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