def do_plot(is_h=True):
from scipy.special._ufuncs import (_struve_power_series,
_struve_asymp_large_z,
_struve_bessel_series)
vs = np.linspace(-1000, 1000, 91)
zs = np.sort(np.r_[1e-5, 1.0, np.linspace(0, 700, 91)[1:]])
rp = _struve_power_series(vs[:,None], zs[None,:], is_h)
ra = _struve_asymp_large_z(vs[:,None], zs[None,:], is_h)
rb = _struve_bessel_series(vs[:,None], zs[None,:], is_h)
mpmath.mp.dps = 50
if is_h:
sh = lambda v, z: float(mpmath.struveh(mpmath.mpf(v), mpmath.mpf(z)))
else:
sh = lambda v, z: float(mpmath.struvel(mpmath.mpf(v), mpmath.mpf(z)))
ex = np.vectorize(sh, otypes='d')(vs[:,None], zs[None,:])
err_a = err_metric(ra[0], ex) + 1e-300
err_p = err_metric(rp[0], ex) + 1e-300
err_b = err_metric(rb[0], ex) + 1e-300
err_est_a = abs(ra[1]/ra[0])
err_est_p = abs(rp[1]/rp[0])
err_est_b = abs(rb[1]/rb[0])
z_cutoff = 0.7*abs(vs) + 12
levels = [-1000, -12]
plt.cla()
plt.hold(1)
plt.contourf(vs, zs, np.log10(err_p).T, levels=levels, colors=['r', 'r'], alpha=0.1)
plt.contourf(vs, zs, np.log10(err_a).T, levels=levels, colors=['b', 'b'], alpha=0.1)
plt.contourf(vs, zs, np.log10(err_b).T, levels=levels, colors=['g', 'g'], alpha=0.1)
plt.contour(vs, zs, np.log10(err_p).T, levels=levels, colors=['r', 'r'], linestyles=[':', ':'])
plt.contour(vs, zs, np.log10(err_a).T, levels=levels, colors=['b', 'b'], linestyles=[':', ':'])
plt.contour(vs, zs, np.log10(err_b).T, levels=levels, colors=['g', 'g'], linestyles=[':', ':'])
lp = plt.contour(vs, zs, np.log10(err_est_p).T, levels=levels, colors=['r', 'r'], linestyles=['-', '-'])
la = plt.contour(vs, zs, np.log10(err_est_a).T, levels=levels, colors=['b', 'b'], linestyles=['-', '-'])
lb = plt.contour(vs, zs, np.log10(err_est_b).T, levels=levels, colors=['g', 'g'], linestyles=['-', '-'])
plt.clabel(lp, fmt={-1000: 'P', -12: 'P'})
plt.clabel(la, fmt={-1000: 'A', -12: 'A'})
plt.clabel(lb, fmt={-1000: 'B', -12: 'B'})
plt.plot(vs, z_cutoff, 'k--')
plt.xlim(vs.min(), vs.max())
plt.ylim(zs.min(), zs.max())
plt.xlabel('v')
plt.ylabel('z')
def make_struve_h_vals():
from mpmath import struveh
nu = [mpf('0.5'), mpf('1.25'), mpf('1.5'), mpf('1.75'), mpf(2), mpf('2.75')]
x = [mpf('0.2'), mpf(1), mpf(2), mpf('2.5'), mpf(3), mpf(5), mpf(10)]
nu, x = zip(*outer(nu, x))
h = [struveh(*vals) for vals in zip(nu, x)]
return make_special_vals('struve_h_vals', ('nu', nu), ('x', x), ('h', h))
def make_struve_h_vals():
from mpmath import struveh
nu = [mpf('0.5'), mpf('1.25'), mpf('1.5'), mpf('1.75'), mpf(2), mpf('2.75')]
x = [mpf('0.2'), mpf(1), mpf(2), mpf('2.5'), mpf(3), mpf(5), mpf(10)]
nu, x = zip(*outer(nu, x))
h = [struveh(*vals) for vals in zip(nu, x)]
return make_special_vals('struve_h_vals', ('nu', nu), ('x', x), ('h', h))
def test_struve(self):
assert_mpmath_equal(sc.struve,
_exception_to_nan(lambda v, x: mpmath.struveh(v, x, **HYPERKW)),
[Arg(-1e30, 1e30), Arg()],
n=2000)
def test_struve(self):
assert_mpmath_equal(
sc.struve,
_exception_to_nan(lambda v, x: mpmath.struveh(v, x, **HYPERKW)),
[Arg(-1e30, 1e30), Arg()],
n=2000)
