Python scipy.special.kve() Examples
The following are 16
code examples of scipy.special.kve().
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scipy.special
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Example #1
| Source File: test_basic.py From Computable with MIT License | 6 votes |
|
def test_ticket_854(self):
"""Real-valued Bessel domains"""
assert_(isnan(special.jv(0.5, -1)))
assert_(isnan(special.iv(0.5, -1)))
assert_(isnan(special.yv(0.5, -1)))
assert_(isnan(special.yv(1, -1)))
assert_(isnan(special.kv(0.5, -1)))
assert_(isnan(special.kv(1, -1)))
assert_(isnan(special.jve(0.5, -1)))
assert_(isnan(special.ive(0.5, -1)))
assert_(isnan(special.yve(0.5, -1)))
assert_(isnan(special.yve(1, -1)))
assert_(isnan(special.kve(0.5, -1)))
assert_(isnan(special.kve(1, -1)))
assert_(isnan(special.airye(-1)[0:2]).all(), special.airye(-1))
assert_(not isnan(special.airye(-1)[2:4]).any(), special.airye(-1))
Example #2
| Source File: test_basic.py From GraphicDesignPatternByPython with MIT License | 6 votes |
|
def test_ticket_854(self):
"""Real-valued Bessel domains"""
assert_(isnan(special.jv(0.5, -1)))
assert_(isnan(special.iv(0.5, -1)))
assert_(isnan(special.yv(0.5, -1)))
assert_(isnan(special.yv(1, -1)))
assert_(isnan(special.kv(0.5, -1)))
assert_(isnan(special.kv(1, -1)))
assert_(isnan(special.jve(0.5, -1)))
assert_(isnan(special.ive(0.5, -1)))
assert_(isnan(special.yve(0.5, -1)))
assert_(isnan(special.yve(1, -1)))
assert_(isnan(special.kve(0.5, -1)))
assert_(isnan(special.kve(1, -1)))
assert_(isnan(special.airye(-1)[0:2]).all(), special.airye(-1))
assert_(not isnan(special.airye(-1)[2:4]).any(), special.airye(-1))
Example #3
| Source File: filter_design.py From lambda-packs with MIT License | 5 votes |
|
def _bessel_zeros(N):
"""
Find zeros of ordinary Bessel polynomial of order `N`, by root-finding of
modified Bessel function of the second kind
"""
if N == 0:
return asarray([])
# Generate starting points
x0 = _campos_zeros(N)
# Zeros are the same for exp(1/x)*K_{N+0.5}(1/x) and Nth-order ordinary
# Bessel polynomial y_N(x)
def f(x):
return special.kve(N+0.5, 1/x)
# First derivative of above
def fp(x):
return (special.kve(N-0.5, 1/x)/(2*x**2) -
special.kve(N+0.5, 1/x)/(x**2) +
special.kve(N+1.5, 1/x)/(2*x**2))
# Starting points converge to true zeros
x = _aberth(f, fp, x0)
# Improve precision using Newton's method on each
for i in range(len(x)):
x[i] = optimize.newton(f, x[i], fp, tol=1e-15)
# Average complex conjugates to make them exactly symmetrical
x = np.mean((x, x[::-1].conj()), 0)
# Zeros should sum to -1
if abs(np.sum(x) + 1) > 1e-15:
raise RuntimeError('Generated zeros are inaccurate')
return x
Example #4
| Source File: test_basic.py From Computable with MIT License | 5 votes |
|
def _check_kve(self):
cephes.kve(1,1)
Example #5
| Source File: test_basic.py From Computable with MIT License | 5 votes |
|
def test_k0e(self):
ozke = special.k0e(.1)
ozker = special.kve(0,.1)
assert_almost_equal(ozke,ozker,8)
Example #6
| Source File: test_basic.py From Computable with MIT License | 5 votes |
|
def test_k1e(self):
o1ke = special.k1e(.1)
o1ker = special.kve(1,.1)
assert_almost_equal(o1ke,o1ker,8)
Example #7
| Source File: test_basic.py From Computable with MIT License | 5 votes |
|
def test_negv_kve(self):
assert_equal(special.kve(3.0, 2.2), special.kve(-3.0, 2.2))
Example #8
| Source File: test_basic.py From Computable with MIT License | 5 votes |
|
def test_kve(self):
kve1 = special.kve(0,.2)
kv1 = special.kv(0,.2)*exp(.2)
assert_almost_equal(kve1,kv1,8)
z = .2+1j
kve2 = special.kve(0,z)
kv2 = special.kv(0,z)*exp(z)
assert_almost_equal(kve2,kv2,8)
Example #9
| Source File: filter_design.py From GraphicDesignPatternByPython with MIT License | 5 votes |
|
def _bessel_zeros(N):
"""
Find zeros of ordinary Bessel polynomial of order `N`, by root-finding of
modified Bessel function of the second kind
"""
if N == 0:
return asarray([])
# Generate starting points
x0 = _campos_zeros(N)
# Zeros are the same for exp(1/x)*K_{N+0.5}(1/x) and Nth-order ordinary
# Bessel polynomial y_N(x)
def f(x):
return special.kve(N+0.5, 1/x)
# First derivative of above
def fp(x):
return (special.kve(N-0.5, 1/x)/(2*x**2) -
special.kve(N+0.5, 1/x)/(x**2) +
special.kve(N+1.5, 1/x)/(2*x**2))
# Starting points converge to true zeros
x = _aberth(f, fp, x0)
# Improve precision using Newton's method on each
for i in range(len(x)):
x[i] = optimize.newton(f, x[i], fp, tol=1e-15)
# Average complex conjugates to make them exactly symmetrical
x = np.mean((x, x[::-1].conj()), 0)
# Zeros should sum to -1
if abs(np.sum(x) + 1) > 1e-15:
raise RuntimeError('Generated zeros are inaccurate')
return x
Example #10
| Source File: test_basic.py From GraphicDesignPatternByPython with MIT License | 5 votes |
|
def _check_kve(self):
cephes.kve(1,1)
Example #11
| Source File: test_basic.py From GraphicDesignPatternByPython with MIT License | 5 votes |
|
def test_k0e(self):
ozke = special.k0e(.1)
ozker = special.kve(0,.1)
assert_almost_equal(ozke,ozker,8)
Example #12
| Source File: test_basic.py From GraphicDesignPatternByPython with MIT License | 5 votes |
|
def test_k1e(self):
o1ke = special.k1e(.1)
o1ker = special.kve(1,.1)
assert_almost_equal(o1ke,o1ker,8)
Example #13
| Source File: test_basic.py From GraphicDesignPatternByPython with MIT License | 5 votes |
|
def test_negv_kve(self):
assert_equal(special.kve(3.0, 2.2), special.kve(-3.0, 2.2))
Example #14
| Source File: test_basic.py From GraphicDesignPatternByPython with MIT License | 5 votes |
|
def test_gh_7909(self):
assert_(special.kv(1.5, 0) == np.inf)
assert_(special.kve(1.5, 0) == np.inf)
Example #15
| Source File: filter_design.py From Splunking-Crime with GNU Affero General Public License v3.0 | 5 votes |
|
def _bessel_zeros(N):
"""
Find zeros of ordinary Bessel polynomial of order `N`, by root-finding of
modified Bessel function of the second kind
"""
if N == 0:
return asarray([])
# Generate starting points
x0 = _campos_zeros(N)
# Zeros are the same for exp(1/x)*K_{N+0.5}(1/x) and Nth-order ordinary
# Bessel polynomial y_N(x)
def f(x):
return special.kve(N+0.5, 1/x)
# First derivative of above
def fp(x):
return (special.kve(N-0.5, 1/x)/(2*x**2) -
special.kve(N+0.5, 1/x)/(x**2) +
special.kve(N+1.5, 1/x)/(2*x**2))
# Starting points converge to true zeros
x = _aberth(f, fp, x0)
# Improve precision using Newton's method on each
for i in range(len(x)):
x[i] = optimize.newton(f, x[i], fp, tol=1e-15)
# Average complex conjugates to make them exactly symmetrical
x = np.mean((x, x[::-1].conj()), 0)
# Zeros should sum to -1
if abs(np.sum(x) + 1) > 1e-15:
raise RuntimeError('Generated zeros are inaccurate')
return x
Example #16
| Source File: test_basic.py From GraphicDesignPatternByPython with MIT License | 4 votes |
|
def test_ticket_853(self):
"""Negative-order Bessels"""
# cephes
assert_allclose(special.jv(-1, 1), -0.4400505857449335)
assert_allclose(special.jv(-2, 1), 0.1149034849319005)
assert_allclose(special.yv(-1, 1), 0.7812128213002887)
assert_allclose(special.yv(-2, 1), -1.650682606816255)
assert_allclose(special.iv(-1, 1), 0.5651591039924851)
assert_allclose(special.iv(-2, 1), 0.1357476697670383)
assert_allclose(special.kv(-1, 1), 0.6019072301972347)
assert_allclose(special.kv(-2, 1), 1.624838898635178)
assert_allclose(special.jv(-0.5, 1), 0.43109886801837607952)
assert_allclose(special.yv(-0.5, 1), 0.6713967071418031)
assert_allclose(special.iv(-0.5, 1), 1.231200214592967)
assert_allclose(special.kv(-0.5, 1), 0.4610685044478945)
# amos
assert_allclose(special.jv(-1, 1+0j), -0.4400505857449335)
assert_allclose(special.jv(-2, 1+0j), 0.1149034849319005)
assert_allclose(special.yv(-1, 1+0j), 0.7812128213002887)
assert_allclose(special.yv(-2, 1+0j), -1.650682606816255)
assert_allclose(special.iv(-1, 1+0j), 0.5651591039924851)
assert_allclose(special.iv(-2, 1+0j), 0.1357476697670383)
assert_allclose(special.kv(-1, 1+0j), 0.6019072301972347)
assert_allclose(special.kv(-2, 1+0j), 1.624838898635178)
assert_allclose(special.jv(-0.5, 1+0j), 0.43109886801837607952)
assert_allclose(special.jv(-0.5, 1+1j), 0.2628946385649065-0.827050182040562j)
assert_allclose(special.yv(-0.5, 1+0j), 0.6713967071418031)
assert_allclose(special.yv(-0.5, 1+1j), 0.967901282890131+0.0602046062142816j)
assert_allclose(special.iv(-0.5, 1+0j), 1.231200214592967)
assert_allclose(special.iv(-0.5, 1+1j), 0.77070737376928+0.39891821043561j)
assert_allclose(special.kv(-0.5, 1+0j), 0.4610685044478945)
assert_allclose(special.kv(-0.5, 1+1j), 0.06868578341999-0.38157825981268j)
assert_allclose(special.jve(-0.5,1+0.3j), special.jv(-0.5, 1+0.3j)*exp(-0.3))
assert_allclose(special.yve(-0.5,1+0.3j), special.yv(-0.5, 1+0.3j)*exp(-0.3))
assert_allclose(special.ive(-0.5,0.3+1j), special.iv(-0.5, 0.3+1j)*exp(-0.3))
assert_allclose(special.kve(-0.5,0.3+1j), special.kv(-0.5, 0.3+1j)*exp(0.3+1j))
assert_allclose(special.hankel1(-0.5, 1+1j), special.jv(-0.5, 1+1j) + 1j*special.yv(-0.5,1+1j))
assert_allclose(special.hankel2(-0.5, 1+1j), special.jv(-0.5, 1+1j) - 1j*special.yv(-0.5,1+1j))
