def test_jacobian():
g = sad.AutoDiff('g', 3)
h = sad.AutoDiff('h', -4)
i = sad.AutoDiff('i', 7)
# Create functions
f1 = g + 4
f2 = h**2 + 2 * h - 12
variables = ['g', 'h', 'i']
functions = [f1, f2]
jacob = sad.jacobian(variables, functions)
test = np.array([[1., 0., 0.], [0., -6., 0.]])
for row in range(jacob.shape[0]):
for col in range(jacob.shape[1]):
assert jacob[row, col] == pytest.approx(test[row, col])
functions = sad.AutoDiffVector([f1, f2])
jacob = sad.jacobian(variables, functions)
test = np.array([[1., 0., 0.], [0., -6., 0.]])
for row in range(jacob.shape[0]):
for col in range(jacob.shape[1]):
assert jacob[row, col] == pytest.approx(test[row, col])
with pytest.raises(ValueError):
sad.jacobian('incorrect', 'input')
def test_eq():
x1 = sad.AutoDiff('x', 1) * 2
y1 = sad.AutoDiff('y', 1) * 2
assert x1 == x1
assert (x1 == y1) == False
y1 = sad.AutoDiff('y', 2) * 2
assert (x1 == y1) == False
assert (x1 == 0) == False
def test_ne():
x1 = sad.AutoDiff('x', 1) * 2
y1 = sad.AutoDiff('y', 2) * 2
assert x1 != y1
y1 = sad.AutoDiff('y', 1) * 2
x2 = sad.AutoDiff('x', 1) * 2
assert (x1 != x1) == False
assert (x1 != x2) == False
assert (x1 != y1)
def test_div_autodiff_other():
x1 = sad.AutoDiff('x', 2.0)
x2 = sad.AutoDiff('x', 2.0)
f = x1 / x2
assert f.der['x'] == pytest.approx(0.0)
#Test other attributes
assert next(iter(f.der)) == 'x'
#assert f.var == 'x'
assert f.val == pytest.approx(1.0)
def test_lt():
x1 = sad.AutoDiff('x', 1) * 1
y1 = sad.AutoDiff('y', 2) * 2
assert x1 < y1
x1 = sad.AutoDiff('x', 2) * 2
y1 = sad.AutoDiff('y', 1) * 2
assert (x1 < x1) == False
assert (x1 < y1) == False
assert (x1 < 0) == False
def test_le():
x1 = sad.AutoDiff('x', 1) * 1
y1 = sad.AutoDiff('y', 2) * 2
assert x1 <= x1
assert x1 <= y1
x1 = sad.AutoDiff('x', 2) * 2
y1 = sad.AutoDiff('y', 1) * 2
assert (x1 <= y1) == False
assert (x1 <= 0) == False
def test_ge():
x1 = sad.AutoDiff('x', 2) * 1
y1 = sad.AutoDiff('y', 1) * 2
assert x1 >= x1
assert x1 >= y1
x1 = sad.AutoDiff('x', 1) * 2
y1 = sad.AutoDiff('y', 2) * 2
assert (x1 >= y1) == False
assert (x1 >= 10) == False
def test_gt():
x1 = sad.AutoDiff('x', 2) * 2
y1 = sad.AutoDiff('y', 1) * 1
assert x1 > y1
x1 = sad.AutoDiff('x', 1) * 2
y1 = sad.AutoDiff('y', 2) * 2
assert (x1 > x1) == False
assert (x1 > y1) == False
assert (x1 > 10) == False
def test_add_autodiff_other():
x1 = sad.AutoDiff('x', 2)
x2 = sad.AutoDiff('x', 2)
f = x1 + x2
assert f.der['x'] == pytest.approx(2.0) # f(x)=x + x; f'(x) = 2; f'(2) = 2
#Test other attributes
assert next(iter(f.der)) == 'x'
#assert f.var == 'x + x'
assert f.val == 4.0
def test_vector_log10():
f1 = sad.AutoDiff('x', 2)
f2 = sad.AutoDiff('y', 2)
other = sad.AutoDiff('z', 2)
# do operations on objects
vec1 = sad.log(sad.AutoDiffVector([f1, f2]), base=10)
vec2 = sad.log(sad.vectorize(['x', 'y'], [2, 2]), base=10)
f3 = sad.log(f1, base=10)
#
der = f3.der['x']
val = f3.val
do_vector_tests_no_other(vec1, vec2, der, val)
def test_vector_rpow():
f1 = sad.AutoDiff('x', 2)
f2 = sad.AutoDiff('y', 2)
other = sad.AutoDiff('z', 2)
# do operations on objects
vec1 = 3.0**sad.AutoDiffVector([f1, f2])
vec2 = 3.0**sad.vectorize(['x', 'y'], [2, 2])
f3 = 3.0**f1
#
der = f3.der['x']
val = f3.val
do_vector_tests_no_other(vec1, vec2, der, val)
def test_vector_tanh():
f1 = sad.AutoDiff('x', 0.5)
f2 = sad.AutoDiff('y', 0.5)
# do operations on objects
vec1 = sad.tanh(sad.AutoDiffVector([f1, f2]))
vec2 = sad.tanh(sad.vectorize(['x', 'y'], [0.5, 0.5]))
f3 = sad.tanh(f1)
#
der = f3.der['x']
val = f3.val
do_vector_tests_no_other(vec1, vec2, der, val)
with pytest.raises(AttributeError):
x1 = sad.AutoDiff('x', 1)
sad._tanhV(x1)
def test_vector_ln():
f1 = sad.AutoDiff('x', 2)
f2 = sad.AutoDiff('y', 2)
other = sad.AutoDiff('z', 2)
# do operations on objects
vec1 = sad.log(sad.AutoDiffVector([f1, f2]))
vec2 = sad.log(sad.vectorize(['x', 'y'], [2, 2]))
f3 = sad.log(f1)
#
der = f3.der['x']
val = f3.val
do_vector_tests_no_other(vec1, vec2, der, val)
with pytest.raises(AttributeError):
x1 = sad.AutoDiff('x', 1)
sad._logV(x1)
def test_sub_autodiff_self():
x1 = sad.AutoDiff('x', 2)
f = x1 - x1
assert f.der['x'] == pytest.approx(0.0)
#Test other attributes
assert next(iter(f.der)) == 'x'
#assert f.var == 'x - x'
assert f.val == pytest.approx(0.0)
def test_rsub_constant():
x1 = sad.AutoDiff('x', 2)
f = 1 - x1
assert f.der['x'] == pytest.approx(1.0)
#Test other attributes
assert next(iter(f.der)) == 'x'
#assert f.var == 'x - 1'
assert f.val == 1.0
def test_mul_autodiff_self():
x1 = sad.AutoDiff('x', 2.0)
f = x1 * x1
assert f.der['x'] == pytest.approx(4.0)
#Test other attributes
assert next(iter(f.der)) == 'x'
#assert f.var == 'x * x'
assert f.val == pytest.approx(4.0)
def test_rmul_constant():
x1 = sad.AutoDiff('x', 2)
f = 3 * x1
assert f.der['x'] == pytest.approx(3.0)
#Test other attributes
assert next(iter(f.der)) == 'x'
#assert f.var == '3 * x'
assert f.val == pytest.approx(6.0)
def test_rdiv_constant():
x1 = sad.AutoDiff('x', 4)
f = 2 / x1
assert f.der['x'] == pytest.approx(-0.125)
#Test other attributes
assert next(iter(f.der)) == 'x'
#assert f.var == 'x'
assert f.val == pytest.approx(0.5)
def test_neg():
x1 = sad.AutoDiff('x', 2)
f = -x1
assert f.der['x'] == pytest.approx(-1.0)
#Test other attributes
assert next(iter(f.der)) == 'x'
#assert f.var == 'x'
assert f.val == pytest.approx(-2.0)
def test_pow():
x1 = sad.AutoDiff('x', 2.0)
f = x1**2
assert f.der['x'] == pytest.approx(4.0)
#Test other attributes
assert next(iter(f.der)) == 'x'
assert f.var == 'x'
assert f.val == pytest.approx(4.0)
def test_add_constant():
x1 = sad.AutoDiff('x', 2)
f = x1 + 1
assert f.der['x'] == pytest.approx(1.0)
#Test other attributes
assert next(iter(f.der)) == 'x'
#assert f.var == 'x + 1'
assert f.val == pytest.approx(3.0)
def test_logistic():
x1 = sad.AutoDiff('x', 4.0)
f = sad.logistic(x1)
assert f.der['x'] == pytest.approx(np.exp(4) / (1 + np.exp(4))**2)
#Test other attributes
assert next(iter(f.der)) == 'x'
assert f.var == 'x'
assert f.val == pytest.approx(1 / (1 + np.exp(-4)))
def test_sqrt():
x1 = sad.AutoDiff('x', 4.0)
f = x1**0.5
assert f.der['x'] == pytest.approx(1 / 4)
#Test other attributes
assert next(iter(f.der)) == 'x'
assert f.var == 'x'
assert f.val == pytest.approx(2.0)
def test_rpow():
x1 = sad.AutoDiff('x', 2.0)
f = 2**x1
assert f.der['x'] == pytest.approx(4 * math.log(2, math.e))
#Test other attributes
assert next(iter(f.der)) == 'x'
assert f.var == 'x'
assert f.val == pytest.approx(4.0)
def test_correct_init():
x1 = sad.AutoDiff('x', 2)
f = x1
assert f.der['x'] == pytest.approx(1.0)
#Test other attributes
assert next(iter(f.der)) == 'x'
assert f.var == 'x'
assert f.val == pytest.approx(2.0)
def test_vector_add():
f1 = sad.AutoDiff('x', 1)
f2 = sad.AutoDiff('y', 1)
other = sad.AutoDiff('z', 2)
# do operations on objects
vec1 = sad.AutoDiffVector([f1, f2]) + 2
vec1_other = sad.AutoDiffVector([f1, f2]) + other
vec2 = sad.vectorize(['x', 'y'], [1, 1]) + 2
vec2_other = sad.vectorize(['x', 'y'], [1, 1]) + other
f3 = f1 + 2
f4 = f1 + other
#
der = f3.der['x']
val = f3.val
der_other = f4.der['x']
val_other = f4.val
do_vector_tests(vec1, vec1_other, vec2, vec2_other, der, der_other, val,
val_other)
def test_tanh():
x1 = sad.AutoDiff('x', 0.5)
f = sad.tanh(x1)
assert f.der['x'] == pytest.approx(2 / (np.cosh(2 * 0.5) + 1))
#Test other attributes
assert next(iter(f.der)) == 'x'
assert f.var == 'x'
assert f.val == pytest.approx(np.tanh(0.5))
assert sad.tanh(0.5) == pytest.approx(np.tanh(0.5))
def test_vector_div():
f1 = sad.AutoDiff('x', 2)
f2 = sad.AutoDiff('y', 2)
other = sad.AutoDiff('z', 2)
# do operations on objects
vec1 = sad.AutoDiffVector([f1, f2]) / 3
vec1_other = sad.AutoDiffVector([f1, f2]) / other
vec2 = sad.vectorize(['x', 'y'], [2, 2]) / 3
vec2_other = sad.vectorize(['x', 'y'], [2, 2]) / other
f3 = f1 / 3
f4 = f1 / other
#
der = f3.der['x']
val = f3.val
der_other = f4.der['x']
val_other = f4.val
do_vector_tests(vec1, vec1_other, vec2, vec2_other, der, der_other, val,
val_other)
def test_vector_rsub():
f1 = sad.AutoDiff('x', 1)
f2 = sad.AutoDiff('y', 1)
other = sad.AutoDiff('z', 1)
# do operations on objects
vec1 = 1 - sad.AutoDiffVector([f1, f2])
vec1_other = other - sad.AutoDiffVector([f1, f2])
vec2 = 1 - sad.vectorize(['x', 'y'], [1, 1])
vec2_other = other - sad.vectorize(['x', 'y'], [1, 1])
f3 = 1 - f1
f4 = other - f1
#
der = f3.der['x']
val = f3.val
der_other = f4.der['x']
val_other = f4.val
do_vector_tests(vec1, vec1_other, vec2, vec2_other, der, der_other, val,
val_other)
def test_vector_rdiv():
f1 = sad.AutoDiff('x', 2)
f2 = sad.AutoDiff('y', 2)
other = sad.AutoDiff('z', 2)
# do operations on objects
vec1 = 3 / sad.AutoDiffVector([f1, f2])
vec1_other = other / sad.AutoDiffVector([f1, f2])
vec2 = 3 / sad.vectorize(['x', 'y'], [2, 2])
vec2_other = other / sad.vectorize(['x', 'y'], [2, 2])
f3 = 3 / f1
f4 = other / f1
#
der = f3.der['x']
val = f3.val
der_other = f4.der['x']
val_other = f4.val
do_vector_tests(vec1, vec1_other, vec2, vec2_other, der, der_other, val,
val_other)