def test_3_points_degree_2():
d = 2
X = [-3, 10, 19]
Y = [3, -4, 30]
spline = interpolating_spline(d, x, X, Y)
assert spline == Piecewise((505*x**2/2574 - x*Rational(4921, 2574) - Rational(1931, 429), (x >= -3) & (x <= 19)))
def test_3_points_degree_2():
d = 2
X = [-3, 10, 19]
Y = [3, -4, 30]
spline = interpolating_spline(d, x, X, Y)
assert spline == Piecewise((505*x**2/2574 - 4921*x/2574 - S(1931)/429, (x >= -3) & (x <= 19)))
def test_3_points_degree_2():
d = 2
X = [-3, 10, 19]
Y = [3, -4, 30]
spline = interpolating_spline(d, x, X, Y)
assert spline == Piecewise((505*x**2/2574 - 4921*x/2574 - S(1931)/429, (x >= -3) & (x <= 19)))
def test_6_points_degree_3():
d = 3
X = [-1, 0, 2, 3, 9, 12]
Y = [-4, 3, 3, 7, 9, 20]
spline = interpolating_spline(d, x, X, Y)
assert spline == Piecewise((6058*x**3/5301 - 18427*x**2/5301 + 12622*x/5301 + 3, (x >= -1) & (x <= 2)),
(-8327*x**3/5301 + 67883*x**2/5301 - 159998*x/5301 + S(43661)/1767, (x >= 2) & (x <= 3)),
(5414*x**3/47709 - 1386*x**2/589 + 4267*x/279 - S(12232)/589, (x >= 3) & (x <= 12)))
def test_5_points_degree_2():
d = 2
X = [-3, 2, 4, 5, 10]
Y = [-1, 2, 5, 10, 14]
spline = interpolating_spline(d, x, X, Y)
assert spline == Piecewise((4*x**2/329 + 1007*x/1645 + S(1196)/1645, (x >= -3) & (x <= 3)),
(2701*x**2/1645 - 15079*x/1645 + S(5065)/329, (x >= 3) & (x <= S(9)/2)),
(-1319*x**2/1645 + 21101*x/1645 - S(11216)/329, (x >= S(9)/2) & (x <= 10)))
def test_6_points_degree_3():
d = 3
X = [-1, 0, 2, 3, 9, 12]
Y = [-4, 3, 3, 7, 9, 20]
spline = interpolating_spline(d, x, X, Y)
assert spline == Piecewise((6058*x**3/5301 - 18427*x**2/5301 + x*Rational(12622, 5301) + 3, (x >= -1) & (x <= 2)),
(-8327*x**3/5301 + 67883*x**2/5301 - x*Rational(159998, 5301) + Rational(43661, 1767), (x >= 2) & (x <= 3)),
(5414*x**3/47709 - 1386*x**2/589 + x*Rational(4267, 279) - Rational(12232, 589), (x >= 3) & (x <= 12)))
def test_5_points_degree_2():
d = 2
X = [-3, 2, 4, 5, 10]
Y = [-1, 2, 5, 10, 14]
spline = interpolating_spline(d, x, X, Y)
assert spline == Piecewise((4*x**2/329 + x*Rational(1007, 1645) + Rational(1196, 1645), (x >= -3) & (x <= 3)),
(2701*x**2/1645 - x*Rational(15079, 1645) + Rational(5065, 329), (x >= 3) & (x <= Rational(9, 2))),
(-1319*x**2/1645 + x*Rational(21101, 1645) - Rational(11216, 329), (x >= Rational(9, 2)) & (x <= 10)))
def test_6_points_degree_3():
d = 3
X = [-1, 0, 2, 3, 9, 12]
Y = [-4, 3, 3, 7, 9, 20]
spline = interpolating_spline(d, x, X, Y)
assert spline == Piecewise((6058*x**3/5301 - 18427*x**2/5301 + 12622*x/5301 + 3, (x >= -1) & (x <= 2)),
(-8327*x**3/5301 + 67883*x**2/5301 - 159998*x/5301 + S(43661)/1767, (x >= 2) & (x <= 3)),
(5414*x**3/47709 - 1386*x**2/589 + 4267*x/279 - S(12232)/589, (x >= 3) & (x <= 12)))
def test_5_points_degree_2():
d = 2
X = [-3, 2, 4, 5, 10]
Y = [-1, 2, 5, 10, 14]
spline = interpolating_spline(d, x, X, Y)
assert spline == Piecewise((4*x**2/329 + 1007*x/1645 + S(1196)/1645, (x >= -3) & (x <= 3)),
(2701*x**2/1645 - 15079*x/1645 + S(5065)/329, (x >= 3) & (x <= S(9)/2)),
(-1319*x**2/1645 + 21101*x/1645 - S(11216)/329, (x >= S(9)/2) & (x <= 10)))
def test_10_points_degree_1():
d = 1
X = [-5, 2, 3, 4, 7, 9, 10, 30, 31, 34]
Y = [-10, -2, 2, 4, 7, 6, 20, 45, 19, 25]
spline = interpolating_spline(d, x, X, Y)
assert spline == Piecewise((8*x/7 - S(30)/7, (x >= -5) & (x <= 2)), (4*x - 10, (x >= 2) & (x <= 3)),
(2*x - 4, (x >= 3) & (x <= 4)), (x, (x >= 4) & (x <= 7)),
(-x/2 + S(21)/2, (x >= 7) & (x <= 9)), (14*x - 120, (x >= 9) & (x <= 10)),
(5*x/4 + S(15)/2, (x >= 10) & (x <= 30)), (-26*x + 825, (x >= 30) & (x <= 31)),
(2*x - 43, (x >= 31) & (x <= 34)))
def test_10_points_degree_1():
d = 1
X = [-5, 2, 3, 4, 7, 9, 10, 30, 31, 34]
Y = [-10, -2, 2, 4, 7, 6, 20, 45, 19, 25]
spline = interpolating_spline(d, x, X, Y)
assert spline == Piecewise((x*Rational(8, 7) - Rational(30, 7), (x >= -5) & (x <= 2)), (4*x - 10, (x >= 2) & (x <= 3)),
(2*x - 4, (x >= 3) & (x <= 4)), (x, (x >= 4) & (x <= 7)),
(-x/2 + Rational(21, 2), (x >= 7) & (x <= 9)), (14*x - 120, (x >= 9) & (x <= 10)),
(x*Rational(5, 4) + Rational(15, 2), (x >= 10) & (x <= 30)), (-26*x + 825, (x >= 30) & (x <= 31)),
(2*x - 43, (x >= 31) & (x <= 34)))
def test_10_points_degree_1():
d = 1
X = [-5, 2, 3, 4, 7, 9, 10, 30, 31, 34]
Y = [-10, -2, 2, 4, 7, 6, 20, 45, 19, 25]
spline = interpolating_spline(d, x, X, Y)
assert spline == Piecewise((8*x/7 - S(30)/7, (x >= -5) & (x <= 2)), (4*x - 10, (x >= 2) & (x <= 3)),
(2*x - 4, (x >= 3) & (x <= 4)), (x, (x >= 4) & (x <= 7)),
(-x/2 + S(21)/2, (x >= 7) & (x <= 9)), (14*x - 120, (x >= 9) & (x <= 10)),
(5*x/4 + S(15)/2, (x >= 10) & (x <= 30)), (-26*x + 825, (x >= 30) & (x <= 31)),
(2*x - 43, (x >= 31) & (x <= 34)))
def test_issue_19262():
Delta = symbols('Delta', positive=True)
knots = [i*Delta for i in range(4)]
basis = bspline_basis_set(1, knots, x)
y = symbols('y', nonnegative=True)
basis2 = bspline_basis_set(1, knots, y)
assert basis[0].subs(x, y) == basis2[0]
assert interpolating_spline(1, x,
[Delta*i for i in [1, 2, 4, 7]], [3, 6, 5, 7]
) == Piecewise((3*x/Delta, (Delta <= x) & (x <= 2*Delta)),
(7 - x/(2*Delta), (x >= 2*Delta) & (x <= 4*Delta)),
(Rational(7, 3) + 2*x/(3*Delta), (x >= 4*Delta) & (x <= 7*Delta)))
