def _get_array():
X, Y, Z = inp = array.array('d', [1, 2, 3])
args = x, y, z = se.symbols('x y z')
exprs = [x+y+z, se.sin(x)*se.log(y)*se.exp(z)]
ref = [X+Y+Z, math.sin(X)*math.log(Y)*math.exp(Z)]
def check(arr):
assert all([abs(x1-x2) < 1e-13 for x1, x2 in zip(ref, arr)])
return args, exprs, inp, check
def test_jacobian2():
import numpy as np
x, y = se.symbols('x, y')
args = se.Matrix(2, 1, [x, y])
v = se.Matrix(2, 1, [x**3 * y, (x+1)*(y+1)])
jac = v.jacobian(args)
lmb = se.Lambdify(args, jac)
out = np.empty((2, 2))
inp = X, Y = 7, 11
out = lmb(inp)
assert np.atleast_1d(out).shape == (2, 2)
assert np.allclose(out, [[3 * X**2 * Y, X**3],
[Y + 1, X + 1]])
def _get_2_to_2by2_numpy():
import numpy as np
args = x, y = se.symbols('x y')
exprs = np.array([[x+y+1.0, x*y],
[x/y, x**y]])
l = se.Lambdify(args, exprs)
def check(A, inp):
X, Y = inp
assert abs(A[0, 0] - (X+Y+1.0)) < 1e-15
assert abs(A[0, 1] - (X*Y)) < 1e-15
assert abs(A[1, 0] - (X/Y)) < 1e-15
assert abs(A[1, 1] - (X**Y)) < 1e-13
return l, check
def _get_1_to_2by3_matrix():
x = se.symbols('x')
args = x,
exprs = se.Matrix(2, 3, [x+1, x+2, x+3,
1/x, 1/(x*x), 1/(x**3.0)])
l = se.Lambdify(args, exprs)
def check(A, inp):
X, = inp
assert abs(A[0, 0] - (X+1)) < 1e-15
assert abs(A[0, 1] - (X+2)) < 1e-15
assert abs(A[0, 2] - (X+3)) < 1e-15
assert abs(A[1, 0] - (1/X)) < 1e-15
assert abs(A[1, 1] - (1/(X*X))) < 1e-15
assert abs(A[1, 2] - (1/(X**3.0))) < 1e-15
return l, check
def test_Lambdify():
n = 7
args = x, y, z = se.symbols('x y z')
l = se.Lambdify(args, [x+y+z, x**2, (x-y)/z, x*y*z])
assert allclose(l(range(n, n+len(args))),
[3*n+3, n**2, -1/(n+2), n*(n+1)*(n+2)])
