def test_interp_spline_akima(self):
xcp = np.array([1.0, 2.0, 4.0, 6.0, 10.0, 12.0])
ycp = np.array([5.0, 12.0, 14.0, 16.0, 21.0, 29.0])
n = 50
x = np.linspace(1.0, 12.0, n)
interp = InterpND(method='akima', points=xcp, x_interp=x, delta_x=0.1)
y = interp.evaluate_spline(ycp)
assert_near_equal(
y,
np.array([
5., 7.20902005, 9.21276849, 10.81097162, 11.80335574,
12.1278001, 12.35869145, 12.58588536, 12.81022332, 13.03254681,
13.25369732, 13.47451633, 13.69584534, 13.91852582,
14.14281484, 14.36710105, 14.59128625, 14.81544619,
15.03965664, 15.26399335, 15.48853209, 15.7133486, 15.93851866,
16.16573502, 16.39927111, 16.63928669, 16.8857123, 17.1384785,
17.39751585, 17.66275489, 17.93412619, 18.21156029,
18.49498776, 18.78433915, 19.07954501, 19.38053589,
19.68724235, 19.99959495, 20.31752423, 20.64096076,
20.96983509, 21.37579297, 21.94811407, 22.66809748,
23.51629844, 24.47327219, 25.51957398, 26.63575905,
27.80238264, 29.
]),
tolerance=1e-6)
def test_interp_spline_bsplines(self):
xcp = np.array([1.0, 2.0, 4.0, 6.0, 10.0, 12.0])
ycp = np.array([5.0, 12.0, 14.0, 16.0, 21.0, 29.0])
n = 50
x = np.linspace(1.0, 12.0, n)
interp = InterpND(method='bsplines', num_cp=6, x_interp=x)
y = interp.evaluate_spline(ycp)
assert_near_equal(
y,
np.array([
9.21614583, 9.90911525, 10.52244151, 11.06231159, 11.53491244,
11.94643105, 12.30305438, 12.61096939, 12.87636305,
13.10542234, 13.30433422, 13.47928566, 13.63646363, 13.7820551,
13.92203064, 14.05954727, 14.19579437, 14.33192094,
14.46907599, 14.60840854, 14.75106758, 14.89820214,
15.05096121, 15.2104938, 15.37794893, 15.5544756, 15.74122282,
15.9393396, 16.14997495, 16.37427787, 16.61339737, 16.86848247,
17.14102103, 17.43486416, 17.75486932, 18.10589772,
18.49281052, 18.92046894, 19.39373414, 19.91746734, 20.4965297,
21.13578243, 21.8400867, 22.61430372, 23.46329467, 24.39192074,
25.40504312, 26.507523, 27.70422156, 29.
]),
tolerance=1e-6)
def test_interp_spline_akima_derivs(self):
import numpy as np
from openmdao.components.interp_util.interp import InterpND
xcp = np.array([1.0, 2.0, 4.0, 6.0, 10.0, 12.0])
ycp = np.array([5.0, 12.0, 14.0, 16.0, 21.0, 29.0])
n = 5
x = np.linspace(1.0, 12.0, n)
interp = InterpND(method='akima', points=xcp, x_interp=x, delta_x=0.1)
y, dy_dycp = interp.evaluate_spline(ycp, compute_derivative=True)
deriv = np.array([[ 1.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[-1.86761492e-06, 3.31278014e-02, 1.05874907e+00,
-9.18750000e-02, 0.00000000e+00, 0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, -2.10964627e-01,
1.19119941e+00, 2.02602810e-02, -4.95062934e-04],
[ 0.00000000e+00, 0.00000000e+00, -2.64126732e-01,
5.82784977e-01, 6.83151998e-01, -1.81024253e-03],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 1.00000000e+00]])
assert_near_equal(deriv, dy_dycp, tolerance=1e-6)
def test_interp_akima_derivs(self):
xcp = np.array([1.0, 2.0, 4.0, 6.0, 10.0, 12.0])
ycp = np.array([5.0, 12.0, 14.0, 16.0, 21.0, 29.0])
n = 23
x = np.linspace(1.0, 12.0, n)
interp = InterpND(method='akima', points=xcp, x_interp=x, delta_x=0.1)
y, dy_dycp = interp.evaluate_spline(ycp, compute_derivative=True)
deriv = np.array([[ 1.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 3.12508538e-01, 7.81237193e-01, -9.37457312e-02,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 0.00000000e+00, 1.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[-1.92097534e-05, 7.05028815e-01, 3.39990395e-01,
-4.50000000e-02, 0.00000000e+00, 0.00000000e+00],
[-1.70753364e-05, 3.80025613e-01, 7.39991462e-01,
-1.20000000e-01, 0.00000000e+00, 0.00000000e+00],
[-6.40325114e-06, 1.15009605e-01, 1.01999680e+00,
-1.35000000e-01, 0.00000000e+00, 0.00000000e+00],
[ 0.00000000e+00, 1.11022302e-16, 1.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 0.00000000e+00, -5.62500000e-03, 7.60412946e-01,
2.45667949e-01, -5.30632175e-04, 7.47369260e-05],
[ 0.00000000e+00, -5.00000000e-03, 5.07767857e-01,
4.98447864e-01, -1.41501913e-03, 1.99298469e-04],
[ 0.00000000e+00, -1.87500000e-03, 2.51238839e-01,
7.52003846e-01, -1.59189652e-03, 2.24210778e-04],
[ 0.00000000e+00, 0.00000000e+00, 1.11022302e-16,
1.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, -2.10964627e-01,
1.19119941e+00, 2.02602810e-02, -4.95062934e-04],
[ 0.00000000e+00, 0.00000000e+00, -3.55003720e-01,
1.28195585e+00, 7.41473347e-02, -1.09946322e-03],
[ 0.00000000e+00, 0.00000000e+00, -4.35442243e-01,
1.27731946e+00, 1.59810592e-01, -1.68780891e-03],
[ 0.00000000e+00, 0.00000000e+00, -4.55605159e-01,
1.18234038e+00, 2.75399483e-01, -2.13470805e-03],
[ 0.00000000e+00, 0.00000000e+00, -4.18817429e-01,
1.00206876e+00, 4.19063438e-01, -2.31476868e-03],
[ 0.00000000e+00, 0.00000000e+00, -3.28404018e-01,
7.41554727e-01, 5.88951889e-01, -2.10259885e-03],
[ 0.00000000e+00, 0.00000000e+00, -1.87689887e-01,
4.05848427e-01, 7.83214266e-01, -1.37280661e-03],
[ 0.00000000e+00, 0.00000000e+00, 2.22044605e-16,
0.00000000e+00, 1.00000000e+00, 4.33680869e-19],
[ 0.00000000e+00, 0.00000000e+00, 1.18164062e-01,
-2.58789062e-01, 1.05371094e+00, 8.69140625e-02],
[ 0.00000000e+00, 0.00000000e+00, 1.05034722e-01,
-2.50868056e-01, 8.32465278e-01, 3.13368056e-01],
[ 0.00000000e+00, 0.00000000e+00, 3.93880208e-02,
-1.17513021e-01, 4.44986979e-01, 6.33138021e-01],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 1.00000000e+00]])
assert_near_equal(deriv, dy_dycp, tolerance=1e-6)
def test_cs_across_interp(self):
# The standalone interpolator is used inside of components, so the imaginary part must
# be carried through all operations to the outputs.
xcp = np.array([1.0, 2.0, 4.0, 6.0, 10.0, 12.0])
ycp = np.array([5.0, 12.0, 14.0, 16.0, 21.0, 29.0])
n = 50
x = np.linspace(1.0, 12.0, n)
ycp = np.array([[5.0 + 1j, 12.0, 14.0, 16.0, 21.0, 29.0],
[5.0, 12.0 + 1j, 14.0, 16.0, 21.0, 29.0]])
for method in SPLINE_METHODS:
# complex step not supported on scipy methods
if method.startswith('scipy'):
continue
interp = InterpND(method=method, points=xcp, x_interp=x)
y, dy = interp.evaluate_spline(ycp, compute_derivative=True)
self.assertTrue(y.dtype == complex)
if method in ['akima']:
# Derivs depend on values only for akima.
self.assertTrue(dy.dtype == complex)
p1 = np.linspace(0, 100, 25)
p2 = np.linspace(-10, 10, 5)
p3 = np.linspace(0, 1, 10)
# can use meshgrid to create a 3D array of test data
P1, P2, P3 = np.meshgrid(p1, p2, p3, indexing='ij')
f = np.sqrt(P1) + P2 * P3
x = np.array([[55.12 + 1j, -2.14, 0.323],
[55.12, -2.14 + 1j, 0.323],
[55.12, -2.14, 0.323 + 1j]])
for method in TABLE_METHODS:
# complex step not supported on scipy methods
if method.startswith('scipy'):
continue
if method in ['1D-akima', 'akima1D']:
# These methods are for fixed grids other than 3d.
continue
interp = InterpND(method=method, points=(p1, p2, p3), values=f)
y, dy = interp.interpolate(x, compute_derivative=True)
self.assertTrue(y.dtype == complex)
self.assertTrue(dy.dtype == complex)
def test_interpolating_spline_derivs(self):
n_cp = 12
n_point = 21
t = np.linspace(0, 3.0*np.pi, n_cp)
tt = np.linspace(0, 3.0*np.pi, n_point)
x = np.sin(t)
for method in self.spline_methods:
interp = InterpND(method=method, points=t, x_interp=tt)
computed, deriv = interp.evaluate_spline(x, compute_derivative=True)
x_expected = np.sin(tt)
delta = computed.flatten() - x_expected
# Here we test that we don't have crazy interpolation error.
self.assertLess(max(delta), .25)
def test_bsplines_interpolating_spline(self):
n_cp = 80
n_point = 160
t = np.linspace(0, 3.0 * np.pi, n_cp)
tt = np.linspace(0, 3.0 * np.pi, n_point)
x = np.sin(t)
# Now, test newer interface for order_reducing spline.
interp = InterpND(method='bsplines', points=t, x_interp=tt)
computed = interp.evaluate_spline(x)
x_expected = np.sin(tt)
delta = computed.flatten() - x_expected
# Here we test that we don't have crazy interpolation error.
self.assertLess(max(delta), .15)
# And that it gets middle points a little better.
self.assertLess(max(delta[15:-15]), .06)
