def calculate_fourier_trasform_cartesian(
symbols: Vector, coords: Vector, dictCGFs: Dict, mo_i: Vector,
kpoints: Vector, chikdic=None) -> Vector:
"""
Calculate the Fourier transform projecting the MO in a set of plane waves
mo_fourier(k) = < phi(r) | exp(i k . r)>
"""
if (chikdic is None):
chikdic = get_fourier_basis(symbols, dictCGFs, kpoints)
result = np.zeros(len(kpoints), dtype=np.complex128)
acc = 0
for symbol, xyz in zip(symbols, coords):
krs = -2j * pi * np.dot(kpoints, xyz)
eikrs = np.exp(krs)
cfgks = chikdic[symbol]
dim_cgfs = len(cfgks)
coefs = mo_i[acc: acc + dim_cgfs]
prod = coefs[:, None] * cfgks * eikrs[None, :]
result += np.sum(prod, axis=0)
acc += dim_cgfs
return result
python类pi()的实例源码
def calculate_fourier_trasform_primitive(l: int, ks: Vector, alpha: float) -> complex:
"""
calculate 1D Fourier transform of single gausian primitive function centred in zero
for given ste of kpoints "ks"
"""
gauss = np.exp(-(pi ** 2 / alpha) * ks ** 2)
if l == 0:
return np.sqrt(pi / alpha) * gauss
elif l == 1:
c = -1j * np.sqrt((pi / alpha) ** 3)
return c * ks * gauss
elif l == 2:
c = np.sqrt(pi / alpha ** 5)
return c * ((alpha / 2.0) - (pi ** 2) * (ks ** 2)) * gauss
else:
msg = ("there is not implementation for the primivite fourier "
"transform of l: {}".format(l))
raise NotImplementedError(msg)
def test_daggered_gate_init():
# Choose gate which does not have an inverse gate:
not_invertible_gate = T
with pytest.raises(NotInvertible):
not_invertible_gate.get_inverse()
# Choose gate which does have an inverse defined:
invertible_gate = Y
assert invertible_gate.get_inverse() == Y
# Test init and matrix
dagger_inv = _metagates.DaggeredGate(not_invertible_gate)
assert dagger_inv._gate == not_invertible_gate
assert np.array_equal(dagger_inv.matrix,
np.matrix([[1, 0],
[0, cmath.exp(-1j * cmath.pi / 4)]]))
inv = _metagates.DaggeredGate(invertible_gate)
assert inv._gate == invertible_gate
assert np.array_equal(inv.matrix, np.matrix([[0, -1j], [1j, 0]]))
# Test matrix
no_matrix_gate = Entangle
with pytest.raises(AttributeError):
no_matrix_gate.matrix
inv_no_matrix_gate = _metagates.DaggeredGate(no_matrix_gate)
with pytest.raises(AttributeError):
inv_no_matrix_gate.matrix
def draw_perpendicular(self, start, guideLine, stepDistance, invert = False):
polR, polPhi = cmath.polar(guideLine)
polR = stepDistance
debugMsg(polPhi)
if invert:
polPhi += (cmath.pi / 2)
else:
polPhi -= (cmath.pi / 2)
debugMsg(polPhi)
debugMsg(cmath.rect(polR, polPhi))
return (cmath.rect(polR, polPhi) + start)
def fft(x):
N = len(x)
if N <= 1: return x
even = fft(x[0::2])
odd = fft(x[1::2])
T= [exp(-2j*pi*k/N)*odd[k] for k in range(N//2)]
return [even[k] + T[k] for k in range(N//2)] + [even[k] - T[k] for k in range(N//2)]
def test_constants(self):
e_expected = 2.71828182845904523536
pi_expected = 3.14159265358979323846
self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))
self.assertAlmostEqual(cmath.e, e_expected, places=9,
msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))
def test_polar(self):
self.assertCISEqual(polar(0), (0., 0.))
self.assertCISEqual(polar(1.), (1., 0.))
self.assertCISEqual(polar(-1.), (1., pi))
self.assertCISEqual(polar(1j), (1., pi/2))
self.assertCISEqual(polar(-1j), (1., -pi/2))
def test_phase(self):
self.assertAlmostEqual(phase(0), 0.)
self.assertAlmostEqual(phase(1.), 0.)
self.assertAlmostEqual(phase(-1.), pi)
self.assertAlmostEqual(phase(-1.+1E-300j), pi)
self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
self.assertAlmostEqual(phase(1j), pi/2)
self.assertAlmostEqual(phase(-1j), -pi/2)
# zeros
self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
self.assertEqual(phase(complex(-0.0, 0.0)), pi)
self.assertEqual(phase(complex(-0.0, -0.0)), -pi)
# infinities
self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
self.assertEqual(phase(complex(INF, -2.3)), -0.0)
self.assertEqual(phase(complex(INF, -0.0)), -0.0)
self.assertEqual(phase(complex(INF, 0.0)), 0.0)
self.assertEqual(phase(complex(INF, 2.3)), 0.0)
self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)
# real or imaginary part NaN
for z in complex_nans:
self.assertTrue(math.isnan(phase(z)))
def test_rect(self):
self.assertCEqual(rect(0, 0), (0, 0))
self.assertCEqual(rect(1, 0), (1., 0))
self.assertCEqual(rect(1, -pi), (-1., 0))
self.assertCEqual(rect(1, pi/2), (0, 1.))
self.assertCEqual(rect(1, -pi/2), (0, -1.))
def set_value(self, number: float):
"""
Sets the value of the graphic
:param number: the number (must be between 0 and 'max_range'
or the scale will peg the limits
:return: None
"""
self.canvas.delete('all')
self.canvas.create_image(0, 0, image=self.image, anchor='nw')
number = number if number <= self.max_value else self.max_value
number = 0.0 if number < 0.0 else number
radius = 0.9 * self.size/2.0
angle_in_radians = (2.0 * cmath.pi / 3.0) \
+ number / self.max_value * (5.0 * cmath.pi / 3.0)
center = cmath.rect(0, 0)
outer = cmath.rect(radius, angle_in_radians)
if self.needle_thickness == 0:
line_width = int(5 * self.size / 200)
line_width = 1 if line_width < 1 else line_width
else:
line_width = self.needle_thickness
self.canvas.create_line(
*self.to_absolute(center.real, center.imag),
*self.to_absolute(outer.real, outer.imag),
width=line_width,
fill=self.needle_color
)
self.readout['text'] = '{}{}'.format(number, self.unit)
def draw_background(self, divisions=10):
"""
Draws the background of the dial
:param divisions: the number of divisions
between 'ticks' shown on the dial
:return: None
"""
self.canvas.create_arc(2, 2, self.size-2, self.size-2,
style=tk.PIESLICE, start=-60, extent=30,
fill='red')
self.canvas.create_arc(2, 2, self.size-2, self.size-2,
style=tk.PIESLICE, start=-30, extent=60,
fill='yellow')
self.canvas.create_arc(2, 2, self.size-2, self.size-2,
style=tk.PIESLICE, start=30, extent=210,
fill='green')
# find the distance between the center and the inner tick radius
inner_tick_radius = int(self.size * 0.4)
outer_tick_radius = int(self.size * 0.5)
for tick in range(divisions):
angle_in_radians = (2.0 * cmath.pi / 3.0) \
+ tick/divisions * (5.0 * cmath.pi / 3.0)
inner_point = cmath.rect(inner_tick_radius, angle_in_radians)
outer_point = cmath.rect(outer_tick_radius, angle_in_radians)
self.canvas.create_line(
*self.to_absolute(inner_point.real, inner_point.imag),
*self.to_absolute(outer_point.real, outer_point.imag),
width=1
)
def test_constants(self):
e_expected = 2.71828182845904523536
pi_expected = 3.14159265358979323846
self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))
self.assertAlmostEqual(cmath.e, e_expected, places=9,
msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))
def check_polar(self, func):
def check(arg, expected):
got = func(arg)
for e, g in zip(expected, got):
self.rAssertAlmostEqual(e, g)
check(0, (0., 0.))
check(1, (1., 0.))
check(-1, (1., pi))
check(1j, (1., pi / 2))
check(-3j, (3., -pi / 2))
inf = float('inf')
check(complex(inf, 0), (inf, 0.))
check(complex(-inf, 0), (inf, pi))
check(complex(3, inf), (inf, pi / 2))
check(complex(5, -inf), (inf, -pi / 2))
check(complex(inf, inf), (inf, pi / 4))
check(complex(inf, -inf), (inf, -pi / 4))
check(complex(-inf, inf), (inf, 3 * pi / 4))
check(complex(-inf, -inf), (inf, -3 * pi / 4))
nan = float('nan')
check(complex(nan, 0), (nan, nan))
check(complex(0, nan), (nan, nan))
check(complex(nan, nan), (nan, nan))
check(complex(inf, nan), (inf, nan))
check(complex(-inf, nan), (inf, nan))
check(complex(nan, inf), (inf, nan))
check(complex(nan, -inf), (inf, nan))
def test_phase(self):
self.assertAlmostEqual(phase(0), 0.)
self.assertAlmostEqual(phase(1.), 0.)
self.assertAlmostEqual(phase(-1.), pi)
self.assertAlmostEqual(phase(-1.+1E-300j), pi)
self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
self.assertAlmostEqual(phase(1j), pi/2)
self.assertAlmostEqual(phase(-1j), -pi/2)
# zeros
self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
self.assertEqual(phase(complex(-0.0, 0.0)), pi)
self.assertEqual(phase(complex(-0.0, -0.0)), -pi)
# infinities
self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
self.assertEqual(phase(complex(INF, -2.3)), -0.0)
self.assertEqual(phase(complex(INF, -0.0)), -0.0)
self.assertEqual(phase(complex(INF, 0.0)), 0.0)
self.assertEqual(phase(complex(INF, 2.3)), 0.0)
self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)
# real or imaginary part NaN
for z in complex_nans:
self.assertTrue(math.isnan(phase(z)))
def test_rect(self):
self.assertCEqual(rect(0, 0), (0, 0))
self.assertCEqual(rect(1, 0), (1., 0))
self.assertCEqual(rect(1, -pi), (-1., 0))
self.assertCEqual(rect(1, pi/2), (0, 1.))
self.assertCEqual(rect(1, -pi/2), (0, -1.))
def test_constants(self):
e_expected = 2.71828182845904523536
pi_expected = 3.14159265358979323846
self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))
self.assertAlmostEqual(cmath.e, e_expected, places=9,
msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))
def check_polar(self, func):
def check(arg, expected):
got = func(arg)
for e, g in zip(expected, got):
self.rAssertAlmostEqual(e, g)
check(0, (0., 0.))
check(1, (1., 0.))
check(-1, (1., pi))
check(1j, (1., pi / 2))
check(-3j, (3., -pi / 2))
inf = float('inf')
check(complex(inf, 0), (inf, 0.))
check(complex(-inf, 0), (inf, pi))
check(complex(3, inf), (inf, pi / 2))
check(complex(5, -inf), (inf, -pi / 2))
check(complex(inf, inf), (inf, pi / 4))
check(complex(inf, -inf), (inf, -pi / 4))
check(complex(-inf, inf), (inf, 3 * pi / 4))
check(complex(-inf, -inf), (inf, -3 * pi / 4))
nan = float('nan')
check(complex(nan, 0), (nan, nan))
check(complex(0, nan), (nan, nan))
check(complex(nan, nan), (nan, nan))
check(complex(inf, nan), (inf, nan))
check(complex(-inf, nan), (inf, nan))
check(complex(nan, inf), (inf, nan))
check(complex(nan, -inf), (inf, nan))
def test_phase(self):
self.assertAlmostEqual(phase(0), 0.)
self.assertAlmostEqual(phase(1.), 0.)
self.assertAlmostEqual(phase(-1.), pi)
self.assertAlmostEqual(phase(-1.+1E-300j), pi)
self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
self.assertAlmostEqual(phase(1j), pi/2)
self.assertAlmostEqual(phase(-1j), -pi/2)
# zeros
self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
self.assertEqual(phase(complex(-0.0, 0.0)), pi)
self.assertEqual(phase(complex(-0.0, -0.0)), -pi)
# infinities
self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
self.assertEqual(phase(complex(INF, -2.3)), -0.0)
self.assertEqual(phase(complex(INF, -0.0)), -0.0)
self.assertEqual(phase(complex(INF, 0.0)), 0.0)
self.assertEqual(phase(complex(INF, 2.3)), 0.0)
self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)
# real or imaginary part NaN
for z in complex_nans:
self.assertTrue(math.isnan(phase(z)))
def test_rect(self):
self.assertCEqual(rect(0, 0), (0, 0))
self.assertCEqual(rect(1, 0), (1., 0))
self.assertCEqual(rect(1, -pi), (-1., 0))
self.assertCEqual(rect(1, pi/2), (0, 1.))
self.assertCEqual(rect(1, -pi/2), (0, -1.))
def test_constants(self):
e_expected = 2.71828182845904523536
pi_expected = 3.14159265358979323846
self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))
self.assertAlmostEqual(cmath.e, e_expected, places=9,
msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))
def test_polar(self):
self.assertCISEqual(polar(0), (0., 0.))
self.assertCISEqual(polar(1.), (1., 0.))
self.assertCISEqual(polar(-1.), (1., pi))
self.assertCISEqual(polar(1j), (1., pi/2))
self.assertCISEqual(polar(-1j), (1., -pi/2))
def test_phase(self):
self.assertAlmostEqual(phase(0), 0.)
self.assertAlmostEqual(phase(1.), 0.)
self.assertAlmostEqual(phase(-1.), pi)
self.assertAlmostEqual(phase(-1.+1E-300j), pi)
self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
self.assertAlmostEqual(phase(1j), pi/2)
self.assertAlmostEqual(phase(-1j), -pi/2)
# zeros
self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
self.assertEqual(phase(complex(-0.0, 0.0)), pi)
self.assertEqual(phase(complex(-0.0, -0.0)), -pi)
# infinities
self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
self.assertEqual(phase(complex(INF, -2.3)), -0.0)
self.assertEqual(phase(complex(INF, -0.0)), -0.0)
self.assertEqual(phase(complex(INF, 0.0)), 0.0)
self.assertEqual(phase(complex(INF, 2.3)), 0.0)
self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)
# real or imaginary part NaN
for z in complex_nans:
self.assertTrue(math.isnan(phase(z)))
def test_rect(self):
self.assertCEqual(rect(0, 0), (0, 0))
self.assertCEqual(rect(1, 0), (1., 0))
self.assertCEqual(rect(1, -pi), (-1., 0))
self.assertCEqual(rect(1, pi/2), (0, 1.))
self.assertCEqual(rect(1, -pi/2), (0, -1.))
def circulate(pos):
theta = 2*pi*pos/len(chords)
x = int(abs(scale+margin+scale*cos(theta)))
y = int(abs(scale+margin+scale*sin(theta)))
return x,y
def test_constants(self):
e_expected = 2.71828182845904523536
pi_expected = 3.14159265358979323846
self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))
self.assertAlmostEqual(cmath.e, e_expected, places=9,
msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))
def test_polar(self):
self.assertCISEqual(polar(0), (0., 0.))
self.assertCISEqual(polar(1.), (1., 0.))
self.assertCISEqual(polar(-1.), (1., pi))
self.assertCISEqual(polar(1j), (1., pi/2))
self.assertCISEqual(polar(-1j), (1., -pi/2))
def test_phase(self):
self.assertAlmostEqual(phase(0), 0.)
self.assertAlmostEqual(phase(1.), 0.)
self.assertAlmostEqual(phase(-1.), pi)
self.assertAlmostEqual(phase(-1.+1E-300j), pi)
self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
self.assertAlmostEqual(phase(1j), pi/2)
self.assertAlmostEqual(phase(-1j), -pi/2)
# zeros
self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
self.assertEqual(phase(complex(-0.0, 0.0)), pi)
self.assertEqual(phase(complex(-0.0, -0.0)), -pi)
# infinities
self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
self.assertEqual(phase(complex(INF, -2.3)), -0.0)
self.assertEqual(phase(complex(INF, -0.0)), -0.0)
self.assertEqual(phase(complex(INF, 0.0)), 0.0)
self.assertEqual(phase(complex(INF, 2.3)), 0.0)
self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)
# real or imaginary part NaN
for z in complex_nans:
self.assertTrue(math.isnan(phase(z)))
def test_rect(self):
self.assertCEqual(rect(0, 0), (0, 0))
self.assertCEqual(rect(1, 0), (1., 0))
self.assertCEqual(rect(1, -pi), (-1., 0))
self.assertCEqual(rect(1, pi/2), (0, 1.))
self.assertCEqual(rect(1, -pi/2), (0, -1.))
def test_constants(self):
e_expected = 2.71828182845904523536
pi_expected = 3.14159265358979323846
self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))
self.assertAlmostEqual(cmath.e, e_expected, places=9,
msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))
def check_polar(self, func):
def check(arg, expected):
got = func(arg)
for e, g in zip(expected, got):
self.rAssertAlmostEqual(e, g)
check(0, (0., 0.))
check(1, (1., 0.))
check(-1, (1., pi))
check(1j, (1., pi / 2))
check(-3j, (3., -pi / 2))
inf = float('inf')
check(complex(inf, 0), (inf, 0.))
check(complex(-inf, 0), (inf, pi))
check(complex(3, inf), (inf, pi / 2))
check(complex(5, -inf), (inf, -pi / 2))
check(complex(inf, inf), (inf, pi / 4))
check(complex(inf, -inf), (inf, -pi / 4))
check(complex(-inf, inf), (inf, 3 * pi / 4))
check(complex(-inf, -inf), (inf, -3 * pi / 4))
nan = float('nan')
check(complex(nan, 0), (nan, nan))
check(complex(0, nan), (nan, nan))
check(complex(nan, nan), (nan, nan))
check(complex(inf, nan), (inf, nan))
check(complex(-inf, nan), (inf, nan))
check(complex(nan, inf), (inf, nan))
check(complex(nan, -inf), (inf, nan))
