Upload files to "tests"

tests/test_basic.py

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+import math
+from numethods import *
+
+def approx_equal(a, b, tol=1e-8):
+    return abs(a-b) <= tol*(1+abs(b))
+
+def test_lu_gauss_seidel():
+    A = Matrix([[10, -1, 2, 0],
+                [-1, 11, -1, 3],
+                [2, -1, 10, -1],
+                [0, 3, -1, 8]])
+    b = Vector([6, 25, -11, 15])
+    x_lu = LUDecomposition(A).solve(b)
+    x_gs = GaussSeidel(A, b, tol=1e-12).solve()
+    for i in range(4):
+        assert approx_equal(x_lu[i], x_gs[i])
+
+def test_cholesky():
+    A = Matrix([[4, 1, 1],
+                [1, 3, 0],
+                [1, 0, 2]])
+    b = Vector([1, 2, 3])
+    x = Cholesky(A).solve(b)
+    Ax = [sum(A.data[i][j]*x[j] for j in range(3)) for i in range(3)]
+    for i in range(3):
+        assert approx_equal(Ax[i], b[i])
+
+def test_roots():
+    f = lambda x: x**3 - 2
+    df = lambda x: 3*x**2
+    r = NewtonRoot(f, df, 1.0).solve()
+    assert approx_equal(r, 2**(1/3))
+    b = Bisection(f, 0, 2).solve()
+    assert approx_equal(b, 2**(1/3))
+
+def test_interp():
+    x = [0,1,2]
+    y = [1,3,2]
+    n = NewtonInterpolation(x,y)
+    l = LagrangeInterpolation(x,y)
+    for t in [0,0.5,1.7,2.0]:
+        assert approx_equal(n.evaluate(t), l.evaluate(t), tol=1e-9)