"""Plot Nyquist
=====================================

:func:`sysplot.plot_nyquist` draws the Nyquist diagram of a frequency
response in the complex plane. A directional arrow marks the direction of
increasing frequency. The complex conjugate (mirror) curve is shown at
reduced opacity, controlled by ``alpha``. The arrow position along the
curve arc length is set by ``arrow_position``.
"""

import numpy as np
import matplotlib.pyplot as plt
import control as ctrl
import sysplot as ssp

ssp.apply_config()

system = ctrl.tf([6.25], [1, 3, 6.25])
omega = np.logspace(-2, 2, 1000)
mag, phase, _ = ctrl.frequency_response(system, omega)
real = mag * np.cos(phase)
imag = mag * np.sin(phase)

fig, axes = plt.subplots(1, 3, figsize=ssp.get_figsize(ncols=3))

# Default: mirror shown at half opacity, arrow at 33 % arc length
ssp.plot_nyquist(real, imag, ax=axes[0])
axes[0].set(title="mirror=True (default)", xlabel=r"Re[$H$]", ylabel=r"Im[$H$]")

# No mirror curve
ssp.plot_nyquist(real, imag, ax=axes[1], mirror=False)
axes[1].set(title="mirror=False", xlabel=r"Re[$H$]")

# Arrow placed later along the curve
ssp.plot_nyquist(real, imag, ax=axes[2], arrow_position=0.8)
axes[2].set(title="arrow_position=0.8", xlabel=r"Re[$H$]")

plt.show()