def test_deviv_integ(self):
" p.deriv() p.integ() "
self.assert_close(self.exp_x.integ().deriv(), self.exp_x)
self.assert_close(self.exp_x.integ(n=2).deriv(n=2), self.exp_x)
self.assert_close(self.exp_x.integ(n=0), self.exp_x)
self.assert_close(self.exp_x.deriv(n=0), self.exp_x)
self.assert_close(self.x.deriv(self.order + 2), PowerSeries([0]))
self.assert_close(self.exp_x.deriv(),
PowerSeries(self.exp_x, order=self.order - 1))
self.assert_close(self.exp_x.integ(x0=0),
exp(PowerSeries(self.x, order=self.order + 1)) - 1)
def test_arith(self):
" x+y x-y x*y x/y x**2 "
x = self.x
y = self.exp_x
self.assert_close(x * x, self.x2)
self.assert_close(y / y, self.one)
self.assert_close((y * y) / y, y)
self.assert_close((x * y) / y, x)
self.assert_close(y - y, self.zero)
self.assert_close((x + y) - x, y)
self.assert_close(x + y - x - y, self.zero)
self.assert_close(x**2, self.x2)
self.assert_close(y * y * y, y**3)
self.assert_close(2**x, self.exp_x**log(2.))
self.assert_close(y + y, 2 * y)
self.assert_close(y + y, y * 2)
self.assert_close(x + 2, PowerSeries([2, 1], order=self.order))
self.assert_close(2 + x, PowerSeries([2, 1], order=self.order))
self.assert_close(x - 2, PowerSeries([-2, 1], order=self.order))
self.assert_close(2 - x, PowerSeries([2, -1], order=self.order))
self.assert_close(2 * (y / 2), y)
self.assert_close(y * (2 / y), 2 * self.one)
self.assertEqual(y**0, 1.)
self.assert_close(y**(-2), 1 / y / y)
# check division where c[0] = 0
self.assert_close(x / x, PowerSeries([1], order=self.order - 1))
self.assert_close((x + x**2) / x,
PowerSeries([1, 1], order=self.order - 1))
self.assert_close((x * x) / self.x2,
PowerSeries([1], order=self.order - 2))
# check error checks
with self.assertRaises(ZeroDivisionError):
self.x / self.zero
def setUp(self):
self.order = 10
self.x = PowerSeries([0.,1.], order=self.order)
self.x2 = PowerSeries([0., 0., 1.], order=self.order)
self.z = PowerSeries([0+0j, 1.+0j], order=self.order)
self.one = PowerSeries([1.], order=self.order)
self.zero = PowerSeries([0.], order=self.order)
coef = 1. / np.cumprod([1.] + (1. + np.arange(0., self.order+1.)).tolist())
self.exp_x = PowerSeries(coef, order=self.order)
osc_coef = coef * (1j)**np.arange(len(coef))
self.cos_x = PowerSeries([xi.real for xi in osc_coef], order=self.order)
self.sin_x = PowerSeries([xi.imag for xi in osc_coef], order=self.order)
def test_constructor(self):
" PowerSeries(c, order) "
x = PowerSeries(1. + np.arange(2 * self.order), order=self.order)
self.assertEqual(len(x.c), self.order + 1)
np.testing.assert_allclose(x.c, 1. + np.arange(self.order + 1))
x = PowerSeries(order=self.order)
y = PowerSeries(numpy.zeros(self.order + 1, object), order=self.order)
self.assertEqual(len(x.c), len(y.c))
for xi, yi in zip(x.c, y.c):
self.assertEqual(xi, yi)
for i in range(self.order + 1):
self.assertEqual(x.c[i], y.c[i])
y = PowerSeries(self.exp_x)
for i in range(self.order + 1):
y.c[i] *= 2
self.assert_close(y, 2 * self.exp_x)
self.assert_close(PowerSeries(), PowerSeries([0.]))
with self.assertRaises(ValueError):
PowerSeries([])
with self.assertRaises(ValueError):
PowerSeries(order=-1)
with self.assertRaises(ValueError):
PowerSeries([1, 2], order=-1)
