def test_double_variable_power_throws(): x, y = ad.Variable(), ad.Variable() f = x**(y + 5.0) g = x**y with pytest.raises(NotImplementedError): g.hessian({x: 1, y: 1}) with pytest.raises(NotImplementedError): f.hessian({x: 1, y: 1})
def test_arithmetic_multivar_hessian(): x, y, z = ad.Variable(), ad.Variable(), ad.Variable() f = 3 * x * x * y + (z - 1.0 / x)**5 h = f.hessian({x: 1, y: 2, z: 3}) assert (equals(h[x][x], 12.0)) assert (equals(h[y][y], 0)) assert (equals(h[z][z], 160)) assert (equals(h[x][y], 6)) assert (equals(h[y][z], 0)) assert (equals(h[x][z], 160))
def test_trig_multivar_hessian_1(): x, y, z = ad.Variable(), ad.Variable(), ad.Variable() f = ad.Sin(x * y) + z * ad.Cos(z * ad.Tan(1 / z)) h = f.hessian({x: 1, y: 3, z: 5}) assert (equals(h[x][x], -1.2700800725)) assert (equals(h[y][y], -0.14112000805)) assert (equals(h[z][z], -0.0050593837)) assert (equals(h[x][y], -1.41335252)) assert (equals(h[y][z], 0)) assert (equals(h[x][z], 0))
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_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_variable_inheritance(): x = ad.Variable() y = ad.Variable() f = x * y assert (x in f.dep_vars) assert (y in f.dep_vars) assert (len(f.dep_vars) == 2) assert (y not in x.dep_vars) assert (x not in y.dep_vars)
def test_arithmetic_multivar_hessian_2(): x, y, z = ad.Variable(), ad.Variable(), ad.Variable() f = -x * (x - y + 1.0)**(-4) + (z / x)**2 h = f.hessian({x: 1, y: 3, z: 5}) assert (equals(h[x][x], 122)) assert (equals(h[y][y], -20)) assert (equals(h[z][z], 2)) assert (equals(h[x][y], 24)) assert (equals(h[y][z], 0)) assert (equals(h[x][z], -20))
def softmaxtest(): x1 = ad.Variable("x1") x2 = ad.Variable("x2") d = ad.Variable("d") d_val = np.array([0, 1, 0]).reshape(3, 1) x1_val = 3 * np.ones((3, 1)) x2_val = 5 * np.ones((3, 1)) J = ad.softmax_crossent(x1 * x2, d) ex = ad.Executor([J] + ad.gradients(J, [x1, x2])) res = ex.run({x1: x1_val, x2: x2_val, d: d_val}) pass
def multiconnection(): x1 = ad.Variable("x1") x2 = ad.Variable("x2") x3 = ad.Variable("x3") s = x1 + x2 y = (s + x3) + (5 * s) grads = ad.gradients(y, [x1, x2, x3]) executor = ad.Executor([y] + grads) feed_dict = {x1: 1, x2: 2, x3: 3} res = executor.run(feed_dict) return
def subtest(): x1 = ad.Variable("x1") x2 = ad.Variable("x2") x1_val = 9 x2_val = 6 y = x1 - x2 z = x1 - 4 u = 8 - x2 Ex_y = ad.Executor([y] + ad.gradients(y, [x1, x2])) Ex_z = ad.Executor([z] + ad.gradients(z, [x1])) Ex_u = ad.Executor([u] + ad.gradients(u, [x2])) print(Ex_y.run(feed_dict={x1: x1_val, x2: x2_val})) print(Ex_z.run(feed_dict={x1: x1_val})) print(Ex_u.run(feed_dict={x2: x2_val})) return
def test_binop(): x = ad.Variable("x") y = x**3 assert np.isclose(y.d_n(n=0, val=2.0), 8.0) assert np.isclose(y.d_n(n=1, val=2.0), 12.0) assert np.isclose(y.d_n(n=3, val=2.0), 6.0) assert np.isclose(y.d_n(n=5, val=2.0), 0.0) y = x + x**3 assert np.isclose(y.d_n(n=0, val=2.0), 10.0) assert np.isclose(y.d_n(n=1, val=2.0), 13.0) assert np.isclose(y.d_n(n=3, val=2.0), 6.0) assert np.isclose(y.d_n(n=5, val=2.0), 0.0) y = x - x**3 assert np.isclose(y.d_n(n=0, val=2.0), -6.0) assert np.isclose(y.d_n(n=1, val=2.0), -11.0) assert np.isclose(y.d_n(n=3, val=2.0), -6.0) y = x * (x**2) assert np.isclose(y.d_n(n=0, val=2.0), 8.0) assert np.isclose(y.d_n(n=1, val=2.0), 12.0) assert np.isclose(y.d_n(n=3, val=2.0), 6.0) assert np.isclose(y.d_n(n=5, val=2.0), 0.0) y = (x**5) / (x**2) assert np.isclose(y.d_n(n=0, val=2.0), 8.0) assert np.isclose(y.d_n(n=1, val=2.0), 12.0) assert np.isclose(y.d_n(n=3, val=2.0), 6.0) assert np.isclose(y.d_n(n=5, val=2.0), 0.0)
def test_single_variable_trig_cos(): """analytic hessian is -25 cos (5 * x + 3)""" x = ad.Variable() f = ad.Cos(5 * x + 3) assert (equals(f.hessian({x: 1}), -25 * np.cos(5 * 1 + 3))) assert (equals(f.hessian({x: 2}), -25 * np.cos(5 * 2 + 3))) assert (equals(f.hessian({x: 3}), -25 * np.cos(5 * 3 + 3)))
def test_single_variable_trig_tan(): """analytic hessian is -25 cos (5 * x + 3)""" x = ad.Variable() f = ad.Cos(5 * x + 3) * ad.Tan(x * x - 5) assert (equals(f.hessian({x: 1}), -48.05115800)) assert (equals(f.hessian({x: 2}), -170.9403025)) assert (equals(f.hessian({x: 3}), 218.2792716))
def test_single_variable_trig_hyperbolic_2(): x = ad.Variable() # x^2 Cosh[Sin[x] + Tanh[Exp[3 * x] + Log[x]]] g = ad.Sin(x) + ad.Tanh(ad.Exp(3 * x) + ad.Log(x)) f = x * x * ad.Cosh(g) assert (equals(f.hessian({x: 1}), 11.464317742)) assert (equals(f.hessian({x: 2}), -13.704377252))
def test_cosine(): x = ad.Variable("x") y = ad.Cos(x) yd1 = y.d_expr() assert np.isclose(yd1.eval({x: pi / 2}), -1.0) assert np.isclose(yd1.eval({x: 0.0}), 0.0) assert np.isclose(yd1.d({x: 0.0}), -1.0)
def test_constant_division(): a = ad.Constant(5) a2 = ad.Constant(-5) b = ad.Variable('b') c = a / b d = b / a2 assert c.eval({b: 5}) == 1 assert d.eval({b: 5}) == -1
def test_constant_subtraction(): a = ad.Constant(5) a2 = ad.Constant(-5) b = ad.Variable('b') c = a - b d = b - a2 assert c.eval({b: 5}) == 0 assert d.eval({b: 5}) == 10
def test_constant_multiplication(): a = ad.Constant(5) a2 = ad.Constant(-5) b = ad.Variable('b') c = a * b d = b * a2 assert c.eval({b: 5}) == 25 assert d.eval({b: 5}) == -25
def test_inverse_trig(): a, b = ad.Variable('a'), ad.Variable('b') c = ad.Arcsin(a / b) assert np.isclose(np.arcsin(0.5), c.eval({a: 1.0, b: 2.0})) d = ad.Arcsin(a) assert np.isclose(1.0 / np.sqrt(1.0 - 0.5**2), d.d({a: 0.5})) c = ad.Arccos(a * b) assert np.isclose(np.arccos(0.25), c.eval({a: 0.5, b: 0.5})) d = ad.Arccos(a) assert np.isclose(-1.0 / np.sqrt(1.0 - 0.5**2), d.d({a: 0.5})) c = ad.Arctan(a / b) assert np.isclose(np.arctan(0.5), c.eval({a: 1.0, b: 2.0})) d = ad.Arctan(a) assert np.isclose(1.0 / (1 + 0.5**2), d.d({a: 0.5}))
def test_variable_inheritance_three(): x = ad.Variable() y = ad.Variable() z = ad.Variable() f = ad.Cos(x) * y g = ad.Sin(f) + z * z * ad.Log(z) + 1 assert (x in f.dep_vars) assert (y in f.dep_vars) assert (len(f.dep_vars) == 2) assert (y not in x.dep_vars) assert (x not in y.dep_vars) assert (len(g.dep_vars) == 3) assert (x in g.dep_vars) assert (y in g.dep_vars) assert (z in g.dep_vars) assert (z not in f.dep_vars)
def test_substration_and_negation(): x = ad.Variable("x") y = ad.Exp(2 * x) - x yd1 = y.d_expr() assert np.isclose(yd1.eval({x: 0.0}), 1.0) y = -ad.Exp(3 * x) yd1 = y.d_expr() assert np.isclose(yd1.eval({x: 0.0}), -3.0)
def test_high_order(): x = ad.Variable("x") y = x**4 yd5 = y.d_expr(5) yd9 = y.d_expr(9) assert np.isclose(yd5.eval({x: 4.0}), 0.0) assert np.isclose(yd5.eval({x: 10.0}), 0.0) assert np.isclose(yd9.eval({x: 4.0}), 0.0) assert np.isclose(yd9.eval({x: 10.0}), 0.0)
def test_inverse_trig_exceptions(): x = ad.Variable('x') y = ad.Variable('y') f5 = ad.Arccos(x) f6 = ad.Arcsin(x) f7 = ad.Arctan(x) f8 = ad.Log(x) f9 = ad.Sin(x) assert f5._d_expr(y).eval({x:0}) == 0 assert np.isclose(f5._d_expr(x).eval({x:0.5}), f5.d({x: 0.5})) assert f6._d_expr(y).eval({x:0}) == 0 assert np.isclose(f6._d_expr(x).eval({x:0}), f6.d({x: 0})) assert f7._d_expr(y).eval({x:0}) == 0 assert np.isclose(f7._d_expr(x).eval({x:0}), f7.d({x: 0})) assert f8._d_expr(y).eval({x:1}) == 0 assert np.isclose(f8._d_expr(x).eval({x:2}), f8.d({x: 2})) assert f9._d_expr(y).eval({x:1}) == 0 assert np.isclose(f9._d_expr(x).eval({x:2}), f9.d({x: 2}))
def test_power(): x = ad.Variable("x") y = x**4 yd1 = y.d_expr() yd2 = yd1.d_expr() yd3 = yd2.d_expr() yd4 = yd3.d_expr() assert np.isclose(yd1.eval({x: 2.0}), 32.0) assert np.isclose(yd2.eval({x: 2.0}), 48.0) assert np.isclose(yd3.eval({x: 2.0}), 48.0) assert np.isclose(yd4.eval({x: 2.0}), 24.0) assert np.isclose(yd4.eval({x: 3.0}), 24.0)
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_power_base0(): a = ad.Variable('a') c = a**2 assert np.isclose(0, c.d_n(2, 0)) assert np.isclose(0, c.d_n(4, 0)) d = a**(-1) with pytest.raises(ZeroDivisionError): d.d_n(2, 0) e = a**(3.5) with pytest.raises(ZeroDivisionError): e.d_n(4, 0)
def test_division(): x = ad.Variable("x") y = 1 / x yd1 = y.d_expr() assert np.isclose(yd1.eval({x: 2.0}), -0.25) y = x / 2 yd1 = y.d_expr() assert np.isclose(yd1.eval({x: 1.0}), 0.5) y = x / x yd1 = y.d_expr() assert np.isclose(yd1.eval({x: 100.0}), 0.0)
def test1(): x1 = ad.Variable(name="x1") x2 = ad.Variable(name="x2") x3 = ad.Variable(name="x3") y = x1 / x2 - x3 executor = ad.Executor([x1, x2, x3, y]) print(executor.run({x1: 0, x2: 2, x3: 3})) print(y) grad_x1, grad_x2, grad_x3 = ad.gradients(y, [x1, x2, x3]) executor_backward = ad.Executor([y, grad_x1, grad_x2, grad_x3]) x1_val = 5 * np.ones(3) x2_val = 2 * np.ones(3) x3_val = 3 * np.ones(3) y_val, grad_x1_val, grad_x2_val, grad_x3_val = executor_backward.run( feed_dict={ x1: x1_val, x2: x2_val, x3: x3_val }) print(y_val, grad_x1_val, grad_x2_val, grad_x3_val)
def test_expression_exceptions(): x = ad.Variable() c = ad.Expression() with pytest.raises(NotImplementedError): c.eval({}) with pytest.raises(NotImplementedError): c.d({}) with pytest.raises(NotImplementedError): c.hessian({}) with pytest.raises(NotImplementedError): c._d_expr(x) with pytest.raises(NotImplementedError): c._d_n(1, {}, {}, {})
def test_exp_exceptions(): x = ad.Variable('x') y = ad.Exp(x) z = ad.Cos(x) a = ad.Log(x) b = ad.Sin(x) f1 = y*2 + y f2 = z*2 + z f3 = a*2 + a f4 = b*2 + b assert np.isclose(f1.d_n(1, 1), 8.154845485377136) assert np.isclose(f2.d_n(1, 1), -2.5244129544236893) assert np.isclose(f3.d_n(1, 1), 3.0) assert np.isclose(f4.d_n(1, 1), 1.6209069176044193)