├── .gitignore
├── name_params.py
├── LICENSE
├── README.md
├── tableLookUpOneImplicit.py
├── flamelet_integration.py
├── tableLookUpTwoImplicit.py
├── beta_integration.py
├── SLFM.py
├── FM2csv.py
├── flameletTableSingleParameter.py
├── plot_S_curve.ipynb
└── test_beta_integration.ipynb


/.gitignore:
--------------------------------------------------------------------------------
 1 | # ignore all
 2 | *
 3 | */
 4 | 
 5 | # unignore all with extensions
 6 | !*.*
 7 | 
 8 | # unignore makefile
 9 | !Makefile
10 | 
11 | # ignore files
12 | *.ipynb
13 | *.eps
14 | *.swp
15 | *.csv
16 | *.npy
17 | *.h5
18 | .DS_store
19 | 
20 | !plot_*.ipynb
21 | !test_*.ipynb
22 | 
23 | 
24 | # ignore folders
25 | .ipynb_checkpoints/
26 | __pycache__/
27 | flamelets/
28 | OutSteady/
29 | OutExtinction/
30 | tables/
31 | 


--------------------------------------------------------------------------------
/name_params.py:
--------------------------------------------------------------------------------
 1 | def params2name(params):
 2 |     params_str = []
 3 |     for k, v in params.items():
 4 |         try:
 5 |             param_str = '{0}-{1:g}'.format(k,v)
 6 |         except ValueError:
 7 |             param_str = '{0}-{1}'.format(k,v)
 8 |         params_str.append(param_str)
 9 |     return '_'.join(params_str)
10 | 
11 | def name2params(name):
12 |     params = {}
13 |     params_str = name.split('_')
14 |     for param_str in params_str:
15 |         param = param_str.split('-',maxsplit=1)
16 |         key = param[0]
17 |         try:
18 |             params[key] = float( param[1] )
19 |         except ValueError:
20 |             params[key] = param[1]
21 |     return params
22 | 


--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
 1 | MIT License
 2 | 
 3 | Copyright (c) 2018 Zhen Lu <albert.lz07@gmail.com>
 4 | 
 5 | Permission is hereby granted, free of charge, to any person obtaining a copy
 6 | of this software and associated documentation files (the "Software"), to deal
 7 | in the Software without restriction, including without limitation the rights
 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 | 
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 | 
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
 1 | # flamelet2table
 2 | python scripts to generate table from flamelet solutions
 3 | 
 4 | FM2csv.py:  convert FlameMaster solutions to csv files. The file "speciestranslated" is required in the folder of FlameMaster solutions, which is generated when converting CK format to FM format. 
 5 | 
 6 | flameletTableSingleParameter.py:  integrate the flamelet solutions to obtain a table, output to a hdf5 file
 7 | 
 8 | Beta distribution is assumed for the independent variable in flamelet solution, e.g., mixture fraction and progress variable for nonpremixed and premixed flames respectively. For the flamelet parameter, such as the stoichiometric scalar dissipation rate and reaction progress parameter, delta and beta distributions are available.
 9 | 
10 | To get the options and help information:
11 | ```
12 | python FM2csv -h
13 | ```
14 | ```
15 | python flameletTableSingleParameter.py -h
16 | ```
17 | 
18 | reference:
19 | ```
20 | @inproceedings{Lu2018,
21 |        author = {{Lu}, Zhen and {Elbaz}, Ayman M. and {Hernandez Perez}, Francisco E. and {Roberts}, William L. and {Im}, Hong G.},
22 |         title = "{LES/flamelet study of vortex-flame interaction in a turbulent nonpremixed swirl burner}",
23 |     booktitle = {14th International Conference on Combustion and Energy Utilization},
24 |          year = "2018",
25 |         month = "November",
26 |       address = "Sendai, Japan"
27 | }
28 | ```
29 | 


--------------------------------------------------------------------------------
/tableLookUpOneImplicit.py:
--------------------------------------------------------------------------------
 1 | import numpy as np
 2 | import h5py
 3 | from scipy import interpolate
 4 | 
 5 | def tableLookUpOneImplicit(
 6 |         x_ave, x_var, p,
 7 |         filename = 'flameletTable.h5',
 8 |         p_name = 'ProgressVariable'):
 9 | 
10 |     with h5py.File(filename,'r') as f:
11 |         table = f['flameletTable']
12 | 
13 |         variable = list(f['variable'])
14 |         x_ave_axis = np.array(f[table.dims[1].label])
15 |         x_var_axis = np.array(f[table.dims[2].label])
16 |         param_axis = np.array(f[table.dims[3].label])
17 | 
18 |         data = np.array(table)
19 | 
20 |     idx_p = variable.index( p_name )
21 | 
22 |     param_table = np.empty(data.shape[3])
23 | 
24 |     # interpolate with explicit index
25 |     for i in range( param_axis.size ):
26 |         f = interpolate.interp2d(x_var_axis, x_ave_axis, 
27 |                                  data[idx_p,:,:,i] )
28 |         param_table[i] = f(x_var, x_ave)
29 | 
30 |     # interpolate with implicit index
31 |     # inverse table
32 |     f = interpolate.interp1d(
33 |         param_table, param_axis, bounds_error=False,
34 |         fill_value=(param_axis[0], param_axis[-1]))
35 |     param = f( p )
36 | 
37 |     # interpolate all variables
38 |     var_table = np.empty((data.shape[0],data.shape[3]))
39 |     for i in range( data.shape[0] ):
40 |         for j in range( param_axis.size ):
41 |             f = interpolate.interp2d(x_var_axis, x_ave_axis, data[i,:,:,j])
42 |             var_table[i,j] = f(x_var, x_ave)
43 | 
44 |     f = interpolate.interp1d( param_axis, var_table )
45 |     phi = f(param)
46 | 
47 |     return phi
48 | 


--------------------------------------------------------------------------------
/flamelet_integration.py:
--------------------------------------------------------------------------------
 1 | import numpy as np
 2 | from name_params import *
 3 | from beta_integration import *
 4 | 
 5 | def single_solution_integration(
 6 |         solution, x_name, x_ave, x_var, y_names):
 7 | 
 8 |     x = solution[x_name]
 9 | 
10 |     f = np.empty((y_names.size, x.size))
11 | 
12 |     for i, name in enumerate(y_names):
13 |         if name.endswith('Variance'):
14 |             f[i,:] = np.square( solution[name[:-8]] )
15 |         else:
16 |             f[i,:] = solution[name]
17 | 
18 |     integration = beta_integration_table(f, x, x_ave, x_var)
19 | 
20 |     return integration
21 | 
22 | def param_solution_integration(
23 |         filenames, x_name, x_ave, x_var, y_names):
24 | 
25 |     table = np.empty((y_names.size, x_ave.size, x_var.size, filenames.size))
26 | 
27 |     for i, filename in enumerate( filenames ):
28 |         solution = np.genfromtxt(filename, names=True, delimiter=',')
29 | 
30 |         table[:,:,:,i] = single_solution_integration(
31 |             solution, x_name, x_ave, x_var, y_names)
32 | 
33 |     return table
34 | 
35 | 
36 | def table_integration( f, x, x_ave, x_var, pdf ):
37 | 
38 |     if pdf == 'beta' :
39 |         table = beta_integration_table(f, x, x_ave, x_var)
40 |     else:
41 |         table = delta_integration(f, x, x_ave)
42 | 
43 |     return table
44 | 
45 | def geometric_progression_01( n, ratio ):
46 | 
47 |     v = np.geomspace( 1., np.power(ratio, n-2), num = n-1 )
48 |     r = np.zeros( n )
49 | 
50 |     for i in range( n-1 ):
51 |         r[i+1] = np.sum( v[:i+1] )
52 |     r /= r[-1]
53 | 
54 |     return r
55 | 
56 | def dependent_variable_names(flamelet, independent_variable):
57 | 
58 |     names = list( flamelet.dtype.names )
59 |     names.remove( independent_variable )
60 | 
61 |     return names
62 | 
63 | def dependent_variable_names_print(filename, independent_variable):
64 |     with open(filename, 'r') as f:
65 |         names = f.readline().rstrip().split(',')
66 | 
67 |     names.remove( independent_variable )
68 | 
69 |     return names
70 | 
71 | def sequence_01(mesh, npts, solution, ratio):
72 | 
73 |     if mesh == 'solution' :
74 |         return solution
75 |     elif mesh == 'geometric' :
76 |         return geometric_progression_01(npts, ratio)
77 |     else :
78 |         return np.linspace(0., 1., num = npts)
79 | 
80 | def reference_solution(filenames, ref_param, p_str, p_end):
81 | 
82 |     ref_var = np.empty(filenames.size)
83 | 
84 |     for i, filename in enumerate(filenames):
85 |         ref_var[i] = name2params(filename[p_str:p_end])[ref_param]
86 | 
87 |     filename = filenames[-1]
88 |     for i in range( filenames.size-2 ):
89 |         if ref_var[i] < ref_var[i+1] and ref_var[i+1] > ref_var[i+2]:
90 |             filename = filenames[i+1]
91 | 
92 |     return np.genfromtxt(filename, names=True, delimiter=',')
93 | 


--------------------------------------------------------------------------------
/tableLookUpTwoImplicit.py:
--------------------------------------------------------------------------------
 1 | import numpy as np
 2 | import h5py
 3 | from scipy import interpolate
 4 | 
 5 | def tableLookUpTwoImplicit(
 6 |         x_ave, x_var, p0, p1,
 7 |         filename = 'flameletTable.h5',
 8 |         p0_name = 'ProgressVariable', 
 9 |         p1_name = 'ProgressVariableVariance'):
10 | 
11 |     with h5py.File(filename,'r') as f:
12 |         table = f['flameletTable']
13 | 
14 |         variable = list(f['variable'])
15 |         x_ave_axis = np.array(f[table.dims[1].label])
16 |         x_var_axis = np.array(f[table.dims[2].label])
17 |         param_axis_0 = np.array(f[table.dims[3].label])
18 |         param_axis_1 = np.array(f[table.dims[4].label])
19 | 
20 |         data = np.array(table)
21 | 
22 |     idx_p0 = variable.index( p0_name )
23 |     idx_p1 = variable.index( p1_name )
24 | 
25 |     param_table = np.empty((2,)+data.shape[3:])
26 | 
27 |     # interpolate with explicit index
28 |     for i in range( param_axis_0.size ):
29 |         for j in range( param_axis_1.size ):
30 |             f = interpolate.interp2d(x_var_axis, x_ave_axis, 
31 |                                      data[idx_p0,:,:,i,j] )
32 |             param_table[0,i,j] = f(x_var, x_ave)
33 | 
34 |             f = interpolate.interp2d(x_var_axis, x_ave_axis,
35 |                                      data[idx_p1,:,:,i,j] )
36 |             param_table[1,i,j] = f(x_var, x_ave)
37 | 
38 |     # interpolate with implicit index
39 |     # inverse table
40 |     table_inverse = np.empty( (2, param_axis_0.size) )
41 |     for i in range( param_axis_0.size ):
42 |         f = interpolate.interp1d(
43 |             param_table[1,i,:], param_table[0,i,:], bounds_error=False,
44 |             fill_value=(param_table[0,i,0], param_table[0,i,-1]) )
45 |         table_inverse[0,i] = f( p1 )
46 | 
47 |         f = interpolate.interp1d(
48 |             param_table[1,i,:], param_axis_1, bounds_error=False,
49 |             fill_value=(param_axis_1[0], param_axis_1[-1]))
50 |         table_inverse[1,i] = f( p1 )
51 | 
52 |     f = interpolate.interp1d(
53 |         table_inverse[0,:], table_inverse[1,:], bounds_error=False,
54 |         fill_value=(table_inverse[1,0], table_inverse[1,-1]))
55 |     param_1 = f( p0 )
56 | 
57 |     f = interpolate.interp1d(
58 |         table_inverse[0,:], param_axis_0, bounds_error=False,
59 |         fill_value=(param_axis_0[0], param_axis_0[-1]))
60 |     param_0 = f( p0 )
61 | 
62 |     # interpolate all variables
63 |     var_table = np.empty((data.shape[0],)+data.shape[3:])
64 |     for k in range( data.shape[0] ):
65 |         for i in range( param_axis_0.size ):
66 |             for j in range( param_axis_1.size ):     
67 |                 f = interpolate.interp2d(x_var_axis, x_ave_axis, data[k,:,:,i,j])
68 |                 var_table[k,i,j] = f(x_var, x_ave)
69 | 
70 |     phi = np.zeros(var_table.shape[0])
71 |     for k in range( var_table.shape[0] ):
72 |         f = interpolate.interp2d( param_axis_1, param_axis_0, var_table[k,:,:] )
73 |         phi[k] = f(param_0, param_1)
74 | 
75 |     return phi
76 | 


--------------------------------------------------------------------------------
/beta_integration.py:
--------------------------------------------------------------------------------
  1 | import numpy as np
  2 | import numpy.polynomial.polynomial as P
  3 | from scipy.stats import beta
  4 | from scipy.interpolate import interp1d
  5 | import scipy as sp
  6 | 
  7 | # calculate the beta pdf coefficients alpha and beta
  8 | def beta_coef(ave, var):
  9 | 
 10 |     a = ave*(1./var-1.)
 11 |     b = (1.-ave)*(1./var-1.)
 12 | 
 13 |     return a, b
 14 | 
 15 | 
 16 | # analytic integration with beta pdf, with linear fit of the target function
 17 | def beta_integration_analytic(f, x, B, CDF0, CDF1):
 18 | 
 19 |     c0 = np.zeros(x.size)
 20 |     c1 = np.zeros(x.size)
 21 | 
 22 |     for i in range(x.size-1):
 23 |         cl1 = (f[i+1] - f[i])/(x[i+1]-x[i])
 24 |         cl0 = f[i] - cl1*x[i]
 25 | 
 26 |         c0[i] -= cl0
 27 |         c0[i+1] += cl0
 28 | 
 29 |         c1[i] -= cl1
 30 |         c1[i+1] += cl1
 31 | 
 32 |     c1 *= B
 33 | 
 34 |     return np.sum(c0*CDF0+c1*CDF1)
 35 | 
 36 | 
 37 | # integration with the delta pdf, implemented as a linear interp
 38 | def delta_integration(f, x, x_ave):
 39 | 
 40 |     y = interp1d(x, f, kind='linear')
 41 | 
 42 |     return y(x_ave)
 43 | 
 44 | 
 45 | # integration with the bimodal pdf
 46 | def bimodal_integration(f, x_ave):
 47 | 
 48 |     return f[0]*(1.-x_ave)+f[-1]*x_ave
 49 | 
 50 | 
 51 | # beta integration of one average and one variance
 52 | def beta_integration(
 53 |         f, x, x_ave, x_nvar,
 54 |         B, CDF0, CDF1, EPS):
 55 | 
 56 |     if x_ave < EPS:
 57 |         return f[0]
 58 |     elif x_ave > 1.-EPS:
 59 |         return f[-1]
 60 |     elif x_nvar < EPS:
 61 |         return delta_integration(f, x, x_ave)
 62 |     elif x_nvar > 1.-EPS:
 63 |         return bimodal_integration(f, x_ave)
 64 |     else:
 65 |         return beta_integration_analytic(
 66 |                 f, x, B, CDF0, CDF1)
 67 | 
 68 | 
 69 | # calculate the coefficients for analytic beta integration
 70 | def beta_integration_coef(x, x_ave, x_nvar):
 71 | 
 72 |     a, b = beta_coef(x_ave, x_nvar)
 73 | 
 74 |     rv0 = beta(a, b)
 75 |     cdf0 = rv0.cdf(x)
 76 |     B0 = sp.special.beta(a, b)
 77 | 
 78 |     rv1 = beta(a+1., b)
 79 |     cdf1 = rv1.cdf(x)
 80 |     B1 = sp.special.beta(a+1, b)
 81 | 
 82 |     B = B1/B0
 83 | 
 84 |     return B, cdf0, cdf1
 85 | 
 86 | 
 87 | # calculate the coefficients for analytic beta integration
 88 | def beta_integration_coef_table(x, x_ave, x_var, EPS):
 89 | 
 90 |     B = np.empty((x_ave.size, x_var.size))
 91 |     CDF0 = np.empty((x_ave.size, x_var.size, x.size))
 92 |     CDF1 = np.empty((x_ave.size, x_var.size, x.size))
 93 | 
 94 |     for j, ave in enumerate(x_ave):
 95 |         for k, var in enumerate(x_var):
 96 |             if ave > EPS and ave < 1.-EPS and var > EPS and var < 1.-EPS :
 97 |                 B[j,k], CDF0[j,k,:], CDF1[j,k,:] = beta_integration_coef(
 98 |                     x, ave, var)
 99 | 
100 |     return B, CDF0, CDF1
101 | 
102 | 
103 | # beta integration of a average and variance table
104 | def beta_integration_table(f, x, x_ave, x_var, EPS=1.e-9):
105 | 
106 |     f_flatten = np.reshape(f, (-1, x.size), order='F')
107 | 
108 |     variable_number = f_flatten.shape[0]
109 | 
110 |     table_flatten = np.empty((variable_number, x_ave.size, x_var.size))
111 | 
112 |     B, CDF0, CDF1 = beta_integration_coef_table(x, x_ave, x_var, EPS)
113 | 
114 |     for i, v in enumerate(f_flatten):
115 |         for j, ave in enumerate(x_ave):
116 |             for k, var in enumerate(x_var):
117 |                 table_flatten[i,j,k] = beta_integration(
118 |                         v, x, ave, var,
119 |                         B[j,k], CDF0[j,k,:], CDF1[j,k,:], EPS)
120 | 
121 |     table = np.reshape(table_flatten, 
122 |                        f.shape[:-1]+(x_ave.size, x_var.size), 
123 |                        order='F')
124 | 
125 |     return table
126 | 


--------------------------------------------------------------------------------
/SLFM.py:
--------------------------------------------------------------------------------
  1 | import os
  2 | import glob
  3 | import argparse
  4 | import numpy as np
  5 | import h5py
  6 | from beta_integration import beta_integration
  7 | from flamelet_integration import *
  8 | from name_params import *
  9 | 
 10 | def table_SLFM(dir_name = 'flamelets',
 11 |                average_mesh = 'solution',
 12 |                average_num = 100,
 13 |                variance_mesh = 'geometric',
 14 |                variance_num = 15,
 15 |                variance_ratio = 1.1):
 16 | 
 17 |     independent_variable = 'Z'
 18 | 
 19 |     # get the flamelet solutions
 20 |     file_suffix = 'csv'
 21 | 
 22 |     chi = np.zeros(1)
 23 |     os.chdir(dir_name)
 24 |     for filename in glob.glob('.'.join(['*', file_suffix])):
 25 |         params = name2params( filename[:-1-len(file_suffix)] )
 26 |         chi = np.append(chi, params['chi'])
 27 |     os.chdir('..')
 28 |     chi = np.delete( chi, 0, 0 )
 29 |     chi = np.sort( chi )
 30 | 
 31 |     # take the flamelet solution with largest chi_st
 32 |     params = { 'chi' : chi[-1] }
 33 |     file_prefix = params2name( params )
 34 | 
 35 |     filename = '{0}/{1}.{2}'.format(dir_name, file_prefix, file_suffix)
 36 |     flamelet = np.genfromtxt(filename, names=True, delimiter=',')
 37 | 
 38 |     # the variables to be integrated
 39 |     variable_names = dependent_variable_names(
 40 |         flamelet, independent_variable, 'chi')
 41 | 
 42 |     # the average axis
 43 |     independent_average = average_sequence(
 44 |         average_mesh,flamelet[independent_variable],average_num)
 45 | 
 46 |     # the variance axis
 47 |     independent_variance = sequence_01(
 48 |         variance_mesh, variance_num, variance_ratio)
 49 | 
 50 |     flamelet_table = np.empty((variable_names.size,
 51 |                                independent_average.size,
 52 |                                independent_variance.size,
 53 |                                chi.size))
 54 | 
 55 |     for l, chi_st in enumerate(chi):
 56 |         params = { 'chi' : chi_st }
 57 |         file_prefix = params2name( params )
 58 | 
 59 |         filename = '{0}/{1}.{2}'.format(dir_name, file_prefix, file_suffix)
 60 |         flamelet = np.genfromtxt(filename, names=True, delimiter=',')    
 61 | 
 62 |         flamelet_table[:,:,:,l] = single_solution_integration(
 63 |             flamelet,
 64 |             independent_variable, 
 65 |             independent_average, 
 66 |             independent_variance, 
 67 |             variable_names)
 68 | 
 69 |     # save the flamelet table
 70 |     with h5py.File('flameletTable.h5', 'w') as f:
 71 |         
 72 |         f['flameletTable'] = flamelet_table
 73 |         
 74 |         # strings
 75 |         dt = h5py.special_dtype(vlen=str)
 76 |         ds = f.create_dataset('variable',
 77 |                               variable_names.shape,
 78 |                               dtype=dt)
 79 |         ds[...] = variable_names
 80 |         
 81 |         f['mixtureFractionAverage'] = independent_average
 82 |         f['mixtureFractionNormalizedVariance'] = independent_variance
 83 |         f['stoichiometricScalarDissipationRate'] = chi
 84 |         
 85 |         f['flameletTable'].dims.create_scale(
 86 |                 f['variable'],
 87 |                 'variable')
 88 |         
 89 |         f['flameletTable'].dims.create_scale(
 90 |                 f['mixtureFractionAverage'],
 91 |                 'mixtureFractionAverage')
 92 |         
 93 |         f['flameletTable'].dims.create_scale(
 94 |                 f['mixtureFractionNormalizedVariance'],
 95 |                 'mixtureFractionNormalizedVariance')
 96 |         
 97 |         f['flameletTable'].dims.create_scale(
 98 |                 f['stoichiometricScalarDissipationRate'],
 99 |                 'stoichiometricScalarDissipationRate')
100 |         
101 |         f['flameletTable'].dims[3].attach_scale(
102 |                 f['stoichiometricScalarDissipationRate'])
103 | 
104 |         f['flameletTable'].dims[2].attach_scale(
105 |                 f['mixtureFractionNormalizedVariance'])
106 | 
107 |         f['flameletTable'].dims[1].attach_scale(
108 |                 f['mixtureFractionAverage'])
109 | 
110 |         f['flameletTable'].dims[0].attach_scale(
111 |                 f['variable'])
112 | 
113 |     return
114 | 
115 | if __name__ == '__main__':
116 | 
117 |     parser = argparse.ArgumentParser()
118 | 
119 |     parser.add_argument(
120 |         '-f', '--folder',
121 |         default = 'flamelets',
122 |         type = str,
123 |         help = 'folder of the flamelet solutions [flamelets]')
124 | 
125 |     parser.add_argument(
126 |         '-a', '--average-mesh',
127 |         default = 'solution',
128 |         type = str,
129 |         help = 'mesh of average [solution]/uniform')
130 | 
131 |     parser.add_argument(
132 |         '--number-average',
133 |         default = 100,
134 |         type = int,
135 |         help = 'the number of points on the axis of average [100]')
136 | 
137 |     parser.add_argument(
138 |         '-v', '--variance-mesh',
139 |         default = 'geometric',
140 |         type = str,
141 |         help = 'mesh of variance [geometric]/uniform')
142 | 
143 |     parser.add_argument(
144 |         '--number-variance',
145 |         default = 15,
146 |         type = int,
147 |         help = 'the number of points on the axis of variance [15]')
148 | 
149 |     parser.add_argument(
150 |         '--ratio-variance',
151 |         default = 1.1,
152 |         type = float,
153 |         help = 'growth rate of the variance mesh [1.1]')
154 | 
155 |     args = parser.parse_args()
156 | 
157 |     table_SLFM(dir_name = args.folder,
158 |                average_mesh = args.average_mesh,
159 |                average_num = args.number_average,
160 |                variance_mesh = args.variance_mesh,
161 |                variance_num = args.number_variance,
162 |                variance_ratio = args.ratio_variance)
163 | 


--------------------------------------------------------------------------------
/FM2csv.py:
--------------------------------------------------------------------------------
  1 | """
  2 | A python script to transfer FlameMaster output to csv tables
  3 | """
  4 | 
  5 | import numpy as np
  6 | from scipy.interpolate import interp1d
  7 | import os
  8 | import sys
  9 | import glob
 10 | import argparse
 11 | from name_params import params2name
 12 | 
 13 | def FM2csv(mode = 'SLFM', 
 14 |            flamelet_prefix = 'CH4_p01_0',
 15 |            FlameMaster_dir = 'OutSteady', 
 16 |            csv_dir = 'flamelets'):
 17 | 
 18 |     if not os.path.exists(FlameMaster_dir):
 19 |         sys.exit('FlameMaster output not found')
 20 | 
 21 |     os.makedirs(csv_dir,exist_ok=True)
 22 | 
 23 |     # the number of columns in FlameMaster output
 24 |     NCOL = 5
 25 |     file_suffix = 'csv'
 26 | 
 27 |     # read the species names into dictionary
 28 |     # key: species names in FlameMaster
 29 |     # value: species names in Chemkin mechanism
 30 |     name_dict = {}
 31 |     with open('{}/speciestranslated'.format(FlameMaster_dir),'r') as f:
 32 |         for line in f:
 33 |             names = line.split()
 34 |             name_dict['-'.join(['massfraction',names[1]])] = names[0] 
 35 | 
 36 |     name_dict['temperature'] = 'T'
 37 |     name_dict['density'] = 'rho'
 38 | 
 39 |     extra_var = ['Z', 'chi', 'lambda', 'cp', 'mu', 'D',
 40 |                  'ProdRateCO2', 'ProdRateH2O', 'ProdRateCO', 'ProdRateH2',
 41 |                  'TotalEnthalpy', 'HeatRelease',
 42 |                  'ProgressVariable', 'ProdRateProgressVariable']
 43 | 
 44 |     prog_var_spe = ['CO2', 'CO', 'H2O', 'H2']
 45 | 
 46 |     for name in extra_var:
 47 |         name_dict[name] = name
 48 | 
 49 |     for flamelet in glob.glob('{0}/{1}*'.format(FlameMaster_dir, 
 50 |                                                 flamelet_prefix)):
 51 | 
 52 |         # skip diverged solution
 53 |         if flamelet.endswith('noC'):
 54 |             continue
 55 | 
 56 |         params = {}
 57 | 
 58 |         params['chi'] = float(
 59 |             flamelet[flamelet.find('chi')+3:flamelet.find('tf')])
 60 | 
 61 |         with open(flamelet,'r') as f:
 62 | 
 63 |             # read the header part
 64 |             for line in f:
 65 |                 if line.startswith('Z_st'):
 66 |                     Zst = float(line.split()[2])
 67 |                 elif line.startswith('gridPoints'):
 68 |                     npts = int(line.split()[-1])
 69 |                     nrow = np.ceil(npts/NCOL)
 70 |                 elif line.startswith('body'):
 71 |                     break
 72 | 
 73 |             name_FlameMaster = list(name_dict.keys())
 74 |             name_csv = list(name_dict.values())
 75 | 
 76 |             data = np.zeros((npts, len(name_FlameMaster)),order='F')
 77 | 
 78 |             for line in f:
 79 | 
 80 |                 if line.strip() == '':
 81 |                     continue
 82 |                 elif line.startswith('trailer'):
 83 |                     break
 84 | 
 85 |                 var_name = line.split()[0]
 86 | 
 87 |                 # read data
 88 |                 var = []
 89 |                 for i in np.arange(nrow):
 90 |                     data_line = f.readline().split()
 91 |                     var.extend([float(x) for x in data_line])
 92 | 
 93 |                 # map names
 94 |                 if var_name in name_FlameMaster :
 95 |                     i = name_csv.index( name_dict[var_name] )
 96 |                     data[:,i] = np.array( var )
 97 | 
 98 |         # calculate Diffusivity with Le = 1
 99 |         idx_D = name_csv.index( 'D' )
100 |         idx_lambda = name_csv.index( 'lambda' )
101 |         idx_rho = name_csv.index( 'rho' )
102 |         idx_cp = name_csv.index( 'cp' )
103 |         data[:,idx_D] = data[:,idx_lambda]/(data[:,idx_rho]*data[:,idx_cp])
104 | 
105 |         # calculate the progress variable based on the list prog_var_spe
106 |         idx_C = name_csv.index( 'ProgressVariable' )
107 |         idx_C_rate = name_csv.index( 'ProdRateProgressVariable' )
108 |         for spe in prog_var_spe:
109 |             idx_spe = name_csv.index( spe )
110 |             idx_spe_rate = name_csv.index( 'ProdRate{}'.format(spe) )
111 | 
112 |             data[:,idx_C] += data[:,idx_spe]
113 |             data[:,idx_C_rate] += data[:,idx_spe_rate]
114 | 
115 | 
116 |         if mode == 'FPV' :
117 |             params['T'] = float(
118 |                 flamelet[flamelet.find('Tst')+3:])
119 | 
120 |             idx_Z = name_csv.index( 'Z' )
121 |             y = interp1d( data[:,idx_Z], data[:,idx_C] )
122 |             params['ProgressVariable'] = y( Zst )
123 | 
124 |         # file name
125 |         file_prefix = params2name( params )
126 | 
127 |         np.savetxt('{}/{}.{}'.format(csv_dir,file_prefix,file_suffix),
128 |                    data,
129 |                    fmt = '%12.6e',
130 |                    delimiter = ',',
131 |                    header = ','.join(name_csv),
132 |                    comments='')
133 | 
134 |     return
135 | 
136 | if __name__ == '__main__' :
137 |     parser = argparse.ArgumentParser()
138 |     parser.add_argument(
139 |         '-m', '--mode',
140 |         default = 'SLFM',
141 |         type = str,
142 |         help = 'use of the flamelet solutions: [SLFM]/FPV')
143 |     parser.add_argument(
144 |         '-p', '--prefix',
145 |         default = 'CH4_p01_0',
146 |         type = str,
147 |         help = 'file prefix of the flamelet solution [CH4_p01_0]')
148 |     parser.add_argument(
149 |         '--FlameMasterFolder',
150 |         default = 'OutSteady',
151 |         type = str,
152 |         help = 'folder of the FlameMaster solutions [OutSteady]')
153 |     parser.add_argument(
154 |         '--csvFolder',
155 |         default = 'flamelets',
156 |         type = str,
157 |         help = 'folder for output csv files [flamelets]')
158 |     args = parser.parse_args()
159 | 
160 |     FM2csv(mode = args.mode,
161 |            flamelet_prefix = args.prefix,
162 |            FlameMaster_dir = args.FlameMasterFolder, 
163 |            csv_dir = args.csvFolder)
164 | 


--------------------------------------------------------------------------------
/flameletTableSingleParameter.py:
--------------------------------------------------------------------------------
  1 | import glob
  2 | import argparse
  3 | import numpy as np
  4 | import h5py
  5 | from flamelet_integration import *
  6 | from beta_integration import delta_integration
  7 | from name_params import name2params
  8 | 
  9 | def single_param_table(
 10 |     mode = 'SLFM', dir_name = 'flamelets', output='flameletTable.h5',
 11 |     param_mesh = 'solution', param_pdf = 'delta',
 12 |     average_mesh = 'solution', average_num = 100,
 13 |     variance_mesh = 'geometric', variance_num = 15, variance_ratio = 1.1):
 14 | 
 15 |     if mode == 'SLFM' :
 16 |         independent_variable = 'Z'
 17 |         param_name = 'chi'
 18 |         ref_param = 'chi'
 19 |     elif mode == 'FPV' :
 20 |         independent_variable = 'Z'
 21 |         param_name = 'ProgressVariable'
 22 |         ref_param = 'chi'
 23 |     elif mode == 'FPI' :
 24 |         independent_variable = 'ProgressVariable'
 25 |         param_name = 'Z'
 26 |         ref_param = 'ProgressVariable'
 27 |     else :
 28 |         print('mode not implemented')
 29 |         return
 30 | 
 31 |     # get the flamelet solutions
 32 |     file_suffix = 'csv'
 33 | 
 34 |     p_str = 1 + len( dir_name )
 35 |     p_end = -1 - len( file_suffix )
 36 | 
 37 |     # get file and parameter list
 38 |     param = []
 39 |     filenames = []
 40 | 
 41 |     for filename in glob.glob('{}/*.{}'.format(dir_name,file_suffix)):
 42 |         params = name2params(filename[p_str:p_end])
 43 |         param.append( params[param_name] )
 44 |         filenames.append( filename )
 45 | 
 46 |     param = np.array(param)
 47 |     idx = np.argsort(param)
 48 | 
 49 |     param = param[idx]
 50 |     param = (param-param[0])/(param[-1]-param[0])
 51 | 
 52 |     filenames = np.array( filenames )[idx]
 53 | 
 54 |     # get the referecen flamelet
 55 |     flamelet = reference_solution(filenames, ref_param, p_str, p_end)
 56 | 
 57 |     # the variables to be integrated
 58 |     names = dependent_variable_names(
 59 |         flamelet, independent_variable)
 60 | 
 61 |     if param_pdf != 'delta' and mode != 'FPI' :
 62 |         names.append('{}Variance'.format(param_name))
 63 | 
 64 |     variable_names = np.array( names )
 65 | 
 66 |     names = dependent_variable_names_print(
 67 |         filenames[0], independent_variable)
 68 | 
 69 |     names_print = np.array( names )
 70 | 
 71 |     # the independent variable average axis
 72 |     independent_average = sequence_01(
 73 |         average_mesh, average_num, flamelet[independent_variable], 1.)
 74 | 
 75 |     # the variance axis
 76 |     normalized_variance = sequence_01(
 77 |         variance_mesh, variance_num, np.linspace(0.,1.), variance_ratio)
 78 | 
 79 |     # the parameter average axis
 80 |     param_average = sequence_01(
 81 |         param_mesh, average_num, param, 1.)
 82 | 
 83 |     # flamelet table with the parameter from solutions
 84 |     flamelet_table_solution = param_solution_integration(
 85 |         filenames, 
 86 |         independent_variable, independent_average, normalized_variance, 
 87 |         variable_names)
 88 | 
 89 |     flamelet_table = table_integration(flamelet_table_solution,
 90 |                                        param,
 91 |                                        param_average,
 92 |                                        normalized_variance,
 93 |                                        param_pdf)
 94 | 
 95 |     if mode == 'FPI' :
 96 |         # integration of the max progress variable for normalization
 97 |         normalization_param = np.zeros( (2, param.size) )
 98 |         for i in range( param.size ):
 99 |             params = name2params( filenames[i][p_str:p_end] )
100 |             normalization_param[0,i] = params[ref_param]
101 |         normalization_param[1,:] = np.square( normalization[0,:] )
102 | 
103 |         normalization_table = table_integration(normalization_param,
104 |                                                 param,
105 |                                                 param_average,
106 |                                                 normalized_variance,
107 |                                                 param_pdf)
108 |     elif param_pdf != 'delta' :
109 |         # variance for implicit parameter
110 |         idx = list(variable_names).index( param_name )
111 |         flamelet_table[-1,:,:,:,:] -= np.square( flamelet_table[idx,:,:,:,:] )
112 | 
113 |     # name of data axis
114 |     axis = []
115 |     axis.append( 'variables' )
116 |     axis.append( '{}Average'.format(independent_variable) )
117 |     axis.append( '{}NormalizedVariance'.format(independent_variable) )
118 |     axis.append( 'Parameter{}Average'.format(param_name) )
119 |     axis.append( 'Parameter{}Variance'.format(param_name) )
120 | 
121 |     # save the flamelet table
122 |     with h5py.File(output, 'w') as f:
123 |         
124 |         f['flameletTable'] = flamelet_table
125 |         
126 |         # strings
127 |         dt = h5py.special_dtype(vlen=str)
128 |         ds = f.create_dataset(axis[0],
129 |                               names_print.shape,
130 |                               dtype=dt)
131 |         ds[...] = names_print
132 | 
133 |         f[axis[1]] = independent_average
134 |         f[axis[2]] = normalized_variance
135 |         f[axis[3]] = param_average
136 | 
137 |         if param_pdf != 'delta':
138 |             f[axis[4]] = normalized_variance
139 |         else:
140 |             del axis[-1]
141 | 
142 |         for i, v in enumerate(axis):
143 |             f['flameletTable'].dims[i].label = v
144 |             f['flameletTable'].dims.create_scale(f[v], v)
145 |             f['flameletTable'].dims[i].attach_scale(f[v])
146 | 
147 |         if mode == 'FPI' :
148 |             f['maxProgressVariable'] = normalization_table
149 | 
150 |             f['maxProgressVariable'].dims[0].label = 'MeanAndSquareMean'
151 |             for i, v in enumerate(axis[3:]):
152 |                 f['maxProgressVariable'].dims[i+1].label = v
153 | 
154 |     return
155 | 
156 | if __name__ == '__main__':
157 | 
158 |     parser = argparse.ArgumentParser()
159 | 
160 |     parser.add_argument(
161 |         '-m', '--mode',
162 |         default = 'FPV',
163 |         type = str,
164 |         help = 'use of the flamelet solutions: SLFM/[FPV]/FPI')
165 | 
166 |     parser.add_argument(
167 |         '-f', '--folder',
168 |         default = 'flamelets',
169 |         type = str,
170 |         help = 'folder of the flamelet solutions [flamelets]')
171 | 
172 |     parser.add_argument(
173 |         '-o', '--output',
174 |         default = 'flameletTable.h5',
175 |         type = str,
176 |         help = 'output file name [flameletTable.h5]')
177 | 
178 |     parser.add_argument(
179 |         '-p', '--parameter-mesh',
180 |         default = 'uniform',
181 |         type = str,
182 |         help = 'mesh of the flamelet parameter solution/[uniform]')
183 | 
184 |     parser.add_argument(
185 |         '--parameter-pdf',
186 |         default = 'delta',
187 |         type = str,
188 |         help = 'pdf of the flamelet parameter [delta]/beta')
189 | 
190 |     parser.add_argument(
191 |         '-a', '--average-mesh',
192 |         default = 'uniform',
193 |         type = str,
194 |         help = 'mesh of average solution/[uniform]')
195 | 
196 |     parser.add_argument(
197 |         '--number-average',
198 |         default = 100,
199 |         type = int,
200 |         help = 'the number of points on the axis of average [100]')
201 | 
202 |     parser.add_argument(
203 |         '-v', '--variance-mesh',
204 |         default = 'geometric',
205 |         type = str,
206 |         help = 'mesh of variance [geometric]/uniform')
207 | 
208 |     parser.add_argument(
209 |         '--number-variance',
210 |         default = 15,
211 |         type = int,
212 |         help = 'the number of points on the axis of variance [15]')
213 | 
214 |     parser.add_argument(
215 |         '--ratio-variance',
216 |         default = 1.1,
217 |         type = float,
218 |         help = 'growth rate of the variance mesh [1.1]')
219 | 
220 |     args = parser.parse_args()
221 | 
222 |     args = parser.parse_args()
223 | 
224 |     single_param_table(
225 |         mode = args.mode, dir_name = args.folder, output = args.output,
226 |         param_mesh = args.parameter_mesh, param_pdf = args.parameter_pdf,
227 |         average_mesh = args.average_mesh, average_num = args.number_average,
228 |         variance_mesh = args.variance_mesh, variance_num = args.number_variance,
229 |         variance_ratio = args.ratio_variance)
230 | 


--------------------------------------------------------------------------------
/plot_S_curve.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 1,
  6 |    "metadata": {},
  7 |    "outputs": [],
  8 |    "source": [
  9 |     "import os\n",
 10 |     "import glob\n",
 11 |     "import numpy as np\n",
 12 |     "import matplotlib.pyplot as plt\n",
 13 |     "from name_params import *\n",
 14 |     "from flamelet_integration import *"
 15 |    ]
 16 |   },
 17 |   {
 18 |    "cell_type": "code",
 19 |    "execution_count": 2,
 20 |    "metadata": {},
 21 |    "outputs": [],
 22 |    "source": [
 23 |     "filenum = 100.\n",
 24 |     "dir_name = 'flamelets'\n",
 25 |     "file_suffix = 'csv'\n",
 26 |     "\n",
 27 |     "filenames = []\n",
 28 |     "chi = np.zeros(1)\n",
 29 |     "T = np.zeros(1)\n",
 30 |     "C = np.zeros(1)\n",
 31 |     "\n",
 32 |     "os.chdir(dir_name)\n",
 33 |     "for filename in glob.glob('.'.join(['*', file_suffix])):\n",
 34 |     "    params = name2params( filename[:-1-len(file_suffix)] )\n",
 35 |     "    chi = np.append(chi, params['chi'])\n",
 36 |     "    T = np.append(T, params['T'])\n",
 37 |     "    C = np.append(C, params['ProgressVariable'])\n",
 38 |     "    filenames.append(filename)\n",
 39 |     "os.chdir('..')\n",
 40 |     "\n",
 41 |     "chi = np.delete( chi, 0, 0 )\n",
 42 |     "T = np.delete( T, 0, 0 )\n",
 43 |     "C = np.delete( C, 0, 0 )"
 44 |    ]
 45 |   },
 46 |   {
 47 |    "cell_type": "code",
 48 |    "execution_count": 3,
 49 |    "metadata": {},
 50 |    "outputs": [],
 51 |    "source": [
 52 |     "idx = np.argsort( T )[::-1]"
 53 |    ]
 54 |   },
 55 |   {
 56 |    "cell_type": "code",
 57 |    "execution_count": 4,
 58 |    "metadata": {},
 59 |    "outputs": [],
 60 |    "source": [
 61 |     "chi = chi[idx]\n",
 62 |     "T = T[idx]\n",
 63 |     "C = C[idx]\n",
 64 |     "filenames = np.array( filenames )[idx]"
 65 |    ]
 66 |   },
 67 |   {
 68 |    "cell_type": "code",
 69 |    "execution_count": 5,
 70 |    "metadata": {},
 71 |    "outputs": [],
 72 |    "source": [
 73 |     "list_delete = []\n",
 74 |     "Lambda = (T-T[-1])/(T[0]-T[-1])\n",
 75 |     "#Lambda = (C-C[-1])/(C[0]-C[-1])\n",
 76 |     "diff_limit = 1./3./filenum\n",
 77 |     "v_old = Lambda[0] + 1.\n",
 78 |     "for i, v in enumerate(Lambda):\n",
 79 |     "    if v_old - v > diff_limit :\n",
 80 |     "        v_old = v\n",
 81 |     "    else:\n",
 82 |     "        list_delete.append(i)"
 83 |    ]
 84 |   },
 85 |   {
 86 |    "cell_type": "code",
 87 |    "execution_count": 6,
 88 |    "metadata": {},
 89 |    "outputs": [
 90 |     {
 91 |      "data": {
 92 |       "text/plain": [
 93 |        "[<matplotlib.lines.Line2D at 0x7f7e026deac8>]"
 94 |       ]
 95 |      },
 96 |      "execution_count": 6,
 97 |      "metadata": {},
 98 |      "output_type": "execute_result"
 99 |     },
100 |     {
101 |      "data": {
102 |       "image/png": 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RpSw77yaSriNWr17dTIhmZi1V5E3jG9FwS0DSRcDZwAVpFw8RsS8iptPnE8DjwPEkV/75P6mVwK5a546IzRExEhEjw8PDjYZoZtZSRd80vhENJQFJZwGfAd4TEXtz5cOSlqXP15EMAE9GxG7gBUmj6aygC4G7m47ezKyDsmmh5YCI4m0a34gFu4Mk3QG8BThG0hRwFclsoCOAe9OZnmPpTKA3A1dLmgXmgEsiIhtU/iTJTKOXkIwh5McRzMwKbSlsGt+IBZNARJxfpfimGsduAbbUeG8cOGlR0ZmZFUSvDQhnfMewmVkdem1AOOMF5MzMFtCLA8IZtwTMzBaQXydI9MaAcMYtATOzefTqgHDGScDMbB5jk9MH1wmC3hkQzjgJmJnNY+jIwUOWNzjxtX/WtVjawUnAzGweM3v3U0oXvimJnhoPACcBM7N5ZVNDS8DgQKmnxgPAScDMrKZenhqa8RRRM7Maxian2T+brBXUa1NDM24JmJnVkO8KWt6DXUHgJGBmVlU/dAWBu4PMzKoam5w+eJcwPbJsdDVuCZiZVZG/P6Ccvu5FTgJmZlVs3/X8wX1xe/H+gIyTgJlZhcr1ggZ6bL2gPCcBM7MKvbqBTDV1JQFJN0t6RtL2XNkrJd0r6bfpz6G0XJKuk7RD0kOSTsl95qL0+N+mG9WbmRXO6LqjGSgJAcuXqWc2kKmm3pbALcBZFWWXAz+OiPXAj9PXAO8i2WB+PbAJuB6SpEGyP/FpwKnAVVniMDMrHOnQnz2qriQQEfcBz1UUbwRuTZ/fCpyTK78tEmPAUZKOBd4J3BsRz0XEDHAvhycWM7Ou27JtigOzyfTQubkyY5PT3Q6pbZoZE3h1ROwGSH++Ki1fATyVO24qLatVbmZWGL2+iUyldgwMV2s7xTzlh59A2iRpXNL4nj17Whqcmdl8+mlQGJpLAk+n3TykP59Jy6eAVbnjVgK75ik/TERsjoiRiBgZHh5uIkQzs8Xpp0FhaC4JbAWyGT4XAXfnyi9MZwmNAs+n3UU/AM6UNJQOCJ+ZlpmZFUufDApD/VNE7wDuB94gaUrSxcAXgHdI+i3wjvQ1wD3AJLADuAH49wAR8Rzw18Av0sfVaZmZWWH006Aw1LmAXEScX+Ott1U5NoBLa5znZuDmuqMzM+ugfhsUBt8xbGZ2UNYKgP4YFAYnATMz4PBWQD8MCoOTgJkZ0H9TQzNOAmZm9N/U0IyTgJlZpo+mhmacBMzM6L+poRknATPre/04NTTjJGBmfa9fB4WhzpvFzMx62dCRg5QkiGBwealvBoXBLQEz63MTO2e4+nuPUI6gVBJXnn1i37QCwC0BM+tzY5PT7DuQDAgTwcze/d0OqaPcEjCzvjZ05ODBAeFy+rqfOAmYWV/bvuv5gztelYRbAmZm/aJyauhAH00NzTgJmFnf6sdVQys5CZhZX+rXVUMrOQmYWV/q5xvE8hpOApLeIOnB3OOPki6T9HlJv8+Vvzv3mSsk7ZD0G0nvbM2vYGa2eKPrjmZwoMQywRF9doNYnpLdIJs8ibQM+D1wGvAx4F8i4m8rjjkBuAM4FXgt8CPg+IiYm+/cIyMjMT4+3nSMZmaVJnbOMDY5zei6o3uqFSBpIiJG6jm2VTeLvQ14PCJ2qvYSrBuBb0bEPuB3knaQJIT7WxSDmdmibFgz1FOVfyNaNSZwHslVfuZTkh6SdLOk7E94BfBU7piptMzMrOMmds7w1X/YwcTOmW6H0lVNJwFJg8B7gL9Pi64HXgecDOwGrs0OrfLxqn1RkjZJGpc0vmfPnmZDNDM7xMTOGS64cYxrf/gbLrhxrK8TQStaAu8CtkXE0wAR8XREzEVEGbiBpMsHkiv/VbnPrQR2VTthRGyOiJGIGBkeHm5BiGZmf7Jl2xT7DpQpBxyY7Z8NZKppRRI4n1xXkKRjc++9F9iePt8KnCfpCEnHAeuBn7fg+83M6tbPG8hU09TAsKQjgXcAn8gV/3dJJ5N09TyRvRcRj0i6E/gVMAtcutDMIDOzVvP9AYdqKglExF7g6Iqyj8xz/DXANc18p5lZM7L7Aw7Mllk+0L/3B2S8n4CZ9Z33nbKSSH/2cysAnATMrI9844EnufLu7cyVgyOWl3hfn7cCwGsHmVmfmNg5w5V3b2e2HASw/0B/zwrKOAmYWV8Ym5ymnFsmp9Tns4IyTgJm1heyAeGSks1jrt54Ut+PB4DHBMysT2xYM8TtHx/tyQXjmuEkYGY9L79a6KVvfX23wykUJwEz62nZOkH7Z8sMDpS4/eOjbgXkeEzAzHra2OQ0+2e9TlAtTgJm1tPyO4gtHyh5RlAFdweZWU/zgPD8nATMrOd5B7Ha3B1kZj3JO4fVxy0BM+s5nhFUP7cEzKzneOew+jkJmFlP8c5hi+MkYGY9xTuHLU7TSUDSE5IelvSgpPG07JWS7pX02/TnUFouSddJ2iHpIUmnNPv9ZmaZiZ0z7PrDiwyUxDLBEcu9c9hCWjUw/NaIeDb3+nLgxxHxBUmXp68/A7yLZIP59cBpwPXpTzOzhk3snOHb26b4+/GnmC0HA8tKfOjUVd45rA7tmh20EXhL+vxW4CckSWAjcFtEBDAm6ShJx0bE7jbFYWY9LpsJtO9A+eA4wNxcmRVHvcQJoA6tSAIB/FBSAF+PiM3Aq7OKPSJ2S3pVeuwK4KncZ6fSskOSgKRNwCaA1atXtyBEM+sl2aqgQ0cO8v3tuw9JAMLLQyxGK5LA6RGxK63o75X063mOVZWyOKwgSSSbAUZGRg5738z6V/4egHIklUqQDHAODJR4/4aV7gZahKaTQETsSn8+I+k7wKnA01k3j6RjgWfSw6eAVbmPrwR2NRuDmfWu/F4AG9YMHbIqKKQJQHD664/hsrcf78p/kZqaHSTppZJenj0HzgS2A1uBi9LDLgLuTp9vBS5MZwmNAs97PMDMasmu+q/94W+44MYxJnbOHLJNJCSV2OBAyQmgQc22BF4NfEdSdq5vRMT/lfQL4E5JFwNPAh9Ij78HeDewA9gLfKzJ7zezHlB5tZ+pthfApW99/cFVQYeOHGRm736vDtqEppJAREwC/6pK+TTwtirlAVzazHea2dJWWeHPt85PdtV/YLZ8yGCvVwVtHS8gZ2ZtUe3qvlqFX+1qPzveewG0n5OAmTWsVjdOrav7ahV+rav9jK/628tJwMyA2hV6rffm68apdXVfrcL31X53OQmY9bD5KvbK42pV6Iu5qq+nL79ahe+r/e5xEjBbYlpRsVear0JfzFV9Zr6re1f4xeIkYNYmi6ms6+0KaVXFXmm+Cn2xV/UZV/ZLg5OA2QIWU0nnP1NPZb3YbRBbVbFXWujK3Vf1vctJwHpeI5V4/rON7FVbb2W9mEodWlex1zq+1jGu7HuXk4B1TDOVcaOfb3bD8cVW0pl6K+vFVOrQ2ordDJwEbB7NVtqV52qmMm73FXkti62kM/VW1o1Mj3TFbq3kJNAFraxc23XuZivtSs1Wxu2+Iq+lmTns9VbWrtStm5wEmtCN7olOnbvZSrtSs5Vxu6/IFzqHK2nrVU4CdLYyb3Xl2q5zN1tpV2q2Mu7EFblZP+rZJNCOG2ryutU90alzt+NW/mYrY1fm1i/a2WVcqSeTQLtuqMnrZvdEp87tStes89rZZVxNTyaBdt1Qk1fU7glX3GZLWzu7jKtpOAlIWgXcBrwGKAObI+LLkj4P/BWwJz30sxFxT/qZK4CLgTngP0bED5qIvaZ23lBT+VlXuGbWSu3sMq5GyWZfDXww2UD+2IjYlu4zPAGcA3wQ+JeI+NuK408A7iDZiP61wI+A4yNibr7vGRkZifHx8UXH18k+NTOzVmq2/pI0EREj9RzbcEsg3SB+d/r8BUmPAivm+chG4JsRsQ/4naQdJAnh/kZjmI+v0s1sqepk/VVqxUkkrQXeBDyQFn1K0kOSbpaU/SYrgKdyH5ti/qRhZmZt1nQSkPQyYAtwWUT8EbgeeB1wMklL4drs0Cofr9oXJWmTpHFJ43v27Kl2iJmZtUBTSUDScpIEcHtEfBsgIp6OiLmIKAM3kHT5QHLlvyr38ZXArmrnjYjNETESESPDw8PNhGhmZvNoOAlIEnAT8GhEfDFXfmzusPcC29PnW4HzJB0h6ThgPfDzRr/fzMya18x9AqcDHwEelvRgWvZZ4HxJJ5N09TwBfAIgIh6RdCfwK2AWuHShmUFmZtZezcwO+keq9/PfM89nrgGuafQ7zcystRq+T6BTJO0BdnYxhGOAZ7v4/ZWKFg8ULybHs7CixeR4FraYmNZERF0DqoVPAt0mabzemy46oWjxQPFicjwLK1pMjmdh7YqpJfcJmJnZ0uQkYGbWx5wEFra52wFUKFo8ULyYHM/CihaT41lYW2LymICZWR9zS8DMrI85CZiZ9TEnATOzPuYk0ABJ50i6QdLdks6sVdbBeNZJuknSXbmyEyTdKel6Se8vQDwlSddI+oqkizoZzzwxvVHS1yTdJemTBYjnpZJuTf8dXdDJeHIxnJH+mdwo6Z+6EUM16Z/NhKSzCxDLYX93XYqjNXVORPTVA7gZeAbYXlF+FvAbYAdweZ3nGgJuWqisg/HclXv+aeCM9PnWAsTzXuAW4IvA27r4d3ZXlbJSQf7OPgL8u/T5t7r8b/sc4BOLjaFdMQFXA58Bzi5CPLX+LXXjz2uxdc5h39nqX6LoD+DNwCn5P2RgGfA4sA4YBP4ZOAH4c+B7FY9X5T53LXBKxfkPK+tgPPkK5VXAV4G/AX5WgHguzyqVxf7naVdM6ev3AP8EfLjb8QBXACenz7/R5X/bdwKvKML/N+DtwHnAR2k+CbTt31IrHouJL/f+ouqcykczq4guSRFxX7oTWt6pwI6ImASQ9E1gY0T8N+Cw5me6jPYXgO9HxLZaZZ2Kp8Z5nwEulbQM+Ha34yHZT2J/+nxRq8e2MSYiYiuwVdL/Ab7R5XimSPbZeJAGumpbFZek1cDzkWwS1ZQW/X97K/BSkor5RUn3RLJfSVfiaafFxJdu6bvoOqeSxwQSi9368j+QXJ28X9Il85R1JB5JR0v6GvAmSVekZWslbQZuI2kNdDUekkT0TklfAe5rMp6WxCTpLZKuk/R15ln9tlPxkPwZvU/S9cD/bjKehuJKXQz8rxZ9fzWLiikiPhcRl5Ek6RsaTQCtiqfG31071YqvJXVO37UEaqh760uAiLgOuG6hsg7GMw1cUlH2BLCpQPHsJalcWqUVMf0E+EmB4vl/wMdaFE9DcaVxXNXiGCotOiaAiLil9aEALfi7a7Oq8bWqznFLIFH31pcd4ngWVrSYihZPpohxFS2mosVTqa3xOQkkfgGsl3ScpEGSQaitjqew8RQxpqLFkyliXEWLqWjxVGpvfK0e3S76A7gD2A0cIMmwF6fl7wYeIxmF/5zjKUY8RYypaPEUOa6ixVS0eIoQnxeQMzPrY+4OMjPrY04CZmZ9zEnAzKyPOQmYmfUxJwEzsz7mJGBm1secBMzM+piTgJlZH3MSMDPrY/8fWUa5wSqxKGYAAAAASUVORK5CYII=\n",
103 |       "text/plain": [
104 |        "<Figure size 432x288 with 1 Axes>"
105 |       ]
106 |      },
107 |      "metadata": {
108 |       "needs_background": "light"
109 |      },
110 |      "output_type": "display_data"
111 |     }
112 |    ],
113 |    "source": [
114 |     "plt.semilogx(chi, T, '.')"
115 |    ]
116 |   },
117 |   {
118 |    "cell_type": "code",
119 |    "execution_count": 7,
120 |    "metadata": {},
121 |    "outputs": [
122 |     {
123 |      "data": {
124 |       "text/plain": [
125 |        "[<matplotlib.lines.Line2D at 0x7f7e0256d710>]"
126 |       ]
127 |      },
128 |      "execution_count": 7,
129 |      "metadata": {},
130 |      "output_type": "execute_result"
131 |     },
132 |     {
133 |      "data": {
134 |       "image/png": "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\n",
135 |       "text/plain": [
136 |        "<Figure size 432x288 with 1 Axes>"
137 |       ]
138 |      },
139 |      "metadata": {
140 |       "needs_background": "light"
141 |      },
142 |      "output_type": "display_data"
143 |     }
144 |    ],
145 |    "source": [
146 |     "plt.plot(chi,T,'.')"
147 |    ]
148 |   },
149 |   {
150 |    "cell_type": "code",
151 |    "execution_count": 8,
152 |    "metadata": {},
153 |    "outputs": [
154 |     {
155 |      "data": {
156 |       "text/plain": [
157 |        "[<matplotlib.lines.Line2D at 0x7f7e02676c50>]"
158 |       ]
159 |      },
160 |      "execution_count": 8,
161 |      "metadata": {},
162 |      "output_type": "execute_result"
163 |     },
164 |     {
165 |      "data": {
166 |       "image/png": 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\n",
167 |       "text/plain": [
168 |        "<Figure size 432x288 with 1 Axes>"
169 |       ]
170 |      },
171 |      "metadata": {
172 |       "needs_background": "light"
173 |      },
174 |      "output_type": "display_data"
175 |     }
176 |    ],
177 |    "source": [
178 |     "plt.plot(C, T)"
179 |    ]
180 |   },
181 |   {
182 |    "cell_type": "code",
183 |    "execution_count": 9,
184 |    "metadata": {},
185 |    "outputs": [],
186 |    "source": [
187 |     "chi_new = np.delete(chi, list_delete)\n",
188 |     "T_new = np.delete(T, list_delete)\n",
189 |     "C_new = np.delete(C, list_delete)"
190 |    ]
191 |   },
192 |   {
193 |    "cell_type": "code",
194 |    "execution_count": 10,
195 |    "metadata": {},
196 |    "outputs": [
197 |     {
198 |      "data": {
199 |       "text/plain": [
200 |        "[<matplotlib.lines.Line2D at 0x7f7e025bb6a0>]"
201 |       ]
202 |      },
203 |      "execution_count": 10,
204 |      "metadata": {},
205 |      "output_type": "execute_result"
206 |     },
207 |     {
208 |      "data": {
209 |       "image/png": "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\n",
210 |       "text/plain": [
211 |        "<Figure size 432x288 with 1 Axes>"
212 |       ]
213 |      },
214 |      "metadata": {
215 |       "needs_background": "light"
216 |      },
217 |      "output_type": "display_data"
218 |     }
219 |    ],
220 |    "source": [
221 |     "plt.plot(C_new, T_new, '.')"
222 |    ]
223 |   },
224 |   {
225 |    "cell_type": "markdown",
226 |    "metadata": {},
227 |    "source": [
228 |     "Lambda"
229 |    ]
230 |   },
231 |   {
232 |    "cell_type": "code",
233 |    "execution_count": 11,
234 |    "metadata": {},
235 |    "outputs": [],
236 |    "source": [
237 |     "for i in list_delete:\n",
238 |     "    os.remove('{}/{}'.format(dir_name,filenames[i]))"
239 |    ]
240 |   },
241 |   {
242 |    "cell_type": "code",
243 |    "execution_count": 12,
244 |    "metadata": {},
245 |    "outputs": [
246 |     {
247 |      "data": {
248 |       "text/plain": [
249 |        "array([2222., 2214., 2203., 2192., 2183., 2175., 2168., 2155., 2145.,\n",
250 |        "       2132., 2120., 2108., 2092., 2079., 2066., 2032., 2019., 2000.,\n",
251 |        "       1987., 1963., 1950., 1926., 1907., 1886., 1865., 1843., 1820.,\n",
252 |        "       1798., 1766., 1743., 1722., 1699., 1676., 1653., 1629., 1605.,\n",
253 |        "       1580., 1557., 1533., 1510., 1486., 1463., 1439., 1418., 1395.,\n",
254 |        "       1376., 1356., 1339., 1322., 1303., 1283., 1261., 1238., 1213.,\n",
255 |        "       1189., 1170., 1142., 1115., 1090., 1068., 1044., 1024., 1002.,\n",
256 |        "        973.,  952.,  931.,  905.,  887.,  855.,  836.,  812.,  796.,\n",
257 |        "        737.,  721.,  680.,  666.,  621.,  564.,  547.,  517.,  506.,\n",
258 |        "        487.,  480.,  461.,  441.,  433.,  424.,  416.,  409.,  402.,\n",
259 |        "        394.,  387.,  380.,  373.,  366.,  359.,  352.,  345.,  338.,\n",
260 |        "        331.,  324.,  317.,  310.,  303.,  298.])"
261 |       ]
262 |      },
263 |      "execution_count": 12,
264 |      "metadata": {},
265 |      "output_type": "execute_result"
266 |     }
267 |    ],
268 |    "source": [
269 |     "T"
270 |    ]
271 |   },
272 |   {
273 |    "cell_type": "code",
274 |    "execution_count": 13,
275 |    "metadata": {},
276 |    "outputs": [
277 |     {
278 |      "data": {
279 |       "text/plain": [
280 |        "array([2222., 2214., 2203., 2192., 2183., 2175., 2168., 2155., 2145.,\n",
281 |        "       2132., 2120., 2108., 2092., 2079., 2066., 2032., 2019., 2000.,\n",
282 |        "       1987., 1963., 1950., 1926., 1907., 1886., 1865., 1843., 1820.,\n",
283 |        "       1798., 1766., 1743., 1722., 1699., 1676., 1653., 1629., 1605.,\n",
284 |        "       1580., 1557., 1533., 1510., 1486., 1463., 1439., 1418., 1395.,\n",
285 |        "       1376., 1356., 1339., 1322., 1303., 1283., 1261., 1238., 1213.,\n",
286 |        "       1189., 1170., 1142., 1115., 1090., 1068., 1044., 1024., 1002.,\n",
287 |        "        973.,  952.,  931.,  905.,  887.,  855.,  836.,  812.,  796.,\n",
288 |        "        737.,  721.,  680.,  666.,  621.,  564.,  547.,  517.,  506.,\n",
289 |        "        487.,  480.,  461.,  441.,  433.,  424.,  416.,  409.,  402.,\n",
290 |        "        394.,  387.,  380.,  373.,  366.,  359.,  352.,  345.,  338.,\n",
291 |        "        331.,  324.,  317.,  310.,  303.])"
292 |       ]
293 |      },
294 |      "execution_count": 13,
295 |      "metadata": {},
296 |      "output_type": "execute_result"
297 |     }
298 |    ],
299 |    "source": [
300 |     "T_new"
301 |    ]
302 |   }
303 |  ],
304 |  "metadata": {
305 |   "kernelspec": {
306 |    "display_name": "Python 3",
307 |    "language": "python",
308 |    "name": "python3"
309 |   },
310 |   "language_info": {
311 |    "codemirror_mode": {
312 |     "name": "ipython",
313 |     "version": 3
314 |    },
315 |    "file_extension": ".py",
316 |    "mimetype": "text/x-python",
317 |    "name": "python",
318 |    "nbconvert_exporter": "python",
319 |    "pygments_lexer": "ipython3",
320 |    "version": "3.7.3"
321 |   }
322 |  },
323 |  "nbformat": 4,
324 |  "nbformat_minor": 2
325 | }
326 | 


--------------------------------------------------------------------------------
/test_beta_integration.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# beta distribution\n",
  8 |     "The distribution is\n",
  9 |     "\\begin{equation}\n",
 10 |     "    \\begin{split}\n",
 11 |     "        f(x;\\alpha,\\beta) &= \\dfrac{x^{\\alpha-1}(1-x)^{\\beta-1}}{\\int_0^1 u^{\\alpha-1}(1-u)^{\\beta-1} du} \\\\\n",
 12 |     "        & = \\dfrac{\\Gamma(\\alpha+\\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)}x^{\\alpha-1}(1-x)^{\\beta-1} \\\\\n",
 13 |     "        & = \\dfrac{1}{B(\\alpha, \\beta)}x^{\\alpha-1}(1-x)^{\\beta-1}\n",
 14 |     "    \\end{split}\n",
 15 |     "\\end{equation}\n",
 16 |     "$\\Gamma$ and $B$ are gamma and beta function respectively.\n",
 17 |     "\n",
 18 |     "Average and variance are,\n",
 19 |     "\\begin{equation}\n",
 20 |     "    \\begin{split}\n",
 21 |     "        \\bar{X} &= \\dfrac{\\alpha}{\\alpha+\\beta} \\\\\n",
 22 |     "        \\bar{X\\prime\\prime^2} &= \\dfrac{\\alpha\\beta}{(\\alpha+\\beta)^2(\\alpha+\\beta+1)} \n",
 23 |     "    \\end{split}\n",
 24 |     "\\end{equation}\n",
 25 |     "With the mean and variance,\n",
 26 |     "\\begin{equation}\n",
 27 |     "    \\begin{split}\n",
 28 |     "        \\alpha & = \\bar{X}\\left(\\dfrac{1}{\\eta_X}-1\\right) \\\\\n",
 29 |     "        \\beta & = \\left(1-\\bar{X}\\right)\\left(\\dfrac{1}{\\eta_X}-1\\right)\n",
 30 |     "    \\end{split}\n",
 31 |     "\\end{equation}\n",
 32 |     "where\n",
 33 |     "\\begin{equation}\n",
 34 |     "    \\eta_X = \\dfrac{\\bar{X\\prime\\prime^2}}{\\bar{X}\\left(1-\\bar{X}\\right)}\n",
 35 |     "\\end{equation}"
 36 |    ]
 37 |   },
 38 |   {
 39 |    "cell_type": "code",
 40 |    "execution_count": 1,
 41 |    "metadata": {},
 42 |    "outputs": [],
 43 |    "source": [
 44 |     "import sys\n",
 45 |     "import numpy as np\n",
 46 |     "import matplotlib.pyplot as plt\n",
 47 |     "import numpy.polynomial.polynomial as P\n",
 48 |     "from scipy.integrate import simps\n",
 49 |     "from scipy.stats import beta\n",
 50 |     "from scipy.interpolate import interp1d\n",
 51 |     "import scipy as sp"
 52 |    ]
 53 |   },
 54 |   {
 55 |    "cell_type": "code",
 56 |    "execution_count": 2,
 57 |    "metadata": {},
 58 |    "outputs": [],
 59 |    "source": [
 60 |     "def beta_coef(ave, var):\n",
 61 |     "    \"\"\"Obtain the coefficients for beta distribution with average and variance\"\"\"\n",
 62 |     "    a = ave*(1./var-1.)\n",
 63 |     "    b = (1.-ave)*(1./var-1.)\n",
 64 |     "    return a, b"
 65 |    ]
 66 |   },
 67 |   {
 68 |    "cell_type": "code",
 69 |    "execution_count": 3,
 70 |    "metadata": {},
 71 |    "outputs": [],
 72 |    "source": [
 73 |     "# Numerical Integration"
 74 |    ]
 75 |   },
 76 |   {
 77 |    "cell_type": "code",
 78 |    "execution_count": 4,
 79 |    "metadata": {},
 80 |    "outputs": [],
 81 |    "source": [
 82 |     "def beta_integration_direct(f, x, a, b, fit='cubic'):\n",
 83 |     "    \"\"\"Integrate over the given sample, intepolate pdf at the boundary\"\"\"\n",
 84 |     "    # f(x): function value\n",
 85 |     "    # x: axis points\n",
 86 |     "    # a: alpha for the beta distribution\n",
 87 |     "    # b: beta for the beta distribution\n",
 88 |     "    # fit: fitting formula\n",
 89 |     "    \n",
 90 |     "    rv = beta(a, b)\n",
 91 |     "    pdf = rv.pdf(x)\n",
 92 |     "    \n",
 93 |     "    y = interp1d(x[1:-1], pdf[1:-1],\n",
 94 |     "                 kind=fit,\n",
 95 |     "                 fill_value='extrapolate'\n",
 96 |     "                )\n",
 97 |     "    \n",
 98 |     "    if a < 1. :\n",
 99 |     "        pdf[0] = y(0.) if y(0.) > 0. else 0.\n",
100 |     "    if b < 1. :\n",
101 |     "        pdf[-1] = y(1.) if y(1.) > 0. else 0.\n",
102 |     "        \n",
103 |     "    return simps(f*pdf, x)"
104 |    ]
105 |   },
106 |   {
107 |    "cell_type": "code",
108 |    "execution_count": 5,
109 |    "metadata": {},
110 |    "outputs": [],
111 |    "source": [
112 |     "def beta_integration_log(f, x, a, b, fit='cubic', epsilon=1.e-9, n_ext=100):\n",
113 |     "    \"\"\"Integrate over the given sample, log spaced intepolation of function and pdf towards the boundary\"\"\"\n",
114 |     "    \n",
115 |     "    f_interp = interp1d(f, x,\n",
116 |     "                        kind = fit,\n",
117 |     "                        fill_value = 'extrapolate'\n",
118 |     "                       )\n",
119 |     "    \n",
120 |     "    if a < 1.:\n",
121 |     "        x_ext = np.logspace(np.log10(epsilon),\n",
122 |     "                            np.log10(x[1]), \n",
123 |     "                            num=n_ext\n",
124 |     "                           )\n",
125 |     "        x_ext = np.insert(x_ext, 0, 0.)\n",
126 |     "        f_ext = f_interp(x_ext)\n",
127 |     "        \n",
128 |     "        x = np.hstack((x_ext, x[2:]))\n",
129 |     "        f = np.hstack((f_ext, f[2:]))\n",
130 |     "    \n",
131 |     "    if b < 1.:\n",
132 |     "        x_ext = np.logspace(np.log10(epsilon), \n",
133 |     "                            np.log10(1.-x[-2]), \n",
134 |     "                            num=n_ext\n",
135 |     "                           )\n",
136 |     "        x_ext = np.flip( 1. - np.insert(x_ext, 0, 0.) )\n",
137 |     "        f_ext = f_interp(x_ext)\n",
138 |     "        \n",
139 |     "        x = np.hstack((x[:-2], x_ext))\n",
140 |     "        f = np.hstack((f[:-2], f_ext))\n",
141 |     "    \n",
142 |     "    rv = beta(a, b)\n",
143 |     "    pdf = rv.pdf(x)\n",
144 |     "    \n",
145 |     "    y = interp1d(x[1:-1], pdf[1:-1],\n",
146 |     "                 kind=fit,\n",
147 |     "                 fill_value='extrapolate'\n",
148 |     "                )\n",
149 |     "    \n",
150 |     "    if a < 1. :\n",
151 |     "        pdf[0] = y(0.) if y(0.) > 0. else 0.\n",
152 |     "    if b < 1. :\n",
153 |     "        pdf[-1] = y(1.) if y(1.) > 0. else 0.\n",
154 |     "        \n",
155 |     "    return simps(f*pdf, x)"
156 |    ]
157 |   },
158 |   {
159 |    "cell_type": "code",
160 |    "execution_count": 6,
161 |    "metadata": {},
162 |    "outputs": [],
163 |    "source": [
164 |     "def beta_integration_linear(f, x, a, b, fit='cubic', n_ext=100):\n",
165 |     "    \"\"\"Integrate over the given sample, linear spaced intepolation of function and pdf towards the boundary\"\"\"\n",
166 |     "    \n",
167 |     "    f_interp = interp1d(f, x,\n",
168 |     "                        kind = fit,\n",
169 |     "                        fill_value = 'extrapolate'\n",
170 |     "                       )\n",
171 |     "    \n",
172 |     "    if a < 1.:\n",
173 |     "        x_ext = np.linspace(0., x[1], num=n_ext)\n",
174 |     "        f_ext = f_interp(x_ext)\n",
175 |     "        \n",
176 |     "        x = np.hstack((x_ext, x[2:]))\n",
177 |     "        f = np.hstack((f_ext, f[2:]))\n",
178 |     "    \n",
179 |     "    if b < 1.:\n",
180 |     "        x_ext = np.linspace(x[-2], 1., num=n_ext)\n",
181 |     "        f_ext = f_interp(x_ext)\n",
182 |     "        \n",
183 |     "        x = np.hstack((x[:-2], x_ext))\n",
184 |     "        f = np.hstack((f[:-2], f_ext))\n",
185 |     "    \n",
186 |     "    rv = beta(a, b)\n",
187 |     "    pdf = rv.pdf(x)\n",
188 |     "    \n",
189 |     "    y = interp1d(x[1:-1], pdf[1:-1],\n",
190 |     "                 kind=fit,\n",
191 |     "                 fill_value='extrapolate'\n",
192 |     "                )\n",
193 |     "    \n",
194 |     "    if a < 1. :\n",
195 |     "        pdf[0] = y(0.) if y(0.) > 0. else 0.\n",
196 |     "    if b < 1. :\n",
197 |     "        pdf[-1] = y(1.) if y(1.) > 0. else 0.\n",
198 |     "        \n",
199 |     "    return simps(f*pdf, x)"
200 |    ]
201 |   },
202 |   {
203 |    "cell_type": "markdown",
204 |    "metadata": {},
205 |    "source": [
206 |     "# Analytical integration of the beta distribution\n",
207 |     "For the polynomial function\n",
208 |     "\\begin{equation}\n",
209 |     "    \\phi(x) = \\sum_{i=0}^n c_i x^i,\n",
210 |     "\\end{equation}\n",
211 |     "integration with the beta distribution\n",
212 |     "\\begin{equation}\n",
213 |     "    \\begin{split}\n",
214 |     "        \\int_{x_1}^{x_2} \\phi(x) f(x;\\alpha, \\beta) dx &= \\int_{x_1}^{x_2} \\sum_{i=0}^n c_i x^i f(x;\\alpha, \\beta) dx \\\\\n",
215 |     "        &= \\sum_{i=0}^n c_i\\dfrac{B(\\alpha+i,\\beta)}{B(\\alpha,\\beta)}\\int_{x_1}^{x_2} f(x;\\alpha+i, \\beta) dx\n",
216 |     "    \\end{split}\n",
217 |     "\\end{equation}"
218 |    ]
219 |   },
220 |   {
221 |    "cell_type": "code",
222 |    "execution_count": 7,
223 |    "metadata": {},
224 |    "outputs": [],
225 |    "source": [
226 |     "def beta_integration_analytic(f, x, a, b):\n",
227 |     "    \n",
228 |     "    rv0 = beta(a, b)\n",
229 |     "    cdf0 = rv0.cdf(x)\n",
230 |     "    B0 = sp.special.beta(a, b)\n",
231 |     "    \n",
232 |     "    rv1 = beta(a+1., b)\n",
233 |     "    cdf1 = rv1.cdf(x)\n",
234 |     "    B1 = sp.special.beta(a+1, b)\n",
235 |     "    \n",
236 |     "    c0 = np.zeros(x.size)\n",
237 |     "    c1 = np.zeros(x.size)\n",
238 |     "    \n",
239 |     "    for i in range(x.size-1):\n",
240 |     "        c = P.polyfit(x[i:i+2], f[i:i+2], 1)\n",
241 |     "        \n",
242 |     "        c0[i] -= c[0]\n",
243 |     "        c0[i+1] += c[0]\n",
244 |     "        \n",
245 |     "        c1[i] -= c[1]\n",
246 |     "        c1[i+1] += c[1]\n",
247 |     "        \n",
248 |     "    c1 *= B1/B0\n",
249 |     "    \n",
250 |     "    return np.sum(c0*cdf0+c1*cdf1)"
251 |    ]
252 |   },
253 |   {
254 |    "cell_type": "code",
255 |    "execution_count": 8,
256 |    "metadata": {},
257 |    "outputs": [],
258 |    "source": [
259 |     "def delta_integration(f, x, x_ave):\n",
260 |     "    y = interp1d(x, f, kind='cubic')\n",
261 |     "    return y(x_ave)"
262 |    ]
263 |   },
264 |   {
265 |    "cell_type": "code",
266 |    "execution_count": 9,
267 |    "metadata": {},
268 |    "outputs": [],
269 |    "source": [
270 |     "def bimodal_integration(f, x_ave):\n",
271 |     "    return f[0]*(1.-x_ave)+f[-1]*x_ave"
272 |    ]
273 |   },
274 |   {
275 |    "cell_type": "code",
276 |    "execution_count": 10,
277 |    "metadata": {},
278 |    "outputs": [],
279 |    "source": [
280 |     "def beta_integration(f, x, x_ave, x_nvar, method='analytic'):\n",
281 |     "    \n",
282 |     "    epsilon = 1.e-9\n",
283 |     "    \n",
284 |     "    if x_ave < epsilon:\n",
285 |     "        return f[0]\n",
286 |     "    elif x_ave > 1.-epsilon:\n",
287 |     "        return f[-1]\n",
288 |     "    elif x_nvar < epsilon:\n",
289 |     "        return delta_integration(f, x, x_ave)\n",
290 |     "    elif x_nvar > 1.-epsilon:\n",
291 |     "        return bimodal_integration(f, x_ave)\n",
292 |     "    else:\n",
293 |     "        a, b = beta_coef(x_ave, x_nvar)\n",
294 |     "        #return beta_integration_analytic(f, x, a, b)\n",
295 |     "        \n",
296 |     "        if method == 'analytic' :\n",
297 |     "            return beta_integration_analytic(f, x, a, b)\n",
298 |     "        elif method == 'log' :\n",
299 |     "            return beta_integration_log(v, v, a, b)\n",
300 |     "        elif method == 'linear' :\n",
301 |     "            return beta_integration_linear(v, v, a, b)\n",
302 |     "        else :\n",
303 |     "            return beta_integration_direct(v, v, a, b)"
304 |    ]
305 |   },
306 |   {
307 |    "cell_type": "code",
308 |    "execution_count": 11,
309 |    "metadata": {},
310 |    "outputs": [],
311 |    "source": [
312 |     "# load flamelet solution\n",
313 |     "flamelet = np.genfromtxt('Table_1.csv', delimiter=',', names=True)"
314 |    ]
315 |   },
316 |   {
317 |    "cell_type": "code",
318 |    "execution_count": 12,
319 |    "metadata": {},
320 |    "outputs": [],
321 |    "source": [
322 |     "methods = ['direct', 'log', 'linear', 'analytic']\n",
323 |     "ls = ['g:', 'b-.', 'c:', 'r--']\n",
324 |     "varName = 'Z'\n",
325 |     "v = flamelet[varName]\n",
326 |     "npts = 1000\n",
327 |     "\n",
328 |     "data = np.zeros((npts, len(methods)))"
329 |    ]
330 |   },
331 |   {
332 |    "cell_type": "code",
333 |    "execution_count": 14,
334 |    "metadata": {},
335 |    "outputs": [],
336 |    "source": [
337 |     "nvar = 0.8\n",
338 |     "for i, ave in enumerate(np.linspace(0., 1., num=npts)):\n",
339 |     "    for j, m in enumerate(methods):\n",
340 |     "        data[i, j] = beta_integration(v, v, ave, nvar, method=m)"
341 |    ]
342 |   },
343 |   {
344 |    "cell_type": "code",
345 |    "execution_count": 15,
346 |    "metadata": {},
347 |    "outputs": [
348 |     {
349 |      "data": {
350 |       "image/png": 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\n",
351 |       "text/plain": [
352 |        "<Figure size 432x288 with 1 Axes>"
353 |       ]
354 |      },
355 |      "metadata": {
356 |       "needs_background": "light"
357 |      },
358 |      "output_type": "display_data"
359 |     }
360 |    ],
361 |    "source": [
362 |     "plt.figure(0)\n",
363 |     "for j, m in enumerate(methods):\n",
364 |     "    plt.plot(np.linspace(0., 1., num=npts), data[:,j], ls[j], label=m, lw=1)\n",
365 |     "plt.legend()"
366 |    ]
367 |   },
368 |   {
369 |    "cell_type": "code",
370 |    "execution_count": 16,
371 |    "metadata": {},
372 |    "outputs": [],
373 |    "source": [
374 |     "ave = 0.1\n",
375 |     "for i, nvar in enumerate(np.linspace(0., 1., num=npts)):\n",
376 |     "    for j, m in enumerate(methods):\n",
377 |     "        data[i, j] = beta_integration(v, v, ave, nvar, method=m)"
378 |    ]
379 |   },
380 |   {
381 |    "cell_type": "code",
382 |    "execution_count": 17,
383 |    "metadata": {},
384 |    "outputs": [
385 |     {
386 |      "data": {
387 |       "text/plain": [
388 |        "<matplotlib.legend.Legend at 0x7f455247add8>"
389 |       ]
390 |      },
391 |      "execution_count": 17,
392 |      "metadata": {},
393 |      "output_type": "execute_result"
394 |     },
395 |     {
396 |      "data": {
397 |       "image/png": 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\n",
398 |       "text/plain": [
399 |        "<Figure size 432x288 with 1 Axes>"
400 |       ]
401 |      },
402 |      "metadata": {
403 |       "needs_background": "light"
404 |      },
405 |      "output_type": "display_data"
406 |     }
407 |    ],
408 |    "source": [
409 |     "plt.figure(1)\n",
410 |     "for j, m in enumerate(methods):\n",
411 |     "    plt.plot(np.linspace(0., 1., num=npts), data[:,j], ls[j], label=m, lw=1)\n",
412 |     "plt.legend()"
413 |    ]
414 |   }
415 |  ],
416 |  "metadata": {
417 |   "kernelspec": {
418 |    "display_name": "Python 3",
419 |    "language": "python",
420 |    "name": "python3"
421 |   },
422 |   "language_info": {
423 |    "codemirror_mode": {
424 |     "name": "ipython",
425 |     "version": 3
426 |    },
427 |    "file_extension": ".py",
428 |    "mimetype": "text/x-python",
429 |    "name": "python",
430 |    "nbconvert_exporter": "python",
431 |    "pygments_lexer": "ipython3",
432 |    "version": "3.7.3"
433 |   }
434 |  },
435 |  "nbformat": 4,
436 |  "nbformat_minor": 2
437 | }
438 | 


--------------------------------------------------------------------------------