def test_grad():
def f(x, y):
return sin(x) * cos(y)
def f_prime(x, y):
return (cos(x) * cos(y), -sin(x) * sin(y))
assert grad(f)(2, 3) == f_prime(2, 3)
def test_pol():
def f(x):
return x**2 + 3 * x + 6
def f_prime(x):
return 2 * x + 3
assert grad(f)(3) == f_prime(3)
def test_trig():
def g(x):
return sin(x**2)
def g_prime(x):
return 2 * x * cos(x**2)
assert grad(g)(6) == g_prime(6)
def test_asin():
for x in range(-1, 1):
assert dmath.asin(x) == math.asin(x)
assert grad(dmath.asin)(x) == approx(1 / math.sqrt(1 - x**2))
def test_cos():
for x in range(-10, 10):
assert dmath.cos(x) == math.cos(x)
assert grad(dmath.cos)(x) == -math.sin(x)
def test_log():
for x in range(1, 10):
assert dmath.log(x) == math.log(x)
assert grad(dmath.log)(x) == 1 / x
def test_exp():
for x in range(-10, 10):
assert dmath.exp(x) == math.exp(x) == grad(dmath.exp)(x)
def test_erfc():
for x in range(-10, 10):
assert dmath.erfc(x) == math.erfc(x)
assert grad(
dmath.erfc)(x) == -2 / math.sqrt(math.pi) * math.exp(-(x**2))
def test_cosh():
for x in range(-10, 10):
assert dmath.cosh(x) == math.cosh(x)
assert grad(dmath.cosh)(x) == math.sinh(x)
def test_log1p():
for x in range(0, 0.1):
assert dmath.log1p(x) == math.log1p(x)
assert grad(dmath.log1p)(x) == 1 / x
def test_sqrt():
for x in range(0, 10):
assert dmath.sqrt(x) == math.sqrt(x)
assert grad(dmath.sqrt)(x) == approx(1 / (2 * math.sqrt(x)))
def test_atanh():
for x in range(-1, 1):
assert dmath.atanh(x) == math.atanh(x)
assert grad(dmath.atanh)(x) == approx(1 / (1 - x**2))
def test_acosh():
for x in range(1, 10):
assert dmath.acosh(x) == math.acosh(x)
assert grad(dmath.acosh)(x) == approx(1 / math.sqrt(x**2 - 1))
def test_asinh():
for x in range(-10, 10):
assert dmath.asinh(x) == math.asinh(x)
assert grad(dmath.asinh)(x) == approx(1 / math.sqrt(x**2 + 1))
def test_acos():
for x in range(-1, 1):
assert dmath.acos(x) == math.acos(x)
assert grad(dmath.acos)(x) == approx(-1 / math.sqrt(1 - x**2))
def test_atan():
for x in range(-10, 10):
assert dmath.atan(x) == math.atan(x)
assert grad(dmath.atan)(x) == approx(1 / (1 + x**2))
def test_log2():
for x in range(0, 10):
assert dmath.log2(x) == math.log2(x)
assert grad(dmath.log2)(x) == approx(1 / (math.log(2) * x))
def test_tanh():
for x in range(-10, 10):
assert dmath.tanh(x) == math.tanh(x)
assert grad(dmath.tanh)(x) == approx(1 / math.cosh(x)**2)
def test_expm1():
for x in range(0, 0.1):
assert dmath.expm1(x) == math.expm1(x)
assert grad(dmath.expm1)(x) == math.expm1(x) + 1.0
