import sys
sys.path.insert(1, '..')
from math import log
import unittest
import numpy as np
from findiff.operators import FinDiff
class TestScaling(unittest.TestCase):
def fit_1d(self, acc):
nx_list = 10 ** np.linspace(1.75, 2., 10)
Lx = np.pi
log_err_list = []
log_dx_list = []
for nx in nx_list:
x = np.linspace(0., Lx, nx)
dx = x[1] - x[0]
f = np.sin(x)
d_dx = FinDiff(0, dx)
fx = d_dx(f, acc=acc)
fxe = np.cos(x)
err = np.max(np.abs(fxe - fx))
log_dx_list.append(log(dx))
log_err_list.append(log(err))
fit = np.polyfit(log_dx_list, log_err_list, deg=1)
return fit[0]
def fit_2d(self, acc):
nx_list = [10, 30, 100, 300]
ny_list = [10, 30, 100, 300]
Lx, Ly = 3, 3
log_err_list = []
log_dx_list = []
for nx, ny in zip(nx_list, ny_list):
x = np.linspace(0, Lx, nx)
y = np.linspace(0, Ly, ny)
dx, dy = x[1] - x[0], y[1] - y[0]
X, Y = np.meshgrid(x, y, indexing='ij')
f = np.sin(X) * np.sin(Y)
d_dx = FinDiff(0, dx)
fx = d_dx(f, acc=acc)
fxe = np.cos(X) * np.sin(Y)
err = np.max(np.abs(fxe - fx))
log_dx_list.append(log(dx))
log_err_list.append(log(err))
fit = np.polyfit(log_dx_list, log_err_list, deg=1)
return fit[0]
def test_1d_acc2(self):
self.assertAlmostEqual(2, self.fit_1d(acc=2), 1)
def test_1d_acc4(self):
self.assertAlmostEqual(4, self.fit_1d(acc=4), 1)
def test_1d_acc6(self):
self.assertAlmostEqual(6, self.fit_1d(acc=6), 1)
def test_2d_acc2(self):
self.assertAlmostEqual(2, self.fit_2d(acc=2), 1)
def test_2d_acc4(self):
self.assertAlmostEqual(4, self.fit_2d(acc=4), 1)
if __name__ == '__main__':
unittest.main()
