Esempio n. 1
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def test_diff():
    assert besselj(n,
                   z).diff(z) == besselj(n - 1, z) / 2 - besselj(n + 1, z) / 2
    assert bessely(n,
                   z).diff(z) == bessely(n - 1, z) / 2 - bessely(n + 1, z) / 2
    assert besseli(n,
                   z).diff(z) == besseli(n - 1, z) / 2 + besseli(n + 1, z) / 2
    assert besselk(n,
                   z).diff(z) == -besselk(n - 1, z) / 2 - besselk(n + 1, z) / 2
    assert hankel1(n,
                   z).diff(z) == hankel1(n - 1, z) / 2 - hankel1(n + 1, z) / 2
    assert hankel2(n,
                   z).diff(z) == hankel2(n - 1, z) / 2 - hankel2(n + 1, z) / 2
Esempio n. 2
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def test_diff():
    assert besselj(n, z).diff(z) == besselj(n - 1, z)/2 - besselj(n + 1, z)/2
    assert bessely(n, z).diff(z) == bessely(n - 1, z)/2 - bessely(n + 1, z)/2
    assert besseli(n, z).diff(z) == besseli(n - 1, z)/2 + besseli(n + 1, z)/2
    assert besselk(n, z).diff(z) == -besselk(n - 1, z)/2 - besselk(n + 1, z)/2
    assert hankel1(n, z).diff(z) == hankel1(n - 1, z)/2 - hankel1(n + 1, z)/2
    assert hankel2(n, z).diff(z) == hankel2(n - 1, z)/2 - hankel2(n + 1, z)/2

    pytest.raises(ArgumentIndexError, lambda: besselj(n, z).fdiff(3))
    pytest.raises(ArgumentIndexError, lambda: jn(n, z).fdiff(3))
    pytest.raises(ArgumentIndexError, lambda: airyai(z).fdiff(2))
    pytest.raises(ArgumentIndexError, lambda: airybi(z).fdiff(2))
    pytest.raises(ArgumentIndexError, lambda: airyaiprime(z).fdiff(2))
    pytest.raises(ArgumentIndexError, lambda: airybiprime(z).fdiff(2))
Esempio n. 3
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def test_diff():
    assert besselj(n, z).diff(z) == besselj(n - 1, z)/2 - besselj(n + 1, z)/2
    assert bessely(n, z).diff(z) == bessely(n - 1, z)/2 - bessely(n + 1, z)/2
    assert besseli(n, z).diff(z) == besseli(n - 1, z)/2 + besseli(n + 1, z)/2
    assert besselk(n, z).diff(z) == -besselk(n - 1, z)/2 - besselk(n + 1, z)/2
    assert hankel1(n, z).diff(z) == hankel1(n - 1, z)/2 - hankel1(n + 1, z)/2
    assert hankel2(n, z).diff(z) == hankel2(n - 1, z)/2 - hankel2(n + 1, z)/2

    pytest.raises(ArgumentIndexError, lambda: besselj(n, z).fdiff(3))
    pytest.raises(ArgumentIndexError, lambda: jn(n, z).fdiff(3))
    pytest.raises(ArgumentIndexError, lambda: airyai(z).fdiff(2))
    pytest.raises(ArgumentIndexError, lambda: airybi(z).fdiff(2))
    pytest.raises(ArgumentIndexError, lambda: airyaiprime(z).fdiff(2))
    pytest.raises(ArgumentIndexError, lambda: airybiprime(z).fdiff(2))
Esempio n. 4
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def test_specfun():
    for f in [besselj, bessely, besseli, besselk]:
        assert octave_code(f(n, x)) == f.__name__ + '(n, x)'
    assert octave_code(hankel1(n, x)) == 'besselh(n, 1, x)'
    assert octave_code(hankel2(n, x)) == 'besselh(n, 2, x)'
    assert octave_code(airyai(x)) == 'airy(0, x)'
    assert octave_code(airyaiprime(x)) == 'airy(1, x)'
    assert octave_code(airybi(x)) == 'airy(2, x)'
    assert octave_code(airybiprime(x)) == 'airy(3, x)'
    assert octave_code(uppergamma(n, x)) == "gammainc(x, n, 'upper')"
    assert octave_code(lowergamma(n, x)) == "gammainc(x, n, 'lower')"
    assert octave_code(jn(
        n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*besselj(n + 1/2, x)/2'
    assert octave_code(yn(
        n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*bessely(n + 1/2, x)/2'
    assert octave_code(Chi(x)) == 'coshint(x)'
    assert octave_code(Ci(x)) == 'cosint(x)'
    assert octave_code(laguerre(n, x)) == 'laguerreL(n, x)'
    assert octave_code(li(x)) == 'logint(x)'
    assert octave_code(loggamma(x)) == 'gammaln(x)'
    assert octave_code(polygamma(n, x)) == 'psi(n, x)'
    assert octave_code(Shi(x)) == 'sinhint(x)'
    assert octave_code(Si(x)) == 'sinint(x)'
    assert octave_code(LambertW(x)) == 'lambertw(x)'
    assert octave_code(LambertW(x, n)) == 'lambertw(n, x)'
    assert octave_code(zeta(x)) == 'zeta(x)'
    assert octave_code(zeta(
        x, y)) == '% Not supported in Octave:\n% zeta\nzeta(x, y)'
Esempio n. 5
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def test_conjugate():
    n, z, x = Symbol('n'), Symbol('z', extended_real=False), Symbol(
        'x', extended_real=True)
    y, t = Symbol('y', extended_real=True,
                  positive=True), Symbol('t', negative=True)

    for f in [besseli, besselj, besselk, bessely, jn, yn, hankel1, hankel2]:
        assert f(n, -1).conjugate() != f(conjugate(n), -1)
        assert f(n, x).conjugate() != f(conjugate(n), x)
        assert f(n, t).conjugate() != f(conjugate(n), t)

    rz = randcplx(b=0.5)

    for f in [besseli, besselj, besselk, bessely, jn, yn]:
        assert f(n, 1 + I).conjugate() == f(conjugate(n), 1 - I)
        assert f(n, 0).conjugate() == f(conjugate(n), 0)
        assert f(n, 1).conjugate() == f(conjugate(n), 1)
        assert f(n, z).conjugate() == f(conjugate(n), conjugate(z))
        assert f(n, y).conjugate() == f(conjugate(n), y)
        assert tn(f(n, rz).conjugate(), f(conjugate(n), conjugate(rz)))

    assert hankel1(n, 1 + I).conjugate() == hankel2(conjugate(n), 1 - I)
    assert hankel1(n, 0).conjugate() == hankel2(conjugate(n), 0)
    assert hankel1(n, 1).conjugate() == hankel2(conjugate(n), 1)
    assert hankel1(n, y).conjugate() == hankel2(conjugate(n), y)
    assert hankel1(n, z).conjugate() == hankel2(conjugate(n), conjugate(z))
    assert tn(hankel1(n, rz).conjugate(), hankel2(conjugate(n), conjugate(rz)))

    assert hankel2(n, 1 + I).conjugate() == hankel1(conjugate(n), 1 - I)
    assert hankel2(n, 0).conjugate() == hankel1(conjugate(n), 0)
    assert hankel2(n, 1).conjugate() == hankel1(conjugate(n), 1)
    assert hankel2(n, y).conjugate() == hankel1(conjugate(n), y)
    assert hankel2(n, z).conjugate() == hankel1(conjugate(n), conjugate(z))
    assert tn(hankel2(n, rz).conjugate(), hankel1(conjugate(n), conjugate(rz)))
Esempio n. 6
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def test_conjugate():
    n, z, x = Symbol('n'), Symbol('z', extended_real=False), Symbol('x', extended_real=True)
    y, t = Symbol('y', extended_real=True, positive=True), Symbol('t', negative=True)

    for f in [besseli, besselj, besselk, bessely, jn, yn, hankel1, hankel2]:
        assert f(n, -1).conjugate() != f(conjugate(n), -1)
        assert f(n, x).conjugate() != f(conjugate(n), x)
        assert f(n, t).conjugate() != f(conjugate(n), t)

    rz = randcplx(b=0.5)

    for f in [besseli, besselj, besselk, bessely, jn, yn]:
        assert f(n, 1 + I).conjugate() == f(conjugate(n), 1 - I)
        assert f(n, 0).conjugate() == f(conjugate(n), 0)
        assert f(n, 1).conjugate() == f(conjugate(n), 1)
        assert f(n, z).conjugate() == f(conjugate(n), conjugate(z))
        assert f(n, y).conjugate() == f(conjugate(n), y)
        assert tn(f(n, rz).conjugate(), f(conjugate(n), conjugate(rz)))

    assert hankel1(n, 1 + I).conjugate() == hankel2(conjugate(n), 1 - I)
    assert hankel1(n, 0).conjugate() == hankel2(conjugate(n), 0)
    assert hankel1(n, 1).conjugate() == hankel2(conjugate(n), 1)
    assert hankel1(n, y).conjugate() == hankel2(conjugate(n), y)
    assert hankel1(n, z).conjugate() == hankel2(conjugate(n), conjugate(z))
    assert tn(hankel1(n, rz).conjugate(), hankel2(conjugate(n), conjugate(rz)))

    assert hankel2(n, 1 + I).conjugate() == hankel1(conjugate(n), 1 - I)
    assert hankel2(n, 0).conjugate() == hankel1(conjugate(n), 0)
    assert hankel2(n, 1).conjugate() == hankel1(conjugate(n), 1)
    assert hankel2(n, y).conjugate() == hankel1(conjugate(n), y)
    assert hankel2(n, z).conjugate() == hankel1(conjugate(n), conjugate(z))
    assert tn(hankel2(n, rz).conjugate(), hankel1(conjugate(n), conjugate(rz)))