`scipy.special._basic:y1p_zeros`

source: /scipy/special/_basic.py :730

Signature

def y1p_zeros ( nt , complex = False )

Summary

Compute nt zeros of Bessel derivative Y1'(z), and value at each zero.

Extended Summary

The values are given by Y1(z1) at each z1 where Y1'(z1)=0.

Parameters

nt : int: Number of zeros to return
complex : bool, default False: Set to False to return only the real zeros; set to True to return only the complex zeros with negative real part and positive imaginary part. Note that the complex conjugates of the latter are also zeros of the function, but are not returned by this routine.

Returns

z1pn : ndarray: Location of nth zero of Y1'(z)
y1z1pn : ndarray: Value of derivative Y1(z1) for nth zero

Examples

Compute the first four roots of :math:`Y_1'` and the values of :math:`Y_1` at these roots.

import numpy as np
from scipy.special import y1p_zeros
y1grad_roots, y1_values = y1p_zeros(4)
with np.printoptions(precision=5):
    print(f"Y1' Roots: {y1grad_roots.real}")
    print(f"Y1 values: {y1_values.real}")

✓

`y1p_zeros` can be used to calculate the extremal points of :math:`Y_1` directly. Here we plot :math:`Y_1` and the first four extrema.

import matplotlib.pyplot as plt
from scipy.special import y1, yvp
y1_roots, y1_values_at_roots = y1p_zeros(4)
real_roots = y1_roots.real
xmax = 15
x = np.linspace(0, xmax, 500)
x[0] += 1e-15
fig, ax = plt.subplots()

✓

ax.plot(x, y1(x), label=r'$Y_1$')
ax.plot(x, yvp(1, x, 1), label=r"$Y_1'$")
ax.scatter(real_roots, np.zeros((4, )), s=30, c='r',
           label=r"Roots of $Y_1'$", zorder=5)
ax.scatter(real_roots, y1_values_at_roots.real, s=30, c='k',
           label=r"Extrema of $Y_1$", zorder=5)
ax.hlines(0, 0, xmax, color='k')
ax.set_ylim(-0.5, 0.5)
ax.set_xlim(0, xmax)
ax.legend(ncol=2, bbox_to_anchor=(1., 0.75))

✗

plt.tight_layout()
plt.show()

✓

Aliases

scipy.special.y1p_zeros