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victor

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def Prominence_from_fft(lambdas, intensities, refractive_index, num_half_space=None, plot=True):
if num_half_space is None:
num_half_space = len(lambdas)
# # # 1. Spectre original
# if plot:
# plt.figure(figsize=(10, 6), dpi=150)
# plt.plot(1/lambdas, intensities, label='Spectre original')
# plt.xlabel('1/Longueur d\'onde (nm-1)')
# plt.ylabel('Intensité')
# plt.legend()
# plt.show()
# 2. Conversion lambda → k = n(λ) / λ
k_vals = refractive_index / lambdas
f_interp = interp1d(k_vals, intensities, kind='linear', fill_value="extrapolate")
# 3. Axe k uniforme + interpolation
k_linspace = np.linspace(k_vals[0], k_vals[-1], 2 * num_half_space)
intensities_k = f_interp(k_linspace)
# 4. FFT
delta_k = (k_vals[-1] - k_vals[0]) / (2 * num_half_space)
fft_vals = fft(intensities_k)
freqs = fftfreq(2 * num_half_space, delta_k)
# 5. Pic FFT
freqs_pos = freqs[freqs > 0]
abs_fft_pos = np.abs(fft_vals[freqs > 0])
idx_max = np.argmax(abs_fft_pos)
F_max = freqs_pos[idx_max]
if plot:
plt.figure(figsize=(10, 6), dpi=150)
plt.plot(freqs_pos, abs_fft_pos, label='|FFT|')
plt.axvline(F_max, color='r', linestyle='--', label='Pic principal')
plt.xlabel('Distance optique [nm]')
plt.ylabel(r'FFT($I^*$)')
plt.xscale('log')
plt.yscale('log')
plt.legend()
plt.show()
# 6. Filtrage (garde hautes fréquences)
cutoff_HF = 2*F_max
mask_HF = np.abs(freqs) >= cutoff_HF
fft_filtered_HF = np.zeros_like(fft_vals, dtype=complex)
fft_filtered_HF[mask_HF] = fft_vals[mask_HF]
# 7. Filtrage (garde basses fréquences)
cutoff_BF = 10*F_max
mask_BF = np.abs(freqs) <= cutoff_BF
fft_filtered_BF = np.zeros_like(fft_vals, dtype=complex)
fft_filtered_BF[mask_BF] = fft_vals[mask_BF]
# 8. Reconstruction
signal_filtered_HF = np.real(ifft(fft_filtered_HF))
signal_filtered_BF = np.real(ifft(fft_filtered_BF))
lambda_reconstructed = np.interp(k_linspace, k_vals[::-1], lambdas[::-1])
# Masque dans la plage [550, 700] nm
mask_Cam_Sensitivity = (lambda_reconstructed >= 550) & (lambda_reconstructed <= 700)
# 9. Affichage reconstruction
if plot:
plt.figure(figsize=(10, 6), dpi=150)
plt.plot(lambda_reconstructed, intensities_k, '--', label='Original interpolé')
plt.plot(lambda_reconstructed, signal_filtered_HF,'--',color='gray')
plt.plot(lambda_reconstructed[mask_Cam_Sensitivity], signal_filtered_HF[mask_Cam_Sensitivity],color='orange', label='Spectre filtré HF')
plt.plot(lambda_reconstructed, signal_filtered_BF, label='Spectre filtré BF')
plt.xlabel('Longueur d\'onde (nm)')
plt.ylabel('Intensité')
plt.legend()
plt.show()
max_amplitude = np.max(np.abs(signal_filtered_HF[mask_Cam_Sensitivity]))
return max_amplitude,signal_filtered_BF,lambda_reconstructed

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<h1>Source code for optifik.fft</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">scipy.interpolate</span><span class="w"> </span><span class="kn">import</span> <span class="n">interp1d</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">scipy.fftpack</span><span class="w"> </span><span class="kn">import</span> <span class="n">fft</span><span class="p">,</span> <span class="n">ifft</span><span class="p">,</span> <span class="n">fftfreq</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">.utils</span><span class="w"> </span><span class="kn">import</span> <span class="n">OptimizeResult</span><span class="p">,</span> <span class="n">setup_matplotlib</span>
<div class="viewcode-block" id="thickness_from_fft">
<a class="viewcode-back" href="../../api_reference.html#optifik.fft.thickness_from_fft">[docs]</a>
<span class="k">def</span><span class="w"> </span><span class="nf">thickness_from_fft</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span> <span class="n">intensities</span><span class="p">,</span>
<span class="n">refractive_index</span><span class="p">,</span>
<span class="n">num_half_space</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">plot</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Determine the tickness by Fast Fourier Transform.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> wavelengths : array</span>
<span class="sd"> Wavelength values in nm.</span>
<span class="sd"> intensities : array</span>
<span class="sd"> Intensity values.</span>
<span class="sd"> refractive_index : scalar, optional</span>
<span class="sd"> Value of the refractive index of the medium.</span>
<span class="sd"> num_half_space : scalar, optional</span>
<span class="sd"> Number of points to compute FFT&#39;s half space.</span>
<span class="sd"> If `None`, default corresponds to `10*len(wavelengths)`.</span>
<span class="sd"> plot : boolean, optional</span>
<span class="sd"> Show plot of the transformed signal and the peak detection.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> results : Instance of `OptimizeResult` class.</span>
<span class="sd"> The attribute `thickness` gives the thickness value in nm.</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">setup_matplotlib</span><span class="p">()</span>
<span class="k">if</span> <span class="n">num_half_space</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">num_half_space</span> <span class="o">=</span> <span class="mi">10</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">)</span>
<span class="c1"># FFT requires evenly spaced data.</span>
<span class="c1"># So, we interpolate the signal.</span>
<span class="c1"># Interpolate to get a linear increase of 1 / wavelengths.</span>
<span class="n">inverse_wavelengths_times_n</span> <span class="o">=</span> <span class="n">refractive_index</span> <span class="o">/</span> <span class="n">wavelengths</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="n">inverse_wavelengths_times_n</span><span class="p">,</span> <span class="n">intensities</span><span class="p">)</span>
<span class="n">inverse_wavelengths_linspace</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">inverse_wavelengths_times_n</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
<span class="n">inverse_wavelengths_times_n</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span>
<span class="mi">2</span><span class="o">*</span><span class="n">num_half_space</span><span class="p">)</span>
<span class="n">intensities_linspace</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">inverse_wavelengths_linspace</span><span class="p">)</span>
<span class="c1"># Perform FFT</span>
<span class="n">density</span> <span class="o">=</span> <span class="p">(</span><span class="n">inverse_wavelengths_times_n</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">inverse_wavelengths_times_n</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">num_half_space</span><span class="p">)</span>
<span class="n">inverse_wavelengths_fft</span> <span class="o">=</span> <span class="n">fftfreq</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">num_half_space</span><span class="p">,</span> <span class="n">density</span><span class="p">)</span>
<span class="n">intensities_fft</span> <span class="o">=</span> <span class="n">fft</span><span class="p">(</span><span class="n">intensities_linspace</span><span class="p">)</span>
<span class="c1"># The FFT is symetrical over [0:N] and [N:2N].</span>
<span class="c1"># Keep over [N:2N], ie for positive freq.</span>
<span class="n">intensities_fft</span> <span class="o">=</span> <span class="n">intensities_fft</span><span class="p">[</span><span class="n">num_half_space</span><span class="p">:</span><span class="mi">2</span><span class="o">*</span><span class="n">num_half_space</span><span class="p">]</span>
<span class="n">inverse_wavelengths_fft</span> <span class="o">=</span> <span class="n">inverse_wavelengths_fft</span><span class="p">[</span><span class="n">num_half_space</span><span class="p">:</span><span class="mi">2</span><span class="o">*</span><span class="n">num_half_space</span><span class="p">]</span>
<span class="n">idx_max_fft</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">intensities_fft</span><span class="p">))</span>
<span class="n">freq_max</span> <span class="o">=</span> <span class="n">inverse_wavelengths_fft</span><span class="p">[</span><span class="n">idx_max_fft</span><span class="p">]</span>
<span class="n">thickness_fft</span> <span class="o">=</span> <span class="n">freq_max</span> <span class="o">/</span> <span class="mf">2.</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">loglog</span><span class="p">(</span><span class="n">inverse_wavelengths_fft</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">intensities_fft</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">loglog</span><span class="p">(</span><span class="n">freq_max</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">intensities_fft</span><span class="p">[</span><span class="n">idx_max_fft</span><span class="p">]),</span> <span class="s1">&#39;o&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Frequency&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;FFT($I^*$)&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Thickness=</span><span class="si">{</span><span class="n">thickness_fft</span><span class="si">:</span><span class="s1">.2f</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">OptimizeResult</span><span class="p">(</span><span class="n">thickness</span><span class="o">=</span><span class="n">thickness_fft</span><span class="p">,)</span></div>
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<h1>Source code for optifik.io</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<div class="viewcode-block" id="load_spectrum">
<a class="viewcode-back" href="../../api_reference.html#optifik.io.load_spectrum">[docs]</a>
<span class="k">def</span><span class="w"> </span><span class="nf">load_spectrum</span><span class="p">(</span><span class="n">spectrum_path</span><span class="p">,</span>
<span class="n">wavelength_min</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
<span class="n">wavelength_max</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">inf</span><span class="p">,</span>
<span class="n">delimiter</span><span class="o">=</span><span class="s1">&#39;,&#39;</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Load a spectrum file.</span>
<span class="sd"> TODO : describe expected format</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> spectrum_path : string</span>
<span class="sd"> File path.</span>
<span class="sd"> wavelength_min : scalar, optional</span>
<span class="sd"> Cut the data at this minimum wavelength (included).</span>
<span class="sd"> wavelength_max : scalar, optional</span>
<span class="sd"> Cut the data at this maximum wavelength (included).</span>
<span class="sd"> delimiter : string, optional</span>
<span class="sd"> Delimiter between columns in the datafile.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> values : arrays</span>
<span class="sd"> (lamdbas, intensities)</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">loadtxt</span><span class="p">(</span><span class="n">spectrum_path</span><span class="p">,</span> <span class="n">delimiter</span><span class="o">=</span><span class="n">delimiter</span><span class="p">)</span>
<span class="n">lambdas</span><span class="p">,</span> <span class="n">intensities</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">column_stack</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">mask</span> <span class="o">=</span> <span class="p">(</span><span class="n">lambdas</span> <span class="o">&gt;=</span> <span class="n">wavelength_min</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">(</span><span class="n">lambdas</span> <span class="o">&lt;=</span> <span class="n">wavelength_max</span><span class="p">)</span>
<span class="k">return</span> <span class="n">lambdas</span><span class="p">[</span><span class="n">mask</span><span class="p">],</span> <span class="n">intensities</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span></div>
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<h1>Source code for optifik.minmax</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">scipy</span><span class="w"> </span><span class="kn">import</span> <span class="n">stats</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">skimage.measure</span><span class="w"> </span><span class="kn">import</span> <span class="n">ransac</span><span class="p">,</span> <span class="n">LineModelND</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">scipy.signal</span><span class="w"> </span><span class="kn">import</span> <span class="n">find_peaks</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">.utils</span><span class="w"> </span><span class="kn">import</span> <span class="n">OptimizeResult</span><span class="p">,</span> <span class="n">setup_matplotlib</span>
<div class="viewcode-block" id="thickness_from_minmax">
<a class="viewcode-back" href="../../api_reference.html#optifik.minmax.thickness_from_minmax">[docs]</a>
<span class="k">def</span><span class="w"> </span><span class="nf">thickness_from_minmax</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span>
<span class="n">intensities</span><span class="p">,</span>
<span class="n">refractive_index</span><span class="p">,</span>
<span class="n">min_peak_prominence</span><span class="p">,</span>
<span class="n">min_peak_distance</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
<span class="n">method</span><span class="o">=</span><span class="s1">&#39;linreg&#39;</span><span class="p">,</span>
<span class="n">plot</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Return the thickness from a min-max detection.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> wavelengths : array</span>
<span class="sd"> Wavelength values in nm.</span>
<span class="sd"> intensities : array</span>
<span class="sd"> Intensity values.</span>
<span class="sd"> refractive_index : scalar, optional</span>
<span class="sd"> Value of the refractive index of the medium.</span>
<span class="sd"> min_peak_prominence : scalar, optional</span>
<span class="sd"> Required prominence of peaks.</span>
<span class="sd"> min_peak_distance : scalar, optional</span>
<span class="sd"> Minimum distance between peaks.</span>
<span class="sd"> method : string, optional</span>
<span class="sd"> Either &#39;linreg&#39; for linear regression or &#39;ransac&#39;</span>
<span class="sd"> for Randon Sampling Consensus.</span>
<span class="sd"> plot : boolean, optional</span>
<span class="sd"> Show plots of peak detection and lin regression.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> results : Instance of `OptimizeResult` class.</span>
<span class="sd"> The attribute `thickness` gives the thickness value in nm.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> For more details about `min_peak_prominence` and `min_peak_distance`,</span>
<span class="sd"> see the documentation of `scipy.signal.find_peaks`. This function</span>
<span class="sd"> is used to find extrema.</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">setup_matplotlib</span><span class="p">()</span>
<span class="n">peaks_max</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">find_peaks</span><span class="p">(</span><span class="n">intensities</span><span class="p">,</span> <span class="n">prominence</span><span class="o">=</span><span class="n">min_peak_prominence</span><span class="p">,</span> <span class="n">distance</span><span class="o">=</span><span class="n">min_peak_distance</span><span class="p">)</span>
<span class="n">peaks_min</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">find_peaks</span><span class="p">(</span><span class="o">-</span><span class="n">intensities</span><span class="p">,</span> <span class="n">prominence</span><span class="o">=</span><span class="n">min_peak_prominence</span><span class="p">,</span> <span class="n">distance</span><span class="o">=</span><span class="n">min_peak_distance</span><span class="p">)</span>
<span class="n">peaks</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">peaks_min</span><span class="p">,</span> <span class="n">peaks_max</span><span class="p">))</span>
<span class="n">peaks</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>
<span class="n">k_values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">peaks</span><span class="p">))</span>
<span class="k">if</span> <span class="n">k_values</span><span class="o">.</span><span class="n">size</span> <span class="o">&lt;</span> <span class="mi">2</span><span class="p">:</span>
<span class="c1"># Can&#39;t fit if less than two points.</span>
<span class="k">return</span> <span class="n">OptimizeResult</span><span class="p">(</span><span class="n">thickness</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">refractive_index</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
<span class="c1">#refractive_index = refractive_index[peaks][::-1]</span>
<span class="n">n_over_lambda</span> <span class="o">=</span> <span class="n">refractive_index</span><span class="p">[</span><span class="n">peaks</span><span class="p">][::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">peaks</span><span class="p">][::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">n_over_lambda</span> <span class="o">=</span> <span class="n">refractive_index</span> <span class="o">/</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">peaks</span><span class="p">][::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="k">if</span> <span class="n">method</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="o">==</span> <span class="s1">&#39;ransac&#39;</span><span class="p">:</span>
<span class="n">residual_threshold</span> <span class="o">=</span> <span class="mf">4e-5</span>
<span class="n">min_samples</span> <span class="o">=</span> <span class="mi">2</span>
<span class="c1"># Scikit-image</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">column_stack</span><span class="p">([</span><span class="n">k_values</span><span class="p">,</span> <span class="n">n_over_lambda</span><span class="p">])</span>
<span class="n">model_robust</span><span class="p">,</span> <span class="n">inliers</span> <span class="o">=</span> <span class="n">ransac</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">LineModelND</span><span class="p">,</span>
<span class="n">min_samples</span><span class="o">=</span><span class="n">min_samples</span><span class="p">,</span>
<span class="n">residual_threshold</span><span class="o">=</span><span class="n">residual_threshold</span><span class="p">,</span>
<span class="n">max_trials</span><span class="o">=</span><span class="mi">100</span><span class="p">)</span>
<span class="n">slope</span> <span class="o">=</span> <span class="n">model_robust</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
<span class="n">thickness_minmax</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">slope</span> <span class="o">/</span> <span class="mi">4</span>
<span class="c1"># Scikit-learn</span>
<span class="c1">#X, y = k_values.reshape(-1, 1), 1/wavelengths[peaks][::-1]</span>
<span class="c1">## Fit line using all data</span>
<span class="c1">#lr = linear_model.LinearRegression()</span>
<span class="c1">#lr.fit(X, y)</span>
<span class="c1">#slransac = linear_model.RANSACRegressor(min_samples=min_samples,</span>
<span class="c1"># residual_threshold=residual_threshold)</span>
<span class="c1">#slransac.fit(X, y)</span>
<span class="c1">#inlier_mask = slransac.inlier_mask_</span>
<span class="c1">#outlier_mask = np.logical_not(inlier_mask)</span>
<span class="c1">## Predict data of estimated models</span>
<span class="c1">#line_X = np.arange(X.min(), X.max())[:, np.newaxis]</span>
<span class="c1">#line_y = lr.predict(line_X)</span>
<span class="c1">#line_y_ransac = slransac.predict(line_X)</span>
<span class="c1">#slope = slransac.estimator_.coef_[0]</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;extremum n°&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">&#39;$n$($\lambda$) / $\lambda$&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">inliers</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">data</span><span class="p">[</span><span class="n">inliers</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;xb&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Inliers&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="o">~</span><span class="n">inliers</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">data</span><span class="p">[</span><span class="o">~</span><span class="n">inliers</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;+r&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Outliers&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">k_values</span><span class="p">,</span> <span class="n">model_robust</span><span class="o">.</span><span class="n">predict_y</span><span class="p">(</span><span class="n">k_values</span><span class="p">),</span> <span class="s1">&#39;-g&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Fit&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Thickness = </span><span class="si">{</span><span class="n">thickness_minmax</span><span class="si">:</span><span class="s1">.2f</span><span class="si">}</span><span class="s1"> nm&#39;</span><span class="p">)</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">inspect</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">currentframe</span><span class="p">()</span><span class="o">.</span><span class="n">f_code</span><span class="o">.</span><span class="n">co_name</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="k">return</span> <span class="n">OptimizeResult</span><span class="p">(</span><span class="n">thickness</span><span class="o">=</span><span class="n">thickness_minmax</span><span class="p">,</span>
<span class="n">num_inliers</span><span class="o">=</span><span class="n">inliers</span><span class="o">.</span><span class="n">sum</span><span class="p">(),</span>
<span class="n">num_outliers</span><span class="o">=</span><span class="p">(</span><span class="o">~</span><span class="n">inliers</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(),</span>
<span class="n">peaks_max</span><span class="o">=</span><span class="n">peaks_max</span><span class="p">,</span>
<span class="n">peaks_min</span><span class="o">=</span><span class="n">peaks_min</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">method</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="o">==</span> <span class="s1">&#39;linreg&#39;</span><span class="p">:</span>
<span class="n">slope</span><span class="p">,</span> <span class="n">intercept</span><span class="p">,</span> <span class="n">r_value</span><span class="p">,</span> <span class="n">p_value</span><span class="p">,</span> <span class="n">std_err</span> <span class="o">=</span> <span class="n">stats</span><span class="o">.</span><span class="n">linregress</span><span class="p">(</span><span class="n">k_values</span><span class="p">,</span> <span class="n">n_over_lambda</span><span class="p">)</span>
<span class="c1">#mean_n = np.mean(refractive_index)</span>
<span class="n">thickness_minmax</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">slope</span> <span class="o">/</span> <span class="mi">4</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;extremum n°&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">&#39;$n$($\lambda$) / $\lambda$&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">k_values</span><span class="p">,</span> <span class="n">n_over_lambda</span><span class="p">,</span> <span class="s1">&#39;s&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Extrema&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">k_values</span><span class="p">,</span> <span class="n">intercept</span> <span class="o">+</span> <span class="n">k_values</span> <span class="o">*</span> <span class="n">slope</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Fit&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Thickness = </span><span class="si">{</span><span class="n">thickness_minmax</span><span class="si">:</span><span class="s1">.2f</span><span class="si">}</span><span class="s1"> nm&#39;</span><span class="p">)</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">inspect</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">currentframe</span><span class="p">()</span><span class="o">.</span><span class="n">f_code</span><span class="o">.</span><span class="n">co_name</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="k">return</span> <span class="n">OptimizeResult</span><span class="p">(</span><span class="n">thickness</span><span class="o">=</span><span class="n">thickness_minmax</span><span class="p">,</span>
<span class="n">peaks_max</span><span class="o">=</span><span class="n">peaks_max</span><span class="p">,</span>
<span class="n">peaks_min</span><span class="o">=</span><span class="n">peaks_min</span><span class="p">,</span>
<span class="n">stderr</span><span class="o">=</span><span class="n">std_err</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;Wrong method&#39;</span><span class="p">)</span></div>
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<h1>Source code for optifik.scheludko</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">scipy.optimize</span><span class="w"> </span><span class="kn">import</span> <span class="n">curve_fit</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">.io</span><span class="w"> </span><span class="kn">import</span> <span class="n">load_spectrum</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">.utils</span><span class="w"> </span><span class="kn">import</span> <span class="n">OptimizeResult</span><span class="p">,</span> <span class="n">setup_matplotlib</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">.analysis</span><span class="w"> </span><span class="kn">import</span> <span class="n">finds_peak</span>
<span class="k">def</span><span class="w"> </span><span class="nf">_thicknesses_scheludko_at_order</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span>
<span class="n">intensities</span><span class="p">,</span>
<span class="n">interference_order</span><span class="p">,</span>
<span class="n">refractive_index</span><span class="p">,</span>
<span class="n">intensities_void</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Compute thicknesses vs wavelength for a given interference order.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> wavelengths : array</span>
<span class="sd"> Wavelength values in nm.</span>
<span class="sd"> intensities : array</span>
<span class="sd"> Intensity values.</span>
<span class="sd"> interference_order : int</span>
<span class="sd"> Interference order.</span>
<span class="sd"> refractive_index : array_like (or float)</span>
<span class="sd"> Refractive index.</span>
<span class="sd"> intensities_void : array, optional</span>
<span class="sd"> Intensities of void.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> thicknesses : array</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">intensities_void</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">Imin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">Imin</span> <span class="o">=</span> <span class="n">intensities_void</span>
<span class="n">n</span> <span class="o">=</span> <span class="n">refractive_index</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">interference_order</span>
<span class="n">I_norm</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">intensities</span><span class="p">)</span> <span class="o">-</span> <span class="n">Imin</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">intensities</span><span class="p">)</span> <span class="o">-</span> <span class="n">Imin</span><span class="p">)</span>
<span class="n">prefactor</span> <span class="o">=</span> <span class="n">wavelengths</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">n</span><span class="p">)</span>
<span class="n">argument</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">I_norm</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">I_norm</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">n</span><span class="o">**</span><span class="mi">2</span><span class="p">)))</span>
<span class="k">if</span> <span class="n">m</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">term1</span> <span class="o">=</span> <span class="p">(</span><span class="n">m</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">term1</span> <span class="o">=</span> <span class="p">((</span><span class="n">m</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
<span class="n">term2</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="n">m</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">arcsin</span><span class="p">(</span><span class="n">argument</span><span class="p">)</span>
<span class="k">return</span> <span class="n">prefactor</span> <span class="o">*</span> <span class="p">(</span><span class="n">term1</span> <span class="o">+</span> <span class="n">term2</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">_Delta</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span> <span class="n">thickness</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">,</span> <span class="n">refractive_index</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Compute the Delta values.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> wavelengths : array</span>
<span class="sd"> Wavelength values in nm.</span>
<span class="sd"> thickness : array_like (or float)</span>
<span class="sd"> Film thickness.</span>
<span class="sd"> interference_order : int</span>
<span class="sd"> Interference order.</span>
<span class="sd"> refractive_index : array_like (or float)</span>
<span class="sd"> Refractive index.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> ndarray</span>
<span class="sd"> Delta values.</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="c1"># ensure that the entries are numpy arrays</span>
<span class="n">wavelengths</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">)</span>
<span class="n">h</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">thickness</span><span class="p">)</span>
<span class="n">n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">refractive_index</span><span class="p">)</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">interference_order</span>
<span class="c1"># Calculation of p as a function of the parity of m</span>
<span class="k">if</span> <span class="n">m</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">m</span> <span class="o">/</span> <span class="mi">2</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">p</span> <span class="o">=</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
<span class="c1"># Calculation of alpha</span>
<span class="n">alpha</span> <span class="o">=</span> <span class="p">((</span><span class="n">n</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">n</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
<span class="c1"># Argument of sinus</span>
<span class="n">angle</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="n">h</span> <span class="o">/</span> <span class="n">wavelengths</span><span class="p">)</span> <span class="o">-</span> <span class="n">p</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
<span class="c1"># A = sin²(argument)</span>
<span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
<span class="c1"># Final calcuation of Delta</span>
<span class="k">return</span> <span class="p">(</span><span class="n">A</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">alpha</span><span class="p">))</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">A</span> <span class="o">*</span> <span class="n">alpha</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">_Delta_fit</span><span class="p">(</span><span class="n">xdata</span><span class="p">,</span> <span class="n">thickness</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Wrapper on Delta() for curve_fit.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> xdata : tuple</span>
<span class="sd"> (wavelengths, refractive_index)</span>
<span class="sd"> thickness : array_like (or float)</span>
<span class="sd"> Film thickness.</span>
<span class="sd"> interference_order : int</span>
<span class="sd"> Interference order.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> ndarray</span>
<span class="sd"> Delta values.</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">lambdas</span><span class="p">,</span> <span class="n">r_index</span> <span class="o">=</span> <span class="n">xdata</span>
<span class="k">return</span> <span class="n">_Delta</span><span class="p">(</span><span class="n">lambdas</span><span class="p">,</span> <span class="n">thickness</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">,</span> <span class="n">r_index</span><span class="p">)</span>
<div class="viewcode-block" id="get_default_start_stop_wavelengths">
<a class="viewcode-back" href="../../api_reference.html#optifik.scheludko.get_default_start_stop_wavelengths">[docs]</a>
<span class="k">def</span><span class="w"> </span><span class="nf">get_default_start_stop_wavelengths</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span>
<span class="n">intensities</span><span class="p">,</span>
<span class="n">refractive_index</span><span class="p">,</span>
<span class="n">min_peak_prominence</span><span class="p">,</span>
<span class="n">plot</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Returns the start and stop wavelength values of the last monotonic branch.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> wavelengths : array</span>
<span class="sd"> Wavelength values in nm.</span>
<span class="sd"> intensities : array</span>
<span class="sd"> Intensity values.</span>
<span class="sd"> refractive_index : scalar, optional</span>
<span class="sd"> Value of the refractive index of the medium.</span>
<span class="sd"> min_peak_prominence : scalar</span>
<span class="sd"> Required prominence of peaks.</span>
<span class="sd"> plot : bool, optional</span>
<span class="sd"> Display a curve, useful for checking or debuging. The default is None.</span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> RuntimeError</span>
<span class="sd"> if at least one maximum and one minimum are not detected.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> wavelength_start : scalar</span>
<span class="sd"> wavelength_stop : scalar</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="c1"># idx_min idx max</span>
<span class="n">idx_peaks_min</span><span class="p">,</span> <span class="n">idx_peaks_max</span> <span class="o">=</span> <span class="n">finds_peak</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span> <span class="n">intensities</span><span class="p">,</span>
<span class="n">min_peak_prominence</span><span class="o">=</span><span class="n">min_peak_prominence</span><span class="p">,</span>
<span class="n">plot</span><span class="o">=</span><span class="n">plot</span><span class="p">)</span>
<span class="n">failure</span><span class="p">,</span> <span class="n">message</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span> <span class="s1">&#39;&#39;</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">idx_peaks_min</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">message</span> <span class="o">+=</span> <span class="s1">&#39;Failed to detect at least one minimum. &#39;</span>
<span class="n">failure</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">idx_peaks_max</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">message</span> <span class="o">+=</span> <span class="s1">&#39;Failed to detect at least one maximum. &#39;</span>
<span class="n">failure</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">if</span> <span class="n">failure</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="n">message</span><span class="p">)</span>
<span class="c1"># Get the last oscillation peaks</span>
<span class="n">lambda_min</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">idx_peaks_min</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span>
<span class="n">lambda_max</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">idx_peaks_max</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span>
<span class="c1"># Order them</span>
<span class="n">wavelength_start</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">lambda_min</span><span class="p">,</span> <span class="n">lambda_max</span><span class="p">)</span>
<span class="n">wavelength_stop</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">lambda_min</span><span class="p">,</span> <span class="n">lambda_max</span><span class="p">)</span>
<span class="k">return</span> <span class="n">wavelength_start</span><span class="p">,</span> <span class="n">wavelength_stop</span></div>
<div class="viewcode-block" id="thickness_from_scheludko">
<a class="viewcode-back" href="../../api_reference.html#optifik.scheludko.thickness_from_scheludko">[docs]</a>
<span class="k">def</span><span class="w"> </span><span class="nf">thickness_from_scheludko</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span>
<span class="n">intensities</span><span class="p">,</span>
<span class="n">refractive_index</span><span class="p">,</span>
<span class="n">wavelength_start</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">wavelength_stop</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">interference_order</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">intensities_void</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">plot</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Compute the film thickness based on Scheludko method.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> wavelengths : array</span>
<span class="sd"> Wavelength values in nm.</span>
<span class="sd"> intensities : array</span>
<span class="sd"> Intensity values.</span>
<span class="sd"> refractive_index : scalar, optional</span>
<span class="sd"> Value of the refractive index of the medium.</span>
<span class="sd"> wavelength_start : scalar, optional</span>
<span class="sd"> Starting value of a monotonic branch.</span>
<span class="sd"> Mandatory if interference_order != 0.</span>
<span class="sd"> wavelength_stop : scalar, optional</span>
<span class="sd"> Stoping value of a monotonic branch.</span>
<span class="sd"> Mandatory if interference_order != 0.</span>
<span class="sd"> interference_order : scalar, optional</span>
<span class="sd"> Interference order, zero or positive integer.</span>
<span class="sd"> If set to None, the value is guessed.</span>
<span class="sd"> intensities_void : array, optional</span>
<span class="sd"> Intensity in absence of a film.</span>
<span class="sd"> Mandatory if interference_order == 0.</span>
<span class="sd"> plot : bool, optional</span>
<span class="sd"> Display a curve, useful for checking or debuging. The default is None.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> results : Instance of `OptimizeResult` class.</span>
<span class="sd"> The attribute `thickness` gives the thickness value in nm.</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">setup_matplotlib</span><span class="p">()</span>
<span class="k">if</span> <span class="n">interference_order</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">interference_order</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">if</span> <span class="n">wavelength_stop</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">wavelength_start</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;wavelength_start and wavelength_stop must be passed for interference_order != 0.&#39;</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="n">wavelength_start</span> <span class="o">&gt;</span> <span class="n">wavelength_stop</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;wavelength_start and wavelength_stop are swapped.&#39;</span><span class="p">)</span>
<span class="n">r_index</span> <span class="o">=</span> <span class="n">refractive_index</span>
<span class="c1"># Handle the interference order</span>
<span class="k">if</span> <span class="n">interference_order</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="c1"># A bit extreme...</span>
<span class="n">max_tested_order</span> <span class="o">=</span> <span class="mi">12</span>
<span class="c1"># mask input data</span>
<span class="n">mask</span> <span class="o">=</span> <span class="p">(</span><span class="n">wavelengths</span> <span class="o">&gt;=</span> <span class="n">wavelength_start</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">(</span><span class="n">wavelengths</span> <span class="o">&lt;=</span> <span class="n">wavelength_stop</span><span class="p">)</span>
<span class="n">wavelengths_masked</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">r_index_masked</span> <span class="o">=</span> <span class="n">r_index</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">intensities_masked</span> <span class="o">=</span> <span class="n">intensities</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">min_difference</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span>
<span class="n">thickness_values</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$h$ ($\mathrm{{nm}}$)&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$\lambda$ ($ \mathrm</span><span class="si">{nm}</span><span class="s1"> $)&#39;</span><span class="p">)</span>
<span class="k">for</span> <span class="n">_order</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_tested_order</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
<span class="n">h_values</span> <span class="o">=</span> <span class="n">_thicknesses_scheludko_at_order</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span>
<span class="n">intensities_masked</span><span class="p">,</span>
<span class="n">_order</span><span class="p">,</span>
<span class="n">r_index_masked</span><span class="p">)</span>
<span class="n">difference</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">h_values</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">h_values</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;h-difference for m=</span><span class="si">{</span><span class="n">_order</span><span class="si">}</span><span class="s2">: </span><span class="si">{</span><span class="n">difference</span><span class="si">:</span><span class="s2">.1f</span><span class="si">}</span><span class="s2"> nm&quot;</span><span class="p">)</span>
<span class="k">if</span> <span class="n">difference</span> <span class="o">&lt;</span> <span class="n">min_difference</span><span class="p">:</span>
<span class="n">min_difference</span> <span class="o">=</span> <span class="n">difference</span>
<span class="n">interference_order</span> <span class="o">=</span> <span class="n">_order</span>
<span class="n">thickness_values</span> <span class="o">=</span> <span class="n">h_values</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">h_values</span><span class="p">,</span> <span class="s1">&#39;.&#39;</span><span class="p">,</span>
<span class="n">markersize</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">f</span><span class="s2">&quot;Order=</span><span class="si">{</span><span class="n">_order</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">interference_order</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">min_peak_prominence</span> <span class="o">=</span> <span class="mf">0.02</span>
<span class="n">peaks_min</span><span class="p">,</span> <span class="n">peaks_max</span> <span class="o">=</span> <span class="n">finds_peak</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span> <span class="n">intensities</span><span class="p">,</span>
<span class="n">min_peak_prominence</span><span class="o">=</span><span class="n">min_peak_prominence</span><span class="p">,</span>
<span class="n">plot</span><span class="o">=</span><span class="n">plot</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">peaks_max</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s1">&#39;Failed to detect a single maximum peak.&#39;</span><span class="p">)</span>
<span class="n">lambda_unique</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">peaks_max</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span>
<span class="c1"># keep rhs from the maximum</span>
<span class="n">mask</span> <span class="o">=</span> <span class="n">wavelengths</span> <span class="o">&gt;=</span> <span class="n">lambda_unique</span>
<span class="n">wavelengths_masked</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">r_index_masked</span> <span class="o">=</span> <span class="n">r_index</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">intensities_masked</span> <span class="o">=</span> <span class="n">intensities</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">intensities_void_masked</span> <span class="o">=</span> <span class="n">intensities_void</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">interference_order</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">thickness_values</span> <span class="o">=</span> <span class="n">_thicknesses_scheludko_at_order</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span>
<span class="n">intensities_masked</span><span class="p">,</span>
<span class="n">interference_order</span><span class="p">,</span>
<span class="n">r_index_masked</span><span class="p">,</span>
<span class="n">intensities_void</span><span class="o">=</span><span class="n">intensities_void_masked</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">interference_order</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">h_values</span> <span class="o">=</span> <span class="n">_thicknesses_scheludko_at_order</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span>
<span class="n">intensities_masked</span><span class="p">,</span>
<span class="n">interference_order</span><span class="p">,</span>
<span class="n">r_index_masked</span><span class="p">)</span>
<span class="n">thickness_values</span> <span class="o">=</span> <span class="n">h_values</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;interference_order must be &gt;= 0.&#39;</span><span class="p">)</span>
<span class="c1"># Compute the thickness for the selected order</span>
<span class="c1"># Delta</span>
<span class="k">if</span> <span class="n">interference_order</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">num</span> <span class="o">=</span> <span class="n">intensities_masked</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities_void_masked</span><span class="p">)</span>
<span class="n">denom</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">intensities_masked</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities_void_masked</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">num</span> <span class="o">=</span> <span class="n">intensities_masked</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities_masked</span><span class="p">)</span>
<span class="n">denom</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">intensities_masked</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities_masked</span><span class="p">)</span>
<span class="n">Delta_from_data</span> <span class="o">=</span> <span class="n">num</span> <span class="o">/</span> <span class="n">denom</span>
<span class="c1"># Delta_from_data = (intensities_masked -np.min(intensities_masked))/(np.max(intensities_masked) -np.min(intensities_masked))</span>
<span class="c1"># Delta_from_data = (intensities_raw_masked -np.min(intensities_raw_masked))/(np.max(intensities_raw_masked) -np.min(intensities_raw_masked))</span>
<span class="n">DeltaScheludko</span> <span class="o">=</span> <span class="n">_Delta</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span>
<span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">thickness_values</span><span class="p">),</span>
<span class="n">interference_order</span><span class="p">,</span>
<span class="n">r_index_masked</span><span class="p">)</span>
<span class="n">xdata</span> <span class="o">=</span> <span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">r_index_masked</span><span class="p">)</span>
<span class="n">popt</span><span class="p">,</span> <span class="n">pcov</span> <span class="o">=</span> <span class="n">curve_fit</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">h</span><span class="p">:</span> <span class="n">_Delta_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">),</span> <span class="n">xdata</span><span class="p">,</span> <span class="n">Delta_from_data</span><span class="p">,</span> <span class="n">p0</span><span class="o">=</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">thickness_values</span><span class="p">)])</span>
<span class="n">fitted_h</span> <span class="o">=</span> <span class="n">popt</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">std_err</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">pcov</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">])</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">Delta_values</span> <span class="o">=</span> <span class="n">_Delta</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">fitted_h</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">,</span> <span class="n">r_index_masked</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">Delta_from_data</span><span class="p">,</span>
<span class="s1">&#39;bo-&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s1">&#39;$\mathrm{{Smoothed}}\ \mathrm{{Data}}$&#39;</span><span class="p">)</span>
<span class="c1"># Scheludko</span>
<span class="n">label</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;$\mathrm</span><span class="se">{{</span><span class="s1">Scheludko</span><span class="se">}}</span><span class="s1">\ (h = </span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">thickness_values</span><span class="p">)</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1"> \pm </span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">thickness_values</span><span class="p">)</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1">\ \mathrm</span><span class="se">{{</span><span class="s1">nm</span><span class="se">}}</span><span class="s1">)$&#39;</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">DeltaScheludko</span><span class="p">,</span>
<span class="s1">&#39;go-&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">label</span><span class="p">)</span>
<span class="c1"># Fit</span>
<span class="n">label</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;$\mathrm</span><span class="se">{{</span><span class="s1">Fit</span><span class="se">}}</span><span class="s1">\ (h = </span><span class="si">{</span><span class="n">fitted_h</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1">\pm </span><span class="si">{</span><span class="n">std_err</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1"> \ \mathrm</span><span class="se">{{</span><span class="s1">nm</span><span class="se">}}</span><span class="s1">)$&#39;</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">Delta_values</span><span class="p">,</span>
<span class="s1">&#39;ro-&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="n">label</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$\Delta$&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$\lambda$ ($ \mathrm</span><span class="si">{nm}</span><span class="s1"> $)&#39;</span><span class="p">)</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">inspect</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">currentframe</span><span class="p">()</span><span class="o">.</span><span class="n">f_code</span><span class="o">.</span><span class="n">co_name</span><span class="p">)</span>
<span class="k">return</span> <span class="n">OptimizeResult</span><span class="p">(</span><span class="n">thickness</span><span class="o">=</span><span class="n">fitted_h</span><span class="p">,</span> <span class="n">stderr</span><span class="o">=</span><span class="n">std_err</span><span class="p">)</span></div>
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&#169;2025, F. Boulogne et al..
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API Reference
=============
Below is the complete reference for Optifik's public API.
io
--
.. automodule:: optifik.io
:members:
:undoc-members:
:show-inheritance:
fft
---
.. automodule:: optifik.fft
:members:
:undoc-members:
:show-inheritance:
minmax
------
.. automodule:: optifik.minmax
:members:
:undoc-members:
:show-inheritance:
scheludko
---------
.. automodule:: optifik.scheludko
:members:
:undoc-members:
:show-inheritance:

34
_sources/examples.rst.txt Normal file
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Examples
========
Basic Optimization
------------------
Here's a simple example using Optifik to solve a quadratic function.
.. code-block:: python
from optifik import minimize
def quadratic(x):
return (x - 3) ** 2
result = minimize(quadratic, x0=0)
print(result)
Constrained Optimization
------------------------
.. code-block:: python
from optifik import minimize
def objective(x):
return x[0] ** 2 + x[1] ** 2
def constraint(x):
return x[0] + x[1] - 1
result = minimize(objective, x0=[0, 0], constraints=[constraint])
print(result)

24
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Optifik Documentation
=====================
Welcome to the documentation for **Optifik**, a Python library for
Contents
--------
.. toctree::
:maxdepth: 2
:caption: Documentation
installation
api_reference
examples
Indices and tables
------------------
* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`

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Installation
============
You can install Optifik using `pip`:
.. code-block:: bash
pip install optifik
Alternatively, you can install it from source:
.. code-block:: bash
git clone https://github.com/yourusername/optifik.git
cd optifik
pip install -e .
Requirements
------------
- Python >= 3.8
- NumPy >= 1.21
Optional for extended functionality:
- SciPy
- Matplotlib

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margin-bottom: 0px;
}
ol.simple ol p,
ol.simple ul p,
ul.simple ol p,
ul.simple ul p {
margin-top: 0;
}
ol.simple > li:not(:first-child) > p,
ul.simple > li:not(:first-child) > p {
margin-top: 0;
}
ol.simple p,
ul.simple p {
margin-bottom: 0;
}
aside.footnote > span,
div.citation > span {
float: left;
}
aside.footnote > span:last-of-type,
div.citation > span:last-of-type {
padding-right: 0.5em;
}
aside.footnote > p {
margin-left: 2em;
}
div.citation > p {
margin-left: 4em;
}
aside.footnote > p:last-of-type,
div.citation > p:last-of-type {
margin-bottom: 0em;
}
aside.footnote > p:last-of-type:after,
div.citation > p:last-of-type:after {
content: "";
clear: both;
}
dl.field-list {
display: grid;
grid-template-columns: fit-content(30%) auto;
}
dl.field-list > dt {
font-weight: bold;
word-break: break-word;
padding-left: 0.5em;
padding-right: 5px;
}
dl.field-list > dd {
padding-left: 0.5em;
margin-top: 0em;
margin-left: 0em;
margin-bottom: 0em;
}
dl {
margin-bottom: 15px;
}
dd > :first-child {
margin-top: 0px;
}
dd ul, dd table {
margin-bottom: 10px;
}
dd {
margin-top: 3px;
margin-bottom: 10px;
margin-left: 30px;
}
.sig dd {
margin-top: 0px;
margin-bottom: 0px;
}
.sig dl {
margin-top: 0px;
margin-bottom: 0px;
}
dl > dd:last-child,
dl > dd:last-child > :last-child {
margin-bottom: 0;
}
dt:target, span.highlighted {
background-color: #fbe54e;
}
rect.highlighted {
fill: #fbe54e;
}
dl.glossary dt {
font-weight: bold;
font-size: 1.1em;
}
.versionmodified {
font-style: italic;
}
.system-message {
background-color: #fda;
padding: 5px;
border: 3px solid red;
}
.footnote:target {
background-color: #ffa;
}
.line-block {
display: block;
margin-top: 1em;
margin-bottom: 1em;
}
.line-block .line-block {
margin-top: 0;
margin-bottom: 0;
margin-left: 1.5em;
}
.guilabel, .menuselection {
font-family: sans-serif;
}
.accelerator {
text-decoration: underline;
}
.classifier {
font-style: oblique;
}
.classifier:before {
font-style: normal;
margin: 0 0.5em;
content: ":";
display: inline-block;
}
abbr, acronym {
border-bottom: dotted 1px;
cursor: help;
}
/* -- code displays --------------------------------------------------------- */
pre {
overflow: auto;
overflow-y: hidden; /* fixes display issues on Chrome browsers */
}
pre, div[class*="highlight-"] {
clear: both;
}
span.pre {
-moz-hyphens: none;
-ms-hyphens: none;
-webkit-hyphens: none;
hyphens: none;
white-space: nowrap;
}
div[class*="highlight-"] {
margin: 1em 0;
}
td.linenos pre {
border: 0;
background-color: transparent;
color: #aaa;
}
table.highlighttable {
display: block;
}
table.highlighttable tbody {
display: block;
}
table.highlighttable tr {
display: flex;
}
table.highlighttable td {
margin: 0;
padding: 0;
}
table.highlighttable td.linenos {
padding-right: 0.5em;
}
table.highlighttable td.code {
flex: 1;
overflow: hidden;
}
.highlight .hll {
display: block;
}
div.highlight pre,
table.highlighttable pre {
margin: 0;
}
div.code-block-caption + div {
margin-top: 0;
}
div.code-block-caption {
margin-top: 1em;
padding: 2px 5px;
font-size: small;
}
div.code-block-caption code {
background-color: transparent;
}
table.highlighttable td.linenos,
span.linenos,
div.highlight span.gp { /* gp: Generic.Prompt */
user-select: none;
-webkit-user-select: text; /* Safari fallback only */
-webkit-user-select: none; /* Chrome/Safari */
-moz-user-select: none; /* Firefox */
-ms-user-select: none; /* IE10+ */
}
div.code-block-caption span.caption-number {
padding: 0.1em 0.3em;
font-style: italic;
}
div.code-block-caption span.caption-text {
}
div.literal-block-wrapper {
margin: 1em 0;
}
code.xref, a code {
background-color: transparent;
font-weight: bold;
}
h1 code, h2 code, h3 code, h4 code, h5 code, h6 code {
background-color: transparent;
}
.viewcode-link {
float: right;
}
.viewcode-back {
float: right;
font-family: sans-serif;
}
div.viewcode-block:target {
margin: -1px -10px;
padding: 0 10px;
}
/* -- math display ---------------------------------------------------------- */
img.math {
vertical-align: middle;
}
div.body div.math p {
text-align: center;
}
span.eqno {
float: right;
}
span.eqno a.headerlink {
position: absolute;
z-index: 1;
}
div.math:hover a.headerlink {
visibility: visible;
}
/* -- printout stylesheet --------------------------------------------------- */
@media print {
div.document,
div.documentwrapper,
div.bodywrapper {
margin: 0 !important;
width: 100%;
}
div.sphinxsidebar,
div.related,
div.footer,
#top-link {
display: none;
}
}

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/*
* Base JavaScript utilities for all Sphinx HTML documentation.
*/
"use strict";
const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([
"TEXTAREA",
"INPUT",
"SELECT",
"BUTTON",
]);
const _ready = (callback) => {
if (document.readyState !== "loading") {
callback();
} else {
document.addEventListener("DOMContentLoaded", callback);
}
};
/**
* Small JavaScript module for the documentation.
*/
const Documentation = {
init: () => {
Documentation.initDomainIndexTable();
Documentation.initOnKeyListeners();
},
/**
* i18n support
*/
TRANSLATIONS: {},
PLURAL_EXPR: (n) => (n === 1 ? 0 : 1),
LOCALE: "unknown",
// gettext and ngettext don't access this so that the functions
// can safely bound to a different name (_ = Documentation.gettext)
gettext: (string) => {
const translated = Documentation.TRANSLATIONS[string];
switch (typeof translated) {
case "undefined":
return string; // no translation
case "string":
return translated; // translation exists
default:
return translated[0]; // (singular, plural) translation tuple exists
}
},
ngettext: (singular, plural, n) => {
const translated = Documentation.TRANSLATIONS[singular];
if (typeof translated !== "undefined")
return translated[Documentation.PLURAL_EXPR(n)];
return n === 1 ? singular : plural;
},
addTranslations: (catalog) => {
Object.assign(Documentation.TRANSLATIONS, catalog.messages);
Documentation.PLURAL_EXPR = new Function(
"n",
`return (${catalog.plural_expr})`
);
Documentation.LOCALE = catalog.locale;
},
/**
* helper function to focus on search bar
*/
focusSearchBar: () => {
document.querySelectorAll("input[name=q]")[0]?.focus();
},
/**
* Initialise the domain index toggle buttons
*/
initDomainIndexTable: () => {
const toggler = (el) => {
const idNumber = el.id.substr(7);
const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`);
if (el.src.substr(-9) === "minus.png") {
el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`;
toggledRows.forEach((el) => (el.style.display = "none"));
} else {
el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`;
toggledRows.forEach((el) => (el.style.display = ""));
}
};
const togglerElements = document.querySelectorAll("img.toggler");
togglerElements.forEach((el) =>
el.addEventListener("click", (event) => toggler(event.currentTarget))
);
togglerElements.forEach((el) => (el.style.display = ""));
if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler);
},
initOnKeyListeners: () => {
// only install a listener if it is really needed
if (
!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS &&
!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS
)
return;
document.addEventListener("keydown", (event) => {
// bail for input elements
if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
// bail with special keys
if (event.altKey || event.ctrlKey || event.metaKey) return;
if (!event.shiftKey) {
switch (event.key) {
case "ArrowLeft":
if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
const prevLink = document.querySelector('link[rel="prev"]');
if (prevLink && prevLink.href) {
window.location.href = prevLink.href;
event.preventDefault();
}
break;
case "ArrowRight":
if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
const nextLink = document.querySelector('link[rel="next"]');
if (nextLink && nextLink.href) {
window.location.href = nextLink.href;
event.preventDefault();
}
break;
}
}
// some keyboard layouts may need Shift to get /
switch (event.key) {
case "/":
if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break;
Documentation.focusSearchBar();
event.preventDefault();
}
});
},
};
// quick alias for translations
const _ = Documentation.gettext;
_ready(Documentation.init);

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const DOCUMENTATION_OPTIONS = {
VERSION: '',
LANGUAGE: 'en',
COLLAPSE_INDEX: false,
BUILDER: 'html',
FILE_SUFFIX: '.html',
LINK_SUFFIX: '.html',
HAS_SOURCE: true,
SOURCELINK_SUFFIX: '.txt',
NAVIGATION_WITH_KEYS: false,
SHOW_SEARCH_SUMMARY: true,
ENABLE_SEARCH_SHORTCUTS: true,
};

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<svg xmlns="http://www.w3.org/2000/svg" width="80" height="80" viewBox="0 0 250 250" fill="#fff">
<path d="M0 0l115 115h15l12 27 108 108V0z" fill="#151513"/>
<path d="M128 109c-15-9-9-19-9-19 3-7 2-11 2-11-1-7 3-2 3-2 4 5 2 11 2 11-3 10 5 15 9 16"/>
<path d="M115 115s4 2 5 0l14-14c3-2 6-3 8-3-8-11-15-24 2-41 5-5 10-7 16-7 1-2 3-7 12-11 0 0 5 3 7 16 4 2 8 5 12 9s7 8 9 12c14 3 17 7 17 7-4 8-9 11-11 11 0 6-2 11-7 16-16 16-30 10-41 2 0 3-1 7-5 11l-12 11c-1 1 1 5 1 5z"/>
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/*
* This script contains the language-specific data used by searchtools.js,
* namely the list of stopwords, stemmer, scorer and splitter.
*/
var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"];
/* Non-minified version is copied as a separate JS file, if available */
/**
* Porter Stemmer
*/
var Stemmer = function() {
var step2list = {
ational: 'ate',
tional: 'tion',
enci: 'ence',
anci: 'ance',
izer: 'ize',
bli: 'ble',
alli: 'al',
entli: 'ent',
eli: 'e',
ousli: 'ous',
ization: 'ize',
ation: 'ate',
ator: 'ate',
alism: 'al',
iveness: 'ive',
fulness: 'ful',
ousness: 'ous',
aliti: 'al',
iviti: 'ive',
biliti: 'ble',
logi: 'log'
};
var step3list = {
icate: 'ic',
ative: '',
alize: 'al',
iciti: 'ic',
ical: 'ic',
ful: '',
ness: ''
};
var c = "[^aeiou]"; // consonant
var v = "[aeiouy]"; // vowel
var C = c + "[^aeiouy]*"; // consonant sequence
var V = v + "[aeiou]*"; // vowel sequence
var mgr0 = "^(" + C + ")?" + V + C; // [C]VC... is m>0
var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$"; // [C]VC[V] is m=1
var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1
var s_v = "^(" + C + ")?" + v; // vowel in stem
this.stemWord = function (w) {
var stem;
var suffix;
var firstch;
var origword = w;
if (w.length < 3)
return w;
var re;
var re2;
var re3;
var re4;
firstch = w.substr(0,1);
if (firstch == "y")
w = firstch.toUpperCase() + w.substr(1);
// Step 1a
re = /^(.+?)(ss|i)es$/;
re2 = /^(.+?)([^s])s$/;
if (re.test(w))
w = w.replace(re,"$1$2");
else if (re2.test(w))
w = w.replace(re2,"$1$2");
// Step 1b
re = /^(.+?)eed$/;
re2 = /^(.+?)(ed|ing)$/;
if (re.test(w)) {
var fp = re.exec(w);
re = new RegExp(mgr0);
if (re.test(fp[1])) {
re = /.$/;
w = w.replace(re,"");
}
}
else if (re2.test(w)) {
var fp = re2.exec(w);
stem = fp[1];
re2 = new RegExp(s_v);
if (re2.test(stem)) {
w = stem;
re2 = /(at|bl|iz)$/;
re3 = new RegExp("([^aeiouylsz])\\1$");
re4 = new RegExp("^" + C + v + "[^aeiouwxy]$");
if (re2.test(w))
w = w + "e";
else if (re3.test(w)) {
re = /.$/;
w = w.replace(re,"");
}
else if (re4.test(w))
w = w + "e";
}
}
// Step 1c
re = /^(.+?)y$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
re = new RegExp(s_v);
if (re.test(stem))
w = stem + "i";
}
// Step 2
re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
suffix = fp[2];
re = new RegExp(mgr0);
if (re.test(stem))
w = stem + step2list[suffix];
}
// Step 3
re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
suffix = fp[2];
re = new RegExp(mgr0);
if (re.test(stem))
w = stem + step3list[suffix];
}
// Step 4
re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;
re2 = /^(.+?)(s|t)(ion)$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
re = new RegExp(mgr1);
if (re.test(stem))
w = stem;
}
else if (re2.test(w)) {
var fp = re2.exec(w);
stem = fp[1] + fp[2];
re2 = new RegExp(mgr1);
if (re2.test(stem))
w = stem;
}
// Step 5
re = /^(.+?)e$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
re = new RegExp(mgr1);
re2 = new RegExp(meq1);
re3 = new RegExp("^" + C + v + "[^aeiouwxy]$");
if (re.test(stem) || (re2.test(stem) && !(re3.test(stem))))
w = stem;
}
re = /ll$/;
re2 = new RegExp(mgr1);
if (re.test(w) && re2.test(w)) {
re = /.$/;
w = w.replace(re,"");
}
// and turn initial Y back to y
if (firstch == "y")
w = firstch.toLowerCase() + w.substr(1);
return w;
}
}

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pre { line-height: 125%; }
td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
.highlight .hll { background-color: #ffffcc }
.highlight { background: #f8f8f8; }
.highlight .c { color: #8F5902; font-style: italic } /* Comment */
.highlight .err { color: #A40000; border: 1px solid #EF2929 } /* Error */
.highlight .g { color: #000 } /* Generic */
.highlight .k { color: #004461; font-weight: bold } /* Keyword */
.highlight .l { color: #000 } /* Literal */
.highlight .n { color: #000 } /* Name */
.highlight .o { color: #582800 } /* Operator */
.highlight .x { color: #000 } /* Other */
.highlight .p { color: #000; font-weight: bold } /* Punctuation */
.highlight .ch { color: #8F5902; font-style: italic } /* Comment.Hashbang */
.highlight .cm { color: #8F5902; font-style: italic } /* Comment.Multiline */
.highlight .cp { color: #8F5902 } /* Comment.Preproc */
.highlight .cpf { color: #8F5902; font-style: italic } /* Comment.PreprocFile */
.highlight .c1 { color: #8F5902; font-style: italic } /* Comment.Single */
.highlight .cs { color: #8F5902; font-style: italic } /* Comment.Special */
.highlight .gd { color: #A40000 } /* Generic.Deleted */
.highlight .ge { color: #000; font-style: italic } /* Generic.Emph */
.highlight .ges { color: #000 } /* Generic.EmphStrong */
.highlight .gr { color: #EF2929 } /* Generic.Error */
.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
.highlight .gi { color: #00A000 } /* Generic.Inserted */
.highlight .go { color: #888 } /* Generic.Output */
.highlight .gp { color: #745334 } /* Generic.Prompt */
.highlight .gs { color: #000; font-weight: bold } /* Generic.Strong */
.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
.highlight .gt { color: #A40000; font-weight: bold } /* Generic.Traceback */
.highlight .kc { color: #004461; font-weight: bold } /* Keyword.Constant */
.highlight .kd { color: #004461; font-weight: bold } /* Keyword.Declaration */
.highlight .kn { color: #004461; font-weight: bold } /* Keyword.Namespace */
.highlight .kp { color: #004461; font-weight: bold } /* Keyword.Pseudo */
.highlight .kr { color: #004461; font-weight: bold } /* Keyword.Reserved */
.highlight .kt { color: #004461; font-weight: bold } /* Keyword.Type */
.highlight .ld { color: #000 } /* Literal.Date */
.highlight .m { color: #900 } /* Literal.Number */
.highlight .s { color: #4E9A06 } /* Literal.String */
.highlight .na { color: #C4A000 } /* Name.Attribute */
.highlight .nb { color: #004461 } /* Name.Builtin */
.highlight .nc { color: #000 } /* Name.Class */
.highlight .no { color: #000 } /* Name.Constant */
.highlight .nd { color: #888 } /* Name.Decorator */
.highlight .ni { color: #CE5C00 } /* Name.Entity */
.highlight .ne { color: #C00; font-weight: bold } /* Name.Exception */
.highlight .nf { color: #000 } /* Name.Function */
.highlight .nl { color: #F57900 } /* Name.Label */
.highlight .nn { color: #000 } /* Name.Namespace */
.highlight .nx { color: #000 } /* Name.Other */
.highlight .py { color: #000 } /* Name.Property */
.highlight .nt { color: #004461; font-weight: bold } /* Name.Tag */
.highlight .nv { color: #000 } /* Name.Variable */
.highlight .ow { color: #004461; font-weight: bold } /* Operator.Word */
.highlight .pm { color: #000; font-weight: bold } /* Punctuation.Marker */
.highlight .w { color: #F8F8F8 } /* Text.Whitespace */
.highlight .mb { color: #900 } /* Literal.Number.Bin */
.highlight .mf { color: #900 } /* Literal.Number.Float */
.highlight .mh { color: #900 } /* Literal.Number.Hex */
.highlight .mi { color: #900 } /* Literal.Number.Integer */
.highlight .mo { color: #900 } /* Literal.Number.Oct */
.highlight .sa { color: #4E9A06 } /* Literal.String.Affix */
.highlight .sb { color: #4E9A06 } /* Literal.String.Backtick */
.highlight .sc { color: #4E9A06 } /* Literal.String.Char */
.highlight .dl { color: #4E9A06 } /* Literal.String.Delimiter */
.highlight .sd { color: #8F5902; font-style: italic } /* Literal.String.Doc */
.highlight .s2 { color: #4E9A06 } /* Literal.String.Double */
.highlight .se { color: #4E9A06 } /* Literal.String.Escape */
.highlight .sh { color: #4E9A06 } /* Literal.String.Heredoc */
.highlight .si { color: #4E9A06 } /* Literal.String.Interpol */
.highlight .sx { color: #4E9A06 } /* Literal.String.Other */
.highlight .sr { color: #4E9A06 } /* Literal.String.Regex */
.highlight .s1 { color: #4E9A06 } /* Literal.String.Single */
.highlight .ss { color: #4E9A06 } /* Literal.String.Symbol */
.highlight .bp { color: #3465A4 } /* Name.Builtin.Pseudo */
.highlight .fm { color: #000 } /* Name.Function.Magic */
.highlight .vc { color: #000 } /* Name.Variable.Class */
.highlight .vg { color: #000 } /* Name.Variable.Global */
.highlight .vi { color: #000 } /* Name.Variable.Instance */
.highlight .vm { color: #000 } /* Name.Variable.Magic */
.highlight .il { color: #900 } /* Literal.Number.Integer.Long */

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/*
* Sphinx JavaScript utilities for the full-text search.
*/
"use strict";
/**
* Simple result scoring code.
*/
if (typeof Scorer === "undefined") {
var Scorer = {
// Implement the following function to further tweak the score for each result
// The function takes a result array [docname, title, anchor, descr, score, filename]
// and returns the new score.
/*
score: result => {
const [docname, title, anchor, descr, score, filename, kind] = result
return score
},
*/
// query matches the full name of an object
objNameMatch: 11,
// or matches in the last dotted part of the object name
objPartialMatch: 6,
// Additive scores depending on the priority of the object
objPrio: {
0: 15, // used to be importantResults
1: 5, // used to be objectResults
2: -5, // used to be unimportantResults
},
// Used when the priority is not in the mapping.
objPrioDefault: 0,
// query found in title
title: 15,
partialTitle: 7,
// query found in terms
term: 5,
partialTerm: 2,
};
}
// Global search result kind enum, used by themes to style search results.
class SearchResultKind {
static get index() { return "index"; }
static get object() { return "object"; }
static get text() { return "text"; }
static get title() { return "title"; }
}
const _removeChildren = (element) => {
while (element && element.lastChild) element.removeChild(element.lastChild);
};
/**
* See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping
*/
const _escapeRegExp = (string) =>
string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
const _displayItem = (item, searchTerms, highlightTerms) => {
const docBuilder = DOCUMENTATION_OPTIONS.BUILDER;
const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX;
const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX;
const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY;
const contentRoot = document.documentElement.dataset.content_root;
const [docName, title, anchor, descr, score, _filename, kind] = item;
let listItem = document.createElement("li");
// Add a class representing the item's type:
// can be used by a theme's CSS selector for styling
// See SearchResultKind for the class names.
listItem.classList.add(`kind-${kind}`);
let requestUrl;
let linkUrl;
if (docBuilder === "dirhtml") {
// dirhtml builder
let dirname = docName + "/";
if (dirname.match(/\/index\/$/))
dirname = dirname.substring(0, dirname.length - 6);
else if (dirname === "index/") dirname = "";
requestUrl = contentRoot + dirname;
linkUrl = requestUrl;
} else {
// normal html builders
requestUrl = contentRoot + docName + docFileSuffix;
linkUrl = docName + docLinkSuffix;
}
let linkEl = listItem.appendChild(document.createElement("a"));
linkEl.href = linkUrl + anchor;
linkEl.dataset.score = score;
linkEl.innerHTML = title;
if (descr) {
listItem.appendChild(document.createElement("span")).innerHTML =
" (" + descr + ")";
// highlight search terms in the description
if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js
highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted"));
}
else if (showSearchSummary)
fetch(requestUrl)
.then((responseData) => responseData.text())
.then((data) => {
if (data)
listItem.appendChild(
Search.makeSearchSummary(data, searchTerms, anchor)
);
// highlight search terms in the summary
if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js
highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted"));
});
Search.output.appendChild(listItem);
};
const _finishSearch = (resultCount) => {
Search.stopPulse();
Search.title.innerText = _("Search Results");
if (!resultCount)
Search.status.innerText = Documentation.gettext(
"Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories."
);
else
Search.status.innerText = Documentation.ngettext(
"Search finished, found one page matching the search query.",
"Search finished, found ${resultCount} pages matching the search query.",
resultCount,
).replace('${resultCount}', resultCount);
};
const _displayNextItem = (
results,
resultCount,
searchTerms,
highlightTerms,
) => {
// results left, load the summary and display it
// this is intended to be dynamic (don't sub resultsCount)
if (results.length) {
_displayItem(results.pop(), searchTerms, highlightTerms);
setTimeout(
() => _displayNextItem(results, resultCount, searchTerms, highlightTerms),
5
);
}
// search finished, update title and status message
else _finishSearch(resultCount);
};
// Helper function used by query() to order search results.
// Each input is an array of [docname, title, anchor, descr, score, filename, kind].
// Order the results by score (in opposite order of appearance, since the
// `_displayNextItem` function uses pop() to retrieve items) and then alphabetically.
const _orderResultsByScoreThenName = (a, b) => {
const leftScore = a[4];
const rightScore = b[4];
if (leftScore === rightScore) {
// same score: sort alphabetically
const leftTitle = a[1].toLowerCase();
const rightTitle = b[1].toLowerCase();
if (leftTitle === rightTitle) return 0;
return leftTitle > rightTitle ? -1 : 1; // inverted is intentional
}
return leftScore > rightScore ? 1 : -1;
};
/**
* Default splitQuery function. Can be overridden in ``sphinx.search`` with a
* custom function per language.
*
* The regular expression works by splitting the string on consecutive characters
* that are not Unicode letters, numbers, underscores, or emoji characters.
* This is the same as ``\W+`` in Python, preserving the surrogate pair area.
*/
if (typeof splitQuery === "undefined") {
var splitQuery = (query) => query
.split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu)
.filter(term => term) // remove remaining empty strings
}
/**
* Search Module
*/
const Search = {
_index: null,
_queued_query: null,
_pulse_status: -1,
htmlToText: (htmlString, anchor) => {
const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html');
for (const removalQuery of [".headerlink", "script", "style"]) {
htmlElement.querySelectorAll(removalQuery).forEach((el) => { el.remove() });
}
if (anchor) {
const anchorContent = htmlElement.querySelector(`[role="main"] ${anchor}`);
if (anchorContent) return anchorContent.textContent;
console.warn(
`Anchored content block not found. Sphinx search tries to obtain it via DOM query '[role=main] ${anchor}'. Check your theme or template.`
);
}
// if anchor not specified or not found, fall back to main content
const docContent = htmlElement.querySelector('[role="main"]');
if (docContent) return docContent.textContent;
console.warn(
"Content block not found. Sphinx search tries to obtain it via DOM query '[role=main]'. Check your theme or template."
);
return "";
},
init: () => {
const query = new URLSearchParams(window.location.search).get("q");
document
.querySelectorAll('input[name="q"]')
.forEach((el) => (el.value = query));
if (query) Search.performSearch(query);
},
loadIndex: (url) =>
(document.body.appendChild(document.createElement("script")).src = url),
setIndex: (index) => {
Search._index = index;
if (Search._queued_query !== null) {
const query = Search._queued_query;
Search._queued_query = null;
Search.query(query);
}
},
hasIndex: () => Search._index !== null,
deferQuery: (query) => (Search._queued_query = query),
stopPulse: () => (Search._pulse_status = -1),
startPulse: () => {
if (Search._pulse_status >= 0) return;
const pulse = () => {
Search._pulse_status = (Search._pulse_status + 1) % 4;
Search.dots.innerText = ".".repeat(Search._pulse_status);
if (Search._pulse_status >= 0) window.setTimeout(pulse, 500);
};
pulse();
},
/**
* perform a search for something (or wait until index is loaded)
*/
performSearch: (query) => {
// create the required interface elements
const searchText = document.createElement("h2");
searchText.textContent = _("Searching");
const searchSummary = document.createElement("p");
searchSummary.classList.add("search-summary");
searchSummary.innerText = "";
const searchList = document.createElement("ul");
searchList.setAttribute("role", "list");
searchList.classList.add("search");
const out = document.getElementById("search-results");
Search.title = out.appendChild(searchText);
Search.dots = Search.title.appendChild(document.createElement("span"));
Search.status = out.appendChild(searchSummary);
Search.output = out.appendChild(searchList);
const searchProgress = document.getElementById("search-progress");
// Some themes don't use the search progress node
if (searchProgress) {
searchProgress.innerText = _("Preparing search...");
}
Search.startPulse();
// index already loaded, the browser was quick!
if (Search.hasIndex()) Search.query(query);
else Search.deferQuery(query);
},
_parseQuery: (query) => {
// stem the search terms and add them to the correct list
const stemmer = new Stemmer();
const searchTerms = new Set();
const excludedTerms = new Set();
const highlightTerms = new Set();
const objectTerms = new Set(splitQuery(query.toLowerCase().trim()));
splitQuery(query.trim()).forEach((queryTerm) => {
const queryTermLower = queryTerm.toLowerCase();
// maybe skip this "word"
// stopwords array is from language_data.js
if (
stopwords.indexOf(queryTermLower) !== -1 ||
queryTerm.match(/^\d+$/)
)
return;
// stem the word
let word = stemmer.stemWord(queryTermLower);
// select the correct list
if (word[0] === "-") excludedTerms.add(word.substr(1));
else {
searchTerms.add(word);
highlightTerms.add(queryTermLower);
}
});
if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js
localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" "))
}
// console.debug("SEARCH: searching for:");
// console.info("required: ", [...searchTerms]);
// console.info("excluded: ", [...excludedTerms]);
return [query, searchTerms, excludedTerms, highlightTerms, objectTerms];
},
/**
* execute search (requires search index to be loaded)
*/
_performSearch: (query, searchTerms, excludedTerms, highlightTerms, objectTerms) => {
const filenames = Search._index.filenames;
const docNames = Search._index.docnames;
const titles = Search._index.titles;
const allTitles = Search._index.alltitles;
const indexEntries = Search._index.indexentries;
// Collect multiple result groups to be sorted separately and then ordered.
// Each is an array of [docname, title, anchor, descr, score, filename, kind].
const normalResults = [];
const nonMainIndexResults = [];
_removeChildren(document.getElementById("search-progress"));
const queryLower = query.toLowerCase().trim();
for (const [title, foundTitles] of Object.entries(allTitles)) {
if (title.toLowerCase().trim().includes(queryLower) && (queryLower.length >= title.length/2)) {
for (const [file, id] of foundTitles) {
const score = Math.round(Scorer.title * queryLower.length / title.length);
const boost = titles[file] === title ? 1 : 0; // add a boost for document titles
normalResults.push([
docNames[file],
titles[file] !== title ? `${titles[file]} > ${title}` : title,
id !== null ? "#" + id : "",
null,
score + boost,
filenames[file],
SearchResultKind.title,
]);
}
}
}
// search for explicit entries in index directives
for (const [entry, foundEntries] of Object.entries(indexEntries)) {
if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) {
for (const [file, id, isMain] of foundEntries) {
const score = Math.round(100 * queryLower.length / entry.length);
const result = [
docNames[file],
titles[file],
id ? "#" + id : "",
null,
score,
filenames[file],
SearchResultKind.index,
];
if (isMain) {
normalResults.push(result);
} else {
nonMainIndexResults.push(result);
}
}
}
}
// lookup as object
objectTerms.forEach((term) =>
normalResults.push(...Search.performObjectSearch(term, objectTerms))
);
// lookup as search terms in fulltext
normalResults.push(...Search.performTermsSearch(searchTerms, excludedTerms));
// let the scorer override scores with a custom scoring function
if (Scorer.score) {
normalResults.forEach((item) => (item[4] = Scorer.score(item)));
nonMainIndexResults.forEach((item) => (item[4] = Scorer.score(item)));
}
// Sort each group of results by score and then alphabetically by name.
normalResults.sort(_orderResultsByScoreThenName);
nonMainIndexResults.sort(_orderResultsByScoreThenName);
// Combine the result groups in (reverse) order.
// Non-main index entries are typically arbitrary cross-references,
// so display them after other results.
let results = [...nonMainIndexResults, ...normalResults];
// remove duplicate search results
// note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept
let seen = new Set();
results = results.reverse().reduce((acc, result) => {
let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(',');
if (!seen.has(resultStr)) {
acc.push(result);
seen.add(resultStr);
}
return acc;
}, []);
return results.reverse();
},
query: (query) => {
const [searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms] = Search._parseQuery(query);
const results = Search._performSearch(searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms);
// for debugging
//Search.lastresults = results.slice(); // a copy
// console.info("search results:", Search.lastresults);
// print the results
_displayNextItem(results, results.length, searchTerms, highlightTerms);
},
/**
* search for object names
*/
performObjectSearch: (object, objectTerms) => {
const filenames = Search._index.filenames;
const docNames = Search._index.docnames;
const objects = Search._index.objects;
const objNames = Search._index.objnames;
const titles = Search._index.titles;
const results = [];
const objectSearchCallback = (prefix, match) => {
const name = match[4]
const fullname = (prefix ? prefix + "." : "") + name;
const fullnameLower = fullname.toLowerCase();
if (fullnameLower.indexOf(object) < 0) return;
let score = 0;
const parts = fullnameLower.split(".");
// check for different match types: exact matches of full name or
// "last name" (i.e. last dotted part)
if (fullnameLower === object || parts.slice(-1)[0] === object)
score += Scorer.objNameMatch;
else if (parts.slice(-1)[0].indexOf(object) > -1)
score += Scorer.objPartialMatch; // matches in last name
const objName = objNames[match[1]][2];
const title = titles[match[0]];
// If more than one term searched for, we require other words to be
// found in the name/title/description
const otherTerms = new Set(objectTerms);
otherTerms.delete(object);
if (otherTerms.size > 0) {
const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase();
if (
[...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0)
)
return;
}
let anchor = match[3];
if (anchor === "") anchor = fullname;
else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname;
const descr = objName + _(", in ") + title;
// add custom score for some objects according to scorer
if (Scorer.objPrio.hasOwnProperty(match[2]))
score += Scorer.objPrio[match[2]];
else score += Scorer.objPrioDefault;
results.push([
docNames[match[0]],
fullname,
"#" + anchor,
descr,
score,
filenames[match[0]],
SearchResultKind.object,
]);
};
Object.keys(objects).forEach((prefix) =>
objects[prefix].forEach((array) =>
objectSearchCallback(prefix, array)
)
);
return results;
},
/**
* search for full-text terms in the index
*/
performTermsSearch: (searchTerms, excludedTerms) => {
// prepare search
const terms = Search._index.terms;
const titleTerms = Search._index.titleterms;
const filenames = Search._index.filenames;
const docNames = Search._index.docnames;
const titles = Search._index.titles;
const scoreMap = new Map();
const fileMap = new Map();
// perform the search on the required terms
searchTerms.forEach((word) => {
const files = [];
// find documents, if any, containing the query word in their text/title term indices
// use Object.hasOwnProperty to avoid mismatching against prototype properties
const arr = [
{ files: terms.hasOwnProperty(word) ? terms[word] : undefined, score: Scorer.term },
{ files: titleTerms.hasOwnProperty(word) ? titleTerms[word] : undefined, score: Scorer.title },
];
// add support for partial matches
if (word.length > 2) {
const escapedWord = _escapeRegExp(word);
if (!terms.hasOwnProperty(word)) {
Object.keys(terms).forEach((term) => {
if (term.match(escapedWord))
arr.push({ files: terms[term], score: Scorer.partialTerm });
});
}
if (!titleTerms.hasOwnProperty(word)) {
Object.keys(titleTerms).forEach((term) => {
if (term.match(escapedWord))
arr.push({ files: titleTerms[term], score: Scorer.partialTitle });
});
}
}
// no match but word was a required one
if (arr.every((record) => record.files === undefined)) return;
// found search word in contents
arr.forEach((record) => {
if (record.files === undefined) return;
let recordFiles = record.files;
if (recordFiles.length === undefined) recordFiles = [recordFiles];
files.push(...recordFiles);
// set score for the word in each file
recordFiles.forEach((file) => {
if (!scoreMap.has(file)) scoreMap.set(file, new Map());
const fileScores = scoreMap.get(file);
fileScores.set(word, record.score);
});
});
// create the mapping
files.forEach((file) => {
if (!fileMap.has(file)) fileMap.set(file, [word]);
else if (fileMap.get(file).indexOf(word) === -1) fileMap.get(file).push(word);
});
});
// now check if the files don't contain excluded terms
const results = [];
for (const [file, wordList] of fileMap) {
// check if all requirements are matched
// as search terms with length < 3 are discarded
const filteredTermCount = [...searchTerms].filter(
(term) => term.length > 2
).length;
if (
wordList.length !== searchTerms.size &&
wordList.length !== filteredTermCount
)
continue;
// ensure that none of the excluded terms is in the search result
if (
[...excludedTerms].some(
(term) =>
terms[term] === file ||
titleTerms[term] === file ||
(terms[term] || []).includes(file) ||
(titleTerms[term] || []).includes(file)
)
)
break;
// select one (max) score for the file.
const score = Math.max(...wordList.map((w) => scoreMap.get(file).get(w)));
// add result to the result list
results.push([
docNames[file],
titles[file],
"",
null,
score,
filenames[file],
SearchResultKind.text,
]);
}
return results;
},
/**
* helper function to return a node containing the
* search summary for a given text. keywords is a list
* of stemmed words.
*/
makeSearchSummary: (htmlText, keywords, anchor) => {
const text = Search.htmlToText(htmlText, anchor);
if (text === "") return null;
const textLower = text.toLowerCase();
const actualStartPosition = [...keywords]
.map((k) => textLower.indexOf(k.toLowerCase()))
.filter((i) => i > -1)
.slice(-1)[0];
const startWithContext = Math.max(actualStartPosition - 120, 0);
const top = startWithContext === 0 ? "" : "...";
const tail = startWithContext + 240 < text.length ? "..." : "";
let summary = document.createElement("p");
summary.classList.add("context");
summary.textContent = top + text.substr(startWithContext, 240).trim() + tail;
return summary;
},
};
_ready(Search.init);

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/* Highlighting utilities for Sphinx HTML documentation. */
"use strict";
const SPHINX_HIGHLIGHT_ENABLED = true
/**
* highlight a given string on a node by wrapping it in
* span elements with the given class name.
*/
const _highlight = (node, addItems, text, className) => {
if (node.nodeType === Node.TEXT_NODE) {
const val = node.nodeValue;
const parent = node.parentNode;
const pos = val.toLowerCase().indexOf(text);
if (
pos >= 0 &&
!parent.classList.contains(className) &&
!parent.classList.contains("nohighlight")
) {
let span;
const closestNode = parent.closest("body, svg, foreignObject");
const isInSVG = closestNode && closestNode.matches("svg");
if (isInSVG) {
span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
} else {
span = document.createElement("span");
span.classList.add(className);
}
span.appendChild(document.createTextNode(val.substr(pos, text.length)));
const rest = document.createTextNode(val.substr(pos + text.length));
parent.insertBefore(
span,
parent.insertBefore(
rest,
node.nextSibling
)
);
node.nodeValue = val.substr(0, pos);
/* There may be more occurrences of search term in this node. So call this
* function recursively on the remaining fragment.
*/
_highlight(rest, addItems, text, className);
if (isInSVG) {
const rect = document.createElementNS(
"http://www.w3.org/2000/svg",
"rect"
);
const bbox = parent.getBBox();
rect.x.baseVal.value = bbox.x;
rect.y.baseVal.value = bbox.y;
rect.width.baseVal.value = bbox.width;
rect.height.baseVal.value = bbox.height;
rect.setAttribute("class", className);
addItems.push({ parent: parent, target: rect });
}
}
} else if (node.matches && !node.matches("button, select, textarea")) {
node.childNodes.forEach((el) => _highlight(el, addItems, text, className));
}
};
const _highlightText = (thisNode, text, className) => {
let addItems = [];
_highlight(thisNode, addItems, text, className);
addItems.forEach((obj) =>
obj.parent.insertAdjacentElement("beforebegin", obj.target)
);
};
/**
* Small JavaScript module for the documentation.
*/
const SphinxHighlight = {
/**
* highlight the search words provided in localstorage in the text
*/
highlightSearchWords: () => {
if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight
// get and clear terms from localstorage
const url = new URL(window.location);
const highlight =
localStorage.getItem("sphinx_highlight_terms")
|| url.searchParams.get("highlight")
|| "";
localStorage.removeItem("sphinx_highlight_terms")
url.searchParams.delete("highlight");
window.history.replaceState({}, "", url);
// get individual terms from highlight string
const terms = highlight.toLowerCase().split(/\s+/).filter(x => x);
if (terms.length === 0) return; // nothing to do
// There should never be more than one element matching "div.body"
const divBody = document.querySelectorAll("div.body");
const body = divBody.length ? divBody[0] : document.querySelector("body");
window.setTimeout(() => {
terms.forEach((term) => _highlightText(body, term, "highlighted"));
}, 10);
const searchBox = document.getElementById("searchbox");
if (searchBox === null) return;
searchBox.appendChild(
document
.createRange()
.createContextualFragment(
'<p class="highlight-link">' +
'<a href="javascript:SphinxHighlight.hideSearchWords()">' +
_("Hide Search Matches") +
"</a></p>"
)
);
},
/**
* helper function to hide the search marks again
*/
hideSearchWords: () => {
document
.querySelectorAll("#searchbox .highlight-link")
.forEach((el) => el.remove());
document
.querySelectorAll("span.highlighted")
.forEach((el) => el.classList.remove("highlighted"));
localStorage.removeItem("sphinx_highlight_terms")
},
initEscapeListener: () => {
// only install a listener if it is really needed
if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return;
document.addEventListener("keydown", (event) => {
// bail for input elements
if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
// bail with special keys
if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return;
if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) {
SphinxHighlight.hideSearchWords();
event.preventDefault();
}
});
},
};
_ready(() => {
/* Do not call highlightSearchWords() when we are on the search page.
* It will highlight words from the *previous* search query.
*/
if (typeof Search === "undefined") SphinxHighlight.highlightSearchWords();
SphinxHighlight.initEscapeListener();
});

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<!DOCTYPE html>
<html lang="en" data-content_root="./">
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
<title>API Reference &#8212; optifik documentation</title>
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=5ecbeea2" />
<link rel="stylesheet" type="text/css" href="_static/basic.css?v=b08954a9" />
<link rel="stylesheet" type="text/css" href="_static/alabaster.css?v=27fed22d" />
<script src="_static/documentation_options.js?v=5929fcd5"></script>
<script src="_static/doctools.js?v=9bcbadda"></script>
<script src="_static/sphinx_highlight.js?v=dc90522c"></script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="Examples" href="examples.html" />
<link rel="prev" title="Installation" href="installation.html" />
<link rel="stylesheet" href="_static/custom.css" type="text/css" />
</head><body>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<section id="api-reference">
<h1>API Reference<a class="headerlink" href="#api-reference" title="Link to this heading"></a></h1>
<p>Below is the complete reference for Optifiks public API.</p>
<section id="module-optifik.io">
<span id="io"></span><h2>io<a class="headerlink" href="#module-optifik.io" title="Link to this heading"></a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="optifik.io.load_spectrum">
<span class="sig-prename descclassname"><span class="pre">optifik.io.</span></span><span class="sig-name descname"><span class="pre">load_spectrum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">spectrum_path</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wavelength_min</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wavelength_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">inf</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">delimiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">','</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/optifik/io.html#load_spectrum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#optifik.io.load_spectrum" title="Link to this definition"></a></dt>
<dd><p>Load a spectrum file.</p>
<p>TODO : describe expected format</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>spectrum_path</strong><span class="classifier">string</span></dt><dd><p>File path.</p>
</dd>
<dt><strong>wavelength_min</strong><span class="classifier">scalar, optional</span></dt><dd><p>Cut the data at this minimum wavelength (included).</p>
</dd>
<dt><strong>wavelength_max</strong><span class="classifier">scalar, optional</span></dt><dd><p>Cut the data at this maximum wavelength (included).</p>
</dd>
<dt><strong>delimiter</strong><span class="classifier">string, optional</span></dt><dd><p>Delimiter between columns in the datafile.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>values</strong><span class="classifier">arrays</span></dt><dd><p>(lamdbas, intensities)</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
</section>
<section id="module-optifik.fft">
<span id="fft"></span><h2>fft<a class="headerlink" href="#module-optifik.fft" title="Link to this heading"></a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="optifik.fft.thickness_from_fft">
<span class="sig-prename descclassname"><span class="pre">optifik.fft.</span></span><span class="sig-name descname"><span class="pre">thickness_from_fft</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wavelengths</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">intensities</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">refractive_index</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">num_half_space</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/optifik/fft.html#thickness_from_fft"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#optifik.fft.thickness_from_fft" title="Link to this definition"></a></dt>
<dd><p>Determine the tickness by Fast Fourier Transform.</p>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>wavelengths</strong><span class="classifier">array</span></dt><dd><p>Wavelength values in nm.</p>
</dd>
<dt><strong>intensities</strong><span class="classifier">array</span></dt><dd><p>Intensity values.</p>
</dd>
<dt><strong>refractive_index</strong><span class="classifier">scalar, optional</span></dt><dd><p>Value of the refractive index of the medium.</p>
</dd>
<dt><strong>num_half_space</strong><span class="classifier">scalar, optional</span></dt><dd><p>Number of points to compute FFTs half space.
If <cite>None</cite>, default corresponds to <cite>10*len(wavelengths)</cite>.</p>
</dd>
<dt><strong>plot</strong><span class="classifier">boolean, optional</span></dt><dd><p>Show plot of the transformed signal and the peak detection.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<dt><strong>results</strong><span class="classifier">Instance of <cite>OptimizeResult</cite> class.</span></dt><dd><p>The attribute <cite>thickness</cite> gives the thickness value in nm.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
</section>
<section id="module-optifik.minmax">
<span id="minmax"></span><h2>minmax<a class="headerlink" href="#module-optifik.minmax" title="Link to this heading"></a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="optifik.minmax.thickness_from_minmax">
<span class="sig-prename descclassname"><span class="pre">optifik.minmax.</span></span><span class="sig-name descname"><span class="pre">thickness_from_minmax</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wavelengths</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">intensities</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">refractive_index</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_peak_prominence</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_peak_distance</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'linreg'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/optifik/minmax.html#thickness_from_minmax"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#optifik.minmax.thickness_from_minmax" title="Link to this definition"></a></dt>
<dd><p>Return the thickness from a min-max detection.</p>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>wavelengths</strong><span class="classifier">array</span></dt><dd><p>Wavelength values in nm.</p>
</dd>
<dt><strong>intensities</strong><span class="classifier">array</span></dt><dd><p>Intensity values.</p>
</dd>
<dt><strong>refractive_index</strong><span class="classifier">scalar, optional</span></dt><dd><p>Value of the refractive index of the medium.</p>
</dd>
<dt><strong>min_peak_prominence</strong><span class="classifier">scalar, optional</span></dt><dd><p>Required prominence of peaks.</p>
</dd>
<dt><strong>min_peak_distance</strong><span class="classifier">scalar, optional</span></dt><dd><p>Minimum distance between peaks.</p>
</dd>
<dt><strong>method</strong><span class="classifier">string, optional</span></dt><dd><p>Either linreg for linear regression or ransac
for Randon Sampling Consensus.</p>
</dd>
<dt><strong>plot</strong><span class="classifier">boolean, optional</span></dt><dd><p>Show plots of peak detection and lin regression.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<dt><strong>results</strong><span class="classifier">Instance of <cite>OptimizeResult</cite> class.</span></dt><dd><p>The attribute <cite>thickness</cite> gives the thickness value in nm.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>For more details about <cite>min_peak_prominence</cite> and <cite>min_peak_distance</cite>,
see the documentation of <cite>scipy.signal.find_peaks</cite>. This function
is used to find extrema.</p>
</dd></dl>
</section>
<section id="module-optifik.scheludko">
<span id="scheludko"></span><h2>scheludko<a class="headerlink" href="#module-optifik.scheludko" title="Link to this heading"></a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="optifik.scheludko.get_default_start_stop_wavelengths">
<span class="sig-prename descclassname"><span class="pre">optifik.scheludko.</span></span><span class="sig-name descname"><span class="pre">get_default_start_stop_wavelengths</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wavelengths</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">intensities</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">refractive_index</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_peak_prominence</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/optifik/scheludko.html#get_default_start_stop_wavelengths"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#optifik.scheludko.get_default_start_stop_wavelengths" title="Link to this definition"></a></dt>
<dd><p>Returns the start and stop wavelength values of the last monotonic branch.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>wavelengths</strong><span class="classifier">array</span></dt><dd><p>Wavelength values in nm.</p>
</dd>
<dt><strong>intensities</strong><span class="classifier">array</span></dt><dd><p>Intensity values.</p>
</dd>
<dt><strong>refractive_index</strong><span class="classifier">scalar, optional</span></dt><dd><p>Value of the refractive index of the medium.</p>
</dd>
<dt><strong>min_peak_prominence</strong><span class="classifier">scalar</span></dt><dd><p>Required prominence of peaks.</p>
</dd>
<dt><strong>plot</strong><span class="classifier">bool, optional</span></dt><dd><p>Display a curve, useful for checking or debuging. The default is None.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>wavelength_start</strong><span class="classifier">scalar</span></dt><dd></dd>
<dt><strong>wavelength_stop</strong><span class="classifier">scalar</span></dt><dd></dd>
</dl>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt>RuntimeError</dt><dd><p>if at least one maximum and one minimum are not detected.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="optifik.scheludko.thickness_from_scheludko">
<span class="sig-prename descclassname"><span class="pre">optifik.scheludko.</span></span><span class="sig-name descname"><span class="pre">thickness_from_scheludko</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wavelengths</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">intensities</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">refractive_index</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wavelength_start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wavelength_stop</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">interference_order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">intensities_void</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/optifik/scheludko.html#thickness_from_scheludko"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#optifik.scheludko.thickness_from_scheludko" title="Link to this definition"></a></dt>
<dd><p>Compute the film thickness based on Scheludko method.</p>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>wavelengths</strong><span class="classifier">array</span></dt><dd><p>Wavelength values in nm.</p>
</dd>
<dt><strong>intensities</strong><span class="classifier">array</span></dt><dd><p>Intensity values.</p>
</dd>
<dt><strong>refractive_index</strong><span class="classifier">scalar, optional</span></dt><dd><p>Value of the refractive index of the medium.</p>
</dd>
<dt><strong>wavelength_start</strong><span class="classifier">scalar, optional</span></dt><dd><p>Starting value of a monotonic branch.
Mandatory if interference_order != 0.</p>
</dd>
<dt><strong>wavelength_stop</strong><span class="classifier">scalar, optional</span></dt><dd><p>Stoping value of a monotonic branch.
Mandatory if interference_order != 0.</p>
</dd>
<dt><strong>interference_order</strong><span class="classifier">scalar, optional</span></dt><dd><p>Interference order, zero or positive integer.
If set to None, the value is guessed.</p>
</dd>
<dt><strong>intensities_void</strong><span class="classifier">array, optional</span></dt><dd><p>Intensity in absence of a film.
Mandatory if interference_order == 0.</p>
</dd>
<dt><strong>plot</strong><span class="classifier">bool, optional</span></dt><dd><p>Display a curve, useful for checking or debuging. The default is None.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<dt><strong>results</strong><span class="classifier">Instance of <cite>OptimizeResult</cite> class.</span></dt><dd><p>The attribute <cite>thickness</cite> gives the thickness value in nm.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
</section>
</section>
</div>
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from collections import OrderedDict
# Data obtained by Lorene Champougny
known_thicknesses = OrderedDict({
'sample1/003582.xy' : 3521,
'sample1/003766.xy' : 3430,
'sample1/003952.xy' : 3494,
'sample1/004136.xy' : 3485,
'sample1/004320.xy' : 3410,
'sample1/004504.xy' : 3280,
'sample1/004689.xy' : 3111,
'sample1/004872.xy' : 2878,
'sample1/005057.xy' : 2629,
'sample1/005241.xy' : 2411,
'sample1/005426.xy' : 2287,
'sample1/005610.xy' : 2180,
'sample1/005794.xy' : 2110,
'sample1/005978.xy' : 2033,
'sample1/006163.xy' : 1958,
'sample1/006347.xy' : 1889,
'sample1/006528.xy' : 1789,
'sample1/006715.xy' : 1703,
'sample1/006900.xy' : 1629,
'sample1/007084.xy' : 1549,
'sample1/007268.xy' : 1459,
'sample1/008188.xy' : 1054,
'sample1/008373.xy' : 1016,
'sample1/008557.xy' : 999,
'sample1/008742.xy' : 982,
'sample1/008926.xy' : 973,
'sample1/009111.xy' : 958,
'sample1/009294.xy' : 940,
'sample1/009479.xy' : 915,
'sample1/009848.xy' : 833,
'sample1/010032.xy' : 804,
'sample1/010215.xy' : 778,
'sample1/010399.xy' : 744,
'sample1/010581.xy' : 717,
'sample1/010768.xy' : 697,
'sample1/010953.xy' : 668,
'sample1/011137.xy' : 643,
'sample1/011321.xy' : 618,
'sample1/011505.xy' : 593,
'sample1/011688.xy' : 572,
'sample1/011873.xy' : 559,
'sample1/012058.xy' : 535,
'sample1/012242.xy' : 509,
'sample1/012426.xy' : 485,
'sample1/012610.xy' : 456,
'sample1/012795.xy' : 432,
'sample1/012979.xy' : 418,
})

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<h1>Source code for optifik.fft</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">scipy.interpolate</span><span class="w"> </span><span class="kn">import</span> <span class="n">interp1d</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">scipy.fftpack</span><span class="w"> </span><span class="kn">import</span> <span class="n">fft</span><span class="p">,</span> <span class="n">ifft</span><span class="p">,</span> <span class="n">fftfreq</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">.utils</span><span class="w"> </span><span class="kn">import</span> <span class="n">OptimizeResult</span><span class="p">,</span> <span class="n">setup_matplotlib</span>
<div class="viewcode-block" id="thickness_from_fft">
<a class="viewcode-back" href="../../api_reference.html#optifik.fft.thickness_from_fft">[docs]</a>
<span class="k">def</span><span class="w"> </span><span class="nf">thickness_from_fft</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span> <span class="n">intensities</span><span class="p">,</span>
<span class="n">refractive_index</span><span class="p">,</span>
<span class="n">num_half_space</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">plot</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Determine the tickness by Fast Fourier Transform.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> wavelengths : array</span>
<span class="sd"> Wavelength values in nm.</span>
<span class="sd"> intensities : array</span>
<span class="sd"> Intensity values.</span>
<span class="sd"> refractive_index : scalar, optional</span>
<span class="sd"> Value of the refractive index of the medium.</span>
<span class="sd"> num_half_space : scalar, optional</span>
<span class="sd"> Number of points to compute FFT&#39;s half space.</span>
<span class="sd"> If `None`, default corresponds to `10*len(wavelengths)`.</span>
<span class="sd"> plot : boolean, optional</span>
<span class="sd"> Show plot of the transformed signal and the peak detection.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> results : Instance of `OptimizeResult` class.</span>
<span class="sd"> The attribute `thickness` gives the thickness value in nm.</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">setup_matplotlib</span><span class="p">()</span>
<span class="k">if</span> <span class="n">num_half_space</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">num_half_space</span> <span class="o">=</span> <span class="mi">10</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">)</span>
<span class="c1"># FFT requires evenly spaced data.</span>
<span class="c1"># So, we interpolate the signal.</span>
<span class="c1"># Interpolate to get a linear increase of 1 / wavelengths.</span>
<span class="n">inverse_wavelengths_times_n</span> <span class="o">=</span> <span class="n">refractive_index</span> <span class="o">/</span> <span class="n">wavelengths</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="n">inverse_wavelengths_times_n</span><span class="p">,</span> <span class="n">intensities</span><span class="p">)</span>
<span class="n">inverse_wavelengths_linspace</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">inverse_wavelengths_times_n</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
<span class="n">inverse_wavelengths_times_n</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span>
<span class="mi">2</span><span class="o">*</span><span class="n">num_half_space</span><span class="p">)</span>
<span class="n">intensities_linspace</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">inverse_wavelengths_linspace</span><span class="p">)</span>
<span class="c1"># Perform FFT</span>
<span class="n">density</span> <span class="o">=</span> <span class="p">(</span><span class="n">inverse_wavelengths_times_n</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">inverse_wavelengths_times_n</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">num_half_space</span><span class="p">)</span>
<span class="n">inverse_wavelengths_fft</span> <span class="o">=</span> <span class="n">fftfreq</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">num_half_space</span><span class="p">,</span> <span class="n">density</span><span class="p">)</span>
<span class="n">intensities_fft</span> <span class="o">=</span> <span class="n">fft</span><span class="p">(</span><span class="n">intensities_linspace</span><span class="p">)</span>
<span class="c1"># The FFT is symetrical over [0:N] and [N:2N].</span>
<span class="c1"># Keep over [N:2N], ie for positive freq.</span>
<span class="n">intensities_fft</span> <span class="o">=</span> <span class="n">intensities_fft</span><span class="p">[</span><span class="n">num_half_space</span><span class="p">:</span><span class="mi">2</span><span class="o">*</span><span class="n">num_half_space</span><span class="p">]</span>
<span class="n">inverse_wavelengths_fft</span> <span class="o">=</span> <span class="n">inverse_wavelengths_fft</span><span class="p">[</span><span class="n">num_half_space</span><span class="p">:</span><span class="mi">2</span><span class="o">*</span><span class="n">num_half_space</span><span class="p">]</span>
<span class="n">idx_max_fft</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">intensities_fft</span><span class="p">))</span>
<span class="n">freq_max</span> <span class="o">=</span> <span class="n">inverse_wavelengths_fft</span><span class="p">[</span><span class="n">idx_max_fft</span><span class="p">]</span>
<span class="n">thickness_fft</span> <span class="o">=</span> <span class="n">freq_max</span> <span class="o">/</span> <span class="mf">2.</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">loglog</span><span class="p">(</span><span class="n">inverse_wavelengths_fft</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">intensities_fft</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">loglog</span><span class="p">(</span><span class="n">freq_max</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">intensities_fft</span><span class="p">[</span><span class="n">idx_max_fft</span><span class="p">]),</span> <span class="s1">&#39;o&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Frequency&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;FFT($I^*$)&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Thickness=</span><span class="si">{</span><span class="n">thickness_fft</span><span class="si">:</span><span class="s1">.2f</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">OptimizeResult</span><span class="p">(</span><span class="n">thickness</span><span class="o">=</span><span class="n">thickness_fft</span><span class="p">,)</span></div>
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<h1>Source code for optifik.io</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<div class="viewcode-block" id="load_spectrum">
<a class="viewcode-back" href="../../api_reference.html#optifik.io.load_spectrum">[docs]</a>
<span class="k">def</span><span class="w"> </span><span class="nf">load_spectrum</span><span class="p">(</span><span class="n">spectrum_path</span><span class="p">,</span>
<span class="n">wavelength_min</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
<span class="n">wavelength_max</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">inf</span><span class="p">,</span>
<span class="n">delimiter</span><span class="o">=</span><span class="s1">&#39;,&#39;</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Load a spectrum file.</span>
<span class="sd"> TODO : describe expected format</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> spectrum_path : string</span>
<span class="sd"> File path.</span>
<span class="sd"> wavelength_min : scalar, optional</span>
<span class="sd"> Cut the data at this minimum wavelength (included).</span>
<span class="sd"> wavelength_max : scalar, optional</span>
<span class="sd"> Cut the data at this maximum wavelength (included).</span>
<span class="sd"> delimiter : string, optional</span>
<span class="sd"> Delimiter between columns in the datafile.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> values : arrays</span>
<span class="sd"> (lamdbas, intensities)</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">loadtxt</span><span class="p">(</span><span class="n">spectrum_path</span><span class="p">,</span> <span class="n">delimiter</span><span class="o">=</span><span class="n">delimiter</span><span class="p">)</span>
<span class="n">lambdas</span><span class="p">,</span> <span class="n">intensities</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">column_stack</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">mask</span> <span class="o">=</span> <span class="p">(</span><span class="n">lambdas</span> <span class="o">&gt;=</span> <span class="n">wavelength_min</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">(</span><span class="n">lambdas</span> <span class="o">&lt;=</span> <span class="n">wavelength_max</span><span class="p">)</span>
<span class="k">return</span> <span class="n">lambdas</span><span class="p">[</span><span class="n">mask</span><span class="p">],</span> <span class="n">intensities</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span></div>
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<h1>Source code for optifik.minmax</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">scipy</span><span class="w"> </span><span class="kn">import</span> <span class="n">stats</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">skimage.measure</span><span class="w"> </span><span class="kn">import</span> <span class="n">ransac</span><span class="p">,</span> <span class="n">LineModelND</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">scipy.signal</span><span class="w"> </span><span class="kn">import</span> <span class="n">find_peaks</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">.utils</span><span class="w"> </span><span class="kn">import</span> <span class="n">OptimizeResult</span><span class="p">,</span> <span class="n">setup_matplotlib</span>
<div class="viewcode-block" id="thickness_from_minmax">
<a class="viewcode-back" href="../../api_reference.html#optifik.minmax.thickness_from_minmax">[docs]</a>
<span class="k">def</span><span class="w"> </span><span class="nf">thickness_from_minmax</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span>
<span class="n">intensities</span><span class="p">,</span>
<span class="n">refractive_index</span><span class="p">,</span>
<span class="n">min_peak_prominence</span><span class="p">,</span>
<span class="n">min_peak_distance</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
<span class="n">method</span><span class="o">=</span><span class="s1">&#39;linreg&#39;</span><span class="p">,</span>
<span class="n">plot</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Return the thickness from a min-max detection.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> wavelengths : array</span>
<span class="sd"> Wavelength values in nm.</span>
<span class="sd"> intensities : array</span>
<span class="sd"> Intensity values.</span>
<span class="sd"> refractive_index : scalar, optional</span>
<span class="sd"> Value of the refractive index of the medium.</span>
<span class="sd"> min_peak_prominence : scalar, optional</span>
<span class="sd"> Required prominence of peaks.</span>
<span class="sd"> min_peak_distance : scalar, optional</span>
<span class="sd"> Minimum distance between peaks.</span>
<span class="sd"> method : string, optional</span>
<span class="sd"> Either &#39;linreg&#39; for linear regression or &#39;ransac&#39;</span>
<span class="sd"> for Randon Sampling Consensus.</span>
<span class="sd"> plot : boolean, optional</span>
<span class="sd"> Show plots of peak detection and lin regression.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> results : Instance of `OptimizeResult` class.</span>
<span class="sd"> The attribute `thickness` gives the thickness value in nm.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> For more details about `min_peak_prominence` and `min_peak_distance`,</span>
<span class="sd"> see the documentation of `scipy.signal.find_peaks`. This function</span>
<span class="sd"> is used to find extrema.</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">setup_matplotlib</span><span class="p">()</span>
<span class="n">peaks_max</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">find_peaks</span><span class="p">(</span><span class="n">intensities</span><span class="p">,</span> <span class="n">prominence</span><span class="o">=</span><span class="n">min_peak_prominence</span><span class="p">,</span> <span class="n">distance</span><span class="o">=</span><span class="n">min_peak_distance</span><span class="p">)</span>
<span class="n">peaks_min</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">find_peaks</span><span class="p">(</span><span class="o">-</span><span class="n">intensities</span><span class="p">,</span> <span class="n">prominence</span><span class="o">=</span><span class="n">min_peak_prominence</span><span class="p">,</span> <span class="n">distance</span><span class="o">=</span><span class="n">min_peak_distance</span><span class="p">)</span>
<span class="n">peaks</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">peaks_min</span><span class="p">,</span> <span class="n">peaks_max</span><span class="p">))</span>
<span class="n">peaks</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>
<span class="n">k_values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">peaks</span><span class="p">))</span>
<span class="k">if</span> <span class="n">k_values</span><span class="o">.</span><span class="n">size</span> <span class="o">&lt;</span> <span class="mi">2</span><span class="p">:</span>
<span class="c1"># Can&#39;t fit if less than two points.</span>
<span class="k">return</span> <span class="n">OptimizeResult</span><span class="p">(</span><span class="n">thickness</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">refractive_index</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
<span class="c1">#refractive_index = refractive_index[peaks][::-1]</span>
<span class="n">n_over_lambda</span> <span class="o">=</span> <span class="n">refractive_index</span><span class="p">[</span><span class="n">peaks</span><span class="p">][::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">peaks</span><span class="p">][::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">n_over_lambda</span> <span class="o">=</span> <span class="n">refractive_index</span> <span class="o">/</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">peaks</span><span class="p">][::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="k">if</span> <span class="n">method</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="o">==</span> <span class="s1">&#39;ransac&#39;</span><span class="p">:</span>
<span class="n">residual_threshold</span> <span class="o">=</span> <span class="mf">4e-5</span>
<span class="n">min_samples</span> <span class="o">=</span> <span class="mi">2</span>
<span class="c1"># Scikit-image</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">column_stack</span><span class="p">([</span><span class="n">k_values</span><span class="p">,</span> <span class="n">n_over_lambda</span><span class="p">])</span>
<span class="n">model_robust</span><span class="p">,</span> <span class="n">inliers</span> <span class="o">=</span> <span class="n">ransac</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">LineModelND</span><span class="p">,</span>
<span class="n">min_samples</span><span class="o">=</span><span class="n">min_samples</span><span class="p">,</span>
<span class="n">residual_threshold</span><span class="o">=</span><span class="n">residual_threshold</span><span class="p">,</span>
<span class="n">max_trials</span><span class="o">=</span><span class="mi">100</span><span class="p">)</span>
<span class="n">slope</span> <span class="o">=</span> <span class="n">model_robust</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
<span class="n">thickness_minmax</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">slope</span> <span class="o">/</span> <span class="mi">4</span>
<span class="c1"># Scikit-learn</span>
<span class="c1">#X, y = k_values.reshape(-1, 1), 1/wavelengths[peaks][::-1]</span>
<span class="c1">## Fit line using all data</span>
<span class="c1">#lr = linear_model.LinearRegression()</span>
<span class="c1">#lr.fit(X, y)</span>
<span class="c1">#slransac = linear_model.RANSACRegressor(min_samples=min_samples,</span>
<span class="c1"># residual_threshold=residual_threshold)</span>
<span class="c1">#slransac.fit(X, y)</span>
<span class="c1">#inlier_mask = slransac.inlier_mask_</span>
<span class="c1">#outlier_mask = np.logical_not(inlier_mask)</span>
<span class="c1">## Predict data of estimated models</span>
<span class="c1">#line_X = np.arange(X.min(), X.max())[:, np.newaxis]</span>
<span class="c1">#line_y = lr.predict(line_X)</span>
<span class="c1">#line_y_ransac = slransac.predict(line_X)</span>
<span class="c1">#slope = slransac.estimator_.coef_[0]</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;extremum n°&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">&#39;$n$($\lambda$) / $\lambda$&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">inliers</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">data</span><span class="p">[</span><span class="n">inliers</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;xb&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Inliers&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="o">~</span><span class="n">inliers</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">data</span><span class="p">[</span><span class="o">~</span><span class="n">inliers</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">&#39;+r&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Outliers&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">k_values</span><span class="p">,</span> <span class="n">model_robust</span><span class="o">.</span><span class="n">predict_y</span><span class="p">(</span><span class="n">k_values</span><span class="p">),</span> <span class="s1">&#39;-g&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Fit&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Thickness = </span><span class="si">{</span><span class="n">thickness_minmax</span><span class="si">:</span><span class="s1">.2f</span><span class="si">}</span><span class="s1"> nm&#39;</span><span class="p">)</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">inspect</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">currentframe</span><span class="p">()</span><span class="o">.</span><span class="n">f_code</span><span class="o">.</span><span class="n">co_name</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="k">return</span> <span class="n">OptimizeResult</span><span class="p">(</span><span class="n">thickness</span><span class="o">=</span><span class="n">thickness_minmax</span><span class="p">,</span>
<span class="n">num_inliers</span><span class="o">=</span><span class="n">inliers</span><span class="o">.</span><span class="n">sum</span><span class="p">(),</span>
<span class="n">num_outliers</span><span class="o">=</span><span class="p">(</span><span class="o">~</span><span class="n">inliers</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(),</span>
<span class="n">peaks_max</span><span class="o">=</span><span class="n">peaks_max</span><span class="p">,</span>
<span class="n">peaks_min</span><span class="o">=</span><span class="n">peaks_min</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">method</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="o">==</span> <span class="s1">&#39;linreg&#39;</span><span class="p">:</span>
<span class="n">slope</span><span class="p">,</span> <span class="n">intercept</span><span class="p">,</span> <span class="n">r_value</span><span class="p">,</span> <span class="n">p_value</span><span class="p">,</span> <span class="n">std_err</span> <span class="o">=</span> <span class="n">stats</span><span class="o">.</span><span class="n">linregress</span><span class="p">(</span><span class="n">k_values</span><span class="p">,</span> <span class="n">n_over_lambda</span><span class="p">)</span>
<span class="c1">#mean_n = np.mean(refractive_index)</span>
<span class="n">thickness_minmax</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">slope</span> <span class="o">/</span> <span class="mi">4</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;extremum n°&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">&#39;$n$($\lambda$) / $\lambda$&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">k_values</span><span class="p">,</span> <span class="n">n_over_lambda</span><span class="p">,</span> <span class="s1">&#39;s&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Extrema&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">k_values</span><span class="p">,</span> <span class="n">intercept</span> <span class="o">+</span> <span class="n">k_values</span> <span class="o">*</span> <span class="n">slope</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Fit&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Thickness = </span><span class="si">{</span><span class="n">thickness_minmax</span><span class="si">:</span><span class="s1">.2f</span><span class="si">}</span><span class="s1"> nm&#39;</span><span class="p">)</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">inspect</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">currentframe</span><span class="p">()</span><span class="o">.</span><span class="n">f_code</span><span class="o">.</span><span class="n">co_name</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="k">return</span> <span class="n">OptimizeResult</span><span class="p">(</span><span class="n">thickness</span><span class="o">=</span><span class="n">thickness_minmax</span><span class="p">,</span>
<span class="n">peaks_max</span><span class="o">=</span><span class="n">peaks_max</span><span class="p">,</span>
<span class="n">peaks_min</span><span class="o">=</span><span class="n">peaks_min</span><span class="p">,</span>
<span class="n">stderr</span><span class="o">=</span><span class="n">std_err</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;Wrong method&#39;</span><span class="p">)</span></div>
</pre></div>
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<h1>Source code for optifik.scheludko</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">scipy.optimize</span><span class="w"> </span><span class="kn">import</span> <span class="n">curve_fit</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">.io</span><span class="w"> </span><span class="kn">import</span> <span class="n">load_spectrum</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">.utils</span><span class="w"> </span><span class="kn">import</span> <span class="n">OptimizeResult</span><span class="p">,</span> <span class="n">setup_matplotlib</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">.analysis</span><span class="w"> </span><span class="kn">import</span> <span class="n">finds_peak</span>
<span class="k">def</span><span class="w"> </span><span class="nf">_thicknesses_scheludko_at_order</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span>
<span class="n">intensities</span><span class="p">,</span>
<span class="n">interference_order</span><span class="p">,</span>
<span class="n">refractive_index</span><span class="p">,</span>
<span class="n">intensities_void</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Compute thicknesses vs wavelength for a given interference order.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> wavelengths : array</span>
<span class="sd"> Wavelength values in nm.</span>
<span class="sd"> intensities : array</span>
<span class="sd"> Intensity values.</span>
<span class="sd"> interference_order : int</span>
<span class="sd"> Interference order.</span>
<span class="sd"> refractive_index : array_like (or float)</span>
<span class="sd"> Refractive index.</span>
<span class="sd"> intensities_void : array, optional</span>
<span class="sd"> Intensities of void.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> thicknesses : array</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">intensities_void</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">Imin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">Imin</span> <span class="o">=</span> <span class="n">intensities_void</span>
<span class="n">n</span> <span class="o">=</span> <span class="n">refractive_index</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">interference_order</span>
<span class="n">I_norm</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">intensities</span><span class="p">)</span> <span class="o">-</span> <span class="n">Imin</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">intensities</span><span class="p">)</span> <span class="o">-</span> <span class="n">Imin</span><span class="p">)</span>
<span class="n">prefactor</span> <span class="o">=</span> <span class="n">wavelengths</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">n</span><span class="p">)</span>
<span class="n">argument</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">I_norm</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">I_norm</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">n</span><span class="o">**</span><span class="mi">2</span><span class="p">)))</span>
<span class="k">if</span> <span class="n">m</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">term1</span> <span class="o">=</span> <span class="p">(</span><span class="n">m</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">term1</span> <span class="o">=</span> <span class="p">((</span><span class="n">m</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
<span class="n">term2</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="n">m</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">arcsin</span><span class="p">(</span><span class="n">argument</span><span class="p">)</span>
<span class="k">return</span> <span class="n">prefactor</span> <span class="o">*</span> <span class="p">(</span><span class="n">term1</span> <span class="o">+</span> <span class="n">term2</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">_Delta</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span> <span class="n">thickness</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">,</span> <span class="n">refractive_index</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Compute the Delta values.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> wavelengths : array</span>
<span class="sd"> Wavelength values in nm.</span>
<span class="sd"> thickness : array_like (or float)</span>
<span class="sd"> Film thickness.</span>
<span class="sd"> interference_order : int</span>
<span class="sd"> Interference order.</span>
<span class="sd"> refractive_index : array_like (or float)</span>
<span class="sd"> Refractive index.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> ndarray</span>
<span class="sd"> Delta values.</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="c1"># ensure that the entries are numpy arrays</span>
<span class="n">wavelengths</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">)</span>
<span class="n">h</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">thickness</span><span class="p">)</span>
<span class="n">n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">refractive_index</span><span class="p">)</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">interference_order</span>
<span class="c1"># Calculation of p as a function of the parity of m</span>
<span class="k">if</span> <span class="n">m</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">m</span> <span class="o">/</span> <span class="mi">2</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">p</span> <span class="o">=</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
<span class="c1"># Calculation of alpha</span>
<span class="n">alpha</span> <span class="o">=</span> <span class="p">((</span><span class="n">n</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">n</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
<span class="c1"># Argument of sinus</span>
<span class="n">angle</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="n">h</span> <span class="o">/</span> <span class="n">wavelengths</span><span class="p">)</span> <span class="o">-</span> <span class="n">p</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
<span class="c1"># A = sin²(argument)</span>
<span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
<span class="c1"># Final calcuation of Delta</span>
<span class="k">return</span> <span class="p">(</span><span class="n">A</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">alpha</span><span class="p">))</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">A</span> <span class="o">*</span> <span class="n">alpha</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">_Delta_fit</span><span class="p">(</span><span class="n">xdata</span><span class="p">,</span> <span class="n">thickness</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Wrapper on Delta() for curve_fit.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> xdata : tuple</span>
<span class="sd"> (wavelengths, refractive_index)</span>
<span class="sd"> thickness : array_like (or float)</span>
<span class="sd"> Film thickness.</span>
<span class="sd"> interference_order : int</span>
<span class="sd"> Interference order.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> ndarray</span>
<span class="sd"> Delta values.</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">lambdas</span><span class="p">,</span> <span class="n">r_index</span> <span class="o">=</span> <span class="n">xdata</span>
<span class="k">return</span> <span class="n">_Delta</span><span class="p">(</span><span class="n">lambdas</span><span class="p">,</span> <span class="n">thickness</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">,</span> <span class="n">r_index</span><span class="p">)</span>
<div class="viewcode-block" id="get_default_start_stop_wavelengths">
<a class="viewcode-back" href="../../api_reference.html#optifik.scheludko.get_default_start_stop_wavelengths">[docs]</a>
<span class="k">def</span><span class="w"> </span><span class="nf">get_default_start_stop_wavelengths</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span>
<span class="n">intensities</span><span class="p">,</span>
<span class="n">refractive_index</span><span class="p">,</span>
<span class="n">min_peak_prominence</span><span class="p">,</span>
<span class="n">plot</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Returns the start and stop wavelength values of the last monotonic branch.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> wavelengths : array</span>
<span class="sd"> Wavelength values in nm.</span>
<span class="sd"> intensities : array</span>
<span class="sd"> Intensity values.</span>
<span class="sd"> refractive_index : scalar, optional</span>
<span class="sd"> Value of the refractive index of the medium.</span>
<span class="sd"> min_peak_prominence : scalar</span>
<span class="sd"> Required prominence of peaks.</span>
<span class="sd"> plot : bool, optional</span>
<span class="sd"> Display a curve, useful for checking or debuging. The default is None.</span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> RuntimeError</span>
<span class="sd"> if at least one maximum and one minimum are not detected.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> wavelength_start : scalar</span>
<span class="sd"> wavelength_stop : scalar</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="c1"># idx_min idx max</span>
<span class="n">idx_peaks_min</span><span class="p">,</span> <span class="n">idx_peaks_max</span> <span class="o">=</span> <span class="n">finds_peak</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span> <span class="n">intensities</span><span class="p">,</span>
<span class="n">min_peak_prominence</span><span class="o">=</span><span class="n">min_peak_prominence</span><span class="p">,</span>
<span class="n">plot</span><span class="o">=</span><span class="n">plot</span><span class="p">)</span>
<span class="n">failure</span><span class="p">,</span> <span class="n">message</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span> <span class="s1">&#39;&#39;</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">idx_peaks_min</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">message</span> <span class="o">+=</span> <span class="s1">&#39;Failed to detect at least one minimum. &#39;</span>
<span class="n">failure</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">idx_peaks_max</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">message</span> <span class="o">+=</span> <span class="s1">&#39;Failed to detect at least one maximum. &#39;</span>
<span class="n">failure</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">if</span> <span class="n">failure</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="n">message</span><span class="p">)</span>
<span class="c1"># Get the last oscillation peaks</span>
<span class="n">lambda_min</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">idx_peaks_min</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span>
<span class="n">lambda_max</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">idx_peaks_max</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span>
<span class="c1"># Order them</span>
<span class="n">wavelength_start</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">lambda_min</span><span class="p">,</span> <span class="n">lambda_max</span><span class="p">)</span>
<span class="n">wavelength_stop</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">lambda_min</span><span class="p">,</span> <span class="n">lambda_max</span><span class="p">)</span>
<span class="k">return</span> <span class="n">wavelength_start</span><span class="p">,</span> <span class="n">wavelength_stop</span></div>
<div class="viewcode-block" id="thickness_from_scheludko">
<a class="viewcode-back" href="../../api_reference.html#optifik.scheludko.thickness_from_scheludko">[docs]</a>
<span class="k">def</span><span class="w"> </span><span class="nf">thickness_from_scheludko</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span>
<span class="n">intensities</span><span class="p">,</span>
<span class="n">refractive_index</span><span class="p">,</span>
<span class="n">wavelength_start</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">wavelength_stop</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">interference_order</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">intensities_void</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">plot</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Compute the film thickness based on Scheludko method.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> wavelengths : array</span>
<span class="sd"> Wavelength values in nm.</span>
<span class="sd"> intensities : array</span>
<span class="sd"> Intensity values.</span>
<span class="sd"> refractive_index : scalar, optional</span>
<span class="sd"> Value of the refractive index of the medium.</span>
<span class="sd"> wavelength_start : scalar, optional</span>
<span class="sd"> Starting value of a monotonic branch.</span>
<span class="sd"> Mandatory if interference_order != 0.</span>
<span class="sd"> wavelength_stop : scalar, optional</span>
<span class="sd"> Stoping value of a monotonic branch.</span>
<span class="sd"> Mandatory if interference_order != 0.</span>
<span class="sd"> interference_order : scalar, optional</span>
<span class="sd"> Interference order, zero or positive integer.</span>
<span class="sd"> If set to None, the value is guessed.</span>
<span class="sd"> intensities_void : array, optional</span>
<span class="sd"> Intensity in absence of a film.</span>
<span class="sd"> Mandatory if interference_order == 0.</span>
<span class="sd"> plot : bool, optional</span>
<span class="sd"> Display a curve, useful for checking or debuging. The default is None.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> results : Instance of `OptimizeResult` class.</span>
<span class="sd"> The attribute `thickness` gives the thickness value in nm.</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">setup_matplotlib</span><span class="p">()</span>
<span class="k">if</span> <span class="n">interference_order</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">interference_order</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">if</span> <span class="n">wavelength_stop</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">wavelength_start</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;wavelength_start and wavelength_stop must be passed for interference_order != 0.&#39;</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="n">wavelength_start</span> <span class="o">&gt;</span> <span class="n">wavelength_stop</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;wavelength_start and wavelength_stop are swapped.&#39;</span><span class="p">)</span>
<span class="n">r_index</span> <span class="o">=</span> <span class="n">refractive_index</span>
<span class="c1"># Handle the interference order</span>
<span class="k">if</span> <span class="n">interference_order</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="c1"># A bit extreme...</span>
<span class="n">max_tested_order</span> <span class="o">=</span> <span class="mi">12</span>
<span class="c1"># mask input data</span>
<span class="n">mask</span> <span class="o">=</span> <span class="p">(</span><span class="n">wavelengths</span> <span class="o">&gt;=</span> <span class="n">wavelength_start</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">(</span><span class="n">wavelengths</span> <span class="o">&lt;=</span> <span class="n">wavelength_stop</span><span class="p">)</span>
<span class="n">wavelengths_masked</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">r_index_masked</span> <span class="o">=</span> <span class="n">r_index</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">intensities_masked</span> <span class="o">=</span> <span class="n">intensities</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">min_difference</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span>
<span class="n">thickness_values</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$h$ ($\mathrm{{nm}}$)&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$\lambda$ ($ \mathrm</span><span class="si">{nm}</span><span class="s1"> $)&#39;</span><span class="p">)</span>
<span class="k">for</span> <span class="n">_order</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_tested_order</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
<span class="n">h_values</span> <span class="o">=</span> <span class="n">_thicknesses_scheludko_at_order</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span>
<span class="n">intensities_masked</span><span class="p">,</span>
<span class="n">_order</span><span class="p">,</span>
<span class="n">r_index_masked</span><span class="p">)</span>
<span class="n">difference</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">h_values</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">h_values</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;h-difference for m=</span><span class="si">{</span><span class="n">_order</span><span class="si">}</span><span class="s2">: </span><span class="si">{</span><span class="n">difference</span><span class="si">:</span><span class="s2">.1f</span><span class="si">}</span><span class="s2"> nm&quot;</span><span class="p">)</span>
<span class="k">if</span> <span class="n">difference</span> <span class="o">&lt;</span> <span class="n">min_difference</span><span class="p">:</span>
<span class="n">min_difference</span> <span class="o">=</span> <span class="n">difference</span>
<span class="n">interference_order</span> <span class="o">=</span> <span class="n">_order</span>
<span class="n">thickness_values</span> <span class="o">=</span> <span class="n">h_values</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">h_values</span><span class="p">,</span> <span class="s1">&#39;.&#39;</span><span class="p">,</span>
<span class="n">markersize</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">f</span><span class="s2">&quot;Order=</span><span class="si">{</span><span class="n">_order</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">interference_order</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">min_peak_prominence</span> <span class="o">=</span> <span class="mf">0.02</span>
<span class="n">peaks_min</span><span class="p">,</span> <span class="n">peaks_max</span> <span class="o">=</span> <span class="n">finds_peak</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span> <span class="n">intensities</span><span class="p">,</span>
<span class="n">min_peak_prominence</span><span class="o">=</span><span class="n">min_peak_prominence</span><span class="p">,</span>
<span class="n">plot</span><span class="o">=</span><span class="n">plot</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">peaks_max</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s1">&#39;Failed to detect a single maximum peak.&#39;</span><span class="p">)</span>
<span class="n">lambda_unique</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">peaks_max</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span>
<span class="c1"># keep rhs from the maximum</span>
<span class="n">mask</span> <span class="o">=</span> <span class="n">wavelengths</span> <span class="o">&gt;=</span> <span class="n">lambda_unique</span>
<span class="n">wavelengths_masked</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">r_index_masked</span> <span class="o">=</span> <span class="n">r_index</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">intensities_masked</span> <span class="o">=</span> <span class="n">intensities</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">intensities_void_masked</span> <span class="o">=</span> <span class="n">intensities_void</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">interference_order</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">thickness_values</span> <span class="o">=</span> <span class="n">_thicknesses_scheludko_at_order</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span>
<span class="n">intensities_masked</span><span class="p">,</span>
<span class="n">interference_order</span><span class="p">,</span>
<span class="n">r_index_masked</span><span class="p">,</span>
<span class="n">intensities_void</span><span class="o">=</span><span class="n">intensities_void_masked</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">interference_order</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">h_values</span> <span class="o">=</span> <span class="n">_thicknesses_scheludko_at_order</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span>
<span class="n">intensities_masked</span><span class="p">,</span>
<span class="n">interference_order</span><span class="p">,</span>
<span class="n">r_index_masked</span><span class="p">)</span>
<span class="n">thickness_values</span> <span class="o">=</span> <span class="n">h_values</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;interference_order must be &gt;= 0.&#39;</span><span class="p">)</span>
<span class="c1"># Compute the thickness for the selected order</span>
<span class="c1"># Delta</span>
<span class="k">if</span> <span class="n">interference_order</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">num</span> <span class="o">=</span> <span class="n">intensities_masked</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities_void_masked</span><span class="p">)</span>
<span class="n">denom</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">intensities_masked</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities_void_masked</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">num</span> <span class="o">=</span> <span class="n">intensities_masked</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities_masked</span><span class="p">)</span>
<span class="n">denom</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">intensities_masked</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities_masked</span><span class="p">)</span>
<span class="n">Delta_from_data</span> <span class="o">=</span> <span class="n">num</span> <span class="o">/</span> <span class="n">denom</span>
<span class="c1"># Delta_from_data = (intensities_masked -np.min(intensities_masked))/(np.max(intensities_masked) -np.min(intensities_masked))</span>
<span class="c1"># Delta_from_data = (intensities_raw_masked -np.min(intensities_raw_masked))/(np.max(intensities_raw_masked) -np.min(intensities_raw_masked))</span>
<span class="n">DeltaScheludko</span> <span class="o">=</span> <span class="n">_Delta</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span>
<span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">thickness_values</span><span class="p">),</span>
<span class="n">interference_order</span><span class="p">,</span>
<span class="n">r_index_masked</span><span class="p">)</span>
<span class="n">xdata</span> <span class="o">=</span> <span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">r_index_masked</span><span class="p">)</span>
<span class="n">popt</span><span class="p">,</span> <span class="n">pcov</span> <span class="o">=</span> <span class="n">curve_fit</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">h</span><span class="p">:</span> <span class="n">_Delta_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">),</span> <span class="n">xdata</span><span class="p">,</span> <span class="n">Delta_from_data</span><span class="p">,</span> <span class="n">p0</span><span class="o">=</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">thickness_values</span><span class="p">)])</span>
<span class="n">fitted_h</span> <span class="o">=</span> <span class="n">popt</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">std_err</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">pcov</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">])</span>
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
<span class="n">Delta_values</span> <span class="o">=</span> <span class="n">_Delta</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">fitted_h</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">,</span> <span class="n">r_index_masked</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">Delta_from_data</span><span class="p">,</span>
<span class="s1">&#39;bo-&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s1">&#39;$\mathrm{{Smoothed}}\ \mathrm{{Data}}$&#39;</span><span class="p">)</span>
<span class="c1"># Scheludko</span>
<span class="n">label</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;$\mathrm</span><span class="se">{{</span><span class="s1">Scheludko</span><span class="se">}}</span><span class="s1">\ (h = </span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">thickness_values</span><span class="p">)</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1"> \pm </span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">thickness_values</span><span class="p">)</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1">\ \mathrm</span><span class="se">{{</span><span class="s1">nm</span><span class="se">}}</span><span class="s1">)$&#39;</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">DeltaScheludko</span><span class="p">,</span>
<span class="s1">&#39;go-&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">label</span><span class="p">)</span>
<span class="c1"># Fit</span>
<span class="n">label</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;$\mathrm</span><span class="se">{{</span><span class="s1">Fit</span><span class="se">}}</span><span class="s1">\ (h = </span><span class="si">{</span><span class="n">fitted_h</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1">\pm </span><span class="si">{</span><span class="n">std_err</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1"> \ \mathrm</span><span class="se">{{</span><span class="s1">nm</span><span class="se">}}</span><span class="s1">)$&#39;</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">Delta_values</span><span class="p">,</span>
<span class="s1">&#39;ro-&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="n">label</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$\Delta$&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$\lambda$ ($ \mathrm</span><span class="si">{nm}</span><span class="s1"> $)&#39;</span><span class="p">)</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">inspect</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">currentframe</span><span class="p">()</span><span class="o">.</span><span class="n">f_code</span><span class="o">.</span><span class="n">co_name</span><span class="p">)</span>
<span class="k">return</span> <span class="n">OptimizeResult</span><span class="p">(</span><span class="n">thickness</span><span class="o">=</span><span class="n">fitted_h</span><span class="p">,</span> <span class="n">stderr</span><span class="o">=</span><span class="n">std_err</span><span class="p">)</span></div>
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&#169;2025, F. Boulogne et al..
|
Powered by <a href="https://www.sphinx-doc.org/">Sphinx 8.2.3</a>
&amp; <a href="https://alabaster.readthedocs.io">Alabaster 1.0.0</a>
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API Reference
=============
Below is the complete reference for Optifik's public API.
io
--
.. automodule:: optifik.io
:members:
:undoc-members:
:show-inheritance:
fft
---
.. automodule:: optifik.fft
:members:
:undoc-members:
:show-inheritance:
minmax
------
.. automodule:: optifik.minmax
:members:
:undoc-members:
:show-inheritance:
scheludko
---------
.. automodule:: optifik.scheludko
:members:
:undoc-members:
:show-inheritance:

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Examples
========
Basic Optimization
------------------
Here's a simple example using Optifik to solve a quadratic function.
.. code-block:: python
from optifik import minimize
def quadratic(x):
return (x - 3) ** 2
result = minimize(quadratic, x0=0)
print(result)
Constrained Optimization
------------------------
.. code-block:: python
from optifik import minimize
def objective(x):
return x[0] ** 2 + x[1] ** 2
def constraint(x):
return x[0] + x[1] - 1
result = minimize(objective, x0=[0, 0], constraints=[constraint])
print(result)

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Optifik Documentation
=====================
Welcome to the documentation for **Optifik**, a Python library for
Contents
--------
.. toctree::
:maxdepth: 2
:caption: Documentation
installation
api_reference
examples
Indices and tables
------------------
* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`

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Installation
============
You can install Optifik using `pip`:
.. code-block:: bash
pip install optifik
Alternatively, you can install it from source:
.. code-block:: bash
git clone https://github.com/yourusername/optifik.git
cd optifik
pip install -e .
Requirements
------------
- Python >= 3.8
- NumPy >= 1.21
Optional for extended functionality:
- SciPy
- Matplotlib

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}
dt:target, .highlight {
background: #FAF3E8;
}
div.warning {
background-color: #FCC;
border: 1px solid #FAA;
}
div.danger {
background-color: #FCC;
border: 1px solid #FAA;
-moz-box-shadow: 2px 2px 4px #D52C2C;
-webkit-box-shadow: 2px 2px 4px #D52C2C;
box-shadow: 2px 2px 4px #D52C2C;
}
div.error {
background-color: #FCC;
border: 1px solid #FAA;
-moz-box-shadow: 2px 2px 4px #D52C2C;
-webkit-box-shadow: 2px 2px 4px #D52C2C;
box-shadow: 2px 2px 4px #D52C2C;
}
div.caution {
background-color: #FCC;
border: 1px solid #FAA;
}
div.attention {
background-color: #FCC;
border: 1px solid #FAA;
}
div.important {
background-color: #EEE;
border: 1px solid #CCC;
}
div.note {
background-color: #EEE;
border: 1px solid #CCC;
}
div.tip {
background-color: #EEE;
border: 1px solid #CCC;
}
div.hint {
background-color: #EEE;
border: 1px solid #CCC;
}
div.seealso {
background-color: #EEE;
border: 1px solid #CCC;
}
div.topic {
background-color: #EEE;
}
p.admonition-title {
display: inline;
}
p.admonition-title:after {
content: ":";
}
pre, tt, code {
font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace;
font-size: 0.9em;
}
.hll {
background-color: #FFC;
margin: 0 -12px;
padding: 0 12px;
display: block;
}
img.screenshot {
}
tt.descname, tt.descclassname, code.descname, code.descclassname {
font-size: 0.95em;
}
tt.descname, code.descname {
padding-right: 0.08em;
}
img.screenshot {
-moz-box-shadow: 2px 2px 4px #EEE;
-webkit-box-shadow: 2px 2px 4px #EEE;
box-shadow: 2px 2px 4px #EEE;
}
table.docutils {
border: 1px solid #888;
-moz-box-shadow: 2px 2px 4px #EEE;
-webkit-box-shadow: 2px 2px 4px #EEE;
box-shadow: 2px 2px 4px #EEE;
}
table.docutils td, table.docutils th {
border: 1px solid #888;
padding: 0.25em 0.7em;
}
table.field-list, table.footnote {
border: none;
-moz-box-shadow: none;
-webkit-box-shadow: none;
box-shadow: none;
}
table.footnote {
margin: 15px 0;
width: 100%;
border: 1px solid #EEE;
background: #FDFDFD;
font-size: 0.9em;
}
table.footnote + table.footnote {
margin-top: -15px;
border-top: none;
}
table.field-list th {
padding: 0 0.8em 0 0;
}
table.field-list td {
padding: 0;
}
table.field-list p {
margin-bottom: 0.8em;
}
/* Cloned from
* https://github.com/sphinx-doc/sphinx/commit/ef60dbfce09286b20b7385333d63a60321784e68
*/
.field-name {
-moz-hyphens: manual;
-ms-hyphens: manual;
-webkit-hyphens: manual;
hyphens: manual;
}
table.footnote td.label {
width: .1px;
padding: 0.3em 0 0.3em 0.5em;
}
table.footnote td {
padding: 0.3em 0.5em;
}
dl {
margin-left: 0;
margin-right: 0;
margin-top: 0;
padding: 0;
}
dl dd {
margin-left: 30px;
}
blockquote {
margin: 0 0 0 30px;
padding: 0;
}
ul, ol {
/* Matches the 30px from the narrow-screen "li > ul" selector below */
margin: 10px 0 10px 30px;
padding: 0;
}
pre {
background: unset;
padding: 7px 30px;
margin: 15px 0px;
line-height: 1.3em;
}
div.viewcode-block:target {
background: #ffd;
}
dl pre, blockquote pre, li pre {
margin-left: 0;
padding-left: 30px;
}
tt, code {
background-color: #ecf0f3;
color: #222;
/* padding: 1px 2px; */
}
tt.xref, code.xref, a tt {
background-color: #FBFBFB;
border-bottom: 1px solid #fff;
}
a.reference {
text-decoration: none;
border-bottom: 1px dotted #004B6B;
}
a.reference:hover {
border-bottom: 1px solid #6D4100;
}
/* Don't put an underline on images */
a.image-reference, a.image-reference:hover {
border-bottom: none;
}
a.footnote-reference {
text-decoration: none;
font-size: 0.7em;
vertical-align: top;
border-bottom: 1px dotted #004B6B;
}
a.footnote-reference:hover {
border-bottom: 1px solid #6D4100;
}
a:hover tt, a:hover code {
background: #EEE;
}
@media screen and (max-width: 940px) {
body {
margin: 0;
padding: 20px 30px;
}
div.documentwrapper {
float: none;
background: #fff;
margin-left: 0;
margin-top: 0;
margin-right: 0;
margin-bottom: 0;
}
div.sphinxsidebar {
display: block;
float: none;
width: unset;
margin: 50px -30px -20px -30px;
padding: 10px 20px;
background: #333;
color: #FFF;
}
div.sphinxsidebar h3, div.sphinxsidebar h4, div.sphinxsidebar p,
div.sphinxsidebar h3 a {
color: #fff;
}
div.sphinxsidebar a {
color: #AAA;
}
div.sphinxsidebar p.logo {
display: none;
}
div.document {
width: 100%;
margin: 0;
}
div.footer {
display: none;
}
div.bodywrapper {
margin: 0;
}
div.body {
min-height: 0;
min-width: auto; /* fixes width on small screens, breaks .hll */
padding: 0;
}
.hll {
/* "fixes" the breakage */
width: max-content;
}
.rtd_doc_footer {
display: none;
}
.document {
width: auto;
}
.footer {
width: auto;
}
.github {
display: none;
}
ul {
margin-left: 0;
}
li > ul {
/* Matches the 30px from the "ul, ol" selector above */
margin-left: 30px;
}
}
/* misc. */
.revsys-inline {
display: none!important;
}
/* Hide ugly table cell borders in ..bibliography:: directive output */
table.docutils.citation, table.docutils.citation td, table.docutils.citation th {
border: none;
/* Below needed in some edge cases; if not applied, bottom shadows appear */
-moz-box-shadow: none;
-webkit-box-shadow: none;
box-shadow: none;
}
/* relbar */
.related {
line-height: 30px;
width: 100%;
font-size: 0.9rem;
}
.related.top {
border-bottom: 1px solid #EEE;
margin-bottom: 20px;
}
.related.bottom {
border-top: 1px solid #EEE;
}
.related ul {
padding: 0;
margin: 0;
list-style: none;
}
.related li {
display: inline;
}
nav#rellinks {
float: right;
}
nav#rellinks li+li:before {
content: "|";
}
nav#breadcrumbs li+li:before {
content: "\00BB";
}
/* Hide certain items when printing */
@media print {
div.related {
display: none;
}
}
img.github {
position: absolute;
top: 0;
border: 0;
right: 0;
}

906
docs/_build/html/_static/basic.css vendored Normal file
View file

@ -0,0 +1,906 @@
/*
* Sphinx stylesheet -- basic theme.
*/
/* -- main layout ----------------------------------------------------------- */
div.clearer {
clear: both;
}
div.section::after {
display: block;
content: '';
clear: left;
}
/* -- relbar ---------------------------------------------------------------- */
div.related {
width: 100%;
font-size: 90%;
}
div.related h3 {
display: none;
}
div.related ul {
margin: 0;
padding: 0 0 0 10px;
list-style: none;
}
div.related li {
display: inline;
}
div.related li.right {
float: right;
margin-right: 5px;
}
/* -- sidebar --------------------------------------------------------------- */
div.sphinxsidebarwrapper {
padding: 10px 5px 0 10px;
}
div.sphinxsidebar {
float: left;
width: 230px;
margin-left: -100%;
font-size: 90%;
word-wrap: break-word;
overflow-wrap : break-word;
}
div.sphinxsidebar ul {
list-style: none;
}
div.sphinxsidebar ul ul,
div.sphinxsidebar ul.want-points {
margin-left: 20px;
list-style: square;
}
div.sphinxsidebar ul ul {
margin-top: 0;
margin-bottom: 0;
}
div.sphinxsidebar form {
margin-top: 10px;
}
div.sphinxsidebar input {
border: 1px solid #98dbcc;
font-family: sans-serif;
font-size: 1em;
}
div.sphinxsidebar #searchbox form.search {
overflow: hidden;
}
div.sphinxsidebar #searchbox input[type="text"] {
float: left;
width: 80%;
padding: 0.25em;
box-sizing: border-box;
}
div.sphinxsidebar #searchbox input[type="submit"] {
float: left;
width: 20%;
border-left: none;
padding: 0.25em;
box-sizing: border-box;
}
img {
border: 0;
max-width: 100%;
}
/* -- search page ----------------------------------------------------------- */
ul.search {
margin-top: 10px;
}
ul.search li {
padding: 5px 0;
}
ul.search li a {
font-weight: bold;
}
ul.search li p.context {
color: #888;
margin: 2px 0 0 30px;
text-align: left;
}
ul.keywordmatches li.goodmatch a {
font-weight: bold;
}
/* -- index page ------------------------------------------------------------ */
table.contentstable {
width: 90%;
margin-left: auto;
margin-right: auto;
}
table.contentstable p.biglink {
line-height: 150%;
}
a.biglink {
font-size: 1.3em;
}
span.linkdescr {
font-style: italic;
padding-top: 5px;
font-size: 90%;
}
/* -- general index --------------------------------------------------------- */
table.indextable {
width: 100%;
}
table.indextable td {
text-align: left;
vertical-align: top;
}
table.indextable ul {
margin-top: 0;
margin-bottom: 0;
list-style-type: none;
}
table.indextable > tbody > tr > td > ul {
padding-left: 0em;
}
table.indextable tr.pcap {
height: 10px;
}
table.indextable tr.cap {
margin-top: 10px;
background-color: #f2f2f2;
}
img.toggler {
margin-right: 3px;
margin-top: 3px;
cursor: pointer;
}
div.modindex-jumpbox {
border-top: 1px solid #ddd;
border-bottom: 1px solid #ddd;
margin: 1em 0 1em 0;
padding: 0.4em;
}
div.genindex-jumpbox {
border-top: 1px solid #ddd;
border-bottom: 1px solid #ddd;
margin: 1em 0 1em 0;
padding: 0.4em;
}
/* -- domain module index --------------------------------------------------- */
table.modindextable td {
padding: 2px;
border-collapse: collapse;
}
/* -- general body styles --------------------------------------------------- */
div.body {
min-width: inherit;
max-width: 800px;
}
div.body p, div.body dd, div.body li, div.body blockquote {
-moz-hyphens: auto;
-ms-hyphens: auto;
-webkit-hyphens: auto;
hyphens: auto;
}
a.headerlink {
visibility: hidden;
}
a:visited {
color: #551A8B;
}
h1:hover > a.headerlink,
h2:hover > a.headerlink,
h3:hover > a.headerlink,
h4:hover > a.headerlink,
h5:hover > a.headerlink,
h6:hover > a.headerlink,
dt:hover > a.headerlink,
caption:hover > a.headerlink,
p.caption:hover > a.headerlink,
div.code-block-caption:hover > a.headerlink {
visibility: visible;
}
div.body p.caption {
text-align: inherit;
}
div.body td {
text-align: left;
}
.first {
margin-top: 0 !important;
}
p.rubric {
margin-top: 30px;
font-weight: bold;
}
img.align-left, figure.align-left, .figure.align-left, object.align-left {
clear: left;
float: left;
margin-right: 1em;
}
img.align-right, figure.align-right, .figure.align-right, object.align-right {
clear: right;
float: right;
margin-left: 1em;
}
img.align-center, figure.align-center, .figure.align-center, object.align-center {
display: block;
margin-left: auto;
margin-right: auto;
}
img.align-default, figure.align-default, .figure.align-default {
display: block;
margin-left: auto;
margin-right: auto;
}
.align-left {
text-align: left;
}
.align-center {
text-align: center;
}
.align-default {
text-align: center;
}
.align-right {
text-align: right;
}
/* -- sidebars -------------------------------------------------------------- */
div.sidebar,
aside.sidebar {
margin: 0 0 0.5em 1em;
border: 1px solid #ddb;
padding: 7px;
background-color: #ffe;
width: 40%;
float: right;
clear: right;
overflow-x: auto;
}
p.sidebar-title {
font-weight: bold;
}
nav.contents,
aside.topic,
div.admonition, div.topic, blockquote {
clear: left;
}
/* -- topics ---------------------------------------------------------------- */
nav.contents,
aside.topic,
div.topic {
border: 1px solid #ccc;
padding: 7px;
margin: 10px 0 10px 0;
}
p.topic-title {
font-size: 1.1em;
font-weight: bold;
margin-top: 10px;
}
/* -- admonitions ----------------------------------------------------------- */
div.admonition {
margin-top: 10px;
margin-bottom: 10px;
padding: 7px;
}
div.admonition dt {
font-weight: bold;
}
p.admonition-title {
margin: 0px 10px 5px 0px;
font-weight: bold;
}
div.body p.centered {
text-align: center;
margin-top: 25px;
}
/* -- content of sidebars/topics/admonitions -------------------------------- */
div.sidebar > :last-child,
aside.sidebar > :last-child,
nav.contents > :last-child,
aside.topic > :last-child,
div.topic > :last-child,
div.admonition > :last-child {
margin-bottom: 0;
}
div.sidebar::after,
aside.sidebar::after,
nav.contents::after,
aside.topic::after,
div.topic::after,
div.admonition::after,
blockquote::after {
display: block;
content: '';
clear: both;
}
/* -- tables ---------------------------------------------------------------- */
table.docutils {
margin-top: 10px;
margin-bottom: 10px;
border: 0;
border-collapse: collapse;
}
table.align-center {
margin-left: auto;
margin-right: auto;
}
table.align-default {
margin-left: auto;
margin-right: auto;
}
table caption span.caption-number {
font-style: italic;
}
table caption span.caption-text {
}
table.docutils td, table.docutils th {
padding: 1px 8px 1px 5px;
border-top: 0;
border-left: 0;
border-right: 0;
border-bottom: 1px solid #aaa;
}
th {
text-align: left;
padding-right: 5px;
}
table.citation {
border-left: solid 1px gray;
margin-left: 1px;
}
table.citation td {
border-bottom: none;
}
th > :first-child,
td > :first-child {
margin-top: 0px;
}
th > :last-child,
td > :last-child {
margin-bottom: 0px;
}
/* -- figures --------------------------------------------------------------- */
div.figure, figure {
margin: 0.5em;
padding: 0.5em;
}
div.figure p.caption, figcaption {
padding: 0.3em;
}
div.figure p.caption span.caption-number,
figcaption span.caption-number {
font-style: italic;
}
div.figure p.caption span.caption-text,
figcaption span.caption-text {
}
/* -- field list styles ----------------------------------------------------- */
table.field-list td, table.field-list th {
border: 0 !important;
}
.field-list ul {
margin: 0;
padding-left: 1em;
}
.field-list p {
margin: 0;
}
.field-name {
-moz-hyphens: manual;
-ms-hyphens: manual;
-webkit-hyphens: manual;
hyphens: manual;
}
/* -- hlist styles ---------------------------------------------------------- */
table.hlist {
margin: 1em 0;
}
table.hlist td {
vertical-align: top;
}
/* -- object description styles --------------------------------------------- */
.sig {
font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace;
}
.sig-name, code.descname {
background-color: transparent;
font-weight: bold;
}
.sig-name {
font-size: 1.1em;
}
code.descname {
font-size: 1.2em;
}
.sig-prename, code.descclassname {
background-color: transparent;
}
.optional {
font-size: 1.3em;
}
.sig-paren {
font-size: larger;
}
.sig-param.n {
font-style: italic;
}
/* C++ specific styling */
.sig-inline.c-texpr,
.sig-inline.cpp-texpr {
font-family: unset;
}
.sig.c .k, .sig.c .kt,
.sig.cpp .k, .sig.cpp .kt {
color: #0033B3;
}
.sig.c .m,
.sig.cpp .m {
color: #1750EB;
}
.sig.c .s, .sig.c .sc,
.sig.cpp .s, .sig.cpp .sc {
color: #067D17;
}
/* -- other body styles ----------------------------------------------------- */
ol.arabic {
list-style: decimal;
}
ol.loweralpha {
list-style: lower-alpha;
}
ol.upperalpha {
list-style: upper-alpha;
}
ol.lowerroman {
list-style: lower-roman;
}
ol.upperroman {
list-style: upper-roman;
}
:not(li) > ol > li:first-child > :first-child,
:not(li) > ul > li:first-child > :first-child {
margin-top: 0px;
}
:not(li) > ol > li:last-child > :last-child,
:not(li) > ul > li:last-child > :last-child {
margin-bottom: 0px;
}
ol.simple ol p,
ol.simple ul p,
ul.simple ol p,
ul.simple ul p {
margin-top: 0;
}
ol.simple > li:not(:first-child) > p,
ul.simple > li:not(:first-child) > p {
margin-top: 0;
}
ol.simple p,
ul.simple p {
margin-bottom: 0;
}
aside.footnote > span,
div.citation > span {
float: left;
}
aside.footnote > span:last-of-type,
div.citation > span:last-of-type {
padding-right: 0.5em;
}
aside.footnote > p {
margin-left: 2em;
}
div.citation > p {
margin-left: 4em;
}
aside.footnote > p:last-of-type,
div.citation > p:last-of-type {
margin-bottom: 0em;
}
aside.footnote > p:last-of-type:after,
div.citation > p:last-of-type:after {
content: "";
clear: both;
}
dl.field-list {
display: grid;
grid-template-columns: fit-content(30%) auto;
}
dl.field-list > dt {
font-weight: bold;
word-break: break-word;
padding-left: 0.5em;
padding-right: 5px;
}
dl.field-list > dd {
padding-left: 0.5em;
margin-top: 0em;
margin-left: 0em;
margin-bottom: 0em;
}
dl {
margin-bottom: 15px;
}
dd > :first-child {
margin-top: 0px;
}
dd ul, dd table {
margin-bottom: 10px;
}
dd {
margin-top: 3px;
margin-bottom: 10px;
margin-left: 30px;
}
.sig dd {
margin-top: 0px;
margin-bottom: 0px;
}
.sig dl {
margin-top: 0px;
margin-bottom: 0px;
}
dl > dd:last-child,
dl > dd:last-child > :last-child {
margin-bottom: 0;
}
dt:target, span.highlighted {
background-color: #fbe54e;
}
rect.highlighted {
fill: #fbe54e;
}
dl.glossary dt {
font-weight: bold;
font-size: 1.1em;
}
.versionmodified {
font-style: italic;
}
.system-message {
background-color: #fda;
padding: 5px;
border: 3px solid red;
}
.footnote:target {
background-color: #ffa;
}
.line-block {
display: block;
margin-top: 1em;
margin-bottom: 1em;
}
.line-block .line-block {
margin-top: 0;
margin-bottom: 0;
margin-left: 1.5em;
}
.guilabel, .menuselection {
font-family: sans-serif;
}
.accelerator {
text-decoration: underline;
}
.classifier {
font-style: oblique;
}
.classifier:before {
font-style: normal;
margin: 0 0.5em;
content: ":";
display: inline-block;
}
abbr, acronym {
border-bottom: dotted 1px;
cursor: help;
}
/* -- code displays --------------------------------------------------------- */
pre {
overflow: auto;
overflow-y: hidden; /* fixes display issues on Chrome browsers */
}
pre, div[class*="highlight-"] {
clear: both;
}
span.pre {
-moz-hyphens: none;
-ms-hyphens: none;
-webkit-hyphens: none;
hyphens: none;
white-space: nowrap;
}
div[class*="highlight-"] {
margin: 1em 0;
}
td.linenos pre {
border: 0;
background-color: transparent;
color: #aaa;
}
table.highlighttable {
display: block;
}
table.highlighttable tbody {
display: block;
}
table.highlighttable tr {
display: flex;
}
table.highlighttable td {
margin: 0;
padding: 0;
}
table.highlighttable td.linenos {
padding-right: 0.5em;
}
table.highlighttable td.code {
flex: 1;
overflow: hidden;
}
.highlight .hll {
display: block;
}
div.highlight pre,
table.highlighttable pre {
margin: 0;
}
div.code-block-caption + div {
margin-top: 0;
}
div.code-block-caption {
margin-top: 1em;
padding: 2px 5px;
font-size: small;
}
div.code-block-caption code {
background-color: transparent;
}
table.highlighttable td.linenos,
span.linenos,
div.highlight span.gp { /* gp: Generic.Prompt */
user-select: none;
-webkit-user-select: text; /* Safari fallback only */
-webkit-user-select: none; /* Chrome/Safari */
-moz-user-select: none; /* Firefox */
-ms-user-select: none; /* IE10+ */
}
div.code-block-caption span.caption-number {
padding: 0.1em 0.3em;
font-style: italic;
}
div.code-block-caption span.caption-text {
}
div.literal-block-wrapper {
margin: 1em 0;
}
code.xref, a code {
background-color: transparent;
font-weight: bold;
}
h1 code, h2 code, h3 code, h4 code, h5 code, h6 code {
background-color: transparent;
}
.viewcode-link {
float: right;
}
.viewcode-back {
float: right;
font-family: sans-serif;
}
div.viewcode-block:target {
margin: -1px -10px;
padding: 0 10px;
}
/* -- math display ---------------------------------------------------------- */
img.math {
vertical-align: middle;
}
div.body div.math p {
text-align: center;
}
span.eqno {
float: right;
}
span.eqno a.headerlink {
position: absolute;
z-index: 1;
}
div.math:hover a.headerlink {
visibility: visible;
}
/* -- printout stylesheet --------------------------------------------------- */
@media print {
div.document,
div.documentwrapper,
div.bodywrapper {
margin: 0 !important;
width: 100%;
}
div.sphinxsidebar,
div.related,
div.footer,
#top-link {
display: none;
}
}

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/* This file intentionally left blank. */

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/*
* Base JavaScript utilities for all Sphinx HTML documentation.
*/
"use strict";
const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([
"TEXTAREA",
"INPUT",
"SELECT",
"BUTTON",
]);
const _ready = (callback) => {
if (document.readyState !== "loading") {
callback();
} else {
document.addEventListener("DOMContentLoaded", callback);
}
};
/**
* Small JavaScript module for the documentation.
*/
const Documentation = {
init: () => {
Documentation.initDomainIndexTable();
Documentation.initOnKeyListeners();
},
/**
* i18n support
*/
TRANSLATIONS: {},
PLURAL_EXPR: (n) => (n === 1 ? 0 : 1),
LOCALE: "unknown",
// gettext and ngettext don't access this so that the functions
// can safely bound to a different name (_ = Documentation.gettext)
gettext: (string) => {
const translated = Documentation.TRANSLATIONS[string];
switch (typeof translated) {
case "undefined":
return string; // no translation
case "string":
return translated; // translation exists
default:
return translated[0]; // (singular, plural) translation tuple exists
}
},
ngettext: (singular, plural, n) => {
const translated = Documentation.TRANSLATIONS[singular];
if (typeof translated !== "undefined")
return translated[Documentation.PLURAL_EXPR(n)];
return n === 1 ? singular : plural;
},
addTranslations: (catalog) => {
Object.assign(Documentation.TRANSLATIONS, catalog.messages);
Documentation.PLURAL_EXPR = new Function(
"n",
`return (${catalog.plural_expr})`
);
Documentation.LOCALE = catalog.locale;
},
/**
* helper function to focus on search bar
*/
focusSearchBar: () => {
document.querySelectorAll("input[name=q]")[0]?.focus();
},
/**
* Initialise the domain index toggle buttons
*/
initDomainIndexTable: () => {
const toggler = (el) => {
const idNumber = el.id.substr(7);
const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`);
if (el.src.substr(-9) === "minus.png") {
el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`;
toggledRows.forEach((el) => (el.style.display = "none"));
} else {
el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`;
toggledRows.forEach((el) => (el.style.display = ""));
}
};
const togglerElements = document.querySelectorAll("img.toggler");
togglerElements.forEach((el) =>
el.addEventListener("click", (event) => toggler(event.currentTarget))
);
togglerElements.forEach((el) => (el.style.display = ""));
if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler);
},
initOnKeyListeners: () => {
// only install a listener if it is really needed
if (
!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS &&
!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS
)
return;
document.addEventListener("keydown", (event) => {
// bail for input elements
if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
// bail with special keys
if (event.altKey || event.ctrlKey || event.metaKey) return;
if (!event.shiftKey) {
switch (event.key) {
case "ArrowLeft":
if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
const prevLink = document.querySelector('link[rel="prev"]');
if (prevLink && prevLink.href) {
window.location.href = prevLink.href;
event.preventDefault();
}
break;
case "ArrowRight":
if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
const nextLink = document.querySelector('link[rel="next"]');
if (nextLink && nextLink.href) {
window.location.href = nextLink.href;
event.preventDefault();
}
break;
}
}
// some keyboard layouts may need Shift to get /
switch (event.key) {
case "/":
if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break;
Documentation.focusSearchBar();
event.preventDefault();
}
});
},
};
// quick alias for translations
const _ = Documentation.gettext;
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const DOCUMENTATION_OPTIONS = {
VERSION: '',
LANGUAGE: 'en',
COLLAPSE_INDEX: false,
BUILDER: 'html',
FILE_SUFFIX: '.html',
LINK_SUFFIX: '.html',
HAS_SOURCE: true,
SOURCELINK_SUFFIX: '.txt',
NAVIGATION_WITH_KEYS: false,
SHOW_SEARCH_SUMMARY: true,
ENABLE_SEARCH_SHORTCUTS: true,
};

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<svg xmlns="http://www.w3.org/2000/svg" width="80" height="80" viewBox="0 0 250 250" fill="#fff">
<path d="M0 0l115 115h15l12 27 108 108V0z" fill="#151513"/>
<path d="M128 109c-15-9-9-19-9-19 3-7 2-11 2-11-1-7 3-2 3-2 4 5 2 11 2 11-3 10 5 15 9 16"/>
<path d="M115 115s4 2 5 0l14-14c3-2 6-3 8-3-8-11-15-24 2-41 5-5 10-7 16-7 1-2 3-7 12-11 0 0 5 3 7 16 4 2 8 5 12 9s7 8 9 12c14 3 17 7 17 7-4 8-9 11-11 11 0 6-2 11-7 16-16 16-30 10-41 2 0 3-1 7-5 11l-12 11c-1 1 1 5 1 5z"/>
</svg>

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/*
* This script contains the language-specific data used by searchtools.js,
* namely the list of stopwords, stemmer, scorer and splitter.
*/
var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"];
/* Non-minified version is copied as a separate JS file, if available */
/**
* Porter Stemmer
*/
var Stemmer = function() {
var step2list = {
ational: 'ate',
tional: 'tion',
enci: 'ence',
anci: 'ance',
izer: 'ize',
bli: 'ble',
alli: 'al',
entli: 'ent',
eli: 'e',
ousli: 'ous',
ization: 'ize',
ation: 'ate',
ator: 'ate',
alism: 'al',
iveness: 'ive',
fulness: 'ful',
ousness: 'ous',
aliti: 'al',
iviti: 'ive',
biliti: 'ble',
logi: 'log'
};
var step3list = {
icate: 'ic',
ative: '',
alize: 'al',
iciti: 'ic',
ical: 'ic',
ful: '',
ness: ''
};
var c = "[^aeiou]"; // consonant
var v = "[aeiouy]"; // vowel
var C = c + "[^aeiouy]*"; // consonant sequence
var V = v + "[aeiou]*"; // vowel sequence
var mgr0 = "^(" + C + ")?" + V + C; // [C]VC... is m>0
var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$"; // [C]VC[V] is m=1
var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1
var s_v = "^(" + C + ")?" + v; // vowel in stem
this.stemWord = function (w) {
var stem;
var suffix;
var firstch;
var origword = w;
if (w.length < 3)
return w;
var re;
var re2;
var re3;
var re4;
firstch = w.substr(0,1);
if (firstch == "y")
w = firstch.toUpperCase() + w.substr(1);
// Step 1a
re = /^(.+?)(ss|i)es$/;
re2 = /^(.+?)([^s])s$/;
if (re.test(w))
w = w.replace(re,"$1$2");
else if (re2.test(w))
w = w.replace(re2,"$1$2");
// Step 1b
re = /^(.+?)eed$/;
re2 = /^(.+?)(ed|ing)$/;
if (re.test(w)) {
var fp = re.exec(w);
re = new RegExp(mgr0);
if (re.test(fp[1])) {
re = /.$/;
w = w.replace(re,"");
}
}
else if (re2.test(w)) {
var fp = re2.exec(w);
stem = fp[1];
re2 = new RegExp(s_v);
if (re2.test(stem)) {
w = stem;
re2 = /(at|bl|iz)$/;
re3 = new RegExp("([^aeiouylsz])\\1$");
re4 = new RegExp("^" + C + v + "[^aeiouwxy]$");
if (re2.test(w))
w = w + "e";
else if (re3.test(w)) {
re = /.$/;
w = w.replace(re,"");
}
else if (re4.test(w))
w = w + "e";
}
}
// Step 1c
re = /^(.+?)y$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
re = new RegExp(s_v);
if (re.test(stem))
w = stem + "i";
}
// Step 2
re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
suffix = fp[2];
re = new RegExp(mgr0);
if (re.test(stem))
w = stem + step2list[suffix];
}
// Step 3
re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
suffix = fp[2];
re = new RegExp(mgr0);
if (re.test(stem))
w = stem + step3list[suffix];
}
// Step 4
re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;
re2 = /^(.+?)(s|t)(ion)$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
re = new RegExp(mgr1);
if (re.test(stem))
w = stem;
}
else if (re2.test(w)) {
var fp = re2.exec(w);
stem = fp[1] + fp[2];
re2 = new RegExp(mgr1);
if (re2.test(stem))
w = stem;
}
// Step 5
re = /^(.+?)e$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
re = new RegExp(mgr1);
re2 = new RegExp(meq1);
re3 = new RegExp("^" + C + v + "[^aeiouwxy]$");
if (re.test(stem) || (re2.test(stem) && !(re3.test(stem))))
w = stem;
}
re = /ll$/;
re2 = new RegExp(mgr1);
if (re.test(w) && re2.test(w)) {
re = /.$/;
w = w.replace(re,"");
}
// and turn initial Y back to y
if (firstch == "y")
w = firstch.toLowerCase() + w.substr(1);
return w;
}
}

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pre { line-height: 125%; }
td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
.highlight .hll { background-color: #ffffcc }
.highlight { background: #f8f8f8; }
.highlight .c { color: #8F5902; font-style: italic } /* Comment */
.highlight .err { color: #A40000; border: 1px solid #EF2929 } /* Error */
.highlight .g { color: #000 } /* Generic */
.highlight .k { color: #004461; font-weight: bold } /* Keyword */
.highlight .l { color: #000 } /* Literal */
.highlight .n { color: #000 } /* Name */
.highlight .o { color: #582800 } /* Operator */
.highlight .x { color: #000 } /* Other */
.highlight .p { color: #000; font-weight: bold } /* Punctuation */
.highlight .ch { color: #8F5902; font-style: italic } /* Comment.Hashbang */
.highlight .cm { color: #8F5902; font-style: italic } /* Comment.Multiline */
.highlight .cp { color: #8F5902 } /* Comment.Preproc */
.highlight .cpf { color: #8F5902; font-style: italic } /* Comment.PreprocFile */
.highlight .c1 { color: #8F5902; font-style: italic } /* Comment.Single */
.highlight .cs { color: #8F5902; font-style: italic } /* Comment.Special */
.highlight .gd { color: #A40000 } /* Generic.Deleted */
.highlight .ge { color: #000; font-style: italic } /* Generic.Emph */
.highlight .ges { color: #000 } /* Generic.EmphStrong */
.highlight .gr { color: #EF2929 } /* Generic.Error */
.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
.highlight .gi { color: #00A000 } /* Generic.Inserted */
.highlight .go { color: #888 } /* Generic.Output */
.highlight .gp { color: #745334 } /* Generic.Prompt */
.highlight .gs { color: #000; font-weight: bold } /* Generic.Strong */
.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
.highlight .gt { color: #A40000; font-weight: bold } /* Generic.Traceback */
.highlight .kc { color: #004461; font-weight: bold } /* Keyword.Constant */
.highlight .kd { color: #004461; font-weight: bold } /* Keyword.Declaration */
.highlight .kn { color: #004461; font-weight: bold } /* Keyword.Namespace */
.highlight .kp { color: #004461; font-weight: bold } /* Keyword.Pseudo */
.highlight .kr { color: #004461; font-weight: bold } /* Keyword.Reserved */
.highlight .kt { color: #004461; font-weight: bold } /* Keyword.Type */
.highlight .ld { color: #000 } /* Literal.Date */
.highlight .m { color: #900 } /* Literal.Number */
.highlight .s { color: #4E9A06 } /* Literal.String */
.highlight .na { color: #C4A000 } /* Name.Attribute */
.highlight .nb { color: #004461 } /* Name.Builtin */
.highlight .nc { color: #000 } /* Name.Class */
.highlight .no { color: #000 } /* Name.Constant */
.highlight .nd { color: #888 } /* Name.Decorator */
.highlight .ni { color: #CE5C00 } /* Name.Entity */
.highlight .ne { color: #C00; font-weight: bold } /* Name.Exception */
.highlight .nf { color: #000 } /* Name.Function */
.highlight .nl { color: #F57900 } /* Name.Label */
.highlight .nn { color: #000 } /* Name.Namespace */
.highlight .nx { color: #000 } /* Name.Other */
.highlight .py { color: #000 } /* Name.Property */
.highlight .nt { color: #004461; font-weight: bold } /* Name.Tag */
.highlight .nv { color: #000 } /* Name.Variable */
.highlight .ow { color: #004461; font-weight: bold } /* Operator.Word */
.highlight .pm { color: #000; font-weight: bold } /* Punctuation.Marker */
.highlight .w { color: #F8F8F8 } /* Text.Whitespace */
.highlight .mb { color: #900 } /* Literal.Number.Bin */
.highlight .mf { color: #900 } /* Literal.Number.Float */
.highlight .mh { color: #900 } /* Literal.Number.Hex */
.highlight .mi { color: #900 } /* Literal.Number.Integer */
.highlight .mo { color: #900 } /* Literal.Number.Oct */
.highlight .sa { color: #4E9A06 } /* Literal.String.Affix */
.highlight .sb { color: #4E9A06 } /* Literal.String.Backtick */
.highlight .sc { color: #4E9A06 } /* Literal.String.Char */
.highlight .dl { color: #4E9A06 } /* Literal.String.Delimiter */
.highlight .sd { color: #8F5902; font-style: italic } /* Literal.String.Doc */
.highlight .s2 { color: #4E9A06 } /* Literal.String.Double */
.highlight .se { color: #4E9A06 } /* Literal.String.Escape */
.highlight .sh { color: #4E9A06 } /* Literal.String.Heredoc */
.highlight .si { color: #4E9A06 } /* Literal.String.Interpol */
.highlight .sx { color: #4E9A06 } /* Literal.String.Other */
.highlight .sr { color: #4E9A06 } /* Literal.String.Regex */
.highlight .s1 { color: #4E9A06 } /* Literal.String.Single */
.highlight .ss { color: #4E9A06 } /* Literal.String.Symbol */
.highlight .bp { color: #3465A4 } /* Name.Builtin.Pseudo */
.highlight .fm { color: #000 } /* Name.Function.Magic */
.highlight .vc { color: #000 } /* Name.Variable.Class */
.highlight .vg { color: #000 } /* Name.Variable.Global */
.highlight .vi { color: #000 } /* Name.Variable.Instance */
.highlight .vm { color: #000 } /* Name.Variable.Magic */
.highlight .il { color: #900 } /* Literal.Number.Integer.Long */

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/*
* Sphinx JavaScript utilities for the full-text search.
*/
"use strict";
/**
* Simple result scoring code.
*/
if (typeof Scorer === "undefined") {
var Scorer = {
// Implement the following function to further tweak the score for each result
// The function takes a result array [docname, title, anchor, descr, score, filename]
// and returns the new score.
/*
score: result => {
const [docname, title, anchor, descr, score, filename, kind] = result
return score
},
*/
// query matches the full name of an object
objNameMatch: 11,
// or matches in the last dotted part of the object name
objPartialMatch: 6,
// Additive scores depending on the priority of the object
objPrio: {
0: 15, // used to be importantResults
1: 5, // used to be objectResults
2: -5, // used to be unimportantResults
},
// Used when the priority is not in the mapping.
objPrioDefault: 0,
// query found in title
title: 15,
partialTitle: 7,
// query found in terms
term: 5,
partialTerm: 2,
};
}
// Global search result kind enum, used by themes to style search results.
class SearchResultKind {
static get index() { return "index"; }
static get object() { return "object"; }
static get text() { return "text"; }
static get title() { return "title"; }
}
const _removeChildren = (element) => {
while (element && element.lastChild) element.removeChild(element.lastChild);
};
/**
* See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping
*/
const _escapeRegExp = (string) =>
string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
const _displayItem = (item, searchTerms, highlightTerms) => {
const docBuilder = DOCUMENTATION_OPTIONS.BUILDER;
const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX;
const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX;
const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY;
const contentRoot = document.documentElement.dataset.content_root;
const [docName, title, anchor, descr, score, _filename, kind] = item;
let listItem = document.createElement("li");
// Add a class representing the item's type:
// can be used by a theme's CSS selector for styling
// See SearchResultKind for the class names.
listItem.classList.add(`kind-${kind}`);
let requestUrl;
let linkUrl;
if (docBuilder === "dirhtml") {
// dirhtml builder
let dirname = docName + "/";
if (dirname.match(/\/index\/$/))
dirname = dirname.substring(0, dirname.length - 6);
else if (dirname === "index/") dirname = "";
requestUrl = contentRoot + dirname;
linkUrl = requestUrl;
} else {
// normal html builders
requestUrl = contentRoot + docName + docFileSuffix;
linkUrl = docName + docLinkSuffix;
}
let linkEl = listItem.appendChild(document.createElement("a"));
linkEl.href = linkUrl + anchor;
linkEl.dataset.score = score;
linkEl.innerHTML = title;
if (descr) {
listItem.appendChild(document.createElement("span")).innerHTML =
" (" + descr + ")";
// highlight search terms in the description
if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js
highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted"));
}
else if (showSearchSummary)
fetch(requestUrl)
.then((responseData) => responseData.text())
.then((data) => {
if (data)
listItem.appendChild(
Search.makeSearchSummary(data, searchTerms, anchor)
);
// highlight search terms in the summary
if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js
highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted"));
});
Search.output.appendChild(listItem);
};
const _finishSearch = (resultCount) => {
Search.stopPulse();
Search.title.innerText = _("Search Results");
if (!resultCount)
Search.status.innerText = Documentation.gettext(
"Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories."
);
else
Search.status.innerText = Documentation.ngettext(
"Search finished, found one page matching the search query.",
"Search finished, found ${resultCount} pages matching the search query.",
resultCount,
).replace('${resultCount}', resultCount);
};
const _displayNextItem = (
results,
resultCount,
searchTerms,
highlightTerms,
) => {
// results left, load the summary and display it
// this is intended to be dynamic (don't sub resultsCount)
if (results.length) {
_displayItem(results.pop(), searchTerms, highlightTerms);
setTimeout(
() => _displayNextItem(results, resultCount, searchTerms, highlightTerms),
5
);
}
// search finished, update title and status message
else _finishSearch(resultCount);
};
// Helper function used by query() to order search results.
// Each input is an array of [docname, title, anchor, descr, score, filename, kind].
// Order the results by score (in opposite order of appearance, since the
// `_displayNextItem` function uses pop() to retrieve items) and then alphabetically.
const _orderResultsByScoreThenName = (a, b) => {
const leftScore = a[4];
const rightScore = b[4];
if (leftScore === rightScore) {
// same score: sort alphabetically
const leftTitle = a[1].toLowerCase();
const rightTitle = b[1].toLowerCase();
if (leftTitle === rightTitle) return 0;
return leftTitle > rightTitle ? -1 : 1; // inverted is intentional
}
return leftScore > rightScore ? 1 : -1;
};
/**
* Default splitQuery function. Can be overridden in ``sphinx.search`` with a
* custom function per language.
*
* The regular expression works by splitting the string on consecutive characters
* that are not Unicode letters, numbers, underscores, or emoji characters.
* This is the same as ``\W+`` in Python, preserving the surrogate pair area.
*/
if (typeof splitQuery === "undefined") {
var splitQuery = (query) => query
.split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu)
.filter(term => term) // remove remaining empty strings
}
/**
* Search Module
*/
const Search = {
_index: null,
_queued_query: null,
_pulse_status: -1,
htmlToText: (htmlString, anchor) => {
const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html');
for (const removalQuery of [".headerlink", "script", "style"]) {
htmlElement.querySelectorAll(removalQuery).forEach((el) => { el.remove() });
}
if (anchor) {
const anchorContent = htmlElement.querySelector(`[role="main"] ${anchor}`);
if (anchorContent) return anchorContent.textContent;
console.warn(
`Anchored content block not found. Sphinx search tries to obtain it via DOM query '[role=main] ${anchor}'. Check your theme or template.`
);
}
// if anchor not specified or not found, fall back to main content
const docContent = htmlElement.querySelector('[role="main"]');
if (docContent) return docContent.textContent;
console.warn(
"Content block not found. Sphinx search tries to obtain it via DOM query '[role=main]'. Check your theme or template."
);
return "";
},
init: () => {
const query = new URLSearchParams(window.location.search).get("q");
document
.querySelectorAll('input[name="q"]')
.forEach((el) => (el.value = query));
if (query) Search.performSearch(query);
},
loadIndex: (url) =>
(document.body.appendChild(document.createElement("script")).src = url),
setIndex: (index) => {
Search._index = index;
if (Search._queued_query !== null) {
const query = Search._queued_query;
Search._queued_query = null;
Search.query(query);
}
},
hasIndex: () => Search._index !== null,
deferQuery: (query) => (Search._queued_query = query),
stopPulse: () => (Search._pulse_status = -1),
startPulse: () => {
if (Search._pulse_status >= 0) return;
const pulse = () => {
Search._pulse_status = (Search._pulse_status + 1) % 4;
Search.dots.innerText = ".".repeat(Search._pulse_status);
if (Search._pulse_status >= 0) window.setTimeout(pulse, 500);
};
pulse();
},
/**
* perform a search for something (or wait until index is loaded)
*/
performSearch: (query) => {
// create the required interface elements
const searchText = document.createElement("h2");
searchText.textContent = _("Searching");
const searchSummary = document.createElement("p");
searchSummary.classList.add("search-summary");
searchSummary.innerText = "";
const searchList = document.createElement("ul");
searchList.setAttribute("role", "list");
searchList.classList.add("search");
const out = document.getElementById("search-results");
Search.title = out.appendChild(searchText);
Search.dots = Search.title.appendChild(document.createElement("span"));
Search.status = out.appendChild(searchSummary);
Search.output = out.appendChild(searchList);
const searchProgress = document.getElementById("search-progress");
// Some themes don't use the search progress node
if (searchProgress) {
searchProgress.innerText = _("Preparing search...");
}
Search.startPulse();
// index already loaded, the browser was quick!
if (Search.hasIndex()) Search.query(query);
else Search.deferQuery(query);
},
_parseQuery: (query) => {
// stem the search terms and add them to the correct list
const stemmer = new Stemmer();
const searchTerms = new Set();
const excludedTerms = new Set();
const highlightTerms = new Set();
const objectTerms = new Set(splitQuery(query.toLowerCase().trim()));
splitQuery(query.trim()).forEach((queryTerm) => {
const queryTermLower = queryTerm.toLowerCase();
// maybe skip this "word"
// stopwords array is from language_data.js
if (
stopwords.indexOf(queryTermLower) !== -1 ||
queryTerm.match(/^\d+$/)
)
return;
// stem the word
let word = stemmer.stemWord(queryTermLower);
// select the correct list
if (word[0] === "-") excludedTerms.add(word.substr(1));
else {
searchTerms.add(word);
highlightTerms.add(queryTermLower);
}
});
if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js
localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" "))
}
// console.debug("SEARCH: searching for:");
// console.info("required: ", [...searchTerms]);
// console.info("excluded: ", [...excludedTerms]);
return [query, searchTerms, excludedTerms, highlightTerms, objectTerms];
},
/**
* execute search (requires search index to be loaded)
*/
_performSearch: (query, searchTerms, excludedTerms, highlightTerms, objectTerms) => {
const filenames = Search._index.filenames;
const docNames = Search._index.docnames;
const titles = Search._index.titles;
const allTitles = Search._index.alltitles;
const indexEntries = Search._index.indexentries;
// Collect multiple result groups to be sorted separately and then ordered.
// Each is an array of [docname, title, anchor, descr, score, filename, kind].
const normalResults = [];
const nonMainIndexResults = [];
_removeChildren(document.getElementById("search-progress"));
const queryLower = query.toLowerCase().trim();
for (const [title, foundTitles] of Object.entries(allTitles)) {
if (title.toLowerCase().trim().includes(queryLower) && (queryLower.length >= title.length/2)) {
for (const [file, id] of foundTitles) {
const score = Math.round(Scorer.title * queryLower.length / title.length);
const boost = titles[file] === title ? 1 : 0; // add a boost for document titles
normalResults.push([
docNames[file],
titles[file] !== title ? `${titles[file]} > ${title}` : title,
id !== null ? "#" + id : "",
null,
score + boost,
filenames[file],
SearchResultKind.title,
]);
}
}
}
// search for explicit entries in index directives
for (const [entry, foundEntries] of Object.entries(indexEntries)) {
if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) {
for (const [file, id, isMain] of foundEntries) {
const score = Math.round(100 * queryLower.length / entry.length);
const result = [
docNames[file],
titles[file],
id ? "#" + id : "",
null,
score,
filenames[file],
SearchResultKind.index,
];
if (isMain) {
normalResults.push(result);
} else {
nonMainIndexResults.push(result);
}
}
}
}
// lookup as object
objectTerms.forEach((term) =>
normalResults.push(...Search.performObjectSearch(term, objectTerms))
);
// lookup as search terms in fulltext
normalResults.push(...Search.performTermsSearch(searchTerms, excludedTerms));
// let the scorer override scores with a custom scoring function
if (Scorer.score) {
normalResults.forEach((item) => (item[4] = Scorer.score(item)));
nonMainIndexResults.forEach((item) => (item[4] = Scorer.score(item)));
}
// Sort each group of results by score and then alphabetically by name.
normalResults.sort(_orderResultsByScoreThenName);
nonMainIndexResults.sort(_orderResultsByScoreThenName);
// Combine the result groups in (reverse) order.
// Non-main index entries are typically arbitrary cross-references,
// so display them after other results.
let results = [...nonMainIndexResults, ...normalResults];
// remove duplicate search results
// note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept
let seen = new Set();
results = results.reverse().reduce((acc, result) => {
let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(',');
if (!seen.has(resultStr)) {
acc.push(result);
seen.add(resultStr);
}
return acc;
}, []);
return results.reverse();
},
query: (query) => {
const [searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms] = Search._parseQuery(query);
const results = Search._performSearch(searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms);
// for debugging
//Search.lastresults = results.slice(); // a copy
// console.info("search results:", Search.lastresults);
// print the results
_displayNextItem(results, results.length, searchTerms, highlightTerms);
},
/**
* search for object names
*/
performObjectSearch: (object, objectTerms) => {
const filenames = Search._index.filenames;
const docNames = Search._index.docnames;
const objects = Search._index.objects;
const objNames = Search._index.objnames;
const titles = Search._index.titles;
const results = [];
const objectSearchCallback = (prefix, match) => {
const name = match[4]
const fullname = (prefix ? prefix + "." : "") + name;
const fullnameLower = fullname.toLowerCase();
if (fullnameLower.indexOf(object) < 0) return;
let score = 0;
const parts = fullnameLower.split(".");
// check for different match types: exact matches of full name or
// "last name" (i.e. last dotted part)
if (fullnameLower === object || parts.slice(-1)[0] === object)
score += Scorer.objNameMatch;
else if (parts.slice(-1)[0].indexOf(object) > -1)
score += Scorer.objPartialMatch; // matches in last name
const objName = objNames[match[1]][2];
const title = titles[match[0]];
// If more than one term searched for, we require other words to be
// found in the name/title/description
const otherTerms = new Set(objectTerms);
otherTerms.delete(object);
if (otherTerms.size > 0) {
const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase();
if (
[...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0)
)
return;
}
let anchor = match[3];
if (anchor === "") anchor = fullname;
else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname;
const descr = objName + _(", in ") + title;
// add custom score for some objects according to scorer
if (Scorer.objPrio.hasOwnProperty(match[2]))
score += Scorer.objPrio[match[2]];
else score += Scorer.objPrioDefault;
results.push([
docNames[match[0]],
fullname,
"#" + anchor,
descr,
score,
filenames[match[0]],
SearchResultKind.object,
]);
};
Object.keys(objects).forEach((prefix) =>
objects[prefix].forEach((array) =>
objectSearchCallback(prefix, array)
)
);
return results;
},
/**
* search for full-text terms in the index
*/
performTermsSearch: (searchTerms, excludedTerms) => {
// prepare search
const terms = Search._index.terms;
const titleTerms = Search._index.titleterms;
const filenames = Search._index.filenames;
const docNames = Search._index.docnames;
const titles = Search._index.titles;
const scoreMap = new Map();
const fileMap = new Map();
// perform the search on the required terms
searchTerms.forEach((word) => {
const files = [];
// find documents, if any, containing the query word in their text/title term indices
// use Object.hasOwnProperty to avoid mismatching against prototype properties
const arr = [
{ files: terms.hasOwnProperty(word) ? terms[word] : undefined, score: Scorer.term },
{ files: titleTerms.hasOwnProperty(word) ? titleTerms[word] : undefined, score: Scorer.title },
];
// add support for partial matches
if (word.length > 2) {
const escapedWord = _escapeRegExp(word);
if (!terms.hasOwnProperty(word)) {
Object.keys(terms).forEach((term) => {
if (term.match(escapedWord))
arr.push({ files: terms[term], score: Scorer.partialTerm });
});
}
if (!titleTerms.hasOwnProperty(word)) {
Object.keys(titleTerms).forEach((term) => {
if (term.match(escapedWord))
arr.push({ files: titleTerms[term], score: Scorer.partialTitle });
});
}
}
// no match but word was a required one
if (arr.every((record) => record.files === undefined)) return;
// found search word in contents
arr.forEach((record) => {
if (record.files === undefined) return;
let recordFiles = record.files;
if (recordFiles.length === undefined) recordFiles = [recordFiles];
files.push(...recordFiles);
// set score for the word in each file
recordFiles.forEach((file) => {
if (!scoreMap.has(file)) scoreMap.set(file, new Map());
const fileScores = scoreMap.get(file);
fileScores.set(word, record.score);
});
});
// create the mapping
files.forEach((file) => {
if (!fileMap.has(file)) fileMap.set(file, [word]);
else if (fileMap.get(file).indexOf(word) === -1) fileMap.get(file).push(word);
});
});
// now check if the files don't contain excluded terms
const results = [];
for (const [file, wordList] of fileMap) {
// check if all requirements are matched
// as search terms with length < 3 are discarded
const filteredTermCount = [...searchTerms].filter(
(term) => term.length > 2
).length;
if (
wordList.length !== searchTerms.size &&
wordList.length !== filteredTermCount
)
continue;
// ensure that none of the excluded terms is in the search result
if (
[...excludedTerms].some(
(term) =>
terms[term] === file ||
titleTerms[term] === file ||
(terms[term] || []).includes(file) ||
(titleTerms[term] || []).includes(file)
)
)
break;
// select one (max) score for the file.
const score = Math.max(...wordList.map((w) => scoreMap.get(file).get(w)));
// add result to the result list
results.push([
docNames[file],
titles[file],
"",
null,
score,
filenames[file],
SearchResultKind.text,
]);
}
return results;
},
/**
* helper function to return a node containing the
* search summary for a given text. keywords is a list
* of stemmed words.
*/
makeSearchSummary: (htmlText, keywords, anchor) => {
const text = Search.htmlToText(htmlText, anchor);
if (text === "") return null;
const textLower = text.toLowerCase();
const actualStartPosition = [...keywords]
.map((k) => textLower.indexOf(k.toLowerCase()))
.filter((i) => i > -1)
.slice(-1)[0];
const startWithContext = Math.max(actualStartPosition - 120, 0);
const top = startWithContext === 0 ? "" : "...";
const tail = startWithContext + 240 < text.length ? "..." : "";
let summary = document.createElement("p");
summary.classList.add("context");
summary.textContent = top + text.substr(startWithContext, 240).trim() + tail;
return summary;
},
};
_ready(Search.init);

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@ -0,0 +1,154 @@
/* Highlighting utilities for Sphinx HTML documentation. */
"use strict";
const SPHINX_HIGHLIGHT_ENABLED = true
/**
* highlight a given string on a node by wrapping it in
* span elements with the given class name.
*/
const _highlight = (node, addItems, text, className) => {
if (node.nodeType === Node.TEXT_NODE) {
const val = node.nodeValue;
const parent = node.parentNode;
const pos = val.toLowerCase().indexOf(text);
if (
pos >= 0 &&
!parent.classList.contains(className) &&
!parent.classList.contains("nohighlight")
) {
let span;
const closestNode = parent.closest("body, svg, foreignObject");
const isInSVG = closestNode && closestNode.matches("svg");
if (isInSVG) {
span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
} else {
span = document.createElement("span");
span.classList.add(className);
}
span.appendChild(document.createTextNode(val.substr(pos, text.length)));
const rest = document.createTextNode(val.substr(pos + text.length));
parent.insertBefore(
span,
parent.insertBefore(
rest,
node.nextSibling
)
);
node.nodeValue = val.substr(0, pos);
/* There may be more occurrences of search term in this node. So call this
* function recursively on the remaining fragment.
*/
_highlight(rest, addItems, text, className);
if (isInSVG) {
const rect = document.createElementNS(
"http://www.w3.org/2000/svg",
"rect"
);
const bbox = parent.getBBox();
rect.x.baseVal.value = bbox.x;
rect.y.baseVal.value = bbox.y;
rect.width.baseVal.value = bbox.width;
rect.height.baseVal.value = bbox.height;
rect.setAttribute("class", className);
addItems.push({ parent: parent, target: rect });
}
}
} else if (node.matches && !node.matches("button, select, textarea")) {
node.childNodes.forEach((el) => _highlight(el, addItems, text, className));
}
};
const _highlightText = (thisNode, text, className) => {
let addItems = [];
_highlight(thisNode, addItems, text, className);
addItems.forEach((obj) =>
obj.parent.insertAdjacentElement("beforebegin", obj.target)
);
};
/**
* Small JavaScript module for the documentation.
*/
const SphinxHighlight = {
/**
* highlight the search words provided in localstorage in the text
*/
highlightSearchWords: () => {
if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight
// get and clear terms from localstorage
const url = new URL(window.location);
const highlight =
localStorage.getItem("sphinx_highlight_terms")
|| url.searchParams.get("highlight")
|| "";
localStorage.removeItem("sphinx_highlight_terms")
url.searchParams.delete("highlight");
window.history.replaceState({}, "", url);
// get individual terms from highlight string
const terms = highlight.toLowerCase().split(/\s+/).filter(x => x);
if (terms.length === 0) return; // nothing to do
// There should never be more than one element matching "div.body"
const divBody = document.querySelectorAll("div.body");
const body = divBody.length ? divBody[0] : document.querySelector("body");
window.setTimeout(() => {
terms.forEach((term) => _highlightText(body, term, "highlighted"));
}, 10);
const searchBox = document.getElementById("searchbox");
if (searchBox === null) return;
searchBox.appendChild(
document
.createRange()
.createContextualFragment(
'<p class="highlight-link">' +
'<a href="javascript:SphinxHighlight.hideSearchWords()">' +
_("Hide Search Matches") +
"</a></p>"
)
);
},
/**
* helper function to hide the search marks again
*/
hideSearchWords: () => {
document
.querySelectorAll("#searchbox .highlight-link")
.forEach((el) => el.remove());
document
.querySelectorAll("span.highlighted")
.forEach((el) => el.classList.remove("highlighted"));
localStorage.removeItem("sphinx_highlight_terms")
},
initEscapeListener: () => {
// only install a listener if it is really needed
if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return;
document.addEventListener("keydown", (event) => {
// bail for input elements
if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
// bail with special keys
if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return;
if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) {
SphinxHighlight.hideSearchWords();
event.preventDefault();
}
});
},
};
_ready(() => {
/* Do not call highlightSearchWords() when we are on the search page.
* It will highlight words from the *previous* search query.
*/
if (typeof Search === "undefined") SphinxHighlight.highlightSearchWords();
SphinxHighlight.initEscapeListener();
});

294
docs/_build/html/api_reference.html vendored Normal file
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@ -0,0 +1,294 @@
<!DOCTYPE html>
<html lang="en" data-content_root="./">
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
<title>API Reference &#8212; optifik documentation</title>
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=5ecbeea2" />
<link rel="stylesheet" type="text/css" href="_static/basic.css?v=b08954a9" />
<link rel="stylesheet" type="text/css" href="_static/alabaster.css?v=27fed22d" />
<script src="_static/documentation_options.js?v=5929fcd5"></script>
<script src="_static/doctools.js?v=9bcbadda"></script>
<script src="_static/sphinx_highlight.js?v=dc90522c"></script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="Examples" href="examples.html" />
<link rel="prev" title="Installation" href="installation.html" />
<link rel="stylesheet" href="_static/custom.css" type="text/css" />
</head><body>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<section id="api-reference">
<h1>API Reference<a class="headerlink" href="#api-reference" title="Link to this heading"></a></h1>
<p>Below is the complete reference for Optifiks public API.</p>
<section id="module-optifik.io">
<span id="io"></span><h2>io<a class="headerlink" href="#module-optifik.io" title="Link to this heading"></a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="optifik.io.load_spectrum">
<span class="sig-prename descclassname"><span class="pre">optifik.io.</span></span><span class="sig-name descname"><span class="pre">load_spectrum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">spectrum_path</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wavelength_min</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wavelength_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">inf</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">delimiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">','</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/optifik/io.html#load_spectrum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#optifik.io.load_spectrum" title="Link to this definition"></a></dt>
<dd><p>Load a spectrum file.</p>
<p>TODO : describe expected format</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>spectrum_path</strong><span class="classifier">string</span></dt><dd><p>File path.</p>
</dd>
<dt><strong>wavelength_min</strong><span class="classifier">scalar, optional</span></dt><dd><p>Cut the data at this minimum wavelength (included).</p>
</dd>
<dt><strong>wavelength_max</strong><span class="classifier">scalar, optional</span></dt><dd><p>Cut the data at this maximum wavelength (included).</p>
</dd>
<dt><strong>delimiter</strong><span class="classifier">string, optional</span></dt><dd><p>Delimiter between columns in the datafile.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>values</strong><span class="classifier">arrays</span></dt><dd><p>(lamdbas, intensities)</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
</section>
<section id="module-optifik.fft">
<span id="fft"></span><h2>fft<a class="headerlink" href="#module-optifik.fft" title="Link to this heading"></a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="optifik.fft.thickness_from_fft">
<span class="sig-prename descclassname"><span class="pre">optifik.fft.</span></span><span class="sig-name descname"><span class="pre">thickness_from_fft</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wavelengths</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">intensities</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">refractive_index</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">num_half_space</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/optifik/fft.html#thickness_from_fft"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#optifik.fft.thickness_from_fft" title="Link to this definition"></a></dt>
<dd><p>Determine the tickness by Fast Fourier Transform.</p>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>wavelengths</strong><span class="classifier">array</span></dt><dd><p>Wavelength values in nm.</p>
</dd>
<dt><strong>intensities</strong><span class="classifier">array</span></dt><dd><p>Intensity values.</p>
</dd>
<dt><strong>refractive_index</strong><span class="classifier">scalar, optional</span></dt><dd><p>Value of the refractive index of the medium.</p>
</dd>
<dt><strong>num_half_space</strong><span class="classifier">scalar, optional</span></dt><dd><p>Number of points to compute FFTs half space.
If <cite>None</cite>, default corresponds to <cite>10*len(wavelengths)</cite>.</p>
</dd>
<dt><strong>plot</strong><span class="classifier">boolean, optional</span></dt><dd><p>Show plot of the transformed signal and the peak detection.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<dt><strong>results</strong><span class="classifier">Instance of <cite>OptimizeResult</cite> class.</span></dt><dd><p>The attribute <cite>thickness</cite> gives the thickness value in nm.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
</section>
<section id="module-optifik.minmax">
<span id="minmax"></span><h2>minmax<a class="headerlink" href="#module-optifik.minmax" title="Link to this heading"></a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="optifik.minmax.thickness_from_minmax">
<span class="sig-prename descclassname"><span class="pre">optifik.minmax.</span></span><span class="sig-name descname"><span class="pre">thickness_from_minmax</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wavelengths</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">intensities</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">refractive_index</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_peak_prominence</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_peak_distance</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'linreg'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/optifik/minmax.html#thickness_from_minmax"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#optifik.minmax.thickness_from_minmax" title="Link to this definition"></a></dt>
<dd><p>Return the thickness from a min-max detection.</p>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>wavelengths</strong><span class="classifier">array</span></dt><dd><p>Wavelength values in nm.</p>
</dd>
<dt><strong>intensities</strong><span class="classifier">array</span></dt><dd><p>Intensity values.</p>
</dd>
<dt><strong>refractive_index</strong><span class="classifier">scalar, optional</span></dt><dd><p>Value of the refractive index of the medium.</p>
</dd>
<dt><strong>min_peak_prominence</strong><span class="classifier">scalar, optional</span></dt><dd><p>Required prominence of peaks.</p>
</dd>
<dt><strong>min_peak_distance</strong><span class="classifier">scalar, optional</span></dt><dd><p>Minimum distance between peaks.</p>
</dd>
<dt><strong>method</strong><span class="classifier">string, optional</span></dt><dd><p>Either linreg for linear regression or ransac
for Randon Sampling Consensus.</p>
</dd>
<dt><strong>plot</strong><span class="classifier">boolean, optional</span></dt><dd><p>Show plots of peak detection and lin regression.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<dt><strong>results</strong><span class="classifier">Instance of <cite>OptimizeResult</cite> class.</span></dt><dd><p>The attribute <cite>thickness</cite> gives the thickness value in nm.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>For more details about <cite>min_peak_prominence</cite> and <cite>min_peak_distance</cite>,
see the documentation of <cite>scipy.signal.find_peaks</cite>. This function
is used to find extrema.</p>
</dd></dl>
</section>
<section id="module-optifik.scheludko">
<span id="scheludko"></span><h2>scheludko<a class="headerlink" href="#module-optifik.scheludko" title="Link to this heading"></a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="optifik.scheludko.get_default_start_stop_wavelengths">
<span class="sig-prename descclassname"><span class="pre">optifik.scheludko.</span></span><span class="sig-name descname"><span class="pre">get_default_start_stop_wavelengths</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wavelengths</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">intensities</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">refractive_index</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_peak_prominence</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/optifik/scheludko.html#get_default_start_stop_wavelengths"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#optifik.scheludko.get_default_start_stop_wavelengths" title="Link to this definition"></a></dt>
<dd><p>Returns the start and stop wavelength values of the last monotonic branch.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>wavelengths</strong><span class="classifier">array</span></dt><dd><p>Wavelength values in nm.</p>
</dd>
<dt><strong>intensities</strong><span class="classifier">array</span></dt><dd><p>Intensity values.</p>
</dd>
<dt><strong>refractive_index</strong><span class="classifier">scalar, optional</span></dt><dd><p>Value of the refractive index of the medium.</p>
</dd>
<dt><strong>min_peak_prominence</strong><span class="classifier">scalar</span></dt><dd><p>Required prominence of peaks.</p>
</dd>
<dt><strong>plot</strong><span class="classifier">bool, optional</span></dt><dd><p>Display a curve, useful for checking or debuging. The default is None.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>wavelength_start</strong><span class="classifier">scalar</span></dt><dd></dd>
<dt><strong>wavelength_stop</strong><span class="classifier">scalar</span></dt><dd></dd>
</dl>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt>RuntimeError</dt><dd><p>if at least one maximum and one minimum are not detected.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="optifik.scheludko.thickness_from_scheludko">
<span class="sig-prename descclassname"><span class="pre">optifik.scheludko.</span></span><span class="sig-name descname"><span class="pre">thickness_from_scheludko</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wavelengths</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">intensities</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">refractive_index</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wavelength_start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wavelength_stop</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">interference_order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">intensities_void</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/optifik/scheludko.html#thickness_from_scheludko"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#optifik.scheludko.thickness_from_scheludko" title="Link to this definition"></a></dt>
<dd><p>Compute the film thickness based on Scheludko method.</p>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>wavelengths</strong><span class="classifier">array</span></dt><dd><p>Wavelength values in nm.</p>
</dd>
<dt><strong>intensities</strong><span class="classifier">array</span></dt><dd><p>Intensity values.</p>
</dd>
<dt><strong>refractive_index</strong><span class="classifier">scalar, optional</span></dt><dd><p>Value of the refractive index of the medium.</p>
</dd>
<dt><strong>wavelength_start</strong><span class="classifier">scalar, optional</span></dt><dd><p>Starting value of a monotonic branch.
Mandatory if interference_order != 0.</p>
</dd>
<dt><strong>wavelength_stop</strong><span class="classifier">scalar, optional</span></dt><dd><p>Stoping value of a monotonic branch.
Mandatory if interference_order != 0.</p>
</dd>
<dt><strong>interference_order</strong><span class="classifier">scalar, optional</span></dt><dd><p>Interference order, zero or positive integer.
If set to None, the value is guessed.</p>
</dd>
<dt><strong>intensities_void</strong><span class="classifier">array, optional</span></dt><dd><p>Intensity in absence of a film.
Mandatory if interference_order == 0.</p>
</dd>
<dt><strong>plot</strong><span class="classifier">bool, optional</span></dt><dd><p>Display a curve, useful for checking or debuging. The default is None.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<dt><strong>results</strong><span class="classifier">Instance of <cite>OptimizeResult</cite> class.</span></dt><dd><p>The attribute <cite>thickness</cite> gives the thickness value in nm.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
</section>
</section>
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<p>Heres a simple example using Optifik to solve a quadratic function.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">optifik</span><span class="w"> </span><span class="kn">import</span> <span class="n">minimize</span>
<span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="mi">3</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">minimize</span><span class="p">(</span><span class="n">quadratic</span><span class="p">,</span> <span class="n">x0</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
</pre></div>
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<section id="constrained-optimization">
<h2>Constrained Optimization<a class="headerlink" href="#constrained-optimization" title="Link to this heading"></a></h2>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">optifik</span><span class="w"> </span><span class="kn">import</span> <span class="n">minimize</span>
<span class="k">def</span><span class="w"> </span><span class="nf">objective</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span>
<span class="k">def</span><span class="w"> </span><span class="nf">constraint</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">minimize</span><span class="p">(</span><span class="n">objective</span><span class="p">,</span> <span class="n">x0</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">constraints</span><span class="o">=</span><span class="p">[</span><span class="n">constraint</span><span class="p">])</span>
<span class="nb">print</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
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<p>You can install Optifik using <cite>pip</cite>:</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>pip<span class="w"> </span>install<span class="w"> </span>optifik
</pre></div>
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<p>Alternatively, you can install it from source:</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>git<span class="w"> </span>clone<span class="w"> </span>https://github.com/yourusername/optifik.git
<span class="nb">cd</span><span class="w"> </span>optifik
pip<span class="w"> </span>install<span class="w"> </span>-e<span class="w"> </span>.
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<h2>Basic Optimization<a class="headerlink" href="#basic-optimization" title="Link to this heading"></a></h2>
<p>Heres a simple example using Optifik to solve a quadratic function.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">optifik</span><span class="w"> </span><span class="kn">import</span> <span class="n">minimize</span>
<span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="mi">3</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">minimize</span><span class="p">(</span><span class="n">quadratic</span><span class="p">,</span> <span class="n">x0</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
</pre></div>
</div>
</section>
<section id="constrained-optimization">
<h2>Constrained Optimization<a class="headerlink" href="#constrained-optimization" title="Link to this heading"></a></h2>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">optifik</span><span class="w"> </span><span class="kn">import</span> <span class="n">minimize</span>
<span class="k">def</span><span class="w"> </span><span class="nf">objective</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span>
<span class="k">def</span><span class="w"> </span><span class="nf">constraint</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">minimize</span><span class="p">(</span><span class="n">objective</span><span class="p">,</span> <span class="n">x0</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">constraints</span><span class="o">=</span><span class="p">[</span><span class="n">constraint</span><span class="p">])</span>
<span class="nb">print</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
</pre></div>
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Metadata-Version: 2.4
Name: optifik
Version: 0.1.0
Summary: Compute film thickness from interferometry
Author-email: François Boulogne <francois.boulogne@cnrs.fr>, Victor Ziapkoff <victor.ziapkoff@universite-paris-saclay.fr>
License-Expression: GPL-3.0-or-later
Project-URL: Homepage, https://github.com/votrecompte/votreprojet
Project-URL: Documentation, https://github.com/votrecompte/votreprojet#readme
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Project-URL: Issues, https://github.com/sciunto-org/optifik/issues
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Description-Content-Type: text/markdown
Requires-Dist: numpy>=1.10.0
Requires-Dist: scipy>=1.1.0
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README.md
pyproject.toml
optifik/__init__.py
optifik/analysis.py
optifik/fft.py
optifik/io.py
optifik/minmax.py
optifik/scheludko.py
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tests/test_SV2o3.py
tests/test_SV2o4.py
tests/test_SV2o5.py
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numpy>=1.10.0
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