Copyright (C) 2020 Andreas Kloeckner
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-1, 1, 5)
xx = np.linspace(-1, 1, 100)
def f(x):
return np.sin(5/(1.6-x))
plt.plot(xx, f(xx))
plt.plot(x, f(x), "o")
[<matplotlib.lines.Line2D at 0x7f071da8f790>]
dmat = x.reshape(-1, 1) - x
np.fill_diagonal(dmat, 1)
dmat[0, 2], x[0]-x[2]
(-1.0, -1.0)
w = 1/dmat.prod(axis=1)
w
array([ 0.66666667, -2.66666667, 4. , -2.66666667, 0.66666667])
def bary_first_form(z, f):
z = z[:, np.newaxis]
ell = (z-x).prod(axis=-1)
return ell * (w / (z - x) * f(x)).sum(axis=-1)
plt.plot(xx, bary_first_form(xx, f))
plt.plot(xx, f(xx))
/home/andreas/src/env-3.7/lib/python3.7/site-packages/ipykernel_launcher.py:4: RuntimeWarning: divide by zero encountered in true_divide after removing the cwd from sys.path. /home/andreas/src/env-3.7/lib/python3.7/site-packages/ipykernel_launcher.py:4: RuntimeWarning: invalid value encountered in multiply after removing the cwd from sys.path.
[<matplotlib.lines.Line2D at 0x7f071be80650>]
def bary_second_form(z, f, weights=None):
if weights is None:
weights = w
z = z[:, np.newaxis]
num = (weights / (z - x) * f(x)).sum(axis=-1)
denom = (weights / (z - x)).sum(axis=-1)
return num/denom
wr = w.copy()
wr[:] = np.random.randn(len(x))
plt.plot(xx, bary_second_form(xx, f))
plt.plot(xx, bary_second_form(xx, f, weights=wr))
plt.plot(xx, f(xx))
plt.plot(x, f(x), "o")
plt.ylim([-2, 2])
/home/andreas/src/env-3.7/lib/python3.7/site-packages/ipykernel_launcher.py:5: RuntimeWarning: divide by zero encountered in true_divide """ /home/andreas/src/env-3.7/lib/python3.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in true_divide /home/andreas/src/env-3.7/lib/python3.7/site-packages/ipykernel_launcher.py:7: RuntimeWarning: invalid value encountered in true_divide import sys
(-2, 2)