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| import pytest | |
| from mpmath import * | |
| from mpmath.calculus.optimization import Secant, Muller, Bisection, Illinois, \ | |
| Pegasus, Anderson, Ridder, ANewton, Newton, MNewton, MDNewton | |
| def test_findroot(): | |
| # old tests, assuming secant | |
| mp.dps = 15 | |
| assert findroot(lambda x: 4*x-3, mpf(5)).ae(0.75) | |
| assert findroot(sin, mpf(3)).ae(pi) | |
| assert findroot(sin, (mpf(3), mpf(3.14))).ae(pi) | |
| assert findroot(lambda x: x*x+1, mpc(2+2j)).ae(1j) | |
| # test all solvers with 1 starting point | |
| f = lambda x: cos(x) | |
| for solver in [Newton, Secant, MNewton, Muller, ANewton]: | |
| x = findroot(f, 2., solver=solver) | |
| assert abs(f(x)) < eps | |
| # test all solvers with interval of 2 points | |
| for solver in [Secant, Muller, Bisection, Illinois, Pegasus, Anderson, | |
| Ridder]: | |
| x = findroot(f, (1., 2.), solver=solver) | |
| assert abs(f(x)) < eps | |
| # test types | |
| f = lambda x: (x - 2)**2 | |
| assert isinstance(findroot(f, 1, tol=1e-10), mpf) | |
| assert isinstance(iv.findroot(f, 1., tol=1e-10), iv.mpf) | |
| assert isinstance(fp.findroot(f, 1, tol=1e-10), float) | |
| assert isinstance(fp.findroot(f, 1+0j, tol=1e-10), complex) | |
| # issue 401 | |
| with pytest.raises(ValueError): | |
| with workprec(2): | |
| findroot(lambda x: x**2 - 4456178*x + 60372201703370, | |
| mpc(real='5.278e+13', imag='-5.278e+13')) | |
| # issue 192 | |
| with pytest.raises(ValueError): | |
| findroot(lambda x: -1, 0) | |
| # issue 387 | |
| with pytest.raises(ValueError): | |
| findroot(lambda p: (1 - p)**30 - 1, 0.9) | |
| def test_bisection(): | |
| # issue 273 | |
| assert findroot(lambda x: x**2-1,(0,2),solver='bisect') == 1 | |
| def test_mnewton(): | |
| f = lambda x: polyval([1,3,3,1],x) | |
| x = findroot(f, -0.9, solver='mnewton') | |
| assert abs(f(x)) < eps | |
| def test_anewton(): | |
| f = lambda x: (x - 2)**100 | |
| x = findroot(f, 1., solver=ANewton) | |
| assert abs(f(x)) < eps | |
| def test_muller(): | |
| f = lambda x: (2 + x)**3 + 2 | |
| x = findroot(f, 1., solver=Muller) | |
| assert abs(f(x)) < eps | |
| def test_multiplicity(): | |
| for i in range(1, 5): | |
| assert multiplicity(lambda x: (x - 1)**i, 1) == i | |
| assert multiplicity(lambda x: x**2, 1) == 0 | |
| def test_multidimensional(): | |
| def f(*x): | |
| return [3*x[0]**2-2*x[1]**2-1, x[0]**2-2*x[0]+x[1]**2+2*x[1]-8] | |
| assert mnorm(jacobian(f, (1,-2)) - matrix([[6,8],[0,-2]]),1) < 1.e-7 | |
| for x, error in MDNewton(mp, f, (1,-2), verbose=0, | |
| norm=lambda x: norm(x, inf)): | |
| pass | |
| assert norm(f(*x), 2) < 1e-14 | |
| # The Chinese mathematician Zhu Shijie was the very first to solve this | |
| # nonlinear system 700 years ago | |
| f1 = lambda x, y: -x + 2*y | |
| f2 = lambda x, y: (x**2 + x*(y**2 - 2) - 4*y) / (x + 4) | |
| f3 = lambda x, y: sqrt(x**2 + y**2) | |
| def f(x, y): | |
| f1x = f1(x, y) | |
| return (f2(x, y) - f1x, f3(x, y) - f1x) | |
| x = findroot(f, (10, 10)) | |
| assert [int(round(i)) for i in x] == [3, 4] | |
| def test_trivial(): | |
| assert findroot(lambda x: 0, 1) == 1 | |
| assert findroot(lambda x: x, 0) == 0 | |
| #assert findroot(lambda x, y: x + y, (1, -1)) == (1, -1) | |