def mpl_plot(filename, outputs=Rx.defaultoutputs, fft=False):
"""Plots electric and magnetic fields and currents from all receiver points in the given output file. Each receiver point is plotted in a new figure window.
Args:
filename (string): Filename (including path) of output file.
outputs (list): List of field/current components to plot.
fft (boolean): Plot FFT switch.
Returns:
plt (object): matplotlib plot object.
"""
# Open output file and read some attributes
f = h5py.File(filename, 'r')
nrx = f.attrs['nrx']
dt = f.attrs['dt']
iterations = f.attrs['Iterations']
time = np.linspace(0, (iterations - 1) * dt, num=iterations)
# Check there are any receivers
if nrx == 0:
raise CmdInputError('No receivers found in {}'.format(filename))
# Check for single output component when doing a FFT
if fft:
if not len(outputs) == 1:
raise CmdInputError('A single output must be specified when using the -fft option')
# New plot for each receiver
for rx in range(1, nrx + 1):
path = '/rxs/rx' + str(rx) + '/'
availableoutputs = list(f[path].keys())
# If only a single output is required, create one subplot
if len(outputs) == 1:
# Check for polarity of output and if requested output is in file
if outputs[0][-1] == '-':
polarity = -1
outputtext = '-' + outputs[0][0:-1]
output = outputs[0][0:-1]
else:
polarity = 1
outputtext = outputs[0]
output = outputs[0]
if output not in availableoutputs:
raise CmdInputError('{} output requested to plot, but the available output for receiver 1 is {}'.format(output, ', '.join(availableoutputs)))
outputdata = f[path + output][:] * polarity
# Plotting if FFT required
if fft:
# FFT
freqs, power = fft_power(outputdata, dt)
freqmaxpower = np.where(np.isclose(power, 0))[0][0]
# Set plotting range to -60dB from maximum power or 4 times
# frequency at maximum power
try:
pltrange = np.where(power[freqmaxpower:] < -60)[0][0] + freqmaxpower + 1
except:
pltrange = freqmaxpower * 4
pltrange = np.s_[0:pltrange]
# Plot time history of output component
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, num='rx' + str(rx), figsize=(20, 10), facecolor='w', edgecolor='w')
line1 = ax1.plot(time, outputdata, 'r', lw=2, label=outputtext)
ax1.set_xlabel('Time [s]')
ax1.set_ylabel(outputtext + ' field strength [V/m]')
ax1.set_xlim([0, np.amax(time)])
ax1.grid(which='both', axis='both', linestyle='-.')
# Plot frequency spectra
markerline, stemlines, baseline = ax2.stem(freqs[pltrange], power[pltrange], '-.')
plt.setp(baseline, 'linewidth', 0)
plt.setp(stemlines, 'color', 'r')
plt.setp(markerline, 'markerfacecolor', 'r', 'markeredgecolor', 'r')
line2 = ax2.plot(freqs[pltrange], power[pltrange], 'r', lw=2)
ax2.set_xlabel('Frequency [Hz]')
ax2.set_ylabel('Power [dB]')
ax2.grid(which='both', axis='both', linestyle='-.')
# Change colours and labels for magnetic field components or currents
if 'H' in outputs[0]:
plt.setp(line1, color='g')
plt.setp(line2, color='g')
plt.setp(ax1, ylabel=outputtext + ' field strength [A/m]')
plt.setp(stemlines, 'color', 'g')
plt.setp(markerline, 'markerfacecolor', 'g', 'markeredgecolor', 'g')
elif 'I' in outputs[0]:
plt.setp(line1, color='b')
plt.setp(line2, color='b')
plt.setp(ax1, ylabel=outputtext + ' current [A]')
plt.setp(stemlines, 'color', 'b')
plt.setp(markerline, 'markerfacecolor', 'b', 'markeredgecolor', 'b')
plt.show()
# Plotting if no FFT required
else:
fig, ax = plt.subplots(subplot_kw=dict(xlabel='Time [s]', ylabel=outputtext + ' field strength [V/m]'), num='rx' + str(rx), figsize=(20, 10), facecolor='w', edgecolor='w')
line = ax.plot(time, outputdata, 'r', lw=2, label=outputtext)
ax.set_xlim([0, np.amax(time)])
# ax.set_ylim([-15, 20])
ax.grid(which='both', axis='both', linestyle='-.')
if 'H' in output:
plt.setp(line, color='g')
plt.setp(ax, ylabel=outputtext + ', field strength [A/m]')
elif 'I' in output:
plt.setp(line, color='b')
plt.setp(ax, ylabel=outputtext + ', current [A]')
# If multiple outputs required, create all nine subplots and populate only the specified ones
else:
fig, ax = plt.subplots(subplot_kw=dict(xlabel='Time [s]'), num='rx' + str(rx), figsize=(20, 10), facecolor='w', edgecolor='w')
if len(outputs) == 9:
gs = gridspec.GridSpec(3, 3, hspace=0.3, wspace=0.3)
else:
gs = gridspec.GridSpec(3, 2, hspace=0.3, wspace=0.3)
for output in outputs:
# Check for polarity of output and if requested output is in file
if output[-1] == 'm':
polarity = -1
outputtext = '-' + output[0:-1]
output = output[0:-1]
else:
polarity = 1
outputtext = output
# Check if requested output is in file
if output not in availableoutputs:
raise CmdInputError('Output(s) requested to plot: {}, but available output(s) for receiver {} in the file: {}'.format(', '.join(outputs), rx, ', '.join(availableoutputs)))
outputdata = f[path + output][:] * polarity
if output == 'Ex':
ax = plt.subplot(gs[0, 0])
ax.plot(time, outputdata, 'r', lw=2, label=outputtext)
ax.set_ylabel(outputtext + ', field strength [V/m]')
# ax.set_ylim([-15, 20])
elif output == 'Ey':
ax = plt.subplot(gs[1, 0])
ax.plot(time, outputdata, 'r', lw=2, label=outputtext)
ax.set_ylabel(outputtext + ', field strength [V/m]')
# ax.set_ylim([-15, 20])
elif output == 'Ez':
ax = plt.subplot(gs[2, 0])
ax.plot(time, outputdata, 'r', lw=2, label=outputtext)
ax.set_ylabel(outputtext + ', field strength [V/m]')
# ax.set_ylim([-15, 20])
elif output == 'Hx':
ax = plt.subplot(gs[0, 1])
ax.plot(time, outputdata, 'g', lw=2, label=outputtext)
ax.set_ylabel(outputtext + ', field strength [A/m]')
# ax.set_ylim([-0.03, 0.03])
elif output == 'Hy':
ax = plt.subplot(gs[1, 1])
ax.plot(time, outputdata, 'g', lw=2, label=outputtext)
ax.set_ylabel(outputtext + ', field strength [A/m]')
# ax.set_ylim([-0.03, 0.03])
elif output == 'Hz':
ax = plt.subplot(gs[2, 1])
ax.plot(time, outputdata, 'g', lw=2, label=outputtext)
ax.set_ylabel(outputtext + ', field strength [A/m]')
# ax.set_ylim([-0.03, 0.03])
elif output == 'Ix':
ax = plt.subplot(gs[0, 2])
ax.plot(time, outputdata, 'b', lw=2, label=outputtext)
ax.set_ylabel(outputtext + ', current [A]')
elif output == 'Iy':
ax = plt.subplot(gs[1, 2])
ax.plot(time, outputdata, 'b', lw=2, label=outputtext)
ax.set_ylabel(outputtext + ', current [A]')
elif output == 'Iz':
ax = plt.subplot(gs[2, 2])
ax.plot(time, outputdata, 'b', lw=2, label=outputtext)
ax.set_ylabel(outputtext + ', current [A]')
for ax in fig.axes:
ax.set_xlim([0, np.amax(time)])
ax.grid(which='both', axis='both', linestyle='-.')
# Save a PDF/PNG of the figure
# fig.savefig(os.path.splitext(os.path.abspath(filename))[0] + '_rx' + str(rx) + '.pdf', dpi=None, format='pdf', bbox_inches='tight', pad_inches=0.1)
# fig.savefig(os.path.splitext(os.path.abspath(filename))[0] + '_rx' + str(rx) + '.png', dpi=150, format='png', bbox_inches='tight', pad_inches=0.1)
return plt
def dispersion_analysis(G):
"""
Analysis of numerical dispersion (Taflove et al, 2005, p112) -
worse case of maximum frequency and minimum wavelength
Args:
G (class): Grid class instance - holds essential parameters describing the model.
Returns:
results (dict): Results from dispersion analysis
"""
# Physical phase velocity error (percentage); grid sampling density;
# material with maximum permittivity; maximum significant frequency; error message
results = {
'deltavp': False,
'N': False,
'material': False,
'maxfreq': [],
'error': ''
}
# Find maximum significant frequency
if G.waveforms:
for waveform in G.waveforms:
if waveform.type == 'sine' or waveform.type == 'contsine':
results['maxfreq'].append(4 * waveform.freq)
elif waveform.type == 'impulse':
results['error'] = 'impulse waveform used.'
else:
# User-defined waveform
if waveform.type == 'user':
iterations = G.iterations
# Built-in waveform
else:
# Time to analyse waveform - 4*pulse_width as using entire
# time window can result in demanding FFT
waveform.calculate_coefficients()
iterations = round_value(4 * waveform.chi / G.dt)
if iterations > G.iterations:
iterations = G.iterations
waveformvalues = np.zeros(G.iterations)
for iteration in range(G.iterations):
waveformvalues[iteration] = waveform.calculate_value(
iteration * G.dt, G.dt)
# Ensure source waveform is not being overly truncated before attempting any FFT
if np.abs(waveformvalues[-1]) < np.abs(
np.amax(waveformvalues)) / 100:
# FFT
freqs, power = fft_power(waveformvalues, G.dt)
# Get frequency for max power
freqmaxpower = np.where(np.isclose(power, 0))[0][0]
# Set maximum frequency to a threshold drop from maximum power, ignoring DC value
try:
freqthres = np.where(
power[freqmaxpower:] < -G.highestfreqthres
)[0][0] + freqmaxpower
results['maxfreq'].append(freqs[freqthres])
except ValueError:
results[
'error'] = 'unable to calculate maximum power from waveform, most likely due to undersampling.'
# Ignore case where someone is using a waveform with zero amplitude, i.e. on a receiver
elif waveform.amp == 0:
pass
# If waveform is truncated don't do any further analysis
else:
results[
'error'] = 'waveform does not fit within specified time window and is therefore being truncated.'
else:
results['error'] = 'no waveform detected.'
if results['maxfreq']:
results['maxfreq'] = max(results['maxfreq'])
# Find minimum wavelength (material with maximum permittivity)
maxer = 0
matmaxer = ''
for x in G.materials:
if x.se != float('inf'):
er = x.er
# If there are dispersive materials calculate the complex relative permittivity
# at maximum frequency and take the real part
if x.poles > 0:
er = x.calculate_er(results['maxfreq'])
er = er.real
if er > maxer:
maxer = er
matmaxer = x.ID
results['material'] = next(x for x in G.materials if x.ID == matmaxer)
# Minimum velocity
minvelocity = c / np.sqrt(maxer)
# Minimum wavelength
minwavelength = minvelocity / results['maxfreq']
# Maximum spatial step
if '3D' in G.mode:
delta = max(G.dx, G.dy, G.dz)
elif '2D' in G.mode:
if G.nx == 1:
delta = max(G.dy, G.dz)
elif G.ny == 1:
delta = max(G.dx, G.dz)
elif G.nz == 1:
delta = max(G.dx, G.dy)
# Courant stability factor
S = (c * G.dt) / delta
# Grid sampling density
results['N'] = minwavelength / delta
# Check grid sampling will result in physical wave propagation
if int(np.floor(results['N'])) >= G.mingridsampling:
# Numerical phase velocity
vp = np.pi / (results['N'] * np.arcsin((1 / S) * np.sin(
(np.pi * S) / results['N'])))
# Physical phase velocity error (percentage)
results['deltavp'] = (((vp * c) - c) / c) * 100
# Store rounded down value of grid sampling density
results['N'] = int(np.floor(results['N']))
return results
def mpl_plot(w, timewindow, dt, iterations, fft=False):
"""Plots waveform and prints useful information about its properties.
Args:
w (class): Waveform class instance.
timewindow (float): Time window.
dt (float): Time discretisation.
iterations (int): Number of iterations.
fft (boolean): Plot FFT switch.
Returns:
plt (object): matplotlib plot object.
"""
time = np.linspace(0, 1, iterations)
time *= (iterations * dt)
waveform = np.zeros(len(time))
timeiter = np.nditer(time, flags=['c_index'])
while not timeiter.finished:
waveform[timeiter.index] = w.calculate_value(timeiter[0], dt)
timeiter.iternext()
print('Waveform characteristics...')
print('Type: {}'.format(w.type))
print('Maximum (absolute) amplitude: {:g}'.format(np.max(
np.abs(waveform))))
if w.freq and not w.type == 'gaussian':
print('Centre frequency: {:g} Hz'.format(w.freq))
if w.type == 'gaussian' or w.type == 'gaussiandot' or w.type == 'gaussiandotnorm' or w.type == 'gaussianprime' or w.type == 'gaussiandoubleprime':
delay = 1 / w.freq
print('Time to centre of pulse: {:g} s'.format(delay))
elif w.type == 'gaussiandotdot' or w.type == 'gaussiandotdotnorm' or w.type == 'ricker':
delay = np.sqrt(2) / w.freq
print('Time to centre of pulse: {:g} s'.format(delay))
print('Time window: {:g} s ({} iterations)'.format(timewindow, iterations))
print('Time step: {:g} s'.format(dt))
if fft:
# FFT
freqs, power = fft_power(waveform, dt)
# Set plotting range to 4 times frequency at max power of waveform or
# 4 times the centre frequency
freqmaxpower = np.where(np.isclose(power, 0))[0][0]
if freqs[freqmaxpower] > w.freq:
pltrange = np.where(freqs > 4 * freqs[freqmaxpower])[0][0]
else:
pltrange = np.where(freqs > 4 * w.freq)[0][0]
pltrange = np.s_[0:pltrange]
fig, (ax1, ax2) = plt.subplots(nrows=1,
ncols=2,
num=w.type,
figsize=(20, 10),
facecolor='w',
edgecolor='w')
# Plot waveform
ax1.plot(time, waveform, 'r', lw=2)
ax1.set_xlabel('Time [s]')
ax1.set_ylabel('Amplitude')
# Plot frequency spectra
markerline, stemlines, baseline = ax2.stem(freqs[pltrange],
power[pltrange], '-.')
plt.setp(baseline, 'linewidth', 0)
plt.setp(stemlines, 'color', 'r')
plt.setp(markerline, 'markerfacecolor', 'r', 'markeredgecolor', 'r')
ax2.plot(freqs[pltrange], power[pltrange], 'r', lw=2)
ax2.set_xlabel('Frequency [Hz]')
ax2.set_ylabel('Power [dB]')
else:
fig, ax1 = plt.subplots(num=w.type,
figsize=(20, 10),
facecolor='w',
edgecolor='w')
# Plot waveform
ax1.plot(time, waveform, 'r', lw=2)
ax1.set_xlabel('Time [s]')
ax1.set_ylabel('Amplitude')
[ax.grid() for ax in fig.axes] # Turn on grid
# Save a PDF/PNG of the figure
# fig.savefig(os.path.dirname(os.path.abspath(__file__)) + os.sep + w.type + '.pdf', dpi=None, format='pdf', bbox_inches='tight', pad_inches=0.1)
# fig.savefig(os.path.dirname(os.path.abspath(__file__)) + os.sep + w.type + '.png', dpi=150, format='png', bbox_inches='tight', pad_inches=0.1)
return plt
