def test_var_div_var(self):
x = self.x
y = self.y
z = self.z
p = self.p
a = self.a
b = self.b
tol_d = self.tol_d
tol_mp = self.tol_mp
#
f = Function(x / y)
self.assertLessEqual(
np.abs(f.eval_d().real /
(-.44755270475041560619657805305047592426404601827) - 1),
tol_d)
self.assertLessEqual(
np.abs(f.eval_d().imag /
(-.13600253041648890000441351713180233327939034617) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float(
"-.44755270475041560619657805305047592426404601827") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float(
"-.13600253041648890000441351713180233327939034617") - 1),
tol_mp)
def test_Float_construct(self):
x_d = self.x_d
y_d = self.y_d
z_d = self.z_d
p_d = self.p_d
tol_d = self.tol_d
x_mp = self.x_mp
y_mp = self.y_mp
z_mp = self.z_mp
p_mp = self.p_mp
tol_mp = self.tol_mp
x = Float("4.3", "-9e-3")
x = Float(y_mp)
x = Float(mpfr_float("9.3"), mpfr_float("-3"))
x = Float("9.2", "-43.2e2")
def test_plus(self):
x = self.x
y = self.y
z = self.z
p = self.p
a = self.a
b = self.b
tol_d = self.tol_d
tol_mp = self.tol_mp
#
f = Function(x + y + a)
self.assertLessEqual(np.abs(f.eval_d().real / (5.53) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.118) - 1), tol_d)
#
self.assertLessEqual(mp.abs(f.eval_mp().real / mpfr_float("5.53") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("-1.118") - 1), tol_mp)
#
f = Function(x + Float("3.87"))
self.assertLessEqual(np.abs(f.eval_d().real / (1.44) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (0.21) - 1), tol_d)
#
f = Function(x + mpfr_complex("3.87", "-2.1"))
self.assertLessEqual(np.abs(f.eval_d().real / (1.44) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.89) - 1), tol_d)
#
self.assertLessEqual(mp.abs(f.eval_mp().real / mpfr_float("1.44") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("-1.89") - 1), tol_mp)
#
f = Function(x + (-5))
self.assertLessEqual(np.abs(f.eval_d().real / (-7.43) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (0.21) - 1), tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float("-7.43") - 1), tol_mp)
self.assertLessEqual(mp.abs(f.eval_mp().imag / mpfr_float("0.21") - 1),
tol_mp)
#
f = Function(x)
f += y
f += a
self.assertLessEqual(np.abs(f.eval_d().real / (5.53) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.118) - 1), tol_d)
#
self.assertLessEqual(mp.abs(f.eval_mp().real / mpfr_float("5.53") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("-1.118") - 1), tol_mp)
#
f = Function(x)
f += Float("3.87")
self.assertLessEqual(np.abs(f.eval_d().real / (1.44) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (0.21) - 1), tol_d)
def test_var_times_var(self):
x = self.x
y = self.y
z = self.z
p = self.p
a = self.a
b = self.b
tol_d = self.tol_d
tol_mp = self.tol_mp
#
f = Function(x * y * z)
self.assertLessEqual(np.abs(f.eval_d().real / (77.7616926) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-28.8346602) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float("77.7616926") - 1), tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("-28.8346602") - 1), tol_mp)
def test_power_rule(self):
x = self.x; y = self.y; z = self.z; p = self.p; a = self.a; b = self.b;
tol_d = self.tol_d; tol_mp = self.tol_mp;
#
f = x**2 + y**3;
df = f.differentiate();
#
self.assertLessEqual(np.abs(df.eval_d(x).real / (-4.86)-1), tol_d)
self.assertLessEqual(np.abs(df.eval_d(x).imag / (0.42)-1), tol_d)
#
self.assertLessEqual(mp.abs(df.eval_mp(x).real / mpfr_float("-4.86")-1), tol_mp)
self.assertLessEqual(mp.abs(df.eval_mp(x).imag / mpfr_float("0.42")-1), tol_mp)
#
df.reset()
self.assertLessEqual(np.abs(df.eval_d(y).real / (58.9860)-1), tol_d)
self.assertLessEqual(np.abs(df.eval_d(y).imag / (-56.3376)-1), tol_d)
#
self.assertLessEqual(mp.abs(df.eval_mp(y).real / mpfr_float("58.9860")-1), tol_mp)
self.assertLessEqual(mp.abs(df.eval_mp(y).imag / mpfr_float("-56.3376")-1), tol_mp)
def test_I_construct(self):
x_d = self.x_d
y_d = self.y_d
z_d = self.z_d
p_d = self.p_d
tol_d = self.tol_d
x_mp = self.x_mp
y_mp = self.y_mp
z_mp = self.z_mp
p_mp = self.p_mp
tol_mp = self.tol_mp
y = make_i()
#
self.assertLessEqual(np.abs(y.eval_d().real - (0)), tol_d)
self.assertLessEqual(np.abs(y.eval_d().imag / (1.0) - 1), tol_d)
#
self.assertLessEqual(mp.abs(y.eval_mp().real - mpfr_float("0")),
tol_mp)
self.assertLessEqual(mp.abs(y.eval_mp().imag / mpfr_float("1.0") - 1),
tol_mp)
def test_trancendental(self):
x = self.x; y = self.y; z = self.z; p = self.p; a = self.a; b = self.b;
tol_d = self.tol_d; tol_mp = self.tol_mp;
#
f = sin(x*y) + exp(z*y) - log(x*x);
df = f.differentiate();
#
self.assertLessEqual(np.abs(df.eval_d(x).real / (-17.648420086229721902138620795382021306411662490)-1), 9e-13)
self.assertLessEqual(np.abs(df.eval_d(x).imag / (-803.11883403426275105632833868183320319093878729)-1), tol_d)
#
self.assertLessEqual(mp.abs(df.eval_mp(x).real / mpfr_float("-17.648420086229721902138620795382021306411662490")-1), tol_mp)
self.assertLessEqual(mp.abs(df.eval_mp(x).imag / mpfr_float("-803.11883403426275105632833868183320319093878729")-1), tol_mp)
#
df.reset()
self.assertLessEqual(np.abs(df.eval_d(y).real / (-100.97157179433748763552280062599971478593963953)-1), tol_d)
self.assertLessEqual(np.abs(df.eval_d(y).imag / (361.98093991820979266721712882115615553425318528)-1), tol_d)
#
self.assertLessEqual(mp.abs(df.eval_mp(y).real / mpfr_float("-100.97157179433748763552280062599971478593963953")-1), tol_mp)
self.assertLessEqual(mp.abs(df.eval_mp(y).imag / mpfr_float("361.98093991820979266721712882115615553425318528")-1), tol_mp)
#
df.reset()
self.assertLessEqual(np.abs(df.eval_d(z).real / (-2.1642907643013779167501866500194314960002972412e-14)-1), tol_d)
self.assertLessEqual(np.abs(df.eval_d(z).imag / (2.1105887207247540399884720817624768568595288922e-14)-1), tol_d)
#
self.assertLessEqual(mp.abs(df.eval_mp(z).real / mpfr_float("-2.1642907643013779167501866500194314960002972412e-14")-1), tol_mp)
self.assertLessEqual(mp.abs(df.eval_mp(z).imag / mpfr_float("2.1105887207247540399884720817624768568595288922e-14")-1), tol_mp)
def test_sum_rule(self):
x = self.x; y = self.y; z = self.z; p = self.p; a = self.a; b = self.b;
tol_d = self.tol_d; tol_mp = self.tol_mp;
#
f = x+y+a;
df = f.differentiate();
#
self.assertLessEqual(np.abs(df.eval_d(x).real/(1.0)-1), tol_d)
self.assertLessEqual(np.abs(df.eval_d(x).imag-0), tol_d)
#
self.assertLessEqual(mp.abs(df.eval_mp(x).real/mpfr_float("1.0")-1), tol_mp)
self.assertLessEqual(mp.abs(df.eval_mp(x).imag-mpfr_float("0")), tol_mp)
#
df.reset()
self.assertLessEqual(np.abs(df.eval_d(y).real/(1.0)-1), tol_d)
self.assertLessEqual(np.abs(df.eval_d(y).imag-0), tol_d)
#
self.assertLessEqual(mp.abs(df.eval_mp(y).real/mpfr_float("1.0")-1), tol_mp)
self.assertLessEqual(mp.abs(df.eval_mp(y).imag-mpfr_float("0")), tol_mp)
#
df.reset()
self.assertLessEqual(np.abs(df.eval_d(z).real-0), tol_d)
self.assertLessEqual(np.abs(df.eval_d(z).imag-0), tol_d)
#
self.assertLessEqual(mp.abs(df.eval_mp(z).real-mpfr_float("0.0")), tol_mp)
self.assertLessEqual(mp.abs(df.eval_mp(z).imag-mpfr_float("0")), tol_mp)
def test_prod_rule(self):
x = self.x; y = self.y; z = self.z; p = self.p; a = self.a; b = self.b;
tol_d = self.tol_d; tol_mp = self.tol_mp;
#
f = x**2*y**4 - a*x*y*z**2;
df = f.differentiate();
#
self.assertLessEqual(np.abs(df.eval_d(x).real / (-559.28968169592)-1), tol_d)
self.assertLessEqual(np.abs(df.eval_d(x).imag / (3577.05276993648)-1), tol_d)
#
self.assertLessEqual(mp.abs(df.eval_mp(x).real / mpfr_float("-559.28968169592")-1), tol_mp)
self.assertLessEqual(mp.abs(df.eval_mp(x).imag / mpfr_float("3577.05276993648")-1), tol_mp)
#
df.reset()
self.assertLessEqual(np.abs(df.eval_d(y).real / (1161.85042980828)-1), tol_d)
self.assertLessEqual(np.abs(df.eval_d(y).imag / (-3157.24325320476)-1), tol_d)
#
self.assertLessEqual(mp.abs(df.eval_mp(y).real / mpfr_float("1161.85042980828")-1), tol_mp)
self.assertLessEqual(mp.abs(df.eval_mp(y).imag / mpfr_float("-3157.24325320476")-1), tol_mp)
#
df.reset()
self.assertLessEqual(np.abs(df.eval_d(z).real / (-520.5265859088)-1), tol_d)
self.assertLessEqual(np.abs(df.eval_d(z).imag / (84.7479679056)-1), tol_d)
#
self.assertLessEqual(mp.abs(df.eval_mp(z).real / mpfr_float("-520.5265859088")-1), tol_mp)
self.assertLessEqual(mp.abs(df.eval_mp(z).imag / mpfr_float("84.7479679056")-1), tol_mp)
def setUp(self):
default_precision(30)
self.x_d = complex(-2.43, .21)
self.y_d = complex(4.84, -1.94)
self.z_d = complex(-6.48, -.731)
self.p_d = complex(-.321, -.72)
self.tol_d = float(1e-15)
#
self.x_mp = mpfr_complex("-2.43", ".21")
self.y_mp = mpfr_complex("4.84", "-1.94")
self.z_mp = mpfr_complex("-6.48", "-.731")
self.p_mp = mpfr_complex("-.321", "-.72")
self.tol_mp = mpfr_float("1e-27")
def test_num_times_var(self):
x = self.x
y = self.y
z = self.z
p = self.p
a = self.a
b = self.b
tol_d = self.tol_d
tol_mp = self.tol_mp
#
f = Function(a * x * b * y)
#
self.assertLessEqual(np.abs(f.eval_d().real / (3.4011196056) - 1),
tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-110.9953448712) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float("3.4011196056") - 1), tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("-110.9953448712") - 1),
tol_mp)
def test_Float_eval(self):
x_d = self.x_d
y_d = self.y_d
z_d = self.z_d
p_d = self.p_d
tol_d = self.tol_d
x_mp = self.x_mp
y_mp = self.y_mp
z_mp = self.z_mp
p_mp = self.p_mp
tol_mp = self.tol_mp
x = Float(x_mp)
y = Float(y_mp)
z = Float(z_mp)
#
self.assertLessEqual(np.abs(x.eval_d().real / (-2.43) - 1), tol_d)
self.assertLessEqual(np.abs(x.eval_d().imag / (.21) - 1), tol_d)
#
self.assertLessEqual(mp.abs(y.eval_mp().real / mpfr_float("4.84") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(y.eval_mp().imag / mpfr_float("-1.94") - 1), tol_mp)
def test_Pi_construct(self):
x_d = self.x_d
y_d = self.y_d
z_d = self.z_d
p_d = self.p_d
tol_d = self.tol_d
x_mp = self.x_mp
y_mp = self.y_mp
z_mp = self.z_mp
p_mp = self.p_mp
tol_mp = self.tol_mp
x = Pi()
y = make_pi()
#
self.assertLessEqual(
np.abs(x.eval_d().real /
(3.1415926535897932384626433832795028841971693994) - 1),
tol_d)
self.assertLessEqual(np.abs(x.eval_d().imag - (0)), tol_d)
#
self.assertLessEqual(
mp.abs(x.eval_mp().real / mpfr_float(
"3.1415926535897932384626433832795028841971693994") - 1),
tol_mp)
self.assertLessEqual(mp.abs(x.eval_mp().imag - mpfr_float("0")),
tol_mp)
#
self.assertLessEqual(
np.abs(y.eval_d().real /
(3.1415926535897932384626433832795028841971693994) - 1),
tol_d)
self.assertLessEqual(np.abs(y.eval_d().imag - (0)), tol_d)
#
self.assertLessEqual(
mp.abs(y.eval_mp().real / mpfr_float(
"3.1415926535897932384626433832795028841971693994") - 1),
tol_mp)
self.assertLessEqual(mp.abs(y.eval_mp().imag - mpfr_float("0")),
tol_mp)
def test_E_construct(self):
x_d = self.x_d
y_d = self.y_d
z_d = self.z_d
p_d = self.p_d
tol_d = self.tol_d
x_mp = self.x_mp
y_mp = self.y_mp
z_mp = self.z_mp
p_mp = self.p_mp
tol_mp = self.tol_mp
x = E()
y = make_e()
#
self.assertLessEqual(
np.abs(x.eval_d().real /
(2.7182818284590452353602874713526624977572470937) - 1),
tol_d)
self.assertLessEqual(np.abs(x.eval_d().imag - (0)), tol_d)
#
self.assertLessEqual(
mp.abs(x.eval_mp().real - mpfr_float(
"2.7182818284590452353602874713526624977572470937")), tol_mp)
self.assertLessEqual(mp.abs(x.eval_mp().imag - mpfr_float("0")),
tol_mp)
#
self.assertLessEqual(
np.abs(y.eval_d().real /
(2.7182818284590452353602874713526624977572470937) - 1),
tol_d)
self.assertLessEqual(np.abs(y.eval_d().imag - (0)), tol_d)
#
self.assertLessEqual(
mp.abs(y.eval_mp().real / mpfr_float(
"2.7182818284590452353602874713526624977572470937") - 1),
tol_mp)
self.assertLessEqual(mp.abs(y.eval_mp().imag - mpfr_float("0")),
tol_mp)
def test_Variable_eval(self):
x_d = self.x_d
y_d = self.y_d
z_d = self.z_d
p_d = self.p_d
tol_d = self.tol_d
x_mp = self.x_mp
y_mp = self.y_mp
z_mp = self.z_mp
p_mp = self.p_mp
tol_mp = self.tol_mp
x = Variable("x")
y = Variable("y")
x.set_current_value(x_d)
x.set_current_value(x_mp)
#
self.assertLessEqual(np.abs(x.eval_d().real / (-2.43) - 1), tol_d)
self.assertLessEqual(np.abs(x.eval_d().imag / (.21) - 1), tol_d)
#
self.assertLessEqual(
mp.abs(x.eval_mp().real / mpfr_float("-2.43") - 1), tol_mp)
self.assertLessEqual(mp.abs(x.eval_mp().imag / mpfr_float(".21") - 1),
tol_mp)
def test_Float_funcs(self):
x_d = self.x_d
y_d = self.y_d
z_d = self.z_d
p_d = self.p_d
tol_d = self.tol_d
x_mp = self.x_mp
y_mp = self.y_mp
z_mp = self.z_mp
p_mp = self.p_mp
tol_mp = self.tol_mp
x = Float(x_mp)
y = Float(y_mp)
z = Float(z_mp)
#
self.assertEqual(x.degree(), 0)
d = y.differentiate()
self.assertLessEqual(mp.abs(d.eval_mp().real - mpfr_float("0")),
tol_mp)
self.assertLessEqual(mp.abs(d.eval_mp().imag - mpfr_float("0")),
tol_mp)
self.assertTrue(y.is_homogeneous())
self.assertTrue(y.is_polynomial())
def test_sub(self):
x = self.x
y = self.y
z = self.z
p = self.p
a = self.a
b = self.b
tol_d = self.tol_d
tol_mp = self.tol_mp
#
f = Function(x - y - a)
self.assertLessEqual(np.abs(f.eval_d().real / (-10.39) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (1.538) - 1), tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float("-10.39") - 1), tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("1.538") - 1), tol_mp)
#
f = Function(y - Float("3.87"))
self.assertLessEqual(np.abs(f.eval_d().real / (0.97) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.94) - 1), tol_d)
#
f = Function(y - Float("3.87", "0"))
self.assertLessEqual(np.abs(f.eval_d().real / (0.97) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.94) - 1), tol_d)
#
#
f = Function(y - mpfr_complex("3.87", "-2.1"))
self.assertLessEqual(np.abs(f.eval_d().real / (0.97) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (0.16) - 1), tol_d)
#
self.assertLessEqual(mp.abs(f.eval_mp().real / mpfr_float("0.97") - 1),
tol_mp)
self.assertLessEqual(mp.abs(f.eval_mp().imag / mpfr_float("0.16") - 1),
tol_mp)
#
f = Function(y - (-5))
self.assertLessEqual(np.abs(f.eval_d().real / (9.84) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.94) - 1), tol_d)
#
f = Function(x)
f -= y
f -= a
self.assertLessEqual(np.abs(f.eval_d().real / (-10.39) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (1.538) - 1), tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float("-10.39") - 1), tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("1.538") - 1), tol_mp)
#
f = Function(y)
f -= Float("3.87")
self.assertLessEqual(np.abs(f.eval_d().real / (0.97) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.94) - 1), tol_d)
def setUp(self):
default_precision(30)
self.x = Variable("x")
self.x.set_current_value(complex(-2.43, .21))
self.y = Variable("y")
self.y.set_current_value(complex(4.84, -1.94))
self.z = Variable("z")
self.z.set_current_value(complex(-6.48, -.731))
self.p = Variable("p")
self.p.set_current_value(complex(-.321, -.72))
self.a = Float(mpfr_complex("3.12", ".612"))
self.b = Float(mpfr_complex("-.823", "2.62"))
self.tol_d = float(9e-14)
#
self.x.set_current_value(mpfr_complex("-2.43", ".21"))
self.y.set_current_value(mpfr_complex("4.84", "-1.94"))
self.z.set_current_value(mpfr_complex("-6.48", "-.731"))
self.p.set_current_value(mpfr_complex("-.321", "-.72"))
self.a = Float(mpfr_complex("3.12", ".612"))
self.b = Float(mpfr_complex("-.823", "2.62"))
self.tol_mp = mpfr_float("1e-27")
def test_power(self):
x = self.x
y = self.y
z = self.z
p = self.p
a = self.a
b = self.b
tol_d = self.tol_d
tol_mp = self.tol_mp
#
f = Function(y**3)
self.assertLessEqual(np.abs(f.eval_d().real / (58.732432) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-129.035608) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float("58.732432") - 1), tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("-129.035608") - 1), tol_mp)
#
f = Function(pow(y, 3))
self.assertLessEqual(np.abs(f.eval_d().real / (58.732432) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-129.035608) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float("58.732432") - 1), tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("-129.035608") - 1), tol_mp)
#
f = Function(x**p)
self.assertLessEqual(
np.abs(f.eval_d().real /
(-.35190932545709434788093164550270669097948909024) - 1),
tol_d)
self.assertLessEqual(
np.abs(f.eval_d().imag /
(-6.7687858345625791466707575744042177964518271087) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float(
"-.35190932545709434788093164550270669097948909024") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float(
"-6.7687858345625791466707575744042177964518271087") - 1),
tol_mp)
#
f = Function(pow(x, p))
self.assertLessEqual(
np.abs(f.eval_d().real /
(-.35190932545709434788093164550270669097948909024) - 1),
tol_d)
self.assertLessEqual(
np.abs(f.eval_d().imag /
(-6.7687858345625791466707575744042177964518271087) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float(
"-.35190932545709434788093164550270669097948909024") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float(
"-6.7687858345625791466707575744042177964518271087") - 1),
tol_mp)
def test_trans_funcs(self):
x = self.x
y = self.y
z = self.z
p = self.p
a = self.a
b = self.b
tol_d = self.tol_d
tol_mp = self.tol_mp
#
f = Function(sin(x))
self.assertLessEqual(
np.abs(f.eval_d().real /
(-.66749329633668695550441899166308616328986315948) - 1),
tol_d)
self.assertLessEqual(
np.abs(f.eval_d().imag /
(-.16020928942503633132090203927960650380076680938) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float(
"-.66749329633668695550441899166308616328986315948") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float(
"-.16020928942503633132090203927960650380076680938") - 1),
tol_mp)
#
f = Function(cos(y))
self.assertLessEqual(
np.abs(f.eval_d().real /
(0.45194679593300564730917329070452033759984813611) - 1),
tol_d)
self.assertLessEqual(
np.abs(f.eval_d().imag /
(-3.3798161097977088705360399142708324234265626016) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float(
"0.45194679593300564730917329070452033759984813611") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float(
"-3.3798161097977088705360399142708324234265626016") - 1),
tol_mp)
#
f = Function(tan(z))
self.assertLessEqual(
np.abs(f.eval_d().real /
(-.11998086808607765336591715593714295443402911227) - 1),
tol_d)
self.assertLessEqual(
np.abs(f.eval_d().imag /
(-.63859741450762243500349270264429166927927928889) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float(
"-.11998086808607765336591715593714295443402911227") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float(
"-.63859741450762243500349270264429166927927928889") - 1),
tol_mp)
#
f = Function(asin(x))
self.assertLessEqual(
np.abs(f.eval_d().real /
(-1.4763431474004472804452143435221887167393328861) - 1),
tol_d)
self.assertLessEqual(
np.abs(f.eval_d().imag /
(1.5406263884278099750127157814537559611048741005) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float(
"-1.4763431474004472804452143435221887167393328861") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float(
"1.5406263884278099750127157814537559611048741005") - 1),
tol_mp)
#
f = Function(acos(y))
self.assertLessEqual(
np.abs(f.eval_d().real /
(0.38769800860408664087229892623614567735197135529) - 1),
tol_d)
self.assertLessEqual(
np.abs(f.eval_d().imag /
(2.3379037587834289977359318611458042347281923566) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float(
"0.38769800860408664087229892623614567735197135529") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float(
"2.3379037587834289977359318611458042347281923566") - 1),
tol_mp)
#
f = Function(atan(z))
self.assertLessEqual(
np.abs(f.eval_d().real /
(-1.4195347801361539102032503530226060969949192059) - 1),
tol_d)
self.assertLessEqual(
np.abs(f.eval_d().imag /
(-0.16801358511827150554928904776095870747673962940e-1) -
1), tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float(
"-1.4195347801361539102032503530226060969949192059") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float(
"-0.16801358511827150554928904776095870747673962940e-1") - 1),
tol_mp)
#
f = Function(exp(y))
self.assertLessEqual(
np.abs(f.eval_d().real /
(-45.639359208255772966298371983389382308765171859) - 1),
tol_d)
self.assertLessEqual(
np.abs(f.eval_d().imag /
(-117.94721623715960520658000231550940351946595854) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float(
"-45.639359208255772966298371983389382308765171859") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float(
"-117.94721623715960520658000231550940351946595854") - 1),
tol_mp)
#
f = Function(log(z))
self.assertLessEqual(
np.abs(f.eval_d().real /
(1.8750432590213669716781046977781508038070552297) - 1),
tol_d)
self.assertLessEqual(
np.abs(f.eval_d().imag /
(-3.0292589170775161726973168096174940982043177322) - 1),
tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float(
"1.8750432590213669716781046977781508038070552297") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float(
"-3.0292589170775161726973168096174940982043177322") - 1),
tol_mp)