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97 lines
2.6 KiB
97 lines
2.6 KiB
6 years ago
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import timeit
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import numpy as np
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import numpy.linalg
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from scipy.linalg import cho_factor, cho_solve
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# We are trying to solve the following system
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# (A.T * A) * x = A.T * b
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# Where x are the polynomial coefficients and b is are the input points
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# First we build A
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deg = 3
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x = np.arange(50 * 1.0)
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A = np.vstack(tuple(x**n for n in range(deg, -1, -1))).T
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# The first way to solve this is using the pseudoinverse, which can be precomputed
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# x = (A.T * A)^-1 * A^T * b = PINV b
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PINV = np.linalg.pinv(A)
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# Another way is using the Cholesky decomposition
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# We can note that at (A.T * A) is always positive definite
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# By precomputing the Cholesky decomposition we can efficiently solve
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# systems of the form (A.T * A) x = c
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CHO = cho_factor(np.dot(A.T, A))
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def model_polyfit_old(points, deg=3):
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A = np.vstack(tuple(x**n for n in range(deg, -1, -1))).T
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pinv = np.linalg.pinv(A)
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return np.dot(pinv, map(float, points))
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def model_polyfit(points, deg=3):
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A = np.vander(x, deg + 1)
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pinv = np.linalg.pinv(A)
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return np.dot(pinv, map(float, points))
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def model_polyfit_cho(points, deg=3):
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A = np.vander(x, deg + 1)
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cho = cho_factor(np.dot(A.T, A))
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c = np.dot(A.T, points)
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return cho_solve(cho, c, check_finite=False)
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def model_polyfit_np(points, deg=3):
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return np.polyfit(x, points, deg)
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def model_polyfit_lstsq(points, deg=3):
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A = np.vander(x, deg + 1)
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return np.linalg.lstsq(A, points, rcond=None)[0]
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TEST_DATA = np.linspace(0, 5, num=50) + 1.
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def time_pinv_old():
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model_polyfit_old(TEST_DATA)
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def time_pinv():
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model_polyfit(TEST_DATA)
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def time_cho():
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model_polyfit_cho(TEST_DATA)
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def time_np():
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model_polyfit_np(TEST_DATA)
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def time_lstsq():
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model_polyfit_lstsq(TEST_DATA)
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if __name__ == "__main__":
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# Verify correct results
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pinv_old = model_polyfit_old(TEST_DATA)
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pinv = model_polyfit(TEST_DATA)
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cho = model_polyfit_cho(TEST_DATA)
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numpy = model_polyfit_np(TEST_DATA)
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lstsq = model_polyfit_lstsq(TEST_DATA)
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assert all(np.isclose(pinv, pinv_old))
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assert all(np.isclose(pinv, cho))
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assert all(np.isclose(pinv, numpy))
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assert all(np.isclose(pinv, lstsq))
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# Run benchmark
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print("Pseudo inverse (old)", timeit.timeit("time_pinv_old()", setup="from __main__ import time_pinv_old", number=10000))
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print("Pseudo inverse", timeit.timeit("time_pinv()", setup="from __main__ import time_pinv", number=10000))
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print("Cholesky", timeit.timeit("time_cho()", setup="from __main__ import time_cho", number=10000))
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print("Numpy leastsq", timeit.timeit("time_lstsq()", setup="from __main__ import time_lstsq", number=10000))
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print("Numpy polyfit", timeit.timeit("time_np()", setup="from __main__ import time_np", number=10000))
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