Python scipy.special.kve() Examples

The following are 16 code examples of scipy.special.kve(). You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. You may also want to check out all available functions/classes of the module scipy.special , or try the search function .
Example #1
Source File: test_basic.py    From Computable with MIT License 6 votes vote down vote up 
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 vote down vote up 
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 vote down vote up 
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 vote down vote up 
def _check_kve(self):
        cephes.kve(1,1)
Example #5
Source File: test_basic.py    From Computable with MIT License 5 votes vote down vote up 
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 vote down vote up 
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 vote down vote up 
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 vote down vote up 
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 vote down vote up 
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 vote down vote up 
def _check_kve(self):
        cephes.kve(1,1)
Example #11
Source File: test_basic.py    From GraphicDesignPatternByPython with MIT License 5 votes vote down vote up 
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 vote down vote up 
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 vote down vote up 
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 vote down vote up 
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 vote down vote up 
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 vote down vote up 
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))