86 lines
1.7 KiB
Python
86 lines
1.7 KiB
Python
import numpy as np
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def rms(errors):
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"""
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root mean square calculation
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"""
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# slow pure python way for reference:
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# r = 0.0
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# for i in errors:
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# r += np.power(i, 2)
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# r = np.sqrt(r / len(errors))
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# return r
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return np.sqrt((errors ** 2).mean())
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def baker_exact_2D(X):
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"""
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the exact function (2D) used from baker's article (for testing,
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slightly modified)
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"""
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x, y = X
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answer = np.power((np.sin(x * np.pi) * np.cos(y * np.pi)), 2)
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return answer
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def friendly_exact_2D(X):
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"""
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A friendlier 2D func
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"""
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x, y = X
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answer = 1.0 + x * x + y * y
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return answer
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def baker_exact_3D(X):
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"""
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the exact function (3D) used from baker's article (for testing)
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"""
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x, y, z = X
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answer = np.power((np.sin(x * np.pi / 2.0) * np.sin(y * np.pi / 2.0) *
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np.sin(z * np.pi / 2.0)), 2)
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return answer
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def exact_me(points, f):
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a = np.array([f(i) for i in points])
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return a
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def friendly_exact_3D(X):
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x, y, z = X
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return 1 + x * x + y * y + z * z
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def scipy_exact_2D(X):
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x, y = X
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return x * (1 - x) * np.cos(4 * np.pi * x) *\
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np.sin(4 * np.pi * y ** 2) ** 2
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def improved_answer(answer, exact):
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if not answer.error:
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# was probably just a linear interpolation
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return False
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if np.abs(answer.final - exact) <= np.abs(answer.qlin - exact):
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return True
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else:
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return False
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def identical_points(a, b):
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return all(set(j[i] for j in a) \
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== set(j[i] for j in b) for i in xrange(len(a[0])))
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def improved(qlin, err, final, exact):
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if np.abs(final - exact) <= np.abs(qlin - exact):
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return True
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else:
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return False
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