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from sympy.functions import bspline_basis_set, interpolating_spline |
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from sympy.core.numbers import Rational |
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from sympy.core.singleton import S |
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from sympy.core.symbol import symbols |
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from sympy.functions.elementary.piecewise import Piecewise |
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from sympy.logic.boolalg import And |
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from sympy.sets.sets import Interval |
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from sympy.testing.pytest import slow |
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x, y = symbols('x,y') |
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def test_basic_degree_0(): |
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d = 0 |
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knots = range(5) |
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splines = bspline_basis_set(d, knots, x) |
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for i in range(len(splines)): |
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assert splines[i] == Piecewise((1, Interval(i, i + 1).contains(x)), |
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(0, True)) |
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def test_basic_degree_1(): |
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d = 1 |
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knots = range(5) |
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splines = bspline_basis_set(d, knots, x) |
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assert splines[0] == Piecewise((x, Interval(0, 1).contains(x)), |
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(2 - x, Interval(1, 2).contains(x)), |
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(0, True)) |
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assert splines[1] == Piecewise((-1 + x, Interval(1, 2).contains(x)), |
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(3 - x, Interval(2, 3).contains(x)), |
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(0, True)) |
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assert splines[2] == Piecewise((-2 + x, Interval(2, 3).contains(x)), |
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(4 - x, Interval(3, 4).contains(x)), |
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(0, True)) |
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def test_basic_degree_2(): |
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d = 2 |
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knots = range(5) |
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splines = bspline_basis_set(d, knots, x) |
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b0 = Piecewise((x**2/2, Interval(0, 1).contains(x)), |
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(Rational(-3, 2) + 3*x - x**2, Interval(1, 2).contains(x)), |
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(Rational(9, 2) - 3*x + x**2/2, Interval(2, 3).contains(x)), |
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(0, True)) |
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b1 = Piecewise((S.Half - x + x**2/2, Interval(1, 2).contains(x)), |
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(Rational(-11, 2) + 5*x - x**2, Interval(2, 3).contains(x)), |
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(8 - 4*x + x**2/2, Interval(3, 4).contains(x)), |
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(0, True)) |
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assert splines[0] == b0 |
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assert splines[1] == b1 |
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def test_basic_degree_3(): |
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d = 3 |
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knots = range(5) |
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splines = bspline_basis_set(d, knots, x) |
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b0 = Piecewise( |
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(x**3/6, Interval(0, 1).contains(x)), |
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(Rational(2, 3) - 2*x + 2*x**2 - x**3/2, Interval(1, 2).contains(x)), |
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(Rational(-22, 3) + 10*x - 4*x**2 + x**3/2, Interval(2, 3).contains(x)), |
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(Rational(32, 3) - 8*x + 2*x**2 - x**3/6, Interval(3, 4).contains(x)), |
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(0, True) |
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) |
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assert splines[0] == b0 |
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def test_repeated_degree_1(): |
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d = 1 |
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knots = [0, 0, 1, 2, 2, 3, 4, 4] |
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splines = bspline_basis_set(d, knots, x) |
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assert splines[0] == Piecewise((1 - x, Interval(0, 1).contains(x)), |
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(0, True)) |
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assert splines[1] == Piecewise((x, Interval(0, 1).contains(x)), |
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(2 - x, Interval(1, 2).contains(x)), |
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(0, True)) |
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assert splines[2] == Piecewise((-1 + x, Interval(1, 2).contains(x)), |
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(0, True)) |
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assert splines[3] == Piecewise((3 - x, Interval(2, 3).contains(x)), |
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(0, True)) |
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assert splines[4] == Piecewise((-2 + x, Interval(2, 3).contains(x)), |
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(4 - x, Interval(3, 4).contains(x)), |
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(0, True)) |
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assert splines[5] == Piecewise((-3 + x, Interval(3, 4).contains(x)), |
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(0, True)) |
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def test_repeated_degree_2(): |
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d = 2 |
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knots = [0, 0, 1, 2, 2, 3, 4, 4] |
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splines = bspline_basis_set(d, knots, x) |
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assert splines[0] == Piecewise(((-3*x**2/2 + 2*x), And(x <= 1, x >= 0)), |
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(x**2/2 - 2*x + 2, And(x <= 2, x >= 1)), |
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(0, True)) |
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assert splines[1] == Piecewise((x**2/2, And(x <= 1, x >= 0)), |
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(-3*x**2/2 + 4*x - 2, And(x <= 2, x >= 1)), |
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(0, True)) |
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assert splines[2] == Piecewise((x**2 - 2*x + 1, And(x <= 2, x >= 1)), |
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(x**2 - 6*x + 9, And(x <= 3, x >= 2)), |
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(0, True)) |
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assert splines[3] == Piecewise((-3*x**2/2 + 8*x - 10, And(x <= 3, x >= 2)), |
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(x**2/2 - 4*x + 8, And(x <= 4, x >= 3)), |
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(0, True)) |
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assert splines[4] == Piecewise((x**2/2 - 2*x + 2, And(x <= 3, x >= 2)), |
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(-3*x**2/2 + 10*x - 16, And(x <= 4, x >= 3)), |
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(0, True)) |
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def test_10_points_degree_1(): |
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d = 1 |
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X = [-5, 2, 3, 4, 7, 9, 10, 30, 31, 34] |
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Y = [-10, -2, 2, 4, 7, 6, 20, 45, 19, 25] |
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spline = interpolating_spline(d, x, X, Y) |
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assert spline == Piecewise((x*Rational(8, 7) - Rational(30, 7), (x >= -5) & (x <= 2)), (4*x - 10, (x >= 2) & (x <= 3)), |
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(2*x - 4, (x >= 3) & (x <= 4)), (x, (x >= 4) & (x <= 7)), |
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(-x/2 + Rational(21, 2), (x >= 7) & (x <= 9)), (14*x - 120, (x >= 9) & (x <= 10)), |
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(x*Rational(5, 4) + Rational(15, 2), (x >= 10) & (x <= 30)), (-26*x + 825, (x >= 30) & (x <= 31)), |
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(2*x - 43, (x >= 31) & (x <= 34))) |
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def test_3_points_degree_2(): |
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d = 2 |
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X = [-3, 10, 19] |
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Y = [3, -4, 30] |
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spline = interpolating_spline(d, x, X, Y) |
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assert spline == Piecewise((505*x**2/2574 - x*Rational(4921, 2574) - Rational(1931, 429), (x >= -3) & (x <= 19))) |
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def test_5_points_degree_2(): |
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d = 2 |
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X = [-3, 2, 4, 5, 10] |
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Y = [-1, 2, 5, 10, 14] |
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spline = interpolating_spline(d, x, X, Y) |
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assert spline == Piecewise((4*x**2/329 + x*Rational(1007, 1645) + Rational(1196, 1645), (x >= -3) & (x <= 3)), |
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(2701*x**2/1645 - x*Rational(15079, 1645) + Rational(5065, 329), (x >= 3) & (x <= Rational(9, 2))), |
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(-1319*x**2/1645 + x*Rational(21101, 1645) - Rational(11216, 329), (x >= Rational(9, 2)) & (x <= 10))) |
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@slow |
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def test_6_points_degree_3(): |
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d = 3 |
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X = [-1, 0, 2, 3, 9, 12] |
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Y = [-4, 3, 3, 7, 9, 20] |
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spline = interpolating_spline(d, x, X, Y) |
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assert spline == Piecewise((6058*x**3/5301 - 18427*x**2/5301 + x*Rational(12622, 5301) + 3, (x >= -1) & (x <= 2)), |
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(-8327*x**3/5301 + 67883*x**2/5301 - x*Rational(159998, 5301) + Rational(43661, 1767), (x >= 2) & (x <= 3)), |
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(5414*x**3/47709 - 1386*x**2/589 + x*Rational(4267, 279) - Rational(12232, 589), (x >= 3) & (x <= 12))) |
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def test_issue_19262(): |
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Delta = symbols('Delta', positive=True) |
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knots = [i*Delta for i in range(4)] |
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basis = bspline_basis_set(1, knots, x) |
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y = symbols('y', nonnegative=True) |
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basis2 = bspline_basis_set(1, knots, y) |
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assert basis[0].subs(x, y) == basis2[0] |
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assert interpolating_spline(1, x, |
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[Delta*i for i in [1, 2, 4, 7]], [3, 6, 5, 7] |
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) == Piecewise((3*x/Delta, (Delta <= x) & (x <= 2*Delta)), |
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(7 - x/(2*Delta), (x >= 2*Delta) & (x <= 4*Delta)), |
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(Rational(7, 3) + 2*x/(3*Delta), (x >= 4*Delta) & (x <= 7*Delta))) |
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