def test_logexp_multivar_hessian_2():
x, y, z = ad.Variable(), ad.Variable(), ad.Variable()
f = ad.Sinh(ad.Exp(x - 3.0) * y) + ad.Log(y + x**2) * z * ad.Sin(x)
h = f.hessian({x: 1, y: 3, z: 5})
assert (equals(h[x][x], -1.5705707143))
assert (equals(h[y][y], -0.2553174360))
assert (equals(h[z][z], 0))
assert (equals(h[x][y], 0.31902899408))
assert (equals(h[y][z], 0.2103677462))
assert (equals(h[x][z], 1.1697535323))
def test_trig_multivar_hessian_2():
x, y, z = ad.Variable(), ad.Variable(), ad.Variable()
f = ad.Sinh(x * y) + (x + y) * (z**2) * ad.Cosh(z * ad.Tanh(1 / z))
h = f.hessian({x: 1, y: 2, z: 3})
assert (equals(h[x][x], 14.50744163138))
assert (equals(h[y][y], 3.6268604078))
assert (equals(h[z][z], 9.3022279093))
assert (equals(h[x][y], 11.015916506))
assert (equals(h[y][z], 9.2426242912))
assert (equals(h[x][z], 9.2426242912))
def test_hyperbolic_expressions():
x = ad.Variable('x')
y = ad.Variable('y')
f1 = ad.Tan(x)
f2 = ad.Sinh(x)
f3 = ad.Cosh(x)
f4 = ad.Tanh(x)
f5 = ad.Exp(x)
f6 = ad.Cos(x)
assert f1._d_expr(y).eval({x:1}) == 0
assert np.isclose(f1._d_expr(x).eval({x:1}), f1.d({x: 1}))
assert f2._d_expr(y).eval({x:1}) == 0
assert np.isclose(f2._d_expr(x).eval({x:1}), f2.d({x: 1}))
assert f3._d_expr(y).eval({x:1}) == 0
assert np.isclose(f3._d_expr(x).eval({x:1}), f3.d({x: 1}))
assert f4._d_expr(y).eval({x:1}) == 0
assert np.isclose(f4._d_expr(x).eval({x:1}), f4.d({x: 1}))
assert f5._d_expr(y).eval({x:1}) == 0
assert np.isclose(f5._d_expr(x).eval({x:1}), f5.d({x: 1}))
assert f6._d_expr(y).eval({x:1}) == 0
assert np.isclose(f6._d_expr(x).eval({x:1}), f6.d({x: 1}))
def test_single_variable_trig_hyperbolic():
x = ad.Variable()
f = x * x * ad.Cosh(0.01 * x + 0.1) + x * ad.Sinh(x * x - 4.0)
assert (equals(f.hessian({x: 1}), 22.351093955))
assert (equals(f.hessian({x: 2}), 14.02444322))
assert (equals(f.hessian({x: 3}), 9351.7592912))
def test_sinh_expression():
a = ad.Variable('a')
b = ad.Sinh(a)
assert np.isclose(b.eval({a: pi/4}), 0.8686709614860095)
assert np.isclose(b.d({a: pi/4}), 1.3246090892520057)