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Code/S_polyfit.py

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+import numpy as np
+import os
+from S_polyfit_utils import getBest
+from S_polyfit_utils import basis_vector
+import itertools
+import sys
+import csv
+import sympy
+from sympy import symbols, Add, Mul, S, simplify
+from scipy.linalg import fractional_matrix_power
+
+def mk_sympy_function(coeffs, num_covariates, deg):
+    generators = [basis_vector(num_covariates+1, i) for i in range(num_covariates+1)]
+    powers = map(sum, itertools.combinations_with_replacement(generators, deg))
+    
+    coeffs = np.round(coeffs,2)
+    
+    xs = (S.One,) + symbols('z0:%d'%num_covariates)
+    if len(coeffs)>1:
+        return Add(*[coeff * Mul(*[x**deg for x, deg in zip(xs, power)])
+                     for power, coeff in zip(powers, coeffs)])
+    else:
+        return coeffs[0]
+
+def polyfit(maxdeg, filename):
+    n_variables = np.loadtxt(filename, dtype='str').shape[1]-1
+    variables = np.loadtxt(filename, usecols=(0,))
+    means = [np.mean(variables)]
+
+    for j in range(1,n_variables):
+        v = np.loadtxt(filename, usecols=(j,))
+        means = means + [np.mean(v)]
+        variables = np.column_stack((variables,v))
+       
+    f_dependent = np.loadtxt(filename, usecols=(n_variables,))
+
+    if n_variables>1:
+        C_1_2 = fractional_matrix_power(np.cov(variables.T),-1/2)
+        
+        x = []
+        z = []
+        for ii in range(len(variables[0])):
+            variables[:,ii] = variables[:,ii] - np.mean(variables[:,ii])
+            x = x + ["x"+str(ii)]
+            z = z + ["z"+str(ii)]
+
+        variables = np.matmul(C_1_2,variables.T).T
+
+        parameters = getBest(variables,f_dependent,maxdeg)[0]
+        params_error = getBest(variables,f_dependent,maxdeg)[1]
+        deg = getBest(variables,f_dependent,maxdeg)[2]     
+
+        x = sympy.Matrix(x)
+        M = sympy.Matrix(C_1_2)
+        b = sympy.Matrix(means)
+        M_x = M*(x-b)
+
+        eq = mk_sympy_function(parameters,n_variables,deg)
+        symb = sympy.Matrix(z)
+
+        for i in range(len(symb)):
+            eq = eq.subs(symb[i],M_x[i])
+
+        eq = simplify(eq)
+        
+    else:
+        parameters = getBest(variables,f_dependent,maxdeg)[0]
+        params_error = getBest(variables,f_dependent,maxdeg)[1]
+        deg = getBest(variables,f_dependent,maxdeg)[2]
+        eq = mk_sympy_function(parameters,n_variables,deg)
+        eq = eq.subs("z0","x0")  
+    
+    return (eq, params_error)
+