def test_basic_degree_0():
d = 0
knots = range(5)
splines = bspline_basis_set(d, knots, x)
for i in range(len(splines)):
assert splines[i] == Piecewise((1, Interval(i, i + 1).contains(x)),
(0, True))
def test_basic_degree_0():
d = 0
knots = range(5)
splines = bspline_basis_set(d, knots, x)
for i in range(len(splines)):
assert splines[i] == Piecewise((1, Interval(i, i + 1).contains(x)),
(0, True))
def test_basic_degree_3():
d = 3
knots = range(5)
splines = bspline_basis_set(d, knots, x)
b0 = Piecewise((x**3 / 6, Interval(0, 1, False, True).contains(x)),
(Rational(2, 3) - 2 * x + 2 * x**2 - x**3 / 2,
Interval(1, 2, False, True).contains(x)),
(Rational(-22, 3) + 10 * x - 4 * x**2 + x**3 / 2,
Interval(2, 3, False, True).contains(x)),
(Rational(32, 3) - 8 * x + 2 * x**2 - x**3 / 6,
Interval(3, 4).contains(x)), (0, True))
assert splines[0] == b0
def test_basic_degree_3():
d = 3
knots = range(5)
splines = bspline_basis_set(d, knots, x)
b0 = Piecewise((x**3/6, Interval(0, 1, False, True).contains(x)),
(Rational(2, 3) - 2*x + 2*x**2 - x**3/2,
Interval(1, 2, False, True).contains(x)),
(Rational(-22, 3) + 10*x - 4*x**2 + x**3/2,
Interval(2, 3, False, True).contains(x)),
(Rational(32, 3) - 8*x + 2*x**2 - x**3/6,
Interval(3, 4).contains(x)), (0, True))
assert splines[0] == b0
def test_basic_degree_1():
d = 1
knots = range(5)
splines = bspline_basis_set(d, knots, x)
assert splines[0] == Piecewise(
(x, Interval(0, 1, False, True).contains(x)),
(2 - x, Interval(1, 2).contains(x)), (0, True))
assert splines[1] == Piecewise(
(-1 + x, Interval(1, 2, False, True).contains(x)),
(3 - x, Interval(2, 3).contains(x)), (0, True))
assert splines[2] == Piecewise(
(-2 + x, Interval(2, 3, False, True).contains(x)),
(4 - x, Interval(3, 4).contains(x)), (0, True))
def test_basic_degree_1():
d = 1
knots = range(5)
splines = bspline_basis_set(d, knots, x)
assert splines[0] == Piecewise((x,
Interval(0, 1, False, True).contains(x)),
(2 - x, Interval(1, 2).contains(x)),
(0, True))
assert splines[1] == Piecewise((-1 + x,
Interval(1, 2, False, True).contains(x)),
(3 - x,
Interval(2, 3).contains(x)), (0, True))
assert splines[2] == Piecewise((-2 + x,
Interval(2, 3, False, True).contains(x)),
(4 - x,
Interval(3, 4).contains(x)), (0, True))
def test_basic_degree_2():
d = 2
knots = range(5)
splines = bspline_basis_set(d, knots, x)
b0 = Piecewise((x**2/2, Interval(0, 1, False, True).contains(x)),
(Rational(-3, 2) + 3*x - x**2,
Interval(1, 2, False, True).contains(x)),
(Rational(9, 2) - 3*x + x**2/2,
Interval(2, 3).contains(x)), (0, True))
b1 = Piecewise((Rational(1, 2) - x + x**2/2,
Interval(1, 2, False, True).contains(x)),
(Rational(-11, 2) + 5*x - x**2,
Interval(2, 3, False, True).contains(x)),
(8 - 4*x + x**2/2,
Interval(3, 4).contains(x)), (0, True))
assert splines[0] == b0
assert splines[1] == b1
def test_repeated_degree_1():
d = 1
knots = [0, 0, 1, 2, 2, 3, 4, 4]
splines = bspline_basis_set(d, knots, x)
assert splines[0] == Piecewise((1 - x, Interval(0, 1).contains(x)),
(0, True))
assert splines[1] == Piecewise(
(x, Interval(0, 1, False, True).contains(x)),
(2 - x, Interval(1, 2).contains(x)), (0, True))
assert splines[2] == Piecewise((-1 + x, Interval(1, 2).contains(x)),
(0, True))
assert splines[3] == Piecewise((3 - x, Interval(2, 3).contains(x)),
(0, True))
assert splines[4] == Piecewise(
(-2 + x, Interval(2, 3, False, True).contains(x)),
(4 - x, Interval(3, 4).contains(x)), (0, True))
assert splines[5] == Piecewise((-3 + x, Interval(3, 4).contains(x)),
(0, True))
def test_basic_degree_2():
d = 2
knots = range(5)
splines = bspline_basis_set(d, knots, x)
b0 = Piecewise(
(x**2 / 2, Interval(0, 1, False, True).contains(x)),
(Rational(-3, 2) + 3 * x - x**2, Interval(1, 2, False,
True).contains(x)),
(Rational(9, 2) - 3 * x + x**2 / 2, Interval(2, 3).contains(x)),
(0, True))
b1 = Piecewise((Rational(1, 2) - x + x**2 / 2, Interval(1, 2, False,
True).contains(x)),
(Rational(-11, 2) + 5 * x - x**2, Interval(
2, 3, False, True).contains(x)),
(8 - 4 * x + x**2 / 2, Interval(3, 4).contains(x)),
(0, True))
assert splines[0] == b0
assert splines[1] == b1
def test_repeated_degree_1():
d = 1
knots = [0, 0, 1, 2, 2, 3, 4, 4]
splines = bspline_basis_set(d, knots, x)
assert splines[0] == Piecewise((1 - x, Interval(0, 1).contains(x)),
(0, True))
assert splines[1] == Piecewise((x,
Interval(0, 1, False, True).contains(x)),
(2 - x,
Interval(1, 2).contains(x)), (0, True))
assert splines[2] == Piecewise((-1 + x, Interval(1, 2).contains(x)),
(0, True))
assert splines[3] == Piecewise((3 - x, Interval(2, 3).contains(x)),
(0, True))
assert splines[4] == Piecewise((-2 + x,
Interval(2, 3, False, True).contains(x)),
(4 - x,
Interval(3, 4).contains(x)), (0, True))
assert splines[5] == Piecewise((-3 + x, Interval(3, 4).contains(x)),
(0, True))
def test_basic_degree_0():
d = 0
knots = range(5)
splines = bspline_basis_set(d, knots, x)
for i, si in enumerate(splines):
assert si == Piecewise((1, Interval(i, i + 1).contains(x)), (0, True))
