def test_guess_symmetry_1(symmetry): C = Circle(0, 3) f = lambda z: z**4 + z**3 + z**2 + z roots = [0,-1,1j,-1j] multiplicities = [1,1,1,1] roots_approx_equal(C.roots(f, verbose=True, guessRootSymmetry=symmetry), (roots, multiplicities))
def test_reevaluation_of_N():
from cxroots import Circle
C = Circle(0, 2)
f = lambda z: (z - 1) * (z - 0.2)**2
roots = [1, 0.2]
multiplicities = [1, 2]
roots_approx_equal(
C.roots(f, NIntAbsTol=10, intMethod='romb', verbose=True),
(roots, multiplicities))
def test_guess_root(guesses): C = Circle(0, 3) f = lambda z: (z-2.5)**2 * (exp(-z)*sin(z/2.) - 1.2*cos(z)) roots = [2.5, 1.44025113016670301345110737, -0.974651035111059787741822566 - 1.381047768247156339633038236j, -0.974651035111059787741822566 + 1.381047768247156339633038236j] multiplicities = [2,1,1,1] roots_approx_equal(C.roots(f, guessRoots=[2.5], verbose=True), (roots, multiplicities))
def calcInt():
plaTrue = ε > -1.0
if plaTrue:
Int = open(f"eps_{ε}_int", "w")
Pla = open(f"eps_{ε}_pla", "w")
else:
Int = open(f"eps_{ε}_int", "w")
for m in range(65):
print(f"m = {m}")
f0 = lambda k: ivp(m, η * k) * hankel1(m, k) / η + iv(m, η * k) * h1vp(
m, k)
f1 = (lambda k: ivp(m, η * k, 2) * hankel1(m, k) + c * ivp(m, η * k) *
h1vp(m, k) + iv(m, η * k) * h1vp(m, k, 2))
t = np.linspace(0.2, 65.0, num=1024)
k = 1j * t
rf = np.real(f0(k))
ind = np.where(rf[1:] * rf[:-1] < 0.0)[0]
roots = np.zeros(np.shape(ind), dtype=complex)
for a, i in enumerate(ind):
C = Circle(center=1j * (t[i] + t[i + 1]) / 2.0,
radius=(t[i + 1] - t[i]))
z = C.roots(f0, df=f1)
roots[a] = z.roots[0]
if plaTrue:
if m:
writeFile(Int, m, roots[1:])
writeFile(Pla, m, roots[[0]])
else:
writeFile(Int, m, roots)
else:
writeFile(Int, m, roots)
if plaTrue:
Int.close()
Pla.close()
else:
Int.close()
def test_guess_symmetry_2(usedf): C = Circle(0, 1.5) f = lambda z: z**27-2*z**11+0.5*z**6-1 df = (lambda z: 27*z**26-22*z**10+3*z**5) if usedf else None symmetry = lambda z: [z.conjugate()] roots = [-1.03509521179240, -0.920332541459108, 1.05026721944263, -0.983563736801535 - 0.382365167035741j, -0.983563736801535 + 0.382365167035741j, -0.792214346729517 - 0.520708613101932j, -0.792214346729517 + 0.520708613101932j, -0.732229626596468 - 0.757345327222341j, -0.732229626596468 + 0.757345327222341j, -0.40289002582335 - 0.825650446354661j, -0.40289002582335 + 0.825650446354661j, -0.383382611408318 - 0.967939747947639j, -0.383382611408318 + 0.967939747947639j, -0.02594227096144 - 1.05524415820652j, -0.02594227096144 + 1.05524415820652j, 0.160356899544475 - 0.927983420797727j, 0.160356899544475 + 0.927983420797727j, 0.41133738621461 - 0.967444751898913j, 0.41133738621461 + 0.967444751898913j, 0.576737152896681 - 0.719511178392941j, 0.576737152896681 + 0.719511178392941j, 0.758074415348703 - 0.724716122470435j, 0.758074415348703 + 0.724716122470435j, 0.903278407433416 - 0.22751872334709j, 0.903278407433416 + 0.22751872334709j, 0.963018623787179 - 0.427294816877434j, 0.963018623787179 + 0.427294816877434j] multiplicities = np.ones_like(roots) roots_approx_equal(C.roots(f, df, verbose=True, guessRootSymmetry=symmetry), (roots, multiplicities))
from numpy import sin, cos
f = lambda z: 1j*z**5 + z*sin(z) # Define f(z)
df = lambda z: 5j*z**4 + z*cos(z) + sin(z) # Define f'(z)
from cxroots import Circle
C = Circle(0, 2) # Define a circle, centered at 0 and with radius 2
r = C.roots(f, df) # Find the roots of f(z) within the circle
r.show('tutorial_roots.png')
from cxroots import Circle C = Circle(0, 2) f = lambda z: z**6 + z**3 df = lambda z: 6 * z**5 + 3 * z**2 r = C.roots(f, df) r.show()
class TestRootfindingContours(unittest.TestCase):
def setUp(self):
self.roots = roots = [0, -1.234, 1 + 1j, 1 - 1j, 2.345]
self.multiplicities = [1, 1, 1, 1, 1]
self.f = lambda z: (z - roots[0]) * (z - roots[1]) * (z - roots[2]) * (
z - roots[3]) * (z - roots[4])
self.df = lambda z: (z - roots[1]) * (z - roots[2]) * (z - roots[
3]) * (z - roots[4]) + (z - roots[0]) * (z - roots[2]) * (
z - roots[3]) * (z - roots[4]) + (z - roots[0]) * (z - roots[
1]) * (z - roots[3]) * (z - roots[4]) + (z - roots[0]) * (
z - roots[1]) * (z - roots[2]) * (z - roots[4]) + (
z - roots[0]) * (z - roots[1]) * (z - roots[2]) * (
z - roots[3])
self.Circle = Circle(0, 3)
self.Rectangle = Rectangle([-2, 2], [-2, 2])
self.halfAnnulus = AnnulusSector(0, [0.5, 3], [-pi / 2, pi / 2])
self.Annulus = Annulus(0, [1, 2])
def test_rootfinding_circle_fdf(self):
roots_approx_equal(self.Circle.roots(self.f, self.df, verbose=True),
(self.roots, self.multiplicities),
decimal=7)
def test_rootfinding_circle_f(self):
roots_approx_equal(self.Circle.roots(self.f, self.df, verbose=True),
(self.roots, self.multiplicities),
decimal=7)
def test_rootfinding_rectangle_fdf(self):
roots_approx_equal(self.Rectangle.roots(self.f, self.df, verbose=True),
(self.roots[:-1], self.multiplicities[:-1]),
decimal=7)
def test_rootfinding_rectangle_f(self):
roots_approx_equal(self.Rectangle.roots(self.f, self.df, verbose=True),
(self.roots[:-1], self.multiplicities[:-1]),
decimal=7)
def test_rootfinding_halfAnnulus_fdf(self):
roots_approx_equal(self.halfAnnulus.roots(self.f,
self.df,
verbose=True),
(self.roots[2:], self.multiplicities[2:]),
decimal=7)
def test_rootfinding_halfAnnulus_f(self):
roots_approx_equal(self.halfAnnulus.roots(self.f,
self.df,
verbose=True),
(self.roots[2:], self.multiplicities[2:]),
decimal=7)
def test_rootfinding_Annulus_fdf(self):
roots_approx_equal(self.Annulus.roots(self.f, self.df, verbose=True),
(self.roots[1:-1], self.multiplicities[1:-1]),
decimal=7)
def test_rootfinding_Annulus_f(self):
roots_approx_equal(self.Annulus.roots(self.f, self.df, verbose=True),
(self.roots[1:-1], self.multiplicities[1:-1]),
decimal=7)
# Taking the derivative
FP = sym.diff(F, Z)
def fp(z):
return complex(FP.evalf(subs={Z: z, C: c}))
print(FP)
#print(complex(FP.evalf(subs={Z: 4+1j, C: 1})))
# Finding the roots
roots = []
cont = Circle(0, 3)
zeroes = cont.roots(f)
zeroes.show()
print(zeroes)
numroots = len(zeroes[0])
for j in range(numroots):
roots.append(complex(zeroes[0][j].real, zeroes[0][j].imag))
print(roots)
# Assign hues for each root
colours = [(90, 190, 155), (0, 190, 155), (150, 255, 255), (90, 190, 155),
(90, 190, 155), (90, 190, 155)]
# Converting to latex
# Write the latex expression to file
exp = sym.Eq(FZ, F)
sym.preview(exp, viewer='file', filename='latex.png')
from numpy import exp, cos, sin
f = lambda z: (exp(2 * z) * cos(z) - 1 - sin(z) + z**5) * (z * (z + 2))**2
from matplotlib import pyplot as plt
plt.figure(figsize=(4.8, 4.8), dpi=80)
from cxroots import Circle
C = Circle(0, 3)
roots = C.roots(f)
roots.show('readmeEx.png')
print(roots)