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))