 | mid_freq = 10 26 | omegas = concatenate((logspace(log10(min_freq),log10(mid_freq),150),linspace(mid_freq,max_freq_to_analyze,140))) 27 | 28 | n = data[0:maxw,1] 29 | k = data[0:maxw,2] 30 | 31 | rawrp = n**2 + k**2 32 | rawcp = 2*n*k 33 | 34 | rp = interp(omegas,rawomegas,rawrp) 35 | cp = interp(omegas,rawomegas,rawcp) 36 | 37 | 38 | 39 | ##---------------------------------------------------------------------------------- 40 | ##---------------------- Define fit function & parameters ------------------------- 41 | ##---------------------------------------------------------------------------------- 42 | 43 | modelT = SpectralModel() 44 | modelT.add(Debye([69, .55] ,[(65,73) ,(.3,.65) ],"Debye")) 45 | modelT.add(Debye([2, 2] ,[(.0001,10) ,(.5,10) ],"2nd Debye")) 46 | modelT.add(DHO([2,60 ,200] ,[(0,10) ,(10 ,100) ,(1 ,400) ],"H-bond bend")) 47 | #modelT.add(DHO([2,150,150] ,[(.1,4) ,(150 ,250) ,(10 ,900) ],"H-bond str.")) 48 | #modelT.add(BrendelDHO([1, 50, 10, 2],[(0,100 ),(1,75),(1,300),(.1,100)],"Brendel Hbond Bend")) 49 | #modelT.add(BrendelDHO([1, 165, 10,50],[(0,100 ),(75,200),(1,300),(1,100)],"Brendel Hbond Str")) 50 | modelT.add(BrendelDHO([.3,460,100,40],[(.01,100),(400,520),(1,500),(1,150)],"Brendel L1")) 51 | modelT.add(BrendelDHO([.3,650,100,40],[(.01,100),(520,750),(1,500),(1,150)],"Brendel L2")) 52 | #modelT.add(DHO([1,1600,100] ,[(.0001,.1),(1500,1700),(.1,500) ],"v2")) 53 | #modelT.add(DHO([1,2120,100],[(.0001,.01) ,(2000,2400) ,(10,600) ],"L+v2")) 54 | ##modelT.add(BrendelDHO([1.4,3500,200,20],[(.01,2),(3000,4500),(.1,500),(1,100) ],"Brendelv1+v3")) 55 | #modelT.add(DHO([1.4,3500,200],[(.01,2),(3000,4500),(.1,500)],"v1+v3")) 56 | modelT.add(constant([0] ,[(1,11)],"eps inf")) 57 | 58 | 59 | ##---------------------- Fitting the model ---------------------------------------- 60 | 61 | print("Fitting transverse model...") 62 | 63 | modelT.fit_model(omegas,rp,cp) 64 | 65 | ## Optional pickling of models (save models) 66 | #pickle.dump(modelT, open('modelT.pkl', 'wb')) 67 | #modelT = pickle.load(open('modelT.pkl', 'rb')) 68 | 69 | 70 | ##---------------------- Plotting the model ---------------------------------------- 71 | plot_model(modelT,omegas,rp,cp,4,.05,max_freq_to_analyze,title='Transverse') 72 | 73 | 74 | ##---------------------- Printing the parameters ----------------------------------- 75 | 76 | modelT.print_model() 77 | 78 | 79 | plt.show(block=True) 80 | -------------------------------------------------------------------------------- /spectrumfitter/spectralmodel.py: -------------------------------------------------------------------------------- 1 | from scipy import optimize 2 | from numpy import * 3 | import time 4 | 5 | class SpectralModel: 6 | """A spectralmodel object is simply a list of lineshape objects""" 7 | 8 | def __init__(self,lineshapes=[]): 9 | self.lineshapes = lineshapes 10 | self.numlineshapes = 0 11 | self.RMS_error = 0 12 | 13 | def add(self,lineshape): 14 | """add a new lineshape object to the spectral model's list of lineshapes""" 15 | self.lineshapes = self.lineshapes + [lineshape] 16 | self.numlineshapes += 1 17 | 18 | def setparams(self,params): 19 | """set parameters in the model from a list of parameters for all lineshapes""" 20 | i = 0 21 | for l in self.lineshapes: 22 | for j in range(len(l.p)): 23 | l.p[j] = params[i] 24 | i += 1 25 | 26 | def getparams(self): 27 | """get parameters for all the lineshapes in a model and return as list""" 28 | params = [] 29 | for lineshape in self.lineshapes: 30 | params = params + lineshape.p 31 | return params 32 | 33 | def getbounds(self): 34 | """get bounds for all the lineshapes in a model and return as list""" 35 | bounds = [] 36 | for lineshape in self.lineshapes: 37 | bounds = bounds + lineshape.bounds 38 | return bounds 39 | 40 | def getfreqs(self): 41 | """get frequencies for all the lineshapes in a model and return as list""" 42 | freqs = zeros(self.numlineshapes) 43 | for i in range(self.numlineshapes): 44 | #if lineshape.type != "Constant": 45 | print(i) 46 | freqs[i] = self.lineshapes[i].p[1] 47 | return freqs 48 | 49 | def fsum(self): 50 | """evaluate the f-sum rule (sum the oscillator strengths)""" 51 | fsum = 0 52 | for i in range(self.numlineshapes): 53 | if (self.lineshapes[i].p[0] == "BrendelDHO"): 54 | fsum = fsum + self.lineshapes[i].f 55 | else: 56 | fsum = fsum + self.lineshapes[i].p[0] 57 | return fsum 58 | 59 | def __call__(self,w): 60 | """compute real and complex parts of the spectral_model model at frequencies in array w 61 | 62 | args: 63 | w: an 1xN array with frequencies 64 | returns: 65 | (rp, cp) a list with rp and cp as 1xN arrays 66 | """ 67 | rp = zeros(len(w)) 68 | cp = zeros(len(w)) 69 | for lineshape in self.lineshapes: 70 | (rpPart, cpPart) = lineshape(w) 71 | rp = rp + rpPart 72 | cp = cp + cpPart 73 | return (rp,cp) 74 | 75 | def longeps(self,w): 76 | ''' computes the longitudinal dielectric function for the spectral_model model at frequencies in array w''' 77 | (rp, cp) = self(w) 78 | denom = rp**2 + cp**2 79 | return (rp/denom, cp/denom) 80 | 81 | def print_model(self): 82 | """Write out info about all of the parameters in the model """ 83 | for lineshape in self.lineshapes: 84 | lineshape.print_params() 85 | 86 | set_printoptions(precision=2) 87 | print( "") 88 | print( "f-sum of oscillator strengths = %6.2f" % self.fsum()) 89 | print( "") 90 | print( "RMS error = %6.3f" % self.RMS_error) 91 | 92 | def print_model_latex(self): 93 | """Write out info about all of the parameters in the model in LaTeX form""" 94 | print("\\begin{table}") 95 | print(" \\begin{tabular}{c c c c c c}") 96 | print("name & $f$ & $\\omega_0$ (cm$^{-1}$) & $\\tau$ (ps) & $\gamma$ (cm$^{-1}) $ & $\sigma$ (cm$^{-1}$) \\\\ ") 97 | print("\hline") 98 | for lineshape in self.lineshapes: 99 | lineshape.print_params_latex() 100 | print(" \\end{tabular}}") 101 | print("\\end{table}") 102 | 103 | def fit_model(self, dataX, datarp, datacp, differential_evolution=True, TNC=True, SLSQP=True, verbose=True): 104 | '''Fit the function using one or multiple optimization methods in serial''' 105 | 106 | def diffsq(params): 107 | self.setparams(params) 108 | 109 | (rp,cp) = self(dataX) 110 | 111 | diffrp = (datarp - rp)/datarp 112 | diffcp = (datacp - cp)/datacp 113 | 114 | #Ldatacp = datacp/(datarp**2 + datacp**2) 115 | #Lfitcp = cp/(rp**2 + cp**2) 116 | #diffLcp = (Ldatacp - Lfitcp)/Ldatacp 117 | 118 | return dot(diffcp, diffcp) + dot(diffrp, diffrp) #+ dot(diffLcp,diffLcp) 119 | 120 | def costfun(params): 121 | """Wrapper function neede for the optimization method 122 | 123 | Args: 124 | params: a list of parameters for the model 125 | Returns: 126 | The cost (real scalar) 127 | """ 128 | Error = diffsq(params) 129 | 130 | fsumpenalty = datarp[0] - self.fsum() 131 | 132 | return Error + fsumpenalty**2 133 | 134 | start_t = time.time() 135 | 136 | params = self.getparams() 137 | bounds = self.getbounds() 138 | 139 | if (differential_evolution == True): 140 | resultobject = optimize.differential_evolution(costfun,bounds,maxiter=2000) 141 | if (verbose == True): print("diff. evolv. number of iterations = ", resultobject.nit) 142 | 143 | if (TNC == True): 144 | resultobject = optimize.minimize(costfun, x0=params, bounds=bounds, method='TNC') 145 | if (verbose == True): print("TNC number of iterations = ", resultobject.nit) 146 | 147 | if (SLSQP == True): 148 | resultobject = optimize.minimize(costfun, x0=params, bounds=bounds, method='SLSQP') 149 | if (verbose == True): print("SLSQP number of iterations = ", resultobject.nit) 150 | 151 | #mybounds = MyBounds(bounds=array(bounds)) 152 | #ret = basinhopping(diffsq, params, niter=10,accept_test=mybounds) 153 | 154 | params = self.getparams() #get updated params 155 | 156 | end_t = time.time() 157 | m, s = divmod(end_t - start_t, 60) 158 | h, m = divmod(m, 60) 159 | print("Fit completed in %02d hr %02d min %02d sec" % (h, m, s)) 160 | 161 | self.RMS_error = sqrt(diffsq(params)/(2*len(dataX))) #Store RMS error -------------------------------------------------------------------------------- /examples/fit_Raman_IR_dielectric.py: -------------------------------------------------------------------------------- 1 | '''Example of how to use spectrum_fitter.py, to fit three spectra (Raman, transverse dielectric function, longitudinal dielectric function) and make a plot of all three''' 2 | __author__ = "Daniel C. Elton" 3 | __maintainer__ = "Daniel C. Elton" 4 | __copyright__ = "Copyright 2015, Daniel C. Elton" 5 | __license__ = "MIT" 6 | __status__ = "Development" 7 | 8 | from pylab import * 9 | from scipy import optimize 10 | from numpy import * 11 | from spectrumfitter.spectrumfitter import * 12 | from spectrumfitter.spectralmodel import * 13 | import pickle 14 | 15 | #---------------------- Load data ------------------------------------- 16 | eps_data = loadtxt(fname='water_full_Siegelstein.RI') 17 | 18 | Raman_data = loadtxt(fname='water_300K_Raman_Castner.dat') 19 | 20 | 21 | #----------------process dielectric data ------------------------------ 22 | max_freq = 1200 23 | maxw = len(eps_data[eps_data[:,0] < max_freq,0]) 24 | rawomegas = eps_data[0:maxw,0] 25 | min_freq = min(rawomegas) 26 | mid_freq = 18 27 | omegas = rawomegas #concatenate((logspace(log10(min_freq),log10(mid_freq),30),linspace(mid_freq,max_freq,80))) 28 | n = eps_data[0:maxw,1] 29 | k = eps_data[0:maxw,2] 30 | rawrp = n**2 + k**2 31 | rawcp = 2*n*k 32 | 33 | rp = rawrp #interp(omegas,rawomegas,rawrp) 34 | cp = rawcp #interp(omegas,rawomegas,rawcp) 35 | 36 | denom = rp**2 + cp**2 37 | (Lrp,Lcp) = (rp/denom, cp/denom) 38 | 39 | #----------------process Raman data ------------------------------------ 40 | maxw = len(Raman_data[Raman_data[:,0] < max_freq,0]) 41 | Raman_omegas = Raman_data[0:maxw,0] 42 | Raman = Raman_data[0:maxw,1]/5000 43 | 44 | 45 | ##------------ Define fit functions & parameters ----------------------- 46 | ##transverse model 47 | modelT = SpectralModel() 48 | modelT.add(Debye([71, .5] ,[(1,80) ,(.4,.8) ],"Debye")) 49 | #modelT.add(Debye([71, .5] ,[(1,80) ,(.4,.8) ],"Debye")) 50 | modelT.add(Debye([2, 6.44] ,[(.01,10) ,(1,15) ],"2nd Debye")) 51 | #modelT.add(StretchedExp([71, 8, 1] ,[(0,20000),(5,15), (0,1) ],"StretchedExp")) 52 | #modelT.add(StretchedExp([200, 6.44, .91],[(0,200000),(1,15), (0,1) ],"2nd StretchedExp")) 53 | #modelT.add(PowerLawDebye([71, .5, 1, 1.2],[(0,100),(.3,.7), (0,100), (1,2)],"PowLawDebye")) 54 | #modelT.add(BrendelDHO([1, 50, 10, 2],[(0,100 ),(1,75),(1,300),(.1,100)],"Brendel")) 55 | modelT.add(BrendelDHO([1, 165, 10,50],[(0,100 ),(75,200),(1,300),(1,100)],"Brendel")) 56 | #modelT.add(BrendelDHO([.3,460,100,50],[(.01,100),(400,520),(1,1000),(1,300)],"Brendel L2")) 57 | #modelT.add(BrendelDHO([.3,650,100,50],[(.01,100),(520,750),(1,1000),(1,300)],"Brendel L2")) 58 | modelT.add(DHO([.3,460,100],[(.01,100),(400,600),(1,1000)],"DHO L1")) 59 | modelT.add(DHO([.3,650,100],[(.01,100),(520,750),(1,1000)],"DHO L2")) 60 | #modelT.add(BrendelDHO([.3,680,244,50],[(.01,100),(650,720),(1,1000),(1,300)],"Brendel L3")) 61 | #modelT.add(Debye([2, 1] ,[(.01,4) ,(.5,15) ],"2nd Debye")) 62 | #modelT.add(Debye([2, 30] ,[(.01,4) ,(1,100) ],"3rd Debye")) 63 | #modelT.add(DHO([2,60 ,200] ,[(0,5) ,(10 ,100) ,(1 ,400) ],"H-bond bend")) 64 | #modelT.add(DHO([2,150,150] ,[(.1,4) ,(150 ,250) ,(10 ,900) ],"H-bond str.")) 65 | modelT.add(constant([2] ,[(1,11)],"eps inf")) 66 | 67 | ##longitudinal model 68 | modelL = SpectralModel() 69 | modelL.add(Debye([1 , 10 ] ,[(.001,1) , (.5 ,50)] ,"Debye")) 70 | modelL.add(Debye([.1 , 10 ] ,[(0,2) , (.5 ,50)] , "2nd Debye")) 71 | #modelL.add(DHO([2,60 ,60 ] ,[(0,5) ,(10 ,100) ,(1 ,400) ],"H-bond bend")) 72 | modelL.add(DHO([2 ,222,200] ,[(0,5) ,(100 ,300) ,(1 ,900) ],"H-bond str.")) 73 | modelL.add(DHO([.2,450,100] ,[(0,2) ,(380 ,600) ,(.1,400) ],"L1")) 74 | modelL.add(DHO([.1,660,244] ,[(0,2) ,(600,770) ,(1,1000)],"L2")) 75 | #modelL.add(BrendelDHO([.3,680,244,50],[(.01,100),(650,720),(1,1000),(1,300)],"Brendel L3")) 76 | modelL.add(constant([2] ,[(1,10)],"eps inf")) 77 | 78 | 79 | 80 | #Raman model 81 | modelR = SpectralModel() 82 | #modelR.add(DHO([.1,65,100] ,[(0,1) ,(10 ,100) ,(10 ,900) ],"H-bond bend")) 83 | #modelR.add(DHO([.1,150,100] ,[(0,1) ,(100 ,200) ,(10 ,900) ],"H-bond str.")) 84 | modelR.add(DHO([.1,433,250] ,[(0,.5),(300,500) ,(.1,400) ],"L1")) 85 | modelR.add(DHO([.04,660,250] ,[(0,.5),(400,750) ,(1,1000)],"L2")) 86 | modelR.add(DHO([.015,802,200] ,[(0,.5) ,(650,800) ,(1,1000)],"L3")) 87 | #modelR.add(constant([0] ,[(0,.4)],"eps inf")) 88 | 89 | 90 | print("Fitting transverse model...") 91 | modelT.fit_model(omegas,rp,cp) 92 | 93 | print("Fitting longitudinal model...") 94 | modelL.fit_model(omegas,Lrp,Lcp) 95 | 96 | print("Fitting Raman model...")# 97 | #modelR.fit_model(Raman_omegas,Raman,Raman) 98 | 99 | #Optional pickling of models (save models) 100 | #pickle.dump(modelL, open('modelL.pkl', 'wb')) 101 | #pickle.dump(modelT, open('modelT.pkl', 'wb')) 102 | #pickle.dump(modelR, open('modelR.pkl', 'wb')) 103 | 104 | 105 | #modelL = pickle.load(open('modelL.pkl', 'rb')) 106 | #modelT = pickle.load(open('modelT2Debye3Brendel.pkl', 'rb')) 107 | #modelT = pickle.load(open('2Debye2DHO3Libr3DHOT.pkl', 'rb')) 108 | 109 | #plot_model(modelT,omegas,rp,cp,1,xmin=min_freq,xmax=max_freq,xscale='log',yscale='log') 110 | #plot_model(modelT,omegas,rp,cp,2,xmin=2,xmax=max_freq,ymin=-.1,ymax=6,xscale='linear',yscale='linear') 111 | #plot_model(modelL,omegas,Lrp,Lcp,1,xmin=min_freq,xmax=max_freq,xscale='log',yscale='log') 112 | #plot_model(modelL,omegas,Lrp,Lcp,2,xmin=2,xmax=max_freq,ymin=-.1,ymax=6,xscale='linear',yscale='linear') 113 | 114 | #plot_model(modelR,Raman_omegas,Raman,Raman,1,xmin=min_freq,xmax=max_freq,xscale='log',yscale='log') 115 | #plot_model(modelR,Raman_omegas,Raman,Raman,2,xmin=2,xmax=max_freq,xscale='linear',yscale='linear') 116 | 117 | 118 | f, (ax1, ax2, ax3) = plt.subplots(3, sharex=True) 119 | 120 | (rpfit, cpfit) = modelT(omegas) 121 | ax1.plot(omegas,cp,'r',omegas,cpfit) 122 | for lineshape in modelT.lineshapes: 123 | (rpPart, cpPart) = lineshape(omegas) 124 | ax1.plot(omegas, cpPart ,'g') 125 | 126 | ax1.set_ylim([0,3]) 127 | 128 | ax2.plot(omegas,Lcp,'r',linewidth=3) 129 | for lineshape in modelL.lineshapes: 130 | (Lrp, Lcp) = lineshape(omegas) 131 | ax2.plot(omegas, Lcp ,'g') 132 | 133 | ax3.plot(Raman_omegas,Raman,'r',linewidth=3) 134 | for lineshape in modelR.lineshapes: 135 | (Rrp, Rcp) = lineshape(omegas) 136 | ax3.plot(omegas, Rcp ,'g') 137 | 138 | ax3.set_ylim([0,.4]) 139 | ax3.set_ylim([0,.4]) 140 | ax3.tick_params(axis='x',labelsize=20) 141 | 142 | plt.xlabel(r"$\omega$ (cm$^{-1}$)",fontsize=25) 143 | 144 | #ax1.text(500, 1.35, 'Transverse dielectric spectra',fontsize=17) 145 | #ax2.text(500, 1.35, 'Longitudinal dielectric spectra',fontsize=17) 146 | #ax3.text(500, 1.35, 'Raman spectra',fontsize=17) 147 | #plt.xlim([10,4000]) 148 | #plt.xlim([-.5,2]) 149 | 150 | modelL.print_model() 151 | modelT.print_model() 152 | #modelR.print_model() 153 | # 154 | 155 | set_printoptions(precision=2) 156 | print("") 157 | print("Eps(0) = ", rp[0]) 158 | 159 | 160 | show(block=True) 161 | 162 | 163 | 164 | 165 | -------------------------------------------------------------------------------- /examples/water_300K_Raman_Castner.dat: -------------------------------------------------------------------------------- 1 | 0 0 2 | 2.4397399 2643.9153 3 | 4.8794899 3891.738 4 | 7.3192301 4321.9575 5 | 9.7589798 4555.1689 6 | 12.1987 4742.7124 7 | 14.6385 4772.1191 8 | 17.078199 4862.354 9 | 19.518 4890.7266 10 | 21.957701 4880.3408 11 | 24.3974 5043.3687 12 | 26.8372 4946.8999 13 | 29.276899 5010.6973 14 | 31.7167 5128.895 15 | 34.156399 5077.5171 16 | 36.596199 5153.8008 17 | 39.0359 5071.2373 18 | 41.4757 5127.9819 19 | 43.915401 5119.6191 20 | 46.355202 5126.4565 21 | 48.794899 5196.6411 22 | 51.2346 5024.8628 23 | 53.6744 4949.6479 24 | 56.114101 5003.8052 25 | 58.553902 4943.958 26 | 60.993599 4769.3784 27 | 63.433399 4730.0708 28 | 65.8731 4648.4609 29 | 68.312897 4578.3423 30 | 70.752602 4443.4326 31 | 73.192398 4353.1509 32 | 75.632103 4332.9858 33 | 78.0718 4233.9253 34 | 80.511597 4189.4326 35 | 82.951302 4002.9639 36 | 85.391098 3984.7471 37 | 87.830803 3948.1672 38 | 90.270599 3880.4067 39 | 92.710297 3780.6675 40 | 95.150101 3679.4902 41 | 97.589798 3708.4807 42 | 100.03 3621.7986 43 | 102.469 3676.8638 44 | 104.909 3586.7563 45 | 107.349 3593.5273 46 | 109.789 3675.4199 47 | 112.228 3714.6196 48 | 114.668 3740.9771 49 | 117.108 3588.0459 50 | 119.548 3682.1094 51 | 121.987 3702.1396 52 | 124.427 3735.0593 53 | 126.867 3734.1389 54 | 129.306 3660.6226 55 | 131.746 3668.1118 56 | 134.186 3637.1064 57 | 136.62601 3675.3865 58 | 139.065 3578.3469 59 | 141.50475 3618.4648 60 | 143.9445 3651.8621 61 | 146.38425 3685.9729 62 | 148.82401 3757.98 63 | 151.26375 3735.2046 64 | 153.70351 3775.2764 65 | 156.14325 3793.9919 66 | 158.58299 3799.8938 67 | 161.02275 3848.1243 68 | 163.46249 3851.79 69 | 165.90225 3822.8723 70 | 168.342 3810.1877 71 | 170.78175 3812.1172 72 | 173.2215 3801.9736 73 | 175.66125 3766.9788 74 | 178.101 3728.0115 75 | 180.54076 3742.78 76 | 182.9805 3682.8086 77 | 185.42026 3607.9851 78 | 187.86 3610.0479 79 | 190.29974 3507.6934 80 | 192.7395 3454.5413 81 | 195.17924 3434.5474 82 | 197.619 3369.3379 83 | 200.05875 3296.6323 84 | 202.4985 3187.6663 85 | 204.93825 3177.9321 86 | 207.37801 3096.7214 87 | 209.81775 3000.3115 88 | 212.25751 2901.7444 89 | 214.69725 2866.4114 90 | 217.13699 2781.9058 91 | 219.57675 2755.2036 92 | 222.01649 2649.5996 93 | 224.45625 2536.3638 94 | 226.896 2541.5649 95 | 229.33575 2457.3413 96 | 231.7755 2431.5063 97 | 234.21526 2312.2769 98 | 236.655 2265.5913 99 | 239.09476 2170.9712 100 | 241.5345 2145.0623 101 | 243.97424 2043.3059 102 | 246.414 1965.0264 103 | 248.85374 1928.0684 104 | 251.2935 1842.3402 105 | 253.73325 1848.615 106 | 256.173 1779.1401 107 | 258.61276 1714.6067 108 | 261.05249 1680.7156 109 | 263.49225 1618.0144 110 | 265.93201 1530.1543 111 | 268.37177 1473.665 112 | 270.81149 1442.8539 113 | 273.25125 1452.3914 114 | 275.69101 1384.7565 115 | 278.13074 1318.6481 116 | 280.5705 1305.9337 117 | 283.01025 1272.4075 118 | 285.45001 1203.5414 119 | 287.88974 1205.9572 120 | 290.3295 1156.2142 121 | 292.76926 1131.1741 122 | 295.20901 1100.8076 123 | 297.64874 1025.6666 124 | 300.0885 1030.0381 125 | 302.52826 1003.0404 126 | 304.96799 984.17993 127 | 307.40775 973.99298 128 | 309.8475 953.11768 129 | 312.28726 939.01886 130 | 314.72699 926.50403 131 | 317.16675 893.47656 132 | 319.60651 879.23944 133 | 322.04626 863.26227 134 | 324.48599 870.14313 135 | 326.92575 861.61841 136 | 329.36551 835.55231 137 | 331.80524 857.7251 138 | 334.245 843.92944 139 | 336.68475 852.67175 140 | 339.12451 855.16455 141 | 341.56424 869.07349 142 | 344.004 831.0351 143 | 346.44376 884.94006 144 | 348.88351 840.97925 145 | 351.32324 842.42413 146 | 353.763 878.70172 147 | 356.20276 856.30359 148 | 358.64249 865.78729 149 | 361.08224 850.9035 150 | 363.522 839.29712 151 | 365.96176 868.57574 152 | 368.40149 857.70209 153 | 370.84125 910.45782 154 | 373.28101 939.67108 155 | 375.72076 918.14691 156 | 378.16049 893.36481 157 | 380.60025 897.73352 158 | 383.04001 874.83649 159 | 385.47974 891.30499 160 | 387.91949 925.51501 161 | 390.35925 926.09491 162 | 392.79901 927.70587 163 | 395.23874 925.36993 164 | 397.6785 941.71222 165 | 400.11826 942.16437 166 | 402.55801 956.51617 167 | 404.99774 945.52942 168 | 407.4375 949.78448 169 | 409.87726 983.51898 170 | 412.31699 959.20441 171 | 414.75674 977.19458 172 | 417.1965 962.52704 173 | 419.63626 950.04352 174 | 422.07599 981.48108 175 | 424.51575 1001.4193 176 | 426.95551 995.88397 177 | 429.39526 953.13867 178 | 431.83499 953.9516 179 | 434.27475 994.75934 180 | 436.71451 967.54047 181 | 439.15424 1006.888 182 | 441.59399 959.17676 183 | 444.03375 993.75488 184 | 446.47351 973.58258 185 | 448.91324 988.32404 186 | 451.353 947.65955 187 | 453.79276 937.49475 188 | 456.23251 920.3493 189 | 458.67224 953.46429 190 | 461.112 938.38568 191 | 463.55176 960.72174 192 | 465.99149 961.16638 193 | 468.43124 966.41217 194 | 470.871 940.23456 195 | 473.31076 942.24976 196 | 475.75049 937.7052 197 | 478.19025 967.86664 198 | 480.63 937.61993 199 | 483.06976 934.80194 200 | 485.50949 929.5144 201 | 487.94925 935.22064 202 | 490.38901 908.86151 203 | 492.82874 904.24133 204 | 495.26849 921.4201 205 | 497.70825 944.45038 206 | 500.14801 944.88202 207 | 502.58774 919.08392 208 | 505.0275 929.59747 209 | 507.46725 898.4165 210 | 509.90701 922.88269 211 | 512.34674 901.9278 212 | 514.7865 865.8313 213 | 517.22626 897.33575 214 | 519.66602 869.16577 215 | 522.10577 888.55743 216 | 524.54547 896.84564 217 | 526.98523 864.14117 218 | 529.42499 872.21759 219 | 531.86475 880.79248 220 | 534.3045 892.58356 221 | 536.74426 895.7937 222 | 539.18402 870.04388 223 | 541.62378 890.07025 224 | 544.06348 833.87408 225 | 546.50323 814.39734 226 | 548.94299 848.18909 227 | 551.38275 832.4903 228 | 553.82251 831.95874 229 | 556.26227 818.22943 230 | 558.70203 818.80573 231 | 561.14172 810.52686 232 | 563.58148 788.19507 233 | 566.02124 790.9873 234 | 568.461 803.38428 235 | 570.90076 812.95111 236 | 573.34052 854.7063 237 | 575.78027 806.10083 238 | 578.21997 808.75116 239 | 580.65973 806.7373 240 | 583.09949 803.93567 241 | 585.53925 790.16504 242 | 587.979 781.2005 243 | 590.41876 777.00873 244 | 592.85852 768.36145 245 | 595.29828 757.1853 246 | 597.73798 746.79608 247 | 600.17773 774.13708 248 | 602.61749 755.35199 249 | 605.05725 779.46826 250 | 607.49701 782.19019 251 | 609.93677 717.00549 252 | 612.37653 706.31189 253 | 614.81622 716.14899 254 | 617.25598 694.62213 255 | 619.69574 705.5415 256 | 622.1355 709.67999 257 | 624.57526 670.74493 258 | 627.01501 688.55237 259 | 629.45477 678.28149 260 | 631.89447 690.7796 261 | 634.33423 698.86182 262 | 636.77399 717.20502 263 | 639.21375 703.74408 264 | 641.6535 691.77856 265 | 644.09326 661.6582 266 | 646.53302 669.39801 267 | 648.97278 679.9054 268 | 651.41248 694.44965 269 | 653.85223 662.26611 270 | 656.29199 665.3548 271 | 658.73175 650.07983 272 | 661.17151 629.24469 273 | 663.61127 646.50574 274 | 666.05103 641.81769 275 | 668.49072 672.49017 276 | 670.93048 615.78094 277 | 673.37024 627.00146 278 | 675.81 661.36426 279 | 678.24976 614.10938 280 | 680.68951 590.50446 281 | 683.12927 573.82062 282 | 685.56897 616.8504 283 | 688.00873 634.23608 284 | 690.44849 595.3623 285 | 692.88824 596.70923 286 | 695.328 550.02332 287 | 697.76776 589.76245 288 | 700.20752 571.35876 289 | 702.64728 584.75305 290 | 705.08698 550.78687 291 | 707.52673 591.12091 292 | 709.96649 568.66663 293 | 712.40625 544.71582 294 | 714.84601 552.49371 295 | 717.28577 516.71887 296 | 719.72552 536.34943 297 | 722.16522 539.48883 298 | 724.60498 547.86163 299 | 727.04474 520.90759 300 | 729.4845 546.14307 301 | 731.92426 536.26251 302 | 734.36401 496.89282 303 | 736.80377 484.40591 304 | 739.24353 514.27679 305 | 741.68323 511.04221 306 | 744.12299 500.94025 307 | 746.56274 464.02896 308 | 749.0025 477.16568 309 | 751.44226 459.41101 310 | 753.88202 441.70703 311 | 756.32178 469.42853 312 | 758.76147 448.46786 313 | 761.20123 485.56638 314 | 763.64099 478.492 315 | 766.08075 448.26303 316 | 768.52051 456.05902 317 | 770.96027 443.72766 318 | 773.40002 464.50211 319 | 775.83972 458.17407 320 | 778.27948 428.3663 321 | 780.71924 423.00388 322 | 783.159 431.45233 323 | 785.59875 458.13132 324 | 788.03851 404.3743 325 | 790.47827 399.28 326 | 792.91803 398.8765 327 | 795.35773 384.58328 328 | 797.79749 394.30078 329 | 800.23724 388.03738 330 | 802.677 361.92819 331 | 805.11676 368.0791 332 | 807.55652 377.80704 333 | 809.99628 353.25082 334 | 812.43597 327.84375 335 | 814.87573 366.82477 336 | 817.31549 352.85254 337 | 819.75525 375.43393 338 | 822.19501 367.08157 339 | 824.63477 354.67609 340 | 827.07452 350.92636 341 | 829.51422 341.26532 342 | 831.95398 332.61304 343 | 834.39374 339.40497 344 | 836.8335 324.13583 345 | 839.27325 327.20706 346 | 841.71301 297.99313 347 | 844.15277 346.17331 348 | 846.59253 301.32697 349 | 849.03223 269.25217 350 | 851.47198 283.04132 351 | 853.91174 313.4682 352 | 856.3515 283.28793 353 | 858.79126 269.51938 354 | 861.23102 264.71301 355 | 863.67078 247.79533 356 | 866.11047 249.94948 357 | 868.55023 255.84656 358 | 870.98999 219.22159 359 | 873.42975 227.11346 360 | 875.86951 201.10995 361 | 878.30927 209.24367 362 | 880.74902 197.98595 363 | 883.18872 204.05627 364 | 885.62848 198.99686 365 | 888.06824 188.16719 366 | 890.508 182.08627 367 | 892.94775 179.89217 368 | 895.38751 184.69533 369 | 897.82727 170.75401 370 | 900.26703 169.80052 371 | 902.70673 184.34039 372 | 905.14648 180.20096 373 | 907.58624 147.88029 374 | 910.026 144.90862 375 | 912.46576 152.19884 376 | 914.90552 142.9668 377 | 917.34528 146.47462 378 | 919.78497 103.17086 379 | 922.22473 109.40102 380 | 924.66449 96.902397 381 | 927.10425 119.56731 382 | 929.54401 98.107162 383 | 931.98376 115.88628 384 | 934.42352 91.293846 385 | 936.86322 94.749397 386 | 939.30298 84.632835 387 | 941.74274 75.468025 388 | 944.1825 71.949165 389 | 946.62225 66.660248 390 | 949.06201 71.05928 391 | 951.50177 72.820633 392 | 953.94153 71.097717 393 | 956.38123 83.795227 394 | 958.82098 67.791306 395 | 961.26074 61.693558 396 | 963.7005 48.041595 397 | 966.14026 53.427692 398 | 968.58002 47.256069 399 | 971.01978 48.854496 400 | 973.45947 53.351479 401 | 975.89923 49.448917 402 | 978.33899 49.420837 403 | 980.77875 51.634781 404 | 983.21851 40.868858 405 | 985.65826 42.850887 406 | 988.09802 22.354353 407 | 990.53772 11.363684 408 | 992.97748 34.676594 409 | 995.41724 -2.1641662 410 | 997.85699 13.41503 411 | 1000.2968 36.966915 412 | 1002.7365 22.063696 413 | 1005.1763 -3.002161 414 | 1007.616 -4.1497684 415 | 1010.0557 21.002785 416 | 1012.4955 14.075428 417 | 1014.9352 6.6108804 418 | 1017.375 5.7113872 419 | 1019.8148 0.80384946 420 | 1022.2545 52.076641 421 | 1024.6942 8.4141235 422 | 1027.134 20.251209 423 | 1029.5737 16.307886 424 | 1032.0135 7.0675249 425 | 1034.4532 25.14929 426 | 1036.8929 9.7398109 427 | 1039.3328 20.487761 428 | 1041.7725 9.6631327 429 | 1044.2123 5.2258015 430 | 1046.652 11.16807 431 | 1049.0918 2.5918784 432 | 1051.5315 29.864304 433 | 1053.9712 -23.122156 434 | 1056.411 1.3877649 435 | 1058.8507 4.1793408 436 | 1061.2905 5.531651 437 | 1063.7302 23.975309 438 | 1066.17 11.84899 439 | 1068.6097 -8.8742924 440 | 1071.0496 28.187889 441 | 1073.4893 1.3482991 442 | 1075.929 1.4734721 443 | 1078.3688 30.731573 444 | 1080.8085 19.463207 445 | 1083.2483 2.496429 446 | 1085.688 9.4053698 447 | 1088.1278 6.2196307 448 | 1090.5675 -15.989283 449 | 1093.0072 -6.0596738 450 | 1095.447 -8.5016403 451 | 1097.8867 -12.238309 452 | 1100.3265 7.451057 453 | 1102.7662 -12.476918 454 | 1105.2061 -1.5000143 455 | 1107.6458 6.3135796 456 | 1110.0854 10.481856 457 | 1112.5253 -12.85174 458 | 1114.965 -13.373502 459 | 1117.4048 -0.34413302 460 | 1119.8445 5.4199195 461 | 1122.2843 -1.8225113 462 | 1124.724 12.222508 463 | 1127.1637 0.42644513 464 | 1129.6035 -3.2090051 465 | 1132.0432 12.141301 466 | 1134.483 3.7536004 467 | 1136.9227 18.320671 468 | 1139.3625 10.752419 469 | 1141.8022 16.881002 470 | 1144.2419 13.466524 471 | 1146.6818 6.3184595 472 | 1149.1215 -24.552118 473 | 1151.5613 -12.063139 474 | 1154.001 6.6630168 475 | 1156.4408 20.142649 476 | 1158.8805 6.8540921 477 | 1161.3202 -28.821178 478 | 1163.76 -35.337326 479 | 1166.1997 -38.098766 480 | 1168.6395 -16.01845 481 | 1171.0792 -4.3596239 482 | 1173.519 1.9881104 483 | 1175.9587 -0.49536726 484 | 1178.3986 -0.58810753 485 | 1180.8383 4.0052252 486 | 1183.278 -2.3914094 487 | 1185.7178 -8.3783484 488 | 1188.1575 -8.2953768 489 | 1190.5973 -18.451151 490 | 1193.037 9.3338804 491 | 1195.4768 -2.1432805 492 | 1197.9165 -9.8731041 493 | 1200.3562 -2.8465831 494 | 1202.796 -14.114304 495 | -------------------------------------------------------------------------------- /examples/water_300.RI: -------------------------------------------------------------------------------- 1 | 1821000000 78 6.49 2 | 2000000000 77.9 7.57 3 | 2200000000 77.5 8.22 4 | 2610000000 76.9 9.77 5 | 2628000000 77.1 9.86 6 | 2800000000 76.6 10.6 7 | 3417000000 76.4 12.9 8 | 3623000000 75.8 13.4 9 | 3733000000 75.3 14.5 10 | 3750000000 75.6 13.7 11 | 3922000000 75.7 14.3 12 | 5300000000 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51 | 16140000000 48.2 35.5 52 | 16600000000 47 35.9 53 | 17170000000 45.4 36.1 54 | 17380000000 45.5 36.4 55 | 17430000000 45.6 36.1 56 | 18020000000 44.4 36.7 57 | 18480000000 42.7 36.6 58 | 19020000000 41.7 36.2 59 | 21010000000 38 36.3 60 | 23530000000 34.4 35.8 61 | 24450000000 32.8 35.2 62 | 26430000000 31.1 34.8 63 | 26640000000 30.8 34.6 64 | 26700000000 31 34.6 65 | 26790000000 30 34.3 66 | 26830000000 31 34.9 67 | 27610000000 29.9 34.1 68 | 28130000000 29.4 34.1 69 | 28580000000 29.2 33.9 70 | 36560000000 21.4 30.1 71 | 36840000000 21.3 30 72 | 37810000000 21.1 29.6 73 | 37970000000 20.8 29.5 74 | 39620000000 20.6 29.1 75 | 52250000000 15.3 23.9 76 | 57780000000 11.5 22.5 77 | 205000000000 6 8.16 78 | 234000000000 6 7.34 79 | 264000000000 5 6.43 80 | 293000000000 5 5.54 81 | 322000000000 5 5.05 82 | 351000000000 5 4.72 83 | 381000000000 5 4.28 84 | 410000000000 5 3.97 85 | 1000000000000000 1.819801 -0.000000043168 86 | 923076923076923 1.811716 -0.0000000290736 87 | 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1.76624099999991 -0.000000778794 108 | 342857142857143 1.76358399999985 -0.000001038496 109 | 333333333333333 1.76358399999976 -0.000001290816 110 | 324324324324324 1.76358399999888 -0.00000281536 111 | 315789473684210 1.76092899999142 -0.00000777622 112 | 307692307692308 1.76092899998789 -0.00000923592 113 | 300000000000000 1.76092899999165 -0.00000767006 114 | 250000000000000 1.75297599990219 -0.00002618872 115 | 214285714285714 1.745040980956 -0.000364596 116 | 187500000000000 1.73448899268975 -0.000225207 117 | 166666666666667 1.721343986775 -0.00030176 118 | 150000000000000 1.70563479 -0.0028732 119 | 136363636363636 1.679615916479 -0.000749088 120 | 125000000000000 1.635840086064 -0.002445448 121 | 115384615384615 1.5425539511 -0.00787428 122 | 113207547169811 1.48591611 -0.0163346 123 | 111111111111111 1.410983 -0.045144 124 | 109090909090909 1.335168 -0.136526 125 | 107142857142857 1.290939 -0.26266 126 | 105263157894737 1.285976 -0.42513 127 | 103448275862069 1.370577 -0.643736 128 | 101694915254237 1.58046 -0.770032 129 | 100000000000000 1.805657 -0.745824 130 | 98360655737704.9 1.975876 -0.68448 131 | 96774193548387.1 2.115225 -0.563328 132 | 95238095238095.2 2.181064 -0.40041 133 | 93750000000000 2.17594624 -0.2731344 134 | 92307692307692.3 2.148368 -0.178974 135 | 90909090909090.9 2.10114576 -0.10672 136 | 89552238805970.1 2.04994279 -0.0747504 137 | 88235294117647.1 2.01601975 -0.05538 138 | 86956521739130.4 1.98792576 -0.037224 139 | 85714285714285.7 1.95991164 -0.02632 140 | 83333333333333.3 1.9181984775 -0.0142655 141 | 81081081081081.1 1.88786304 -0.0098928 142 | 78947368421052.6 1.86048444 -0.0092752 143 | 76923076923076.9 1.84143456 -0.0103132 144 | 75000000000000 1.82517984 -0.0124292 145 | 73170731707317.1 1.8116844156 -0.01512904 146 | 71428571428571.4 1.8009166656 -0.01846592 147 | 69767441860465.1 1.7901725975 -0.0226122 148 | 68181818181818.2 1.77944991 -0.0274804 149 | 66666666666666.7 1.77404444 -0.0356976 150 | 65217391304347.8 1.76868391 -0.039102 151 | 63829787234042.6 1.76865351 -0.041762 152 | 62500000000000 1.768675 -0.0399 153 | 61224489795918.4 1.76339631 -0.0363872 154 | 60000000000000 1.75547124 -0.03286 155 | 58823529411764.7 1.74756079 -0.0293484 156 | 57692307692307.7 1.73438699 -0.0266034 157 | 56603773584905.7 1.72124796 -0.0257152 158 | 55555555555555.6 1.70291891 -0.026883 159 | 54545454545454.6 1.68466944 -0.0301136 160 | 53571428571428.6 1.66131936 -0.0366076 161 | 52631578947368.4 1.63031691 -0.0518462 162 | 51724137931034.5 1.591555 -0.083292 163 | 50847457627118.6 1.55363516 -0.1552512 164 | 50000000000000 1.588776 -0.27071 165 | 49180327868852.5 1.7226 -0.345578 166 | 48387096774193.6 1.850025 -0.239888 167 | 47619047619047.6 1.8382 -0.154698 168 | 46875000000000 1.81239299 -0.1209606 169 | 46153846153846.2 1.79138436 -0.1049776 170 | 45454545454545.5 1.77828864 -0.0949808 171 | 44776119402985.1 1.76510531 -0.0895746 172 | 44117647058823.5 1.75190671 -0.0865896 173 | 43478260869565.2 1.74400416 -0.0850724 174 | 42857142857142.9 1.733465 -0.084288 175 | 42253521126760.6 1.725572 -0.084096 176 | 41666666666666.7 1.72031359 -0.0842304 177 | 41095890410958.9 1.71244416 -0.0842996 178 | 40540540540540.5 1.70719924 -0.0846936 179 | 40000000000000 1.69935324 -0.0850208 180 | 39473684210526.3 1.69412816 -0.0854112 181 | 38961038961039 1.68630539 -0.0859938 182 | 38461538461538.5 1.68108675 -0.086899 183 | 37974683544303.8 1.67328679 -0.0877332 184 | 37500000000000 1.66550451 -0.0885626 185 | 36585365853658.5 1.65256399 -0.0902772 186 | 35714285714285.7 1.63965779 -0.0924882 187 | 34883720930232.6 1.62424116 -0.09486 188 | 34090909090909.1 1.60887875 -0.097713 189 | 33333333333333.3 1.59105199 -0.1007076 190 | 32608695652173.9 1.57330275 -0.104165 191 | 31914893617021.3 1.55313411 -0.1079902 192 | 31250000000000 1.53305984 -0.1125012 193 | 30612244897959.2 1.50814659 -0.1177382 194 | 30000000000000 1.48094336 -0.1237488 195 | 28571428571428.6 1.39984256 -0.156894 196 | 27272727272727.3 1.32003876 -0.2232208 197 | 26086956521739.1 1.247712 -0.319784 198 | 25000000000000 1.19472 -0.442178 199 | 24000000000000 1.194048 -0.581714 200 | 23076923076923.1 1.220291 -0.69906 201 | 22222222222222.2 1.26768 -0.807422 202 | 21428571428571.4 1.3272 -0.8954 203 | 20689655172413.8 1.389537 -0.963016 204 | 20000000000000 1.451296 -1.02108 205 | 19354838709677.4 1.510813 -1.073916 206 | 18750000000000 1.577541 -1.1183 207 | 18181818181818.2 1.642017 -1.156456 208 | 17647058823529.4 1.709335 -1.180608 209 | 17142857142857.1 1.77876 -1.202058 210 | 16666666666666.7 1.843453 -1.212396 211 | 16216216216216.2 1.905008 -1.215006 212 | 15789473684210.5 1.963125 -1.209708 213 | 15384615384615.4 2.01536 -1.192608 214 | 15000000000000 2.035951 -1.16328 215 | 14285714285714.3 2.065245 -1.136068 216 | 13636363636363.6 2.110871 -1.119 217 | 13043478260869.6 2.148432 -1.109074 218 | 12500000000000 2.18312 -1.098162 219 | 12000000000000 2.217225 -1.090072 220 | 11538461538461.5 2.246021 -1.0773 221 | 11111111111111.1 2.268689 -1.06296 222 | 10714285714285.7 2.285157 -1.047124 223 | 10344827586206.9 2.294712 -1.032966 224 | 10000000000000 2.298017 -1.017456 225 | 9375000000000 2.28514 -1.001808 226 | 8823529411764.71 2.251055 -1.010688 227 | 8333333333333.33 2.21408 -1.047522 228 | 7894736842105.26 2.186163 -1.098884 229 | 7500000000000 2.159136 -1.16963 230 | 7142857142857.14 2.149203 -1.244996 231 | 6818181818181.82 2.150804 -1.33416 232 | 6521739130434.78 2.161237 -1.423884 233 | 6250000000000 2.179881 -1.51768 234 | 6000000000000 2.254373 -1.631436 235 | 5000000000000 2.55564 -1.999322 236 | 4285714285714.29 2.984265 -2.097792 237 | 3750000000000 3.257787 -2.063284 238 | 3333333333333.33 3.41448 -2.062528 239 | 3000000000000 3.546825 -2.082248 240 | 2727272727272.73 3.583195 -2.087892 241 | 2500000000000 3.73934 -2.108208 242 | 2307692307692.31 3.8811 -2.093008 243 | 2142857142857.14 3.977136 -2.056 244 | 2000000000000 4.035736 -2.04831 245 | 1875000000000 4.084545 -2.064352 246 | 1764705882352.94 4.137827 -2.081436 247 | 1666666666666.67 4.190448 -2.102786 248 | 1578947368421.05 4.23916 -2.123238 249 | 1500000000000 4.282884 -2.14704 250 | 1.72523E+11 7.33 8.5 251 | 2.29931E+11 5.92 6.32 252 | 2.87339E+11 5.42 5.42 253 | 3.44747E+11 5.19 4.76 254 | 4.59862E+11 4.9 3.72 255 | 5.74678E+11 4.65 3.23 256 | 6.89793E+11 4.53 2.88 257 | 8.6112E+11 4.27 2.52 258 | 1.03454E+12 4.06 2.26 259 | 1.20796E+12 3.98 2.11 260 | 1.495E+12 3.9 1.91 261 | 1.794E+12 3.81 1.75 262 | 2.093E+12 3.7 1.66 263 | 2.392E+12 3.66 1.64 264 | 2.691E+12 3.59 1.61 265 | 2.99E+12 3.53 1.69 266 | 3.289E+12 3.43 1.77 267 | 3.887E+12 3.2 1.88 268 | 4.485E+12 3 1.89 269 | 5.083E+12 2.68 1.81 270 | 5.681E+12 2.44 1.65 271 | 6.279E+12 2.29 1.44 272 | 6.877E+12 2.21 1.22 273 | 7.475E+12 2.22 1.05 274 | 8.073E+12 2.25 0.94 275 | 8.671E+12 2.29 0.887 276 | 9.269E+12 2.36 0.872 277 | 9.867E+12 2.39 0.874 278 | 1.0465E+13 2.38 0.92 279 | 1.1063E+13 2.37 0.972 280 | 1.1661E+13 2.33 1.02 281 | 1.2259E+13 2.29 1.06 282 | 1.2857E+13 2.24 1.1 283 | 1.3455E+13 2.14 1.13 -------------------------------------------------------------------------------- /spectrumfitter/spectrumfitter.py: -------------------------------------------------------------------------------- 1 | 2 | 3 | ''' Spectrum_fitter.py : an obect-oriented framework for fitting dielectric spectra. ''' 4 | from numpy import * 5 | import matplotlib.pyplot as plt 6 | from scipy import optimize 7 | from scipy import special as sp 8 | 9 | class Lineshape: 10 | """Class that holds some things common to all Lineshapes""" 11 | def __init__(self,params,bounds,name): 12 | self.p = params 13 | self.bounds = bounds 14 | self.name = name 15 | 16 | class Debye(Lineshape): 17 | """Debye lineshape object. 18 | Note: the wD parameter is assumed to be in units of cm^-1 19 | """ 20 | def __init__(self,params=[1,1],bounds=[(-float('inf'),+float('inf')),(-float('inf'),+float('inf'))],name="Debye"): 21 | Lineshape.__init__(self, params, bounds, name) 22 | self.pnames = ["f", "wD"] 23 | self.type = "Debye" 24 | 25 | def __call__(self, w): 26 | rp = self.p[0]*self.p[1]**2/(self.p[1]**2 + w**2) 27 | cp = rp*w/self.p[1] 28 | return (rp, cp) 29 | 30 | def get_freq(self): 31 | return self.p[1] 32 | 33 | def get_abs_freq(self): 34 | return self.p[1] 35 | 36 | def print_params(self): 37 | print(u"%20s f =%7.5f \u03C9 = %6.2f 1/cm (%5.2f ps)" % (self.name, self.p[0], self.p[1], 33.34/(2*3.14159*self.p[1]))) 38 | 39 | def print_params_latex(self): 40 | print(u"%20s & %7.5f & %6.2f & %5.2f & & \\\\" % (self.name, self.p[0], self.p[1], 33.333/(2*3.14159*self.p[1]))) 41 | 42 | 43 | class DHO(Lineshape): 44 | """Damped harmonic oscillator object""" 45 | def __init__(self,params=[1,1,1],bounds=[(-float('inf'),+float('inf')),(-float('inf'),+float('inf'))],name="DHO"): 46 | Lineshape.__init__(self, params, bounds, name) 47 | self.pnames = ["f", "w", "gamma"] 48 | self.type = "DHO" 49 | 50 | def __call__(self, w): 51 | denom = (self.p[1]**2 - w**2)**2 + w**2*self.p[2]**2 52 | rp = self.p[0]*(self.p[1]**2)*(self.p[1]**2 - w**2)/denom 53 | cp = self.p[0]*(self.p[1]**2)*self.p[2]*w/denom 54 | return (rp, cp) 55 | 56 | def get_freq(self): 57 | return self.p[1] 58 | 59 | def get_abs_freq(self): 60 | return sqrt( self.p[1]**2 + self.p[2]**2 ) 61 | 62 | def print_params(self): 63 | print(u"%20s f =%7.5f \u03C9 = %6.2f + %6.2f i (%6.3f ps)" % (self.name, self.p[0], self.p[1], self.p[2], 33.34/(2*3.141*self.p[1]))) 64 | 65 | def print_params_latex(self): 66 | print(u"%20s & %7.5f & %6.2f & %6.3f & %6.2f & \\\\" % (self.name, self.p[0], self.p[1], 33.34/(2*3.141*self.p[1]), self.p[2] )) 67 | 68 | 69 | class BrendelDHO(Lineshape): 70 | """"Brendel model for amorphous materials - Gaussian distribution of DHOs. Ref: J. Appl. Phys. 71, 1 (1992)""" 71 | def __init__(self,params=[1,1,1,1],bounds=[(0,+float('inf')),(0,+float('inf')),(0,+float('inf')),(0,+float('inf'))],name="BrendelDHO"): 72 | Lineshape.__init__(self, params, bounds, name) 73 | self.pnames = ["wp**2/w0**2", "wT", "gamma","sigma"] 74 | self.type = "BrendelDHO" 75 | self.f = 0 76 | 77 | def __call__(self, w): 78 | sigma = self.p[3] 79 | x0 = self.p[1] 80 | g = self.p[2] 81 | a = sqrt(w**2 - 1j*g*w) 82 | a = a.real - 1j*a.imag #we want the imaginary part to the root to be positive 83 | prefac = 1j*sqrt(3.14149)*self.p[0]*x0**2/(sqrt(22)*sigma) 84 | eps = prefac*exp(-.5)*(1/a)*( sp.erfcx(-1j*(a-x0)/sigma) + sp.erfcx(-1j*(a+x0)/sigma) ) 85 | #self.f = 2*prefac*exp(-x0**2/(2*sigma**2))*(1 + sp.erf(1j*x0/sigma)) 86 | self.f = eps.real[1] 87 | return (eps.real, eps.imag) 88 | 89 | def get_freq(self): 90 | return self.p[1] 91 | 92 | def get_abs_freq(self): 93 | return sqrt( self.p[1]**2 + self.p[2]**2 ) 94 | 95 | def print_params(self): 96 | print( u"%20s f =%7.5f \u03C9 = %6.2f + %6.2f i (%5.3f ps) \u03C3 = %6.2f cm^-1" % (self.name, self.p[0], self.p[1], self.p[2], 33.34/self.p[1], self.p[3])) 97 | 98 | def print_params_latex(self): 99 | print( u"%20s & %7.5f & %6.2f & %5.3f & %6.2f & %6.2f \\\\" % (self.name, self.p[0], self.p[1], 33.34/self.p[1], self.p[2], self.p[3])) 100 | 101 | class DistributionOfDebye(Lineshape): 102 | '''Under construction''' 103 | 104 | def __init__(self,params=[1,1],bounds=[(0,+float('inf')),(0,+float('inf'))],name="BrendelDHO"): 105 | Lineshape.__init__(self, params, bounds, name) 106 | #self.pnames = ["wp**2/w0**2", "wT", "gamma","sigma"] 107 | #self.type = "BrendelDHO" 108 | #self.f = 0 109 | #self.num_tau_pts=10000 110 | ##self.min_tau= 111 | ##self.max_tau= 112 | 113 | #tau_values = logspace(min_tau, max_tau, num_tau_pts) 114 | 115 | #def __call__(self, w): 116 | 117 | #for m in xrange(1,num_tau_pts+1): 118 | #gtau(m)*tau 119 | 120 | #def TikhonovRegularization(self): 121 | #der1 = gradient(gdist) 122 | #der2 = gradient(der1) 123 | #return linalg.norm(der2)**2 124 | 125 | class StretchedExp(Lineshape): 126 | """Stretched Exponential lineshape """ 127 | def __init__(self,params=[1,1,1],bounds=[(0,10000),(0,10000),(0,1)],name="Str exp"): 128 | Lineshape.__init__(self, params, bounds, name) 129 | self.pnames = ["f", "tau", "beta"] 130 | self.type = "StretchedExp" 131 | 132 | def __call__(self, w): 133 | (f, eps_omega) = self.calc_eps(w) 134 | rp = interp(w,f,real(eps_omega)) 135 | cp = interp(w,f,imag(eps_omega)) 136 | return (rp, cp) 137 | 138 | def calc_eps(self,w): 139 | deltaeps = self.p[0] 140 | tau = self.p[1] 141 | beta = self.p[2] 142 | timestep = 1/(2*3.141*max(w)) #timestep in ps 143 | maxt = 3*tau #length of corr function 144 | npts = int(maxt/timestep) 145 | times = array(range(0,npts))*timestep 146 | corr_fun = exp(-(times/tau)**beta) 147 | nextpow2 = int(2**ceil(log2(npts))) 148 | f = (1/(2.99*.01))*array(range(0,npts))/(timestep*nextpow2) #Frequencies (evenly spaced), inverse cm 149 | tderiv = -diff(corr_fun)/timestep #time derivative of corr fun 150 | eps_omega = deltaeps*ifft(tderiv,nextpow2) #inverse one-sided fourier 151 | return (f, eps_omega[0:npts]) 152 | 153 | def get_freq(self): 154 | return self.p[1] 155 | 156 | def get_abs_freq(self): 157 | return sqrt( self.p[1]**2 + self.p[2]**2 ) 158 | 159 | def print_params(self): 160 | print( u"%20s f =%7.5f \u03C9 %6.2f 1/cm (%5.2f ps) \u03B2 = %6.2f" % (self.name, self.p[0], self.p[1], 33.34/(self.p[1]), self.p[2] )) 161 | 162 | 163 | class PowerLawDebye(Lineshape): 164 | """Debye lineshape with additional "power law" wing. 165 | See J. Phys. Chem. B, 2005, 109 (12), pp 6031-6035 166 | 167 | Note: the wD parameter is assumed to be in units of cm^-1 168 | """ 169 | def __init__(self,params=[1,1],bounds=[(0,+float('inf')),(0,+float('inf')),(0,+float('inf')),(1,10)],name="unnamed"): 170 | Lineshape.__init__(self, params, bounds, name) 171 | self.pnames = ["f", "wD","A","q"] 172 | self.type = "PowerLawDebye" 173 | self.convfac = 1.0#/(2*3.141*2.99*.01) 174 | 175 | def __call__(self, w): 176 | A = self.p[2] 177 | q = self.p[3] 178 | tau = self.convfac/self.p[1] 179 | numomegas = len(w) 180 | start = numomegas - len(w[w[:] > self.p[1]]) 181 | HighFreqOmegas = w#0.0*array(w) 182 | #HighFreqOmegas[start:numomegas] = w[start:numomegas] 183 | TheWing = 1 + A*(HighFreqOmegas*tau)**q 184 | rp = TheWing*self.p[0]/(1 + (tau*w)**2) 185 | cp = TheWing*self.p[0]*w*tau/(1 + (tau*w)**2) 186 | return (rp, cp) 187 | 188 | def get_freq(self): 189 | return self.p[1] 190 | 191 | def get_abs_freq(self): 192 | return self.p[1] 193 | 194 | def print_params(self): 195 | print(u"%20s f =%7.5f \u03C9 %6.2f 1/cm (%5.2f ps) A = %6.2f q = %6.2f" % (self.name, self.p[0], self.p[1], 33.34/self.p[1], self.p[2], self.p[3] )) 196 | 197 | class ColeCole(Lineshape): 198 | """Cole-Cole lineshape object. 199 | 200 | Note: the wD parameter is assumed to be in units of cm^-1 201 | """ 202 | def __init__(self,params=[1,1,1],bounds=[(0,+float('inf')),(0,+float('inf')),(0,2)],name="unnamed"): 203 | Lineshape.__init__(self, params, bounds, name) 204 | self.pnames = ["f", "wD","alpha"] 205 | self.type = "Debye" 206 | 207 | def __call__(self, w): 208 | rp = self.p[0]*self.p[1]**2/(self.p[1]**2 + w**2) 209 | cp = rp*w/self.p[1] 210 | return (rp, cp) 211 | 212 | def get_freq(self): 213 | return self.p[1] 214 | 215 | def get_abs_freq(self): 216 | return self.p[1] 217 | 218 | def print_params(self): 219 | print( u"%20s f =%7.5f \u03C9 %6.2f 1/cm (%5.2f ps) \u03B1 %6.2f" % (self.name, self.p[0], self.p[1], 33.34/self.p[1], self.p[2] )) 220 | 221 | class VanVleck(Lineshape): 222 | """Van Vleck and Weisskopf lineshape Rev. Mod. Phys., 17:227 236, Apr 1945.""" 223 | def __init__(self,params=[1,1,1],bounds=[(-float('inf'),+float('inf')),(-float('inf'),+float('inf'))],name="VanVleck"): 224 | Lineshape.__init__(self, params, bounds, name) 225 | self.pnames = ["f", "wT","gamma"] 226 | self.type = "VanVleck" 227 | 228 | #the real part has not been tested or checked to see if it is mathematically correct!!! 229 | def __call__(self, w): 230 | rp = .5*self.p[0]*(self.p[1]**2 + self.p[2]**2)( 1/((self.p[1] - w)**2 + self.p[2]**2) + 1.00/((self.p[1] + w)**2 + self.p[2]**2) ) 231 | cp = .5*self.p[0]*self.p[2]*w*( 1/((self.p[1] - w)**2 + self.p[2]**2) + 1.00/((self.p[1] + w)**2 + self.p[2]**2) ) 232 | return (rp, cp) 233 | 234 | def get_freq(self): 235 | return self.p[1] 236 | 237 | def get_abs_freq(self): 238 | return sqrt( self.p[1]**2 + self.p[2]**2 ) 239 | 240 | def print_params(self): 241 | print( u"%20s f =%7.5f \u03C9= %6.2f + %6.2f i %6.3f ps" % (self.name, self.p[0], self.p[1], self.p[2], 33.34/(2*3.141*self.p[2])) ) 242 | 243 | 244 | class Gaussian(Lineshape): 245 | """Gaussian peak in the imaginary part, ie. inertial absorption or homogenous broadening""" 246 | def __init__(self,params=[1,1,1],bounds=[(-float('inf'),+float('inf')),(-float('inf'),+float('inf'))],name="Gaussian"): 247 | Lineshape.__init__(self, params, bounds, name) 248 | self.pnames = ["f", "wT","gamma"] 249 | self.type = "BRO" 250 | 251 | def __call__(self, w): 252 | # sp.dawsn 253 | rp = .5*self.p[0]*(self.p[1]**2 + self.p[2]**2)( 1/((self.p[1] - w)**2 + self.p[2]**2) + 1.00/((self.p[1] + w)**2 + self.p[2]**2) ) 254 | cp = .5*self.p[0]*self.p[2]*w*( 1/((self.p[1] - w)**2 + self.p[2]**2) + 1.00/((self.p[1] + w)**2 + self.p[2]**2) ) 255 | return (rp, cp) 256 | 257 | def get_freq(self): 258 | return self.p[1] 259 | 260 | def get_abs_freq(self): 261 | return sqrt( self.p[1]**2 + self.p[2]**2 ) 262 | 263 | def print_params(self): 264 | print( u"%20s f =%7.5f \u03C9= %6.2f + %6.2f i %6.3f" % (self.name, self.p[0], self.p[1], self.p[2], 33.34/(2*3.141*self.p[2]))) 265 | 266 | 267 | class constant(Lineshape): 268 | """this "lineshape" object is merely a constant term""" 269 | def __init__(self,params=[1],bounds=[(0,100)],name="constant"): 270 | Lineshape.__init__(self, params, bounds, name) 271 | self.pnames = ["Eps float('inf')."] 272 | self.type = "Constant" 273 | 274 | def __call__(self,w): 275 | rp = 0*w + self.p[0] 276 | cp = 0*w 277 | return (rp, cp) 278 | 279 | def print_params(self): 280 | print("%20s f =%7.5f" % (self.name, self.p[0])) 281 | 282 | def print_params_latex(self): 283 | print("%20s & %7.5f & & & & \\\\" % (self.name, self.p[0])) 284 | 285 | #----------------------------------------------------------------------------------------------------------- 286 | def fit_model_gLST_constraint(modelL, modelT, dataX, Tdatarp, Tdatacp): 287 | ''' fit both the transverse and longitudinal models at the same time with the gLST constraint ''' 288 | 289 | Ldatarp = 1.0 - Tdatarp/(Tdatarp**2 + Tdatacp**2) 290 | Ldatacp = Tdatacp/(Tdatarp**2 + Tdatacp**2) 291 | 292 | def diffsq(paramsL, paramsT): 293 | 294 | modelL.setparams(paramsL) 295 | modelT.setparams(paramsT) 296 | 297 | (Lrp, Lcp) = modelL(dataX) 298 | (Trp, Tcp) = modelT(dataX) 299 | 300 | Ldiff = (Ldatarp - Lrp)/Ldatarp + (Ldatacp - Lcp)/Ldatacp 301 | Tdiff = (Tdatarp - Trp)/Tdatarp + (Tdatacp - Tcp)/Tdatacp 302 | 303 | err = dot(Tdiff, Tdiff) + dot(Ldiff, Ldiff) 304 | 305 | return err 306 | 307 | def costfun(params): 308 | """Wrapper function needed for differential_evolution() 309 | 310 | Args: 311 | params: a list of parameters for the model 312 | Returns: 313 | The cost function 314 | """ 315 | 316 | paramsL = params[0:len(params)//2] 317 | paramsT = params[len(params)//2:] 318 | 319 | eps0 = Tdatarp[0] 320 | eps_inf = Tdatarp[-1] 321 | 322 | fsumpenalty = ( ( eps0 - modelT.fsum())/Tdatarp[0] )**2 323 | 324 | gLST_RHS = eps0/eps_inf 325 | 326 | gLSTpenalty = ( gLST_LHS(modelL, modelT) - gLST_RHS )**2 327 | 328 | #print(diffsq(paramsL, paramsT) , gLSTpenalty , 100*fsumpenalty) 329 | 330 | return diffsq(paramsL, paramsT) + 100*fsumpenalty + gLSTpenalty 331 | 332 | Lparams = modelL.getparams() 333 | Tparams = modelT.getparams() 334 | 335 | params = Lparams + Tparams 336 | 337 | boundsL = modelL.getbounds() 338 | boundsT = modelT.getbounds() 339 | 340 | bounds = boundsL + boundsT 341 | 342 | assert len(boundsL) == len(boundsT) 343 | assert len(params) == len(bounds) 344 | 345 | resultobject = optimize.minimize(costfun, x0=params, bounds=bounds, method='TNC') 346 | print("number of iterations = ", resultobject.nit) 347 | 348 | resultobject = optimize.minimize(costfun, x0=params, bounds=bounds, method='SLSQP') 349 | print("number of iterations = ", resultobject.nit) 350 | 351 | 352 | #optimize.fmin_l_bfgs_b(costfun, bounds=bounds) 353 | #optimize.differential_evolution(costfun, bounds) 354 | 355 | Lparams = modelL.getparams() 356 | Tparams = modelT.getparams() 357 | 358 | print("RMS error = ",sqrt(diffsq(Lparams, Tparams))) 359 | 360 | #---------------------------------------------------------------------------------------------------- 361 | def print_gLST_ratios(modelL, modelT): 362 | '''try to print out the ratios for different modes. Note this may not be very accurate as the ordering of modes in the longitudinal and transverse model 363 | may not be the same''' 364 | 365 | ratios = ones(modelL.numlineshapes) 366 | 367 | if (modelL.numlineshapes == modelT.numlineshapes): 368 | 369 | for i in range(modelL.numlineshapes): 370 | if modelL.lineshapes[i].type == "Debye": 371 | ratios[i] = modelL.lineshapes[i].p[1]/modelT.lineshapes[i].p[1] 372 | 373 | if (modelL.lineshapes[i].type == "DHO") or (modelL.lineshapes[i].type == "VanVleck") or (modelL.lineshapes[i].type == "BrendelDHO"): 374 | ratios[i] = (modelL.lineshapes[i].p[1]**2 + modelL.lineshapes[i].p[2]**2)/modelT.lineshapes[i].p[1]**2 375 | 376 | set_printoptions(precision=2) 377 | print("LST Ratios = ", ratios) 378 | print("Prod of ratios =", prod(ratios)) 379 | else: 380 | print("Can't compute gLST ratios, number of lineshapes in transverse not equal to number in longitudinal") 381 | 382 | #---------------------------------------------------------------------------------------------------- 383 | def gLST_LHS(modelL,modelT): 384 | '''calculate the left hand side of the GLST equation''' 385 | 386 | numerator = ones(modelL.numlineshapes) 387 | denominator = ones(modelT.numlineshapes) 388 | 389 | for i in range(modelL.numlineshapes): 390 | if modelL.lineshapes[i].type == "Debye": 391 | numerator[i] = modelL.lineshapes[i].p[1] 392 | 393 | if (modelL.lineshapes[i].type == "DHO") or (modelL.lineshapes[i].type == "VanVleck") or (modelL.lineshapes[i].type == "BrendelDHO"): 394 | numerator[i] = (modelL.lineshapes[i].p[1]**2 + modelL.lineshapes[i].p[2]**2) 395 | 396 | for i in range(modelT.numlineshapes): 397 | if modelT.lineshapes[i].type == "Debye": 398 | denominator[i] = modelT.lineshapes[i].p[1] 399 | 400 | if (modelT.lineshapes[i].type == "DHO") or (modelT.lineshapes[i].type == "VanVleck") or (modelT.lineshapes[i].type == "BrendelDHO"): 401 | denominator[i] = modelT.lineshapes[i].p[1]**2 402 | 403 | return prod(numerator)/prod(denominator) 404 | 405 | 406 | ##---------------------------------------------------------------------------------- 407 | ##----- Printout all frequencies in system and left side of gLST equation -------- 408 | ##---------------------------------------------------------------------------------- 409 | def print_gLST_LHS_stuff(modelL, modelT, Tdatarp, Tdatacp): 410 | 411 | print("longitudinal model:") 412 | modelL.print_model() 413 | print("transverse model:") 414 | modelT.print_model() 415 | 416 | print_gLST_ratios(modelL, modelT) 417 | 418 | eps0 = Tdatarp[0] 419 | eps_inf = Tdatarp[-1] 420 | gLST_RHS = eps0/eps_inf 421 | 422 | print("LST LHS = %6.2f" % gLST_LHS(modelL,modelT)) 423 | print("LST RHS = %6.2f" % gLST_RHS) 424 | 425 | 426 | #------------------------------------------------------------------------------------------------------------- 427 | def plot_model(model,dataX,dataYrp,dataYcp,Myhandle,xmin=None,xmax=None,xscale='linear',yscale='log',ymin=None,ymax=None,show=False,Block=True,longitudinal=False,title='',peaks=[]): 428 | """displays a pretty plot of the real and complex parts of the model and data using matplotlib 429 | 430 | args: 431 | model: a spectral_model object 432 | dataX: a numpy array giving the experimental x-data 433 | dataYrp: a numpy array giving the real part of the experimental y-data 434 | dataYcp: a numpy array giving the complex part of the experimental y-data 435 | handle: an integer giving the plot window number 436 | xmin: scalar, minimum frequency to plot 437 | xmax: scalar, maximum frequency to plot 438 | xscale: string, xscale type 'linear' or 'log' 439 | yscale: string, yscale type 'linear' or 'log' 440 | show: logical, option to display plot 441 | blockoption: logical, option to block further processing after displaying window (Default True, False is experimental) 442 | """ 443 | if (xmin == None): 444 | xmin = min(dataX) 445 | if (xmax == None): 446 | xmax = max(dataX) 447 | if (ymin == None): 448 | ymin = min(dataYrp)/600 449 | if (ymax == None): 450 | ymax = max(dataYrp) 451 | if (xscale == 'log'): 452 | plotomegas = logspace(log10(xmin), log10(xmax), 10000) 453 | else: 454 | plotomegas = linspace(xmin, xmax, 10000) 455 | 456 | #if (longitudinal == True): 457 | # (rp, cp) = model.longeps(plotomegas) 458 | # denom = dataYrp**2 + dataYcp**2 459 | # (dataYrp,dataYcp) = (dataYrp/denom, dataYcp/denom) 460 | # (xmin,xmax) = (min(dataX),max(dataX)) 461 | # (ymin,ymax) = (min(dataYrp),max(dataYrp)) 462 | #else: 463 | (rp, cp) = model(plotomegas) 464 | 465 | # Two subplots, unpack the axes array immediately 466 | f, (ax1, ax2) = plt.subplots(nrows=2, sharex=True, sharey=False ) 467 | 468 | ax1.plot(dataX, dataYrp, "g", plotomegas, rp,'b') 469 | #ax1.set_title('Real part') 470 | 471 | ax2.plot(dataX, dataYcp, "g", plotomegas, cp,'b') 472 | #ax2.set_title('Complex part') 473 | 474 | #plot all of the components 475 | for lineshape in model.lineshapes: 476 | (rpPart, cpPart) = lineshape(plotomegas) 477 | ax1.plot(plotomegas, rpPart ,'b--',linewidth=1) 478 | ax2.plot(plotomegas, cpPart ,'b--',linewidth=1) 479 | 480 | ax1.set_xscale(xscale) 481 | ax1.set_xlim([xmin,xmax]) 482 | ax1.set_yscale(yscale) 483 | ax1.set_ylim([ymin,ymax]) 484 | 485 | ax2.set_xscale(xscale) 486 | ax2.set_xlim([xmin,xmax]) 487 | ax2.set_yscale(yscale) 488 | ax2.set_ylim([ymin,ymax]) 489 | 490 | ax1.set_xlabel(r"$\omega$ (cm$^{-1}$)") 491 | ax2.set_xlabel(r"$\omega$ (cm$^{-1}$)") 492 | 493 | 494 | if (longitudinal == True): 495 | ax1.set_ylabel(r"Re$\lbrace\frac{1}{\varepsilon(\omega)}\rbrace$") 496 | ax2.set_ylabel(r"Im$\lbrace\frac{1}{\varepsilon(\omega)}\rbrace$") 497 | else: 498 | ax1.set_ylabel(r"Re$\lbrace\varepsilon(\omega)\rbrace$") 499 | ax2.set_ylabel(r"Im$\lbrace\varepsilon(\omega)\rbrace$") 500 | 501 | ax1.set_title(title) 502 | 503 | 504 | 505 | #ax.annotate('local max', xy=(3, 1), xycoords='data') 506 | 507 | 508 | #----------------------------------------------------------------------- 509 | # Function to find the maxima of a dataset by looking where the sign of the slope changes 510 | #----------------------------------------------------------------------- 511 | def find_peaks(dataset,omegas): 512 | #Smooth dataset 513 | smoothing_length = 5 514 | dataset = np.convolve(dataset, np.ones(smoothing_length)/smoothing_length) 515 | 516 | # lowess = sm.nonparametric.lowess(dataset, omegas, frac=0.5) 517 | #dataset = lowess[:,1] 518 | 519 | npoints = len(dataset) 520 | data_shift = np.r_[0, dataset] 521 | diff = data_shift[0:npoints] - dataset 522 | peaks = [] 523 | npoints = len(omegas) -1 524 | for i in range(0, npoints): 525 | if np.sign(diff[i]) != np.sign(diff[i+1]): 526 | #check if in useful range 527 | if ( 580 <= omegas[i] <= 1000 ) | ( 3000 <= omegas[i] <= 3500 ): #(1500 <= omegas[i] <= 1700) 528 | peaks = peaks + [(omegas[i] + omegas[i+1])/2] 529 | return peaks 530 | -------------------------------------------------------------------------------- /examples/water_full_Siegelstein.RI: -------------------------------------------------------------------------------- 1 | 0.001000 8.848600 0.006931 2 | 0.001009 8.848600 0.007011 3 | 0.001021 8.848600 0.007060 4 | 0.001030 8.848600 0.007142 5 | 0.001042 8.848600 0.007208 6 | 0.001052 8.848600 0.007291 7 | 0.001064 8.848600 0.007359 8 | 0.001076 8.848599 0.007444 9 | 0.001086 8.848599 0.007530 10 | 0.001099 8.848599 0.007600 11 | 0.001112 8.848599 0.007688 12 | 0.001125 8.848599 0.007759 13 | 0.001138 8.848599 0.007849 14 | 0.001148 8.848599 0.007958 15 | 0.001164 8.848599 0.008031 16 | 0.001178 8.848598 0.008124 17 | 0.001191 8.848598 0.008218 18 | 0.001205 8.848598 0.008333 19 | 0.001219 8.848598 0.008429 20 | 0.001236 8.848598 0.008527 21 | 0.001250 8.848598 0.008626 22 | 0.001265 8.848598 0.008746 23 | 0.001282 8.848597 0.008847 24 | 0.001300 8.848597 0.008949 25 | 0.001315 8.848597 0.009095 26 | 0.001334 8.848597 0.009200 27 | 0.001352 8.848596 0.009328 28 | 0.001371 8.848596 0.009458 29 | 0.001390 8.848596 0.009567 30 | 0.001409 8.848596 0.009700 31 | 0.001429 8.848595 0.009858 32 | 0.001449 8.848595 0.009995 33 | 0.001469 8.848595 0.010160 34 | 0.001493 8.848594 0.010300 35 | 0.001514 8.848594 0.010440 36 | 0.001538 8.848594 0.010610 37 | 0.001563 8.848593 0.010760 38 | 0.001589 8.848593 0.010910 39 | 0.001614 8.848592 0.011110 40 | 0.001641 8.848592 0.011290 41 | 0.001667 8.848591 0.011480 42 | 0.001694 8.848591 0.011660 43 | 0.001726 8.848590 0.011850 44 | 0.001754 8.848589 0.012070 45 | 0.001786 8.848589 0.012270 46 | 0.001820 8.848588 0.012500 47 | 0.001854 8.848587 0.012730 48 | 0.001888 8.848586 0.012970 49 | 0.001923 8.848585 0.013210 50 | 0.001959 8.848585 0.013480 51 | 0.002000 8.848584 0.013730 52 | 0.002042 8.848582 0.013990 53 | 0.002085 8.848581 0.014280 54 | 0.002128 8.848580 0.014580 55 | 0.002172 8.848579 0.014920 56 | 0.002223 8.848577 0.015230 57 | 0.002275 8.848576 0.015590 58 | 0.002328 8.848574 0.015910 59 | 0.002382 8.848572 0.016320 60 | 0.002438 8.848570 0.016700 61 | 0.002501 8.848568 0.017130 62 | 0.002565 8.848566 0.017570 63 | 0.002630 8.848563 0.018020 64 | 0.002704 8.848560 0.018480 65 | 0.002780 8.848557 0.019000 66 | 0.002858 8.848554 0.019530 67 | 0.002945 8.848550 0.020080 68 | 0.003027 8.848546 0.020740 69 | 0.003126 8.848541 0.021320 70 | 0.003229 8.848536 0.022020 71 | 0.003334 8.848531 0.022740 72 | 0.003452 8.848524 0.023480 73 | 0.003573 8.848518 0.024370 74 | 0.003706 8.848510 0.025220 75 | 0.003846 8.848501 0.026230 76 | 0.004000 8.848491 0.027210 77 | 0.004168 8.848480 0.028370 78 | 0.004346 8.848467 0.029570 79 | 0.004550 8.848452 0.030890 80 | 0.004764 8.848435 0.032340 81 | 0.005000 8.848415 0.033950 82 | 0.005260 8.848392 0.035710 83 | 0.005559 8.848364 0.037650 84 | 0.005889 8.848330 0.039790 85 | 0.006250 8.848291 0.042340 86 | 0.006667 8.848243 0.045060 87 | 0.007143 8.848183 0.048280 88 | 0.007692 8.848109 0.051970 89 | 0.008340 8.848013 0.056210 90 | 0.009099 8.847889 0.061210 91 | 0.010000 8.847727 0.067270 92 | 0.010093 8.847710 0.068040 93 | 0.010209 8.847688 0.068520 94 | 0.010304 8.847671 0.069310 95 | 0.010423 8.847648 0.069950 96 | 0.010520 8.847630 0.070760 97 | 0.010642 8.847606 0.071420 98 | 0.010764 8.847582 0.072240 99 | 0.010865 8.847563 0.073080 100 | 0.010990 8.847537 0.073750 101 | 0.011117 8.847512 0.074610 102 | 0.011246 8.847485 0.075470 103 | 0.011377 8.847459 0.076170 104 | 0.011481 8.847437 0.077230 105 | 0.011641 8.847403 0.077950 106 | 0.011776 8.847374 0.078850 107 | 0.011912 8.847344 0.079760 108 | 0.012050 8.847314 0.080870 109 | 0.012189 8.847283 0.081810 110 | 0.012359 8.847244 0.082750 111 | 0.012503 8.847212 0.083910 112 | 0.012647 8.847178 0.084880 113 | 0.012824 8.847137 0.085860 114 | 0.013002 8.847094 0.087050 115 | 0.013153 8.847058 0.088270 116 | 0.013335 8.847013 0.089290 117 | 0.013521 8.846967 0.090530 118 | 0.013708 8.846920 0.091790 119 | 0.013900 8.846871 0.092850 120 | 0.014092 8.846821 0.094360 121 | 0.014290 8.846769 0.095670 122 | 0.014489 8.846716 0.097000 123 | 0.014689 8.846662 0.098580 124 | 0.014928 8.846596 0.099950 125 | 0.015135 8.846538 0.101300 126 | 0.015382 8.846468 0.103000 127 | 0.015632 8.846396 0.104400 128 | 0.015886 8.846321 0.106100 129 | 0.016145 8.846244 0.107600 130 | 0.016407 8.846164 0.109300 131 | 0.016672 8.846082 0.111400 132 | 0.016943 8.845997 0.113200 133 | 0.017259 8.845896 0.115000 134 | 0.017538 8.845804 0.117200 135 | 0.017864 8.845696 0.119100 136 | 0.018198 8.845583 0.121300 137 | 0.018536 8.845467 0.123300 138 | 0.018879 8.845345 0.125800 139 | 0.019231 8.845220 0.128200 140 | 0.019589 8.845089 0.130900 141 | 0.020000 8.844936 0.133300 142 | 0.020416 8.844776 0.135800 143 | 0.020846 8.844609 0.138600 144 | 0.021281 8.844436 0.141500 145 | 0.021725 8.844254 0.144800 146 | 0.022232 8.844044 0.147800 147 | 0.022753 8.843823 0.150900 148 | 0.023283 8.843591 0.154500 149 | 0.023821 8.843349 0.158000 150 | 0.024378 8.843095 0.162100 151 | 0.025006 8.842801 0.165900 152 | 0.025648 8.842491 0.170100 153 | 0.026302 8.842166 0.174500 154 | 0.027042 8.841790 0.179000 155 | 0.027801 8.841394 0.184000 156 | 0.028580 8.840974 0.189100 157 | 0.029446 8.840491 0.194400 158 | 0.030266 8.840020 0.200800 159 | 0.031260 8.839434 0.206400 160 | 0.032289 8.838809 0.213200 161 | 0.033344 8.838141 0.220200 162 | 0.034518 8.837375 0.227400 163 | 0.035727 8.836475 0.235600 164 | 0.037064 8.835449 0.244100 165 | 0.038462 8.834348 0.253500 166 | 0.040000 8.833091 0.263400 167 | 0.041684 8.831656 0.274100 168 | 0.043459 8.830103 0.286000 169 | 0.045496 8.828230 0.298300 170 | 0.047642 8.826184 0.312300 171 | 0.050000 8.823834 0.327700 172 | 0.052604 8.821129 0.344800 173 | 0.055586 8.817867 0.363000 174 | 0.058893 8.814082 0.383700 175 | 0.062500 8.809677 0.407300 176 | 0.066667 8.804337 0.433700 177 | 0.071429 8.797836 0.463600 178 | 0.076923 8.788091 0.498300 179 | 0.083403 8.776133 0.538000 180 | 0.090992 8.761392 0.584500 181 | 0.100000 8.743107 0.640900 182 | 0.101020 8.741029 0.647100 183 | 0.102051 8.738919 0.653400 184 | 0.103082 8.736776 0.659800 185 | 0.104156 8.734549 0.666300 186 | 0.105274 8.732236 0.673000 187 | 0.106394 8.729884 0.679800 188 | 0.107527 8.727494 0.686700 189 | 0.108696 8.725011 0.693800 190 | 0.109902 8.722432 0.700900 191 | 0.111123 8.719808 0.708300 192 | 0.112360 8.717139 0.715900 193 | 0.113636 8.714366 0.723600 194 | 0.114943 8.711486 0.731400 195 | 0.116279 8.708553 0.739400 196 | 0.117647 8.705507 0.747600 197 | 0.119048 8.702404 0.756000 198 | 0.120482 8.699181 0.764500 199 | 0.121951 8.695941 0.773300 200 | 0.123457 8.692637 0.782200 201 | 0.125000 8.689204 0.791400 202 | 0.126582 8.685638 0.800700 203 | 0.128205 8.681999 0.810400 204 | 0.129870 8.678217 0.820100 205 | 0.131579 8.674287 0.830200 206 | 0.133316 8.670273 0.840600 207 | 0.135153 8.666029 0.850900 208 | 0.136986 8.661691 0.861800 209 | 0.138908 8.657181 0.872800 210 | 0.140825 8.652568 0.884500 211 | 0.142857 8.647693 0.896000 212 | 0.144949 8.642623 0.907800 213 | 0.147059 8.637431 0.920200 214 | 0.149254 8.632030 0.932800 215 | 0.151538 8.626323 0.945600 216 | 0.153846 8.620473 0.958900 217 | 0.156250 8.614382 0.972700 218 | 0.158755 8.607948 0.986700 219 | 0.161290 8.601342 1.001000 220 | 0.163934 8.594362 1.016000 221 | 0.166639 8.587191 1.031000 222 | 0.169463 8.579613 1.047000 223 | 0.172414 8.571605 1.063000 224 | 0.175439 8.563363 1.080000 225 | 0.178571 8.554652 1.097000 226 | 0.181818 8.545560 1.115000 227 | 0.185185 8.535947 1.133000 228 | 0.188679 8.526995 1.152000 229 | 0.192308 8.517490 1.171000 230 | 0.196078 8.507814 1.191000 231 | 0.200000 8.497290 1.212000 232 | 0.204082 8.486470 1.233000 233 | 0.208333 8.474673 1.256000 234 | 0.212766 8.462521 1.278000 235 | 0.217391 8.449912 1.302000 236 | 0.222222 8.435660 1.327000 237 | 0.227273 8.420858 1.352000 238 | 0.232558 8.405156 1.378000 239 | 0.238095 8.389151 1.405000 240 | 0.243902 8.371979 1.434000 241 | 0.250000 8.352700 1.463000 242 | 0.256410 8.332788 1.493000 243 | 0.263158 8.311297 1.525000 244 | 0.270270 8.288448 1.557000 245 | 0.277778 8.264599 1.591000 246 | 0.285714 8.238281 1.627000 247 | 0.294118 8.209818 1.663000 248 | 0.303030 8.179843 1.701000 249 | 0.312500 8.147128 1.741000 250 | 0.322581 8.112180 1.781000 251 | 0.333333 8.074469 1.824000 252 | 0.344828 8.033791 1.868000 253 | 0.357143 7.989355 1.914000 254 | 0.370370 7.941322 1.961000 255 | 0.384615 7.889643 2.011000 256 | 0.400000 7.831158 2.064000 257 | 0.416667 7.768902 2.113000 258 | 0.434783 7.701126 2.170000 259 | 0.454545 7.625553 2.224000 260 | 0.476190 7.544423 2.280000 261 | 0.500000 7.455943 2.338000 262 | 0.526316 7.358822 2.397000 263 | 0.555556 7.252419 2.461000 264 | 0.588235 7.135674 2.519000 265 | 0.625000 7.007965 2.576000 266 | 0.666667 6.867192 2.630000 267 | 0.714286 6.711149 2.685000 268 | 0.769231 6.538143 2.733000 269 | 0.833333 6.346035 2.773000 270 | 0.909091 6.131865 2.807000 271 | 1.000000 5.879378 2.830000 272 | 1.010101 5.853423 2.828000 273 | 1.020408 5.827179 2.831000 274 | 1.030928 5.800631 2.835000 275 | 1.041667 5.773802 2.832000 276 | 1.052632 5.746661 2.835000 277 | 1.063830 5.719272 2.831000 278 | 1.075269 5.691521 2.833000 279 | 1.086957 5.663535 2.835000 280 | 1.098901 5.635201 2.830000 281 | 1.111111 5.606586 2.832000 282 | 1.123596 5.577699 2.833000 283 | 1.136364 5.548489 2.833000 284 | 1.149425 5.519027 2.827000 285 | 1.162791 5.489262 2.827000 286 | 1.176471 5.459208 2.826000 287 | 1.190476 5.428878 2.825000 288 | 1.204819 5.398286 2.824000 289 | 1.219512 5.367389 2.816000 290 | 1.234568 5.336323 2.814000 291 | 1.250000 5.304929 2.811000 292 | 1.265823 5.273172 2.808000 293 | 1.282051 5.241539 2.805000 294 | 1.298701 5.209531 2.801000 295 | 1.315789 5.177179 2.796000 296 | 1.333156 5.146161 2.792000 297 | 1.351534 5.116001 2.786000 298 | 1.369863 5.083439 2.787000 299 | 1.389082 5.047771 2.780000 300 | 1.408252 5.013994 2.774000 301 | 1.428571 4.979800 2.766000 302 | 1.449485 4.946351 2.758000 303 | 1.470588 4.915201 2.750000 304 | 1.492537 4.881015 2.747000 305 | 1.515381 4.844068 2.737000 306 | 1.538462 4.811400 2.727000 307 | 1.562500 4.776470 2.723000 308 | 1.587554 4.740422 2.711000 309 | 1.612903 4.704528 2.705000 310 | 1.639344 4.667698 2.692000 311 | 1.666389 4.631138 2.685000 312 | 1.694628 4.593558 2.671000 313 | 1.724138 4.555811 2.662000 314 | 1.754386 4.518750 2.647000 315 | 1.785714 4.482558 2.636000 316 | 1.818182 4.442443 2.625000 317 | 1.851852 4.403706 2.607000 318 | 1.886792 4.367201 2.595000 319 | 1.923077 4.328263 2.581000 320 | 1.960784 4.288766 2.567000 321 | 2.000000 4.248425 2.551000 322 | 2.040816 4.207585 2.535000 323 | 2.083333 4.166540 2.518000 324 | 2.127660 4.125763 2.500000 325 | 2.173913 4.084851 2.481000 326 | 2.222222 4.045111 2.460000 327 | 2.272727 4.003601 2.445000 328 | 2.325581 3.960586 2.423000 329 | 2.380952 3.917021 2.404000 330 | 2.439024 3.873564 2.380000 331 | 2.500000 3.829496 2.360000 332 | 2.564103 3.785136 2.333000 333 | 2.631579 3.741930 2.310000 334 | 2.702703 3.695213 2.286000 335 | 2.777778 3.650102 2.255000 336 | 2.857143 3.607096 2.228000 337 | 2.941176 3.563346 2.199000 338 | 3.030303 3.516889 2.174000 339 | 3.125000 3.468221 2.142000 340 | 3.225806 3.422465 2.110000 341 | 3.333333 3.374610 2.079000 342 | 3.448276 3.326631 2.043000 343 | 3.571429 3.279470 2.009000 344 | 3.703704 3.228984 1.973000 345 | 3.846154 3.179887 1.931000 346 | 4.000000 3.133464 1.891000 347 | 4.166667 3.084049 1.853000 348 | 4.347826 3.032401 1.809000 349 | 4.545455 2.983258 1.763000 350 | 4.761905 2.933900 1.718000 351 | 5.000000 2.881863 1.670000 352 | 5.263158 2.831974 1.617000 353 | 5.555556 2.781861 1.567000 354 | 5.882353 2.729264 1.511000 355 | 6.250000 2.679108 1.452000 356 | 6.666667 2.629097 1.393000 357 | 7.142857 2.577344 1.330000 358 | 7.692308 2.527536 1.261000 359 | 8.333333 2.481153 1.191000 360 | 9.090909 2.436760 1.120000 361 | 10.000000 2.399111 1.042000 362 | 10.519672 2.385313 1.011000 363 | 11.117287 2.363856 0.983500 364 | 11.775789 2.337241 0.950100 365 | 12.503126 2.312599 0.911600 366 | 13.335111 2.290196 0.872500 367 | 14.289797 2.270109 0.831400 368 | 15.382249 2.254575 0.792100 369 | 16.672224 2.236685 0.761700 370 | 17.259234 2.228339 0.747800 371 | 17.863523 2.220374 0.735900 372 | 18.535681 2.210869 0.724100 373 | 19.230769 2.200349 0.712500 374 | 20.000000 2.188736 0.699500 375 | 20.846362 2.177335 0.685200 376 | 21.724962 2.166254 0.672700 377 | 22.753129 2.153213 0.658900 378 | 23.820867 2.139507 0.645300 379 | 25.006252 2.125742 0.629200 380 | 26.301946 2.112811 0.613500 381 | 27.800945 2.099543 0.596700 382 | 29.446408 2.086956 0.580500 383 | 31.259769 2.073976 0.566000 384 | 33.344448 2.059773 0.550500 385 | 34.518467 2.052476 0.543000 386 | 35.727045 2.045135 0.535500 387 | 37.064492 2.037243 0.528200 388 | 38.461538 2.029224 0.520900 389 | 40.000000 2.020318 0.513800 390 | 41.684035 2.010446 0.505600 391 | 43.459365 2.001418 0.496400 392 | 45.495905 1.992287 0.487300 393 | 47.641734 1.983438 0.478400 394 | 50.000000 1.974559 0.469700 395 | 52.603893 1.965156 0.461100 396 | 55.586437 1.955736 0.450600 397 | 58.892815 1.948419 0.440300 398 | 62.500000 1.941655 0.433300 399 | 66.666667 1.934154 0.426400 400 | 71.428571 1.927412 0.420500 401 | 76.923077 1.919973 0.418600 402 | 83.402836 1.911671 0.416700 403 | 90.991811 1.907505 0.417600 404 | 100.000000 1.899131 0.438300 405 | 102.092905 1.895435 0.443400 406 | 104.231812 1.891384 0.448500 407 | 106.416942 1.886330 0.454800 408 | 108.648414 1.880545 0.460000 409 | 111.172874 1.874242 0.465400 410 | 113.765643 1.867327 0.471800 411 | 116.414435 1.859854 0.477300 412 | 119.118523 1.851943 0.483900 413 | 121.891760 1.842330 0.490700 414 | 125.031258 1.830882 0.496400 415 | 128.238010 1.819110 0.502100 416 | 131.527029 1.805539 0.507900 417 | 135.208221 1.790800 0.510300 418 | 139.004726 1.777162 0.513800 419 | 142.897971 1.762824 0.517400 420 | 146.886016 1.747333 0.520900 421 | 151.354624 1.729441 0.523300 422 | 156.323277 1.709762 0.524600 423 | 161.446561 1.690223 0.524600 424 | 166.722241 1.669053 0.525800 425 | 172.592337 1.643739 0.523300 426 | 178.635227 1.619157 0.516200 427 | 185.356812 1.594131 0.507900 428 | 192.307692 1.567492 0.497500 429 | 200.000000 1.542270 0.477300 430 | 204.164965 1.531473 0.467500 431 | 208.463623 1.520272 0.457900 432 | 212.811236 1.508821 0.446500 433 | 217.249620 1.499424 0.432300 434 | 222.321032 1.491543 0.417600 435 | 227.531286 1.485266 0.402500 436 | 232.828871 1.480747 0.388000 437 | 238.208671 1.477194 0.373900 438 | 243.783520 1.475642 0.358700 439 | 250.062516 1.476571 0.344200 440 | 256.476019 1.478232 0.331700 441 | 263.019463 1.481006 0.319000 442 | 270.416441 1.486740 0.306800 443 | 278.009452 1.492960 0.299100 444 | 285.795942 1.498932 0.291600 445 | 294.464075 1.505906 0.286300 446 | 302.663438 1.511879 0.283000 447 | 312.597687 1.519076 0.279800 448 | 322.893122 1.527225 0.279100 449 | 333.444481 1.535500 0.281700 450 | 345.184674 1.542658 0.288900 451 | 357.270454 1.546272 0.299100 452 | 370.644922 1.546670 0.310300 453 | 384.615385 1.544080 0.322700 454 | 400.000000 1.537967 0.335600 455 | 416.840350 1.529309 0.348200 456 | 434.593655 1.516402 0.362900 457 | 454.959054 1.499422 0.372200 458 | 476.417342 1.483693 0.381800 459 | 500.000000 1.467642 0.393400 460 | 501.253133 1.467249 0.394300 461 | 502.260171 1.467000 0.395200 462 | 503.524673 1.466543 0.397000 463 | 504.540868 1.465400 0.398800 464 | 505.816894 1.463349 0.400700 465 | 508.130081 1.460391 0.400700 466 | 509.424350 1.459690 0.401600 467 | 510.464523 1.458719 0.402500 468 | 511.770727 1.457713 0.403500 469 | 512.820513 1.456898 0.404400 470 | 514.138817 1.455604 0.406200 471 | 515.198351 1.453825 0.407200 472 | 516.528926 1.452188 0.408100 473 | 517.598344 1.450255 0.409100 474 | 520.020801 1.447502 0.409100 475 | 521.104742 1.446666 0.410000 476 | 522.466040 1.445486 0.411000 477 | 523.560209 1.444197 0.411900 478 | 524.934383 1.442846 0.412800 479 | 526.038927 1.441618 0.413800 480 | 527.148129 1.439563 0.415700 481 | 529.661017 1.435881 0.415700 482 | 530.785563 1.434643 0.416700 483 | 532.197978 1.432797 0.417600 484 | 533.333333 1.431240 0.417600 485 | 534.473544 1.429982 0.418600 486 | 535.905681 1.428308 0.419600 487 | 537.056928 1.426178 0.420500 488 | 539.374326 1.422820 0.420500 489 | 540.832883 1.421557 0.421500 490 | 542.005420 1.419809 0.422500 491 | 543.183053 1.417548 0.423400 492 | 544.365814 1.415276 0.423400 493 | 547.045952 1.412092 0.423400 494 | 548.245614 1.410419 0.424400 495 | 549.450549 1.408657 0.424400 496 | 550.660793 1.406786 0.425400 497 | 552.181115 1.404604 0.425400 498 | 554.631170 1.401123 0.425400 499 | 555.864369 1.399826 0.425400 500 | 557.103064 1.398169 0.426400 501 | 558.347292 1.396377 0.426400 502 | 559.910414 1.394313 0.427400 503 | 562.429696 1.390838 0.426400 504 | 563.697858 1.389417 0.427400 505 | 564.971751 1.387734 0.427400 506 | 566.251416 1.385875 0.428300 507 | 567.536890 1.383660 0.428300 508 | 570.125428 1.380029 0.428300 509 | 571.428571 1.378598 0.428300 510 | 572.737686 1.376758 0.429300 511 | 574.052813 1.374519 0.429300 512 | 576.701269 1.370751 0.429300 513 | 578.034682 1.369211 0.429300 514 | 579.374276 1.367219 0.430300 515 | 580.720093 1.364655 0.430300 516 | 583.430572 1.361083 0.429300 517 | 584.795322 1.359301 0.430300 518 | 586.166471 1.356772 0.430300 519 | 588.928151 1.352834 0.429300 520 | 590.318772 1.351233 0.429300 521 | 591.715976 1.349696 0.429300 522 | 592.768228 1.347481 0.430300 523 | 595.592615 1.342949 0.429300 524 | 597.014925 1.341074 0.429300 525 | 598.444045 1.338869 0.429300 526 | 601.322910 1.334869 0.428300 527 | 602.409639 1.333056 0.428300 528 | 603.864734 1.330870 0.428300 529 | 606.796117 1.326773 0.427400 530 | 608.272506 1.324631 0.427400 531 | 609.384522 1.322675 0.426400 532 | 610.873549 1.320901 0.426400 533 | 613.873542 1.317122 0.425400 534 | 615.006150 1.315327 0.425400 535 | 616.522811 1.313112 0.425400 536 | 619.578686 1.308540 0.424400 537 | 620.732464 1.306556 0.423400 538 | 623.830318 1.303145 0.422500 539 | 625.000000 1.301310 0.422500 540 | 626.566416 1.298872 0.422500 541 | 629.326621 1.294706 0.420500 542 | 630.914826 1.292723 0.420500 543 | 632.511069 1.290576 0.419600 544 | 635.324015 1.286576 0.418600 545 | 636.942675 1.284709 0.417600 546 | 638.162093 1.282639 0.417600 547 | 641.025641 1.278233 0.415700 548 | 642.673522 1.276473 0.414800 549 | 645.577792 1.272559 0.413800 550 | 647.249191 1.270391 0.412800 551 | 648.508431 1.268440 0.411900 552 | 651.465798 1.265082 0.410000 553 | 653.167864 1.263173 0.410000 554 | 656.167979 1.258880 0.408100 555 | 657.462196 1.256977 0.407200 556 | 660.501982 1.253631 0.405300 557 | 662.251656 1.251704 0.405300 558 | 663.570007 1.249380 0.404400 559 | 666.666667 1.245318 0.402500 560 | 668.449198 1.243348 0.401600 561 | 671.591672 1.239445 0.399800 562 | 672.947510 1.237500 0.398800 563 | 676.132522 1.233597 0.397000 564 | 677.506775 1.231631 0.396100 565 | 680.735194 1.227627 0.394300 566 | 682.128240 1.225566 0.393400 567 | 685.400960 1.220973 0.391600 568 | 687.285223 1.218762 0.389800 569 | 690.131125 1.215328 0.387100 570 | 692.041522 1.213645 0.386200 571 | 694.927033 1.209428 0.384400 572 | 696.864111 1.207465 0.382600 573 | 699.790063 1.203552 0.380900 574 | 701.262272 1.201594 0.379100 575 | 704.721635 1.197623 0.377400 576 | 706.214689 1.195603 0.375700 577 | 709.723208 1.191399 0.373900 578 | 711.237553 1.189086 0.372200 579 | 714.285714 1.184740 0.369600 580 | 716.332378 1.182458 0.368000 581 | 719.424460 1.178513 0.364600 582 | 722.543353 1.174089 0.362100 583 | 724.637681 1.172049 0.359600 584 | 727.802038 1.167947 0.357100 585 | 729.394602 1.165763 0.354600 586 | 732.600733 1.161869 0.351400 587 | 734.753857 1.160150 0.349000 588 | 738.007380 1.156338 0.346600 589 | 741.289844 1.151643 0.342600 590 | 742.942051 1.149628 0.340200 591 | 746.268657 1.145850 0.336300 592 | 749.625187 1.141428 0.332500 593 | 751.879699 1.139515 0.329500 594 | 755.287009 1.135773 0.325700 595 | 757.002271 1.133825 0.322700 596 | 760.456274 1.130583 0.318300 597 | 763.941940 1.126485 0.313900 598 | 765.696784 1.124841 0.310300 599 | 769.230769 1.122067 0.306000 600 | 772.797527 1.118262 0.301200 601 | 774.593338 1.116753 0.297700 602 | 778.210117 1.114243 0.292900 603 | 781.860829 1.110319 0.288300 604 | 783.699060 1.108999 0.283700 605 | 786.782061 1.107403 0.279100 606 | 790.513834 1.104624 0.274000 607 | 794.281176 1.100816 0.269000 608 | 796.178344 1.099603 0.264100 609 | 800.000000 1.098011 0.259300 610 | 803.212851 1.095643 0.252800 611 | 807.102502 1.092375 0.247600 612 | 809.061489 1.091270 0.242000 613 | 813.008130 1.090913 0.235900 614 | 816.326531 1.089721 0.229500 615 | 820.344545 1.087212 0.223800 616 | 822.368421 1.086723 0.217700 617 | 825.763832 1.087993 0.211200 618 | 829.875519 1.087926 0.205500 619 | 834.028357 1.087480 0.199000 620 | 837.520938 1.086163 0.192700 621 | 839.630563 1.086474 0.186500 622 | 843.170320 1.089062 0.180200 623 | 847.457627 1.090622 0.174100 624 | 851.063830 1.092339 0.167800 625 | 855.431993 1.094339 0.162100 626 | 859.106529 1.096068 0.157000 627 | 862.812770 1.096584 0.152000 628 | 865.051903 1.097503 0.147200 629 | 868.809731 1.100705 0.142200 630 | 872.600349 1.103057 0.137000 631 | 877.192982 1.105361 0.132100 632 | 881.057269 1.107674 0.127000 633 | 884.955752 1.110334 0.121800 634 | 888.888889 1.113289 0.117200 635 | 893.655049 1.116059 0.112900 636 | 897.666068 1.118841 0.108300 637 | 901.713255 1.122010 0.103900 638 | 905.797101 1.125466 0.099950 639 | 909.918107 1.128640 0.096780 640 | 914.076782 1.131445 0.093280 641 | 918.273646 1.134419 0.089700 642 | 922.509225 1.137372 0.086460 643 | 926.784059 1.140345 0.082940 644 | 931.098696 1.143601 0.079580 645 | 935.453695 1.146959 0.076520 646 | 939.849624 1.150368 0.073590 647 | 944.287063 1.153843 0.070920 648 | 948.766603 1.157248 0.068520 649 | 952.380952 1.160584 0.066190 650 | 956.937799 1.163960 0.063940 651 | 961.538462 1.167354 0.061910 652 | 966.183575 1.170827 0.059950 653 | 970.873786 1.174182 0.058450 654 | 974.658869 1.178360 0.056340 655 | 979.431929 1.180893 0.058050 656 | 986.193294 1.183900 0.053800 657 | 991.080278 1.187365 0.052700 658 | 995.024876 1.190334 0.051740 659 | 1000.000000 1.193164 0.050790 660 | 1004.621258 1.195932 0.049980 661 | 1009.285426 1.198600 0.049290 662 | 1016.260163 1.202228 0.048510 663 | 1020.929045 1.204471 0.047840 664 | 1025.641026 1.206729 0.047180 665 | 1030.396703 1.208909 0.046640 666 | 1035.089535 1.211068 0.046000 667 | 1042.318115 1.214136 0.045370 668 | 1047.120419 1.216115 0.044750 669 | 1051.967179 1.218113 0.044340 670 | 1059.209829 1.220909 0.043730 671 | 1064.169416 1.222699 0.043330 672 | 1069.061364 1.224439 0.042930 673 | 1076.426265 1.226967 0.042340 674 | 1081.431816 1.228589 0.041960 675 | 1086.484137 1.230259 0.041480 676 | 1093.972213 1.232659 0.041100 677 | 1099.021871 1.234142 0.040720 678 | 1104.118361 1.235657 0.040350 679 | 1111.728738 1.237862 0.039880 680 | 1116.819299 1.239322 0.039520 681 | 1124.606388 1.241424 0.039160 682 | 1129.815840 1.242789 0.038800 683 | 1137.656428 1.244791 0.038440 684 | 1142.857143 1.246095 0.038090 685 | 1148.105626 1.247433 0.037830 686 | 1156.069364 1.249353 0.037480 687 | 1164.144354 1.251193 0.037140 688 | 1169.453865 1.252405 0.036880 689 | 1177.578898 1.254220 0.036540 690 | 1183.011948 1.255384 0.036370 691 | 1191.185229 1.257072 0.036040 692 | 1196.744854 1.258240 0.035790 693 | 1204.964454 1.259903 0.035630 694 | 1213.444970 1.261488 0.035300 695 | 1218.917601 1.262564 0.035140 696 | 1227.445686 1.264125 0.034900 697 | 1235.941169 1.265652 0.034660 698 | 1241.619071 1.266657 0.034500 699 | 1250.312578 1.268163 0.034260 700 | 1258.970162 1.269613 0.034100 701 | 1264.702163 1.270543 0.033950 702 | 1273.560876 1.271952 0.033710 703 | 1282.380097 1.273363 0.033480 704 | 1291.155584 1.274794 0.033250 705 | 1300.221038 1.276220 0.033100 706 | 1306.165099 1.277123 0.033020 707 | 1315.270288 1.278508 0.032790 708 | 1324.327904 1.279895 0.032720 709 | 1333.511135 1.281248 0.032570 710 | 1342.822613 1.282606 0.032490 711 | 1352.082207 1.283912 0.032420 712 | 1361.470388 1.285242 0.032270 713 | 1370.801919 1.286624 0.032200 714 | 1380.452789 1.287944 0.032200 715 | 1390.047262 1.289296 0.032050 716 | 1399.580126 1.290696 0.032050 717 | 1409.244645 1.292093 0.031970 718 | 1419.043565 1.293609 0.031900 719 | 1428.979708 1.295193 0.031970 720 | 1438.848921 1.296751 0.032120 721 | 1448.855404 1.298382 0.032200 722 | 1458.789205 1.300125 0.032420 723 | 1468.860165 1.301901 0.032720 724 | 1482.579689 1.304521 0.033100 725 | 1492.760113 1.306716 0.033710 726 | 1503.081317 1.309021 0.034500 727 | 1513.546239 1.311404 0.035630 728 | 1527.650474 1.314837 0.037310 729 | 1538.224888 1.317726 0.039250 730 | 1548.706830 1.320468 0.041760 731 | 1563.232765 1.325038 0.044850 732 | 1574.059499 1.329242 0.049520 733 | 1588.562351 1.335754 0.056990 734 | 1599.488164 1.339863 0.069470 735 | 1614.465612 1.341605 0.087860 736 | 1625.487646 1.330121 0.117200 737 | 1640.689089 1.295314 0.130900 738 | 1652.073352 1.268459 0.125000 739 | 1667.222407 1.242862 0.106900 740 | 1678.697331 1.231892 0.086460 741 | 1694.340901 1.229289 0.062200 742 | 1709.986320 1.234896 0.043230 743 | 1725.923369 1.242239 0.032950 744 | 1737.921446 1.248370 0.024820 745 | 1753.770607 1.256584 0.020310 746 | 1770.224819 1.262994 0.016590 747 | 1786.352269 1.268802 0.014180 748 | 1803.101334 1.273883 0.012580 749 | 1819.836215 1.278291 0.011580 750 | 1836.547291 1.282194 0.010780 751 | 1853.568119 1.285729 0.010300 752 | 1870.557426 1.289015 0.009881 753 | 1887.861053 1.292117 0.009790 754 | 1905.487805 1.294933 0.009904 755 | 1923.076923 1.297550 0.010110 756 | 1940.993789 1.299910 0.010610 757 | 1958.863859 1.301965 0.011110 758 | 1981.375074 1.304258 0.011800 759 | 2000.000000 1.305885 0.012410 760 | 2018.163471 1.307228 0.013120 761 | 2041.649653 1.308720 0.013700 762 | 2060.581084 1.309721 0.014410 763 | 2084.636231 1.310657 0.014990 764 | 2103.934357 1.311148 0.015520 765 | 2128.112364 1.311451 0.015700 766 | 2152.852530 1.311588 0.015480 767 | 2172.496198 1.311785 0.014720 768 | 2197.802198 1.312483 0.013610 769 | 2223.210316 1.313587 0.012380 770 | 2249.212776 1.314920 0.011400 771 | 2275.312856 1.316398 0.010300 772 | 2301.495972 1.318113 0.009307 773 | 2328.288708 1.319948 0.008449 774 | 2355.157796 1.321906 0.007600 775 | 2382.086708 1.323997 0.006883 776 | 2409.638554 1.326183 0.006220 777 | 2437.835202 1.328504 0.005621 778 | 2471.576866 1.331403 0.005067 779 | 2500.625156 1.333929 0.004600 780 | 2529.084471 1.336658 0.004157 781 | 2564.760195 1.340174 0.003800 782 | 2600.104004 1.343958 0.003530 783 | 2630.194634 1.347393 0.003402 784 | 2666.666667 1.351891 0.003402 785 | 2704.164413 1.356937 0.003596 786 | 2741.228070 1.362546 0.004234 787 | 2780.094523 1.368863 0.005150 788 | 2818.489290 1.376092 0.006789 789 | 2857.959417 1.384213 0.009393 790 | 2897.710808 1.393260 0.013210 791 | 2944.640754 1.404875 0.019490 792 | 2985.074627 1.417064 0.026110 793 | 3026.634383 1.432585 0.036880 794 | 3075.976623 1.449409 0.061060 795 | 3125.976868 1.461522 0.092430 796 | 3176.620076 1.466753 0.134800 797 | 3228.931224 1.452013 0.191800 798 | 3280.839895 1.411876 0.239800 799 | 3334.444815 1.352917 0.272100 800 | 3350.083752 1.334533 0.272100 801 | 3356.831151 1.326310 0.275900 802 | 3372.681282 1.307891 0.278500 803 | 3380.662610 1.297762 0.281700 804 | 3388.681803 1.285942 0.282400 805 | 3403.675970 1.263935 0.280400 806 | 3411.804845 1.252073 0.279800 807 | 3419.972640 1.240033 0.275900 808 | 3428.179637 1.229654 0.271500 809 | 3443.526171 1.208002 0.264700 810 | 3451.846738 1.195889 0.258100 811 | 3459.010723 1.185419 0.249300 812 | 3467.406380 1.178446 0.239200 813 | 3483.106931 1.162372 0.229000 814 | 3491.620112 1.152284 0.218200 815 | 3498.950315 1.145545 0.206000 816 | 3507.541214 1.142386 0.194000 817 | 3523.608175 1.133346 0.179800 818 | 3532.320735 1.127523 0.167000 819 | 3539.823009 1.125351 0.154100 820 | 3548.616040 1.125532 0.142200 821 | 3556.187767 1.128413 0.131200 822 | 3572.704537 1.129478 0.121000 823 | 3580.379520 1.127558 0.111900 824 | 3589.375449 1.127959 0.102000 825 | 3597.122302 1.130913 0.092850 826 | 3614.022407 1.132778 0.083520 827 | 3621.876132 1.131711 0.074440 828 | 3631.082062 1.132860 0.064830 829 | 3639.010189 1.136183 0.054800 830 | 3646.973012 1.142068 0.046220 831 | 3664.345914 1.149520 0.038000 832 | 3672.420125 1.152876 0.028170 833 | 3681.885125 1.160993 0.020500 834 | 3690.036900 1.168874 0.018610 835 | 3698.224852 1.174582 0.016400 836 | 3706.449222 1.179962 0.014510 837 | 3724.394786 1.188087 0.012700 838 | 3732.736096 1.191390 0.010490 839 | 3741.114852 1.195340 0.008547 840 | 3749.531309 1.199289 0.007325 841 | 3757.985720 1.202951 0.006278 842 | 3766.478343 1.206519 0.005368 843 | 3775.009438 1.209954 0.004828 844 | 3793.626707 1.215699 0.004363 845 | 3802.281369 1.218078 0.004016 846 | 3810.975610 1.220535 0.003302 847 | 3819.709702 1.223082 0.002977 848 | 3828.483920 1.225483 0.002703 849 | 3837.298542 1.227769 0.002575 850 | 3855.050116 1.231834 0.002476 851 | 3863.987635 1.233679 0.002425 852 | 3872.966692 1.235426 0.002387 853 | 3881.987578 1.237089 0.002338 854 | 3891.050584 1.238670 0.002311 855 | 3900.156006 1.240167 0.002269 856 | 3916.960439 1.243014 0.002142 857 | 3935.458481 1.245672 0.002069 858 | 3954.132068 1.248127 0.002017 859 | 3971.405878 1.250383 0.001990 860 | 3980.891720 1.251445 0.001953 861 | 4000.000000 1.253465 0.001900 862 | 4017.677782 1.255347 0.001810 863 | 4037.141704 1.257102 0.001709 864 | 4045.307443 1.257969 0.001580 865 | 4065.040650 1.259683 0.001472 866 | 4083.299306 1.261297 0.001348 867 | 4101.722724 1.262824 0.001250 868 | 4111.842105 1.263577 0.001150 869 | 4130.524577 1.265059 0.001071 870 | 4149.377593 1.266450 0.000990 871 | 4168.403501 1.267787 0.000910 872 | 4187.604690 1.269059 0.000849 873 | 4198.152813 1.269682 0.000792 874 | 4217.629692 1.270902 0.000743 875 | 4237.288136 1.272062 0.000685 876 | 4255.319149 1.273184 0.000637 877 | 4275.331338 1.274257 0.000599 878 | 4295.532646 1.275295 0.000543 879 | 4315.925766 1.276305 0.000511 880 | 4325.259516 1.276797 0.000492 881 | 4345.936549 1.277755 0.000469 882 | 4364.906155 1.278675 0.000451 883 | 4385.964912 1.279561 0.000429 884 | 4405.286344 1.280421 0.000408 885 | 4426.737494 1.281256 0.000390 886 | 4446.420631 1.282064 0.000374 887 | 4466.279589 1.282852 0.000357 888 | 4488.330341 1.283619 0.000346 889 | 4508.566276 1.284365 0.000341 890 | 4528.985507 1.285087 0.000339 891 | 4549.590537 1.285790 0.000338 892 | 4570.383912 1.286474 0.000340 893 | 4591.368228 1.287139 0.000343 894 | 4612.546125 1.287787 0.000351 895 | 4633.920297 1.288418 0.000359 896 | 4655.493482 1.289033 0.000371 897 | 4677.268475 1.289634 0.000383 898 | 4699.248120 1.290221 0.000397 899 | 4721.435316 1.290795 0.000418 900 | 4741.583689 1.291353 0.000440 901 | 4764.173416 1.291899 0.000464 902 | 4786.979416 1.292438 0.000488 903 | 4807.692308 1.292966 0.000529 904 | 4830.917874 1.293476 0.000572 905 | 4852.013586 1.293973 0.000621 906 | 4875.670405 1.294457 0.000674 907 | 4897.159647 1.294919 0.000739 908 | 4930.966469 1.295606 0.000805 909 | 4955.401388 1.296066 0.000889 910 | 4977.600796 1.296499 0.000990 911 | 5000.000000 1.296913 0.001101 912 | 5022.601708 1.297292 0.001250 913 | 5045.408678 1.297607 0.001402 914 | 5081.300813 1.298051 0.001548 915 | 5104.645227 1.298308 0.001717 916 | 5128.205128 1.298472 0.001848 917 | 5151.983514 1.298590 0.001909 918 | 5175.983437 1.298681 0.001922 919 | 5211.047421 1.298793 0.001827 920 | 5235.602094 1.298791 0.001678 921 | 5260.389269 1.298998 0.001161 922 | 5296.610169 1.299545 0.000922 923 | 5321.979776 1.299860 0.000722 924 | 5344.735436 1.300214 0.000521 925 | 5370.569280 1.300633 0.000320 926 | 5408.328826 1.301291 0.000186 927 | 5431.830527 1.301709 0.000155 928 | 5470.459519 1.302269 0.000142 929 | 5494.505495 1.302616 0.000138 930 | 5521.811154 1.302947 0.000137 931 | 5558.643691 1.303418 0.000136 932 | 5583.472920 1.303718 0.000133 933 | 5624.296963 1.304155 0.000122 934 | 5649.717514 1.304442 0.000112 935 | 5675.368899 1.304727 0.000105 936 | 5714.285714 1.305142 0.000100 937 | 5740.528129 1.305413 0.000095 938 | 5780.346821 1.305809 0.000089 939 | 5807.200929 1.306070 0.000084 940 | 5847.953216 1.306453 0.000081 941 | 5889.281508 1.306829 0.000077 942 | 5917.159763 1.307073 0.000076 943 | 5955.926147 1.307435 0.000075 944 | 5984.440455 1.307672 0.000074 945 | 6024.096386 1.308021 0.000074 946 | 6067.961165 1.308341 0.000076 947 | 6093.845216 1.308548 0.000079 948 | 6138.735421 1.308855 0.000081 949 | 6165.228113 1.309055 0.000083 950 | 6207.324643 1.309352 0.000088 951 | 6250.000000 1.309642 0.000093 952 | 6293.266205 1.309928 0.000099 953 | 6325.110689 1.310114 0.000107 954 | 6369.426752 1.310387 0.000114 955 | 6410.256410 1.310659 0.000124 956 | 6455.777921 1.310923 0.000135 957 | 6485.084306 1.311097 0.000144 958 | 6531.678641 1.311352 0.000160 959 | 6574.621959 1.311604 0.000174 960 | 6622.516556 1.311852 0.000196 961 | 6666.666667 1.312093 0.000225 962 | 6715.916723 1.312318 0.000266 963 | 6761.325220 1.312525 0.000302 964 | 6807.351940 1.312715 0.000339 965 | 6854.009596 1.312888 0.000360 966 | 6901.311249 1.313055 0.000364 967 | 6949.270327 1.313220 0.000363 968 | 6997.900630 1.313373 0.000354 969 | 7047.216350 1.313518 0.000320 970 | 7097.232079 1.313671 0.000254 971 | 7142.857143 1.313871 0.000153 972 | 7194.244604 1.314104 0.000106 973 | 7246.376812 1.314329 0.000078 974 | 7293.946025 1.314547 0.000058 975 | 7347.538575 1.314760 0.000045 976 | 7412.898443 1.315031 0.000040 977 | 7462.686567 1.315228 0.000028 978 | 7518.796992 1.315425 0.000023 979 | 7570.022710 1.315618 0.000019 980 | 7639.419404 1.315868 0.000016 981 | 7692.307692 1.316052 0.000014 982 | 7745.933385 1.316233 0.000012 983 | 7818.608288 1.316470 0.000011 984 | 7867.820614 1.316645 0.000011 985 | 7942.811755 1.316873 0.000011 986 | 8000.000000 1.317042 0.000011 987 | 8071.025020 1.317263 0.000011 988 | 8130.081301 1.317427 0.000012 989 | 8203.445447 1.317641 0.000012 990 | 8257.638315 1.317799 0.000012 991 | 8340.283570 1.318008 0.000012 992 | 8396.305626 1.318162 0.000012 993 | 8474.576271 1.318366 0.000012 994 | 8554.319932 1.318566 0.000011 995 | 8628.127696 1.318763 0.000011 996 | 8688.097307 1.318909 0.000009 997 | 8771.929825 1.319103 0.000006 998 | 8849.557522 1.319296 0.000004 999 | 8936.550492 1.319488 0.000003 1000 | 9017.132552 1.319678 0.000002 1001 | 9099.181074 1.319865 0.000002 1002 | 9182.736455 1.320051 0.000001 1003 | 9267.840593 1.320233 0.000001 1004 | 9354.536950 1.320416 0.000001 1005 | 9442.870633 1.320596 0.000001 1006 | 9523.809524 1.320775 0.000001 1007 | 9615.384615 1.320952 0.000002 1008 | 9708.737864 1.321128 0.000002 1009 | 9794.319295 1.321303 0.000002 1010 | 9910.802775 1.321521 0.000003 1011 | 10000.000000 1.321695 0.000003 1012 | 10046.212578 1.321780 0.000003 1013 | 10092.854259 1.321866 0.000003 1014 | 10162.601626 1.321994 0.000003 1015 | 10209.290454 1.322080 0.000003 1016 | 10256.410256 1.322165 0.000003 1017 | 10303.967027 1.322249 0.000004 1018 | 10350.895352 1.322333 0.000003 1019 | 10423.181155 1.322462 0.000003 1020 | 10471.204188 1.322546 0.000003 1021 | 10519.671786 1.322630 0.000003 1022 | 10592.098295 1.322757 0.000003 1023 | 10641.694158 1.322842 0.000002 1024 | 10690.613641 1.322926 0.000002 1025 | 10764.262648 1.323054 0.000001 1026 | 10814.318157 1.323138 0.000001 1027 | 10864.841373 1.323222 0.000001 1028 | 10939.722131 1.323351 0.000001 1029 | 10990.218705 1.323434 0.000001 1030 | 11041.183615 1.323520 0.000001 1031 | 11117.287382 1.323648 0.000000 1032 | 11168.192986 1.323732 0.000000 1033 | 11246.063878 1.323859 0.000000 1034 | 11298.158400 1.323946 0.000000 1035 | 11376.564278 1.324074 0.000000 1036 | 11428.571429 1.324159 0.000000 1037 | 11481.056257 1.324244 0.000000 1038 | 11560.693642 1.324373 0.000000 1039 | 11641.443539 1.324502 0.000000 1040 | 11694.538650 1.324590 0.000000 1041 | 11775.788978 1.324718 0.000000 1042 | 11830.119484 1.324805 0.000000 1043 | 11911.852293 1.324937 0.000000 1044 | 11967.448540 1.325025 0.000000 1045 | 12049.644535 1.325157 0.000000 1046 | 12134.449703 1.325290 0.000000 1047 | 12189.176012 1.325379 0.000000 1048 | 12274.456855 1.325512 0.000000 1049 | 12359.411692 1.325648 0.000000 1050 | 12416.190713 1.325739 0.000000 1051 | 12503.125781 1.325874 0.000000 1052 | 12589.701624 1.326012 0.000000 1053 | 12647.021626 1.326104 0.000000 1054 | 12735.608762 1.326244 0.000000 1055 | 12823.800975 1.326382 0.000000 1056 | 12911.555842 1.326524 0.000000 1057 | 13002.210376 1.326667 0.000000 1058 | 13061.650993 1.326764 0.000000 1059 | 13152.702880 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-6.3298690e-07 994 | 9.9499499e+14 1.0027340e+00 5.1084065e-05 995 | 9.9599600e+14 1.0027707e+00 8.2868840e-05 996 | 9.9699700e+14 1.0028151e+00 9.0900062e-05 997 | 9.9799800e+14 1.0028563e+00 7.5927593e-05 998 | 9.9899900e+14 1.0028852e+00 4.2908081e-05 999 | 1.0000000e+15 1.0028956e+00 6.9957957e-13 1000 | --------------------------------------------------------------------------------