bootstrap

prior-art/Code/S_polyfit_utils.py

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+import numpy as np
+from numpy import linalg, zeros, ones, hstack, asarray
+import itertools
+from matplotlib import pyplot as plt
+from scipy.sparse.linalg import lsqr
+import os
+from sympy import symbols, Add, Mul, S
+
+
+def basis_vector(n, i):
+    x = zeros(n, dtype=int)
+    x[i] = 1
+    return x
+
+def as_tall(x):
+    return x.reshape(x.shape + (1,))
+
+
+def multipolyfit(xs, y, deg):
+    
+    y = asarray(y).squeeze()
+    rows = y.shape[0]
+    xs = asarray(xs)
+    try:
+        num_covariates = xs.shape[1]
+    except:
+        num_covariates = 1
+        xs = np.reshape(xs,(len(xs),1))
+
+    xs = hstack((ones((xs.shape[0], 1), dtype=xs.dtype) , xs))
+    
+    generators = [basis_vector(num_covariates+1, i) for i in range(num_covariates+1)]
+        
+    # All combinations of degrees
+    powers = map(sum, itertools.combinations_with_replacement(generators, deg))
+
+    # Raise data to specified degree pattern, stack in order
+    A = hstack(asarray([as_tall((xs**p).prod(1)) for p in powers]))
+    params = lsqr(A, y)[0] # get the best params of the fit
+    rms = lsqr(A, y)[4] # get the rms params of the fit
+    
+    return (params, rms)
+
+
+def getBest(xs,y,max_deg):
+    results = []
+    for i in range(0,max_deg+1):
+        results = results + [multipolyfit(xs,y,i)]
+    results = np.array(results)
+    # get the parameters and error of the fit with the lowest rms error
+    params = results[np.argmin(results[:,1:])][0]
+    error = results[np.argmin(results[:,1:])][1]
+    deg = np.argmin(results[:,1:])
+    return (params, error, deg)
+