Python scipy.special.hankel1() Examples

The following are 15 code examples of scipy.special.hankel1(). 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: sph.py    From sound_field_analysis-py with MIT License 6 votes vote down vote up 
def neumann(n, z):
    """Bessel function of second kind (Neumann / Weber function) of order n at kr.
    Implemented as (hankel1(n, z) - besselj(n, z)) / 1j

    Parameters
    ----------
    n : array_like
       Order
    z: array_like
       Argument

    Returns
    -------
    Y : array_like
       Values of Hankel function of order n at position z
    """
    return (hankel1(n, z) - besselj(n, z)) / 1j
Example #2
Source File: sph.py    From sound_field_analysis-py with MIT License 6 votes vote down vote up 
def hankel1(n, z):
    """Bessel function of third kind (Hankel function) of order n at kr.
    Wraps scipy.special.hankel1(n, z)

    Parameters
    ----------
    n : array_like
       Order
    z: array_like
       Argument

    Returns
    -------
    H1 : array_like
       Values of Hankel function of order n at position z
    """
    return scy.hankel1(n, z)
Example #3
Source File: sph.py    From sound_field_analysis-py with MIT License 6 votes vote down vote up 
def sphankel1(n, kr):
    """Spherical Hankel (first kind) of order n at kr

    Parameters
    ----------
    n : array_like
       Order
    kr: array_like
       Argument

    Returns
    -------
    hn1 : complex float
       Spherical Hankel function hn (first kind)
    """
    n, kr = scalar_broadcast_match(n, kr)
    hn1 = _np.full(n.shape, _np.nan, dtype=_np.complex_)
    kr_nonzero = kr != 0
    hn1[kr_nonzero] = _np.sqrt(_np.pi / 2) / _np.lib.scimath.sqrt(kr[kr_nonzero]) * hankel1(n[kr_nonzero] + 0.5,
                                                                                            kr[kr_nonzero])
    return hn1
Example #4
Source File: analytical.py    From sharpy with BSD 3-Clause "New" or "Revised" License 6 votes vote down vote up 
def sears_CL_freq_resp(k):
    """
    Frequency response of lift coefficient according Sear's solution.
    Ref. Palacios and Cesnik, Chap.3
    """

    # hanckel functions
    H1 = scsp.hankel1(1, k)
    H0 = scsp.hankel1(0, k)

    # Sear's function
    S12star = 2. / (np.pi * k * (H0 + 1.j * H1))
    S0 = np.exp(-1.0j * k) * S12star.conj(S12star)

    # CL frequency response
    CL = 2. * np.pi * S0

    return CL
Example #5
Source File: test_basic.py    From Computable with MIT License 5 votes vote down vote up 
def test_hankel1(self):
        cephes.hankel1(1,1)
Example #6
Source File: test_basic.py    From Computable with MIT License 5 votes vote down vote up 
def test_negv1(self):
        assert_almost_equal(special.hankel1(-3,2), -special.hankel1(3,2), 14)
Example #7
Source File: test_basic.py    From Computable with MIT License 5 votes vote down vote up 
def test_hankel1(self):
        hank1 = special.hankel1(1,.1)
        hankrl = (special.jv(1,.1) + special.yv(1,.1)*1j)
        assert_almost_equal(hank1,hankrl,8)
Example #8
Source File: test_basic.py    From Computable with MIT License 5 votes vote down vote up 
def test_hankel1e(self):
        hank1e = special.hankel1e(1,.1)
        hankrle = special.hankel1(1,.1)*exp(-.1j)
        assert_almost_equal(hank1e,hankrle,8)
Example #9
Source File: test_basic.py    From GraphicDesignPatternByPython with MIT License 5 votes vote down vote up 
def test_hankel1(self):
        cephes.hankel1(1,1)
Example #10
Source File: test_basic.py    From GraphicDesignPatternByPython with MIT License 5 votes vote down vote up 
def test_negv1(self):
        assert_almost_equal(special.hankel1(-3,2), -special.hankel1(3,2), 14)
Example #11
Source File: test_basic.py    From GraphicDesignPatternByPython with MIT License 5 votes vote down vote up 
def test_hankel1(self):
        hank1 = special.hankel1(1,.1)
        hankrl = (special.jv(1,.1) + special.yv(1,.1)*1j)
        assert_almost_equal(hank1,hankrl,8)
Example #12
Source File: test_basic.py    From GraphicDesignPatternByPython with MIT License 5 votes vote down vote up 
def test_hankel1e(self):
        hank1e = special.hankel1e(1,.1)
        hankrle = special.hankel1(1,.1)*exp(-.1j)
        assert_almost_equal(hank1e,hankrle,8)
Example #13
Source File: analytical.py    From sharpy with BSD 3-Clause "New" or "Revised" License 5 votes vote down vote up 
def sears_fun(kg):
    """
    Produces Sears function
    """

    S12 = 2. / np.pi / kg / (scsp.hankel1(0, kg) + 1.j * scsp.hankel1(1, kg))
    S = np.exp(-1.j * kg) * S12.conj()

    return S
Example #14
Source File: test_basic.py    From Computable with MIT License 4 votes vote down vote up 
def test_ticket_853(self):
        """Negative-order Bessels"""
        # cephes
        assert_tol_equal(special.jv(-1, 1), -0.4400505857449335)
        assert_tol_equal(special.jv(-2, 1), 0.1149034849319005)
        assert_tol_equal(special.yv(-1, 1), 0.7812128213002887)
        assert_tol_equal(special.yv(-2, 1), -1.650682606816255)
        assert_tol_equal(special.iv(-1, 1), 0.5651591039924851)
        assert_tol_equal(special.iv(-2, 1), 0.1357476697670383)
        assert_tol_equal(special.kv(-1, 1), 0.6019072301972347)
        assert_tol_equal(special.kv(-2, 1), 1.624838898635178)
        assert_tol_equal(special.jv(-0.5, 1), 0.43109886801837607952)
        assert_tol_equal(special.yv(-0.5, 1), 0.6713967071418031)
        assert_tol_equal(special.iv(-0.5, 1), 1.231200214592967)
        assert_tol_equal(special.kv(-0.5, 1), 0.4610685044478945)
        # amos
        assert_tol_equal(special.jv(-1, 1+0j), -0.4400505857449335)
        assert_tol_equal(special.jv(-2, 1+0j), 0.1149034849319005)
        assert_tol_equal(special.yv(-1, 1+0j), 0.7812128213002887)
        assert_tol_equal(special.yv(-2, 1+0j), -1.650682606816255)

        assert_tol_equal(special.iv(-1, 1+0j), 0.5651591039924851)
        assert_tol_equal(special.iv(-2, 1+0j), 0.1357476697670383)
        assert_tol_equal(special.kv(-1, 1+0j), 0.6019072301972347)
        assert_tol_equal(special.kv(-2, 1+0j), 1.624838898635178)

        assert_tol_equal(special.jv(-0.5, 1+0j), 0.43109886801837607952)
        assert_tol_equal(special.jv(-0.5, 1+1j), 0.2628946385649065-0.827050182040562j)
        assert_tol_equal(special.yv(-0.5, 1+0j), 0.6713967071418031)
        assert_tol_equal(special.yv(-0.5, 1+1j), 0.967901282890131+0.0602046062142816j)

        assert_tol_equal(special.iv(-0.5, 1+0j), 1.231200214592967)
        assert_tol_equal(special.iv(-0.5, 1+1j), 0.77070737376928+0.39891821043561j)
        assert_tol_equal(special.kv(-0.5, 1+0j), 0.4610685044478945)
        assert_tol_equal(special.kv(-0.5, 1+1j), 0.06868578341999-0.38157825981268j)

        assert_tol_equal(special.jve(-0.5,1+0.3j), special.jv(-0.5, 1+0.3j)*exp(-0.3))
        assert_tol_equal(special.yve(-0.5,1+0.3j), special.yv(-0.5, 1+0.3j)*exp(-0.3))
        assert_tol_equal(special.ive(-0.5,0.3+1j), special.iv(-0.5, 0.3+1j)*exp(-0.3))
        assert_tol_equal(special.kve(-0.5,0.3+1j), special.kv(-0.5, 0.3+1j)*exp(0.3+1j))

        assert_tol_equal(special.hankel1(-0.5, 1+1j), special.jv(-0.5, 1+1j) + 1j*special.yv(-0.5,1+1j))
        assert_tol_equal(special.hankel2(-0.5, 1+1j), special.jv(-0.5, 1+1j) - 1j*special.yv(-0.5,1+1j))
Example #15
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))