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### import ####################################################################
import matplotlib.pyplot as plt
plt.close('all')
import numpy as np
import WrightTools as wt
### define ####################################################################
def get_signal(d, tau, pulsewidth=10, offset=0):
# pulse
pulse = np.exp((-d**2)/(pulsewidth**2))
# signal
sig = np.zeros(d.shape)
sig[d<=0] = np.exp(d[d<=0]/tau)
sig[d<=0] += offset
sig /= sig.max()
# finish
#sig = np.convolve(sig, pulse, mode='same')
return sig
def logarithmic_stepping(p_tau, p_npts, n_tau, n_npts):
# positive
p_xi = np.arange(0, p_npts)
p_delays = p_tau * np.log((p_xi.size+1)/(p_xi+1))
# negative
n_xi = np.arange(0, n_npts)
n_delays = -n_tau * np.log((n_xi.size+1)/(n_xi+1))
return np.hstack((n_delays, [0], p_delays))
tau = 200
d = logarithmic_stepping(50, 3, 200, 15)
### workspace #################################################################
if True:
fig, gs = wt.artists.create_figure(width=13, cols=[1, 1], nrows=1)
# delay space
ax = plt.subplot(gs[0, 0])
ds = np.linspace(-1500, 1500, 1000)
sig = get_signal(ds, tau)
plt.plot(ds, sig, c='b', lw=2, alpha=0.5)
sig = get_signal(ds, tau, offset=0.5)
plt.plot(ds, sig, c='r', lw=2, alpha=0.5)
sig = get_signal(ds, tau*2, offset=0)
plt.plot(ds, sig, c='g', lw=2, alpha=0.5)
plt.xlim(-1250, 100)
plt.ylim(-0.1, 1.1)
for x in d:
plt.axvline(x, c='k', zorder=0)
plt.axvline(0, lw=3, c='k')
ax.set_xlabel('delay', fontsize=18)
ax.set_ylabel('signal', fontsize=18)
plt.grid(ls=':')
# index space
ax = plt.subplot(gs[0, 1])
d = logarithmic_stepping(50, 3, 200, 15)
sig = get_signal(d, tau)
plt.scatter(np.arange(sig.size), sig, c='b', edgecolor='none', s=50, alpha=0.5)
sig = get_signal(d, tau, offset=0.5)
plt.scatter(np.arange(sig.size), sig, c='r', edgecolor='none', s=50, alpha=0.5)
sig = get_signal(d, tau*2, offset=0)
plt.scatter(np.arange(sig.size), sig, c='g', edgecolor='none', s=50, alpha=0.5)
i = np.argmin(np.abs(d))
plt.axvline(i, lw=3, c='k')
plt.grid(ls=':')
plt.ylim(-0.1, 1.1)
plt.setp(ax.get_yticklabels(), visible=False)
ax.set_xlim(0-1, sig.size)
ax.set_xlabel('index', fontsize=18)
# finish
wt.artists.savefig('exponential.png')
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