def test_add_different_AD():
x = AD(val=[3], index=0, magnitude=2)
y = AD(val=[4], index=1, magnitude=2)
z = x + y
assert z.val == pytest.approx([7])
for d in z.der:
assert d == pytest.approx([1])
def test_neg_different_AD_many_val():
x = AD(val=[10, -1, 3.2, 4], index=0, magnitude=2)
y = AD(val=[-2, 0, 1, 100], index=1, magnitude=2)
z = -(x + y)
assert z.val == pytest.approx([-8, 1, -4.2, -104])
for d in z.der:
assert d == pytest.approx([-1, -1, -1, -1])
def test_div_different_AD():
x = AD(val=[2], index=0, magnitude=2)
y = AD(val=[4], index=1, magnitude=2)
z = x / y
assert z.val == pytest.approx([0.5])
assert z.der[0] == pytest.approx([0.25])
assert z.der[1] == pytest.approx([-0.125])
def test_add_different_AD_many_val():
x = AD(val=[10, -1, 3.2, 4], index=0, magnitude=2)
y = AD(val=[-2, 0, 1, 100], index=1, magnitude=2)
z = x + y
assert z.val == pytest.approx([8, -1, 4.2, 104])
for d in z.der:
assert d == pytest.approx([1, 1, 1, 1])
def test_mul_different_AD():
x = AD(val=[3], index=0, magnitude=2)
y = AD(val=[4], index=1, magnitude=2)
z = x * y
assert z.val == pytest.approx([12])
assert z.der[0] == pytest.approx([4])
assert z.der[1] == pytest.approx([3])
def test_sub_different_AD():
x = AD(val=[3], index=0, magnitude=2)
y = AD(val=[4], index=1, magnitude=2)
z = x - y
assert z.val == pytest.approx([-1])
assert z.der[0] == pytest.approx([1])
assert z.der[1] == pytest.approx([-1])
def test_sub_different_AD_many_val():
x = AD(val=[10, -1, 3.2, 4], index=0, magnitude=2)
y = AD(val=[-2, 0, 1, 100], index=1, magnitude=2)
z = x - y
assert z.val == pytest.approx([12, -1, 2.2, -96])
assert z.der[0] == pytest.approx([1, 1, 1, 1])
assert z.der[1] == pytest.approx([-1, -1, -1, -1])
def test_pow_different_AD():
x = AD(val=[2], index=0, magnitude=2)
y = AD(val=[3], index=1, magnitude=2)
z = x**y
assert z.val == pytest.approx([8])
assert z.der[0] == pytest.approx([12])
assert z.der[1] == pytest.approx([5.545177444479562])
def test_pos_different_AD():
x = AD(val=[10], index=0, magnitude=2)
y = AD(val=[-20], index=1, magnitude=2)
z = +(x + y)
assert z.val == pytest.approx([-10])
for d in z.der:
assert d == pytest.approx([1])
def test_div_different_AD_many_val():
x = AD(val=[-2, 4, 10, 100], index=0, magnitude=2)
y = AD(val=[1, 2, 2, 4], index=1, magnitude=2)
z = x / y
assert z.val == pytest.approx([-2, 2, 5, 25])
assert z.der[0] == pytest.approx([1, 0.5, 0.5, 0.25])
assert z.der[1] == pytest.approx([2, -1, -2.5, -6.25])
def test_neg_different_AD():
x = AD(val=[10], index=0, magnitude=2)
y = AD(val=[20], index=1, magnitude=2)
z = -(x + y)
assert z.val == pytest.approx([-30])
for d in z.der:
assert d == pytest.approx([-1])
def test_mul_different_AD_many_val():
x = AD(val=[10, -1, 3.2, 4], index=0, magnitude=2)
y = AD(val=[-2, 0, 1, 100], index=1, magnitude=2)
z = x * y
assert z.val == pytest.approx([-20, 0, 3.2, 400])
assert z.der[0] == pytest.approx([-2, 0, 1, 100])
assert z.der[1] == pytest.approx([10, -1, 3.2, 4])
def test_pow_different_AD_many_val():
x = AD(val=[1, 2, 3, 4], index=0, magnitude=2)
y = AD(val=[4, 3, 2, 1], index=1, magnitude=2)
z = x**y
assert z.val == pytest.approx([1, 8, 9, 4])
assert z.der[0] == pytest.approx([4, 12, 6, 1])
assert z.der[1] == pytest.approx(
[0, 5.545177444479562, 9.887510598012987, 5.545177444479562])
def test_arctan4():
# AD object with .val=[1,2]
x1 = AD(val=[0.3, 0.4], index=0, magnitude=2)
# AD object with .val=[2,3]
x2 = AD(val=[0.4, 0.5], index=1, magnitude=2)
y = ef.arctan(x1 + x2)
assert y.val == pytest.approx(np.arctan([0.7, 0.9]))
assert y.der[0] == pytest.approx([0.6711409395973155, 0.5524861878453039])
assert y.der[1] == pytest.approx([0.6711409395973155, 0.5524861878453039])
def test_arcsin4():
# AD object with .val=[1,2]
x1 = AD(val=[0.1, 0.2], index=0, magnitude=2)
# AD object with .val=[2,3]
x2 = AD(val=[0.2, 0.3], index=1, magnitude=2)
y = ef.arcsin(x1 + x2)
assert y.val == pytest.approx(np.arcsin([0.3, 0.5]))
assert y.der[0] == pytest.approx([1.0482848367219182, 1.1547005383792517])
assert y.der[1] == pytest.approx([1.0482848367219182, 1.1547005383792517])
def test_tanh3():
# AD object with .val=[1]
x1 = AD(val=[1], index=0, magnitude=2)
# AD object with .val=[2]
x2 = AD(val=[2], index=1, magnitude=2)
y = ef.tanh(x1 + x2)
assert y.val == pytest.approx(np.tanh([3]))
assert y.der[0] == pytest.approx(1 / np.cosh(3))
assert y.der[1] == pytest.approx(1 / np.cosh(3))
def test_log4():
# AD object with .val=[1,2]
x1 = AD(val=[1, 2], index=0, magnitude=2)
# AD object with .val=[2,3]
x2 = AD(val=[2, 3], index=1, magnitude=2)
y = ef.log(x1 + x2)
assert y.val == pytest.approx(np.log([3, 5]))
assert y.der[0] == pytest.approx([0.3333333333333333, 0.2])
assert y.der[1] == pytest.approx([0.3333333333333333, 0.2])
def test_logistic4():
# AD object with .val=[1,2]
x1 = AD(val=[1, 2], index=0, magnitude=2)
# AD object with .val=[2,3]
x2 = AD(val=[2, 3], index=1, magnitude=2)
y = ef.logistic(x1 + x2)
assert y.val == pytest.approx([0.95257412, 0.99330714])
assert y.der[0] == pytest.approx([0.045176659730, 0.006648056670])
assert y.der[1] == pytest.approx([0.045176659730, 0.006648056670])
def test_tanh4():
# AD object with .val=[1,2]
x1 = AD(val=[1, 2], index=0, magnitude=2)
# AD object with .val=[2,3]
x2 = AD(val=[2, 3], index=1, magnitude=2)
y = ef.tanh(x1 + x2)
assert y.val == pytest.approx(np.tanh([3, 5]))
assert y.der[0] == pytest.approx(np.sinh(1 / np.cosh([3, 5])), rel=1e-2)
assert y.der[1] == pytest.approx(np.sinh(1 / np.cosh([3, 5])), rel=1e-2)
def test_cos4():
# AD object with .val=[1,2]
x1 = AD(val=[1, 2], index=0, magnitude=2)
# AD object with .val=[2,3]
x2 = AD(val=[2, 3], index=1, magnitude=2)
y = ef.cos(x1 + x2)
assert y.val == pytest.approx(np.cos([3, 5]))
assert y.der[0] == pytest.approx(-np.sin([3, 5]) * 1)
assert y.der[1] == pytest.approx(-np.sin([3, 5]) * 1)
def test_sqrt4():
# AD object with .val=[1,2]
x1 = AD(val=[1, 2], index=0, magnitude=2)
# AD object with .val=[2,3]
x2 = AD(val=[2, 3], index=1, magnitude=2)
y = ef.sqrt(x1 + x2)
assert y.val == pytest.approx(np.sqrt([3, 5]))
assert y.der[0] == pytest.approx(0.5 / np.sqrt([3, 5]) * 1)
assert y.der[1] == pytest.approx(0.5 / np.sqrt([3, 5]) * 1)
def test_sin3():
# AD object with .val=[1]
x1 = AD(val=[1], index=0, magnitude=2)
# AD object with .val=[2]
x2 = AD(val=[2], index=1, magnitude=2)
y = ef.sin(x1 + x2)
assert y.val == pytest.approx(np.sin([3]))
assert y.der[0] == pytest.approx(np.cos(3) * 1)
assert y.der[1] == pytest.approx(np.cos(3) * 1)
def test_tan4():
# AD object with .val=[1,2]
x1 = AD(val=[1, 2], index=0, magnitude=2)
# AD object with .val=[2,3]
x2 = AD(val=[2, 3], index=1, magnitude=2)
y = ef.tan(x1 + x2)
assert y.val == pytest.approx(np.tan([3, 5]))
assert y.der[0] == pytest.approx((1 / np.cos([3, 5]))**2 * 1)
assert y.der[1] == pytest.approx((1 / np.cos([3, 5]))**2 * 1)
def test_arccos4():
# AD object with .val=[1,2]
x1 = AD(val=[0.3, 0.4], index=0, magnitude=2)
# AD object with .val=[2,3]
x2 = AD(val=[0.4, 0.5], index=1, magnitude=2)
y = ef.arccos(x1 + x2)
assert y.val == pytest.approx(np.arccos([0.7, 0.9]))
assert y.der[0] == pytest.approx([-1.4002800840280099, -2.294157338705618])
assert y.der[1] == pytest.approx([-1.4002800840280099, -2.294157338705618])
def test_log2_4():
# AD object with .val=[1,2]
x1 = AD(val=[1, 2], index=0, magnitude=2)
# AD object with .val=[2,3]
x2 = AD(val=[2, 3], index=1, magnitude=2)
y = ef.log2(x1 + x2)
assert y.val == pytest.approx(np.log2([3, 5]))
assert y.der[0] == pytest.approx(
[0.48089834696298783, 0.28853900817779266])
assert y.der[1] == pytest.approx(
[0.48089834696298783, 0.28853900817779266])
def test_log10_4():
# AD object with .val=[1,2]
x1 = AD(val=[1, 2], index=0, magnitude=2)
# AD object with .val=[2,3]
x2 = AD(val=[2, 3], index=1, magnitude=2)
y = ef.log10(x1 + x2)
assert y.val == pytest.approx(np.log10([3, 5]))
assert y.der[0] == pytest.approx(
[0.14476482730108392, 0.08685889638065035])
assert y.der[1] == pytest.approx(
[0.14476482730108392, 0.08685889638065035])
def test_logb4():
# AD object with .val=[1,2]
x1 = AD(val=[1, 2], index=0, magnitude=2)
# AD object with .val=[2,3]
x2 = AD(val=[2, 3], index=1, magnitude=2)
y = ef.logb(x1 + x2, 3)
assert y.val[0] == pytest.approx(math.log(3, 3))
assert y.val[1] == pytest.approx(math.log(5, 3))
assert y.der[0] == pytest.approx(
[0.30341307554227914, 0.18204784532536747])
assert y.der[1] == pytest.approx(
[0.30341307554227914, 0.18204784532536747])
def test_getters():
x = AD(val=[10])
value = x.val
derivative = x.der
assert value == pytest.approx([10], rel=1e-4)
for d in derivative:
assert d == pytest.approx([1])
def test_pow_AD_many_val():
x = AD(val=[1, 2, 5, 10])
y = x**x
assert y.val == pytest.approx([1, 4, 3125, 10000000000])
for d in y.der:
assert d == pytest.approx(
[1, 6.772588722239782, 8154.493476356564, 33025850929.94046])
def test_rdiv_const_many_val():
x = AD(val=[-1, 1, 7, 14])
y = 7 / x
assert y.val == pytest.approx([-7, 7, 1, 0.5])
for d in y.der:
assert d == pytest.approx(
[-7, -7, -0.14285714285714285, -0.03571428571428571])