def test_basis_func(self):
p = poly.Chebyshev([1, 2, 3])
assert_equal(self.as_latex(p),
r'$x \mapsto 1.0\,{T}_{0}(x) + 2.0\,{T}_{1}(x) + 3.0\,{T}_{2}(x)$')
# affine input - check no surplus parens are added
p = poly.Chebyshev([1, 2, 3], domain=[-1, 0])
assert_equal(self.as_latex(p),
r'$x \mapsto 1.0\,{T}_{0}(1.0 + 2.0x) + 2.0\,{T}_{1}(1.0 + 2.0x) + 3.0\,{T}_{2}(1.0 + 2.0x)$')
def __get_collocation_nodes(self, m, kind):
"""Computes the collocation nodes."""
# basis coefs
coefs = np.zeros(m + 1)
coefs[-1] = 1
if kind == 'polynomial':
nodes = polynomial.Polynomial(coefs).roots()
elif kind == 'chebyshev':
domain = [self.a, self.b]
nodes = polynomial.Chebyshev(coefs, domain).roots()
elif kind == 'legendre':
domain = [self.a, self.b]
nodes = polynomial.Legendre(coefs, domain).roots()
elif kind == 'laguerre':
domain = [self.a, self.b]
nodes = polynomial.Laguerre(coefs, domain).roots()
elif kind == 'hermite':
domain = [self.a, self.b]
nodes = polynomial.Hermite(coefs, domain).roots()
else:
raise ValueError
return nodes
def test_set_default_printoptions():
p = poly.Polynomial([1, 2, 3])
c = poly.Chebyshev([1, 2, 3])
poly.set_default_printstyle("ascii")
assert_equal(str(p), "1.0 + 2.0 x**1 + 3.0 x**2")
assert_equal(str(c), "1.0 + 2.0 T_1(x) + 3.0 T_2(x)")
poly.set_default_printstyle("unicode")
assert_equal(str(p), "1.0 + 2.0·x¹ + 3.0·x²")
assert_equal(str(c), "1.0 + 2.0·T₁(x) + 3.0·T₂(x)")
with pytest.raises(ValueError):
poly.set_default_printstyle("invalid_input")
def __get_cheb_yhat(self, coefs):
"""Constructs a Chebyshev polynomial approximation to the solution."""
# the solution y is in R^n
n = coefs.shape[0]
# create the approximation yhat
domain = [self.a, self.b]
yhat = [polynomial.Chebyshev(coefs[i], domain) for i in range(n)]
# create the approximation of yhat_prime
yhat_prime = [yhat[i].deriv() for i in range(n)]
return [yhat, yhat_prime]
def __init__(self, rect, n=11):
super().__init__()
self.image = pygame.Surface(rect.size, depth=32)
self.rect = self.image.get_rect(topleft=rect.topleft)
self.image.set_colorkey(self.clear)
p = P.Chebyshev(tycho).linspace(n)
# scale x terms to rect width
w2 = self.rect.w / 2
X = (p[0] * w2) + w2
# scale y terms to rect height
Y = abs(p[1] - p[1][0])
Y *= (self.rect.h - 10) / Y.max()
# self.points = [self.rect.rect.topleft
pts = [(int(x), int(y)) for x, y in zip(X, Y)]
self.pads = [LandingPad(p, 30) for p in pts[1:-1]]
self.points = [pts[0]]
for p in self.pads:
self.points.append(p.rect.bottomleft)
self.points.append(p.rect.bottomright)
self.points.extend(
[pts[-1], self.rect.bottomright, self.rect.bottomleft])
# relocate the pad to world coordinates
for pad in self.pads:
x, y = pad.rect.center
a, b = self.rect.topleft
pad.rect.center = a + x, b + y
self.render()
def test_chebyshev_str(self):
res = repr(poly.Chebyshev([0, 1]))
tgt = 'Chebyshev([0., 1.], domain=[-1, 1], window=[-1, 1])'
assert_equal(res, tgt)
def test_chebyshev_str(self):
res = str(poly.Chebyshev([0, 1]))
tgt = 'cheb([0. 1.])'
assert_equal(res, tgt)
def test_chebyshev_str(self):
res = repr(poly.Chebyshev([0,1]))
tgt = 'Chebyshev([0., 1.], [-1., 1.], [-1., 1.])'
assert_(res, tgt)
def test_chebyshev_str(self):
res = str(poly.Chebyshev([0,1]))
tgt = 'leg([0., 1.])'
assert_(res, tgt)
def test_chebyshev_str(self, inp, tgt):
res = str(poly.Chebyshev(inp))
assert_equal(res, tgt)
# In[24]: p3 # In[25]: p3.roots() # In[26]: p2 # In[27]: c1 = P.Chebyshev([1, 2, 3]) # In[28]: c1 # In[29]: c1.roots() # In[30]: c = P.Chebyshev.fromroots([-1, 1]) # In[31]:
def test_chebyshev_str(self):
res = repr(poly.Chebyshev([0, 1]))
tgt = ("Chebyshev([0., 1.], domain=[-1, 1], window=[-1, 1], "
"symbol='x')")
assert_equal(res, tgt)
# Programa de Franco Benassi
# Proyecto #3 Interfaces Graficas 2020
# Ejercicio 6
import numpy as np
from numpy.linalg import linalg
import numpy.polynomial as P
import matplotlib.pyplot as pt
data = np.load("/home/franco-os/Documentos/Informática/Interfaces de Grafica de Usuario/Proyecto 3/datas/cheby.npy")
x = data[0]
y = data[1]
deg = len(x)-1
A = P.chebyshev.chebvander(x,deg)
c = linalg.solve(A,y)
Resutl = P.Chebyshev(c)
xx = np.linspace(x.min(),x.max(),100)
pt.plot(xx,Resutl(xx),'r',label="Interpolación Chebychev")
pt.scatter(x,y,label="Puntos de datos")
pt.ylabel("F(x)")
pt.xlabel("T(s)")
pt.legend()
pt.show()
