initial commit

.gitignore

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+.vscode
+.DS_Store
+
+# Byte-compiled / optimized / DLL files
+__pycache__/
+*.py[cod]
+*$py.class
+
+# C extensions
+*.so
+
+# Distribution / packaging
+.Python
+build/
+develop-eggs/
+dist/
+downloads/
+eggs/
+.eggs/
+lib/
+lib64/
+parts/
+sdist/
+var/
+wheels/
+share/python-wheels/
+*.egg-info/
+.installed.cfg
+*.egg
+MANIFEST
+
+# PyInstaller
+#  Usually these files are written by a python script from a template
+#  before PyInstaller builds the exe, so as to inject date/other infos into it.
+*.manifest
+*.spec
+
+# Installer logs
+pip-log.txt
+pip-delete-this-directory.txt
+
+# Unit test / coverage reports
+htmlcov/
+.tox/
+.nox/
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+.coverage.*
+.cache
+nosetests.xml
+coverage.xml
+*.cover
+*.py,cover
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+# Translations
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+*.pot
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+# Django stuff:
+*.log
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+db.sqlite3
+db.sqlite3-journal
+
+# Flask stuff:
+instance/
+.webassets-cache
+
+# Scrapy stuff:
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+# Sphinx documentation
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+
+# PyBuilder
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+target/
+
+# Jupyter Notebook
+.ipynb_checkpoints
+
+# IPython
+profile_default/
+ipython_config.py
+
+# pyenv
+#   For a library or package, you might want to ignore these files since the code is
+#   intended to run in multiple environments; otherwise, check them in:
+# .python-version
+
+# pipenv
+#   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
+#   However, in case of collaboration, if having platform-specific dependencies or dependencies
+#   having no cross-platform support, pipenv may install dependencies that don't work, or not
+#   install all needed dependencies.
+#Pipfile.lock
+
+# poetry
+#   Similar to Pipfile.lock, it is generally recommended to include poetry.lock in version control.
+#   This is especially recommended for binary packages to ensure reproducibility, and is more
+#   commonly ignored for libraries.
+#   https://python-poetry.org/docs/basic-usage/#commit-your-poetrylock-file-to-version-control
+#poetry.lock
+
+# pdm
+#   Similar to Pipfile.lock, it is generally recommended to include pdm.lock in version control.
+#pdm.lock
+#   pdm stores project-wide configurations in .pdm.toml, but it is recommended to not include it
+#   in version control.
+#   https://pdm.fming.dev/#use-with-ide
+.pdm.toml
+
+# PEP 582; used by e.g. github.com/David-OConnor/pyflow and github.com/pdm-project/pdm
+__pypackages__/
+
+# Celery stuff
+celerybeat-schedule
+celerybeat.pid
+
+# SageMath parsed files
+*.sage.py
+
+# Environments
+.env
+.venv
+env/
+venv/
+ENV/
+env.bak/
+venv.bak/
+
+# Spyder project settings
+.spyderproject
+.spyproject
+
+# Rope project settings
+.ropeproject
+
+# mkdocs documentation
+/site
+
+# mypy
+.mypy_cache/
+.dmypy.json
+dmypy.json
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+# Pyre type checker
+.pyre/
+
+# pytype static type analyzer
+.pytype/
+
+# Cython debug symbols
+cython_debug/
+
+# PyCharm
+#  JetBrains specific template is maintained in a separate JetBrains.gitignore that can
+#  be found at https://github.com/github/gitignore/blob/main/Global/JetBrains.gitignore
+#  and can be added to the global gitignore or merged into this file.  For a more nuclear
+#  option (not recommended) you can uncomment the following to ignore the entire idea folder.
+#.idea/

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+ 750.9920,6.305E-009
+ 750.9960,7.803E-009
+ 751.0000,6.260E-009
+ 751.0040,6.632E-009
+ 751.0080,8.439E-009
+ 751.0120,6.287E-009
+ 751.0160,9.148E-009
+ 751.0200,8.275E-009
+ 751.0240,8.422E-009
+ 751.0280,7.888E-009
+ 751.0320,8.916E-009
+ 751.0360,7.581E-009
+ 751.0400,9.430E-009
+ 751.0440,9.312E-009
+ 751.0480,9.281E-009
+ 751.0520,9.729E-009
+ 751.0560,1.015E-008
+ 751.0600,9.065E-009
+ 751.0640,1.002E-008
+ 751.0680,7.607E-009
+ 751.0720,8.622E-009
+ 751.0760,1.189E-008
+ 751.0800,9.802E-009
+ 751.0840,8.685E-009
+ 751.0880,6.030E-009
+ 751.0920,9.090E-009
+ 751.0960,1.158E-008
+ 751.1000,5.451E-009
+ 751.1040,9.767E-009
+ 751.1080,6.368E-009
+ 751.1120,7.536E-009
+ 751.1160,1.124E-008
+ 751.1200,1.017E-008
+ 751.1240,9.669E-009
+ 751.1280,9.600E-009
+ 751.1320,8.671E-009
+ 751.1360,1.134E-008
+ 751.1400,9.225E-009
+ 751.1440,1.207E-008
+ 751.1480,8.720E-009
+ 751.1520,5.573E-009
+ 751.1560,9.581E-009
+ 751.1600,9.566E-009
+ 751.1640,1.122E-008
+ 751.1680,1.144E-008
+ 751.1720,1.069E-008
+ 751.1760,1.181E-008
+ 751.1800,1.227E-008

deconvolution.py

@@ -0,0 +1,400 @@
+from dataclasses import dataclass, field
+from pathlib import Path
+from typing import Callable
+
+import click
+import labmodule as lab
+import numpy as np
+from customfunc.app import PlotApp
+from numpy.fft import fft, fftshift, ifft
+from scipy.optimize import curve_fit
+
+LN2 = np.log(2)
+
+
+@click.group()
+def main():
+    pass
+
+
+@dataclass
+class FitResult:
+    curve: np.ndarray = field(repr=False)
+    covariance: np.ndarray
+    amp: float
+    width: float
+    x0: float = 0
+    params: tuple[float, ...] = field(default_factory=tuple)
+
+
+@dataclass
+class VoigtFitResult:
+    name: str
+    curve: np.ndarray = field(repr=False)
+    covariance: np.ndarray
+    gaussian_width: float
+    lorentzian_width: float
+
+    @property
+    def descr(self) -> str:
+        return (
+            f"{self.name} - Gaussian width : {self.gaussian_width:.2f}, "
+            f"Lorentzian width : {self.lorentzian_width:.2f}"
+        )
+
+
+def setup_axes(n: int, lims=(-10, 10)) -> tuple[np.ndarray, float, np.ndarray, float]:
+    """Creates a time-like and a frequency-like array and returns their respective spacing"""
+    x, dx = np.linspace(*lims, n, retstep=True)
+    f = np.fft.fftfreq(n, dx)
+    return x, dx, f, f[1] - f[0]
+
+
+def freq_axis(x: np.ndarray) -> tuple[np.ndarray, np.ndarray, float]:
+    """
+    given an array with equally spaced values, returns a corresponding frequency array,
+    an array of indices to automatically sort ffts and the x spacing
+    """
+    dx = np.diff(x).mean()
+    f = np.fft.fftfreq(len(x), dx)
+    ind = np.argsort(f)
+    return f[ind], ind, dx
+
+
+def lorentzian(x: np.ndarray, amp: float, width: float, x0: float) -> np.ndarray:
+    """Lorentzian function of max `amp`, FWHM `width` and position `x0`"""
+    gamma = (width * 0.5) ** 2
+    return amp * gamma / ((x - x0) ** 2 + gamma)
+
+
+def unit_lorentzian(x: np.ndarray, width: float, x0: float) -> np.ndarray:
+    """Normalized Lorentzian function of FWHM `width` and position `x0`"""
+    return lorentzian(x, 1 / (np.pi * width * 0.5), width, x0)
+
+
+def peak_func(x: np.ndarray, amp: float, width: float, x0: float) -> np.ndarray:
+    """2-sided decaying exp of max `amp`, FWHM `width` and position `x0`"""
+    a = 2 * LN2 / width
+    return amp * np.exp(-np.abs(x - x0) * a)
+
+
+def fft_lorentzian(f: np.ndarray, dx: float, amp: float, width: float) -> np.ndarray:
+    """
+    Same as `peak_func` but parametrized as the fourier transform
+    of a Lorentzian function of max `amp` and FWHM `width`
+    """
+    gamma_sqrt = width / 2
+    return amp * np.pi * gamma_sqrt * np.exp(-2 * np.pi * gamma_sqrt * np.abs(f)) / dx
+
+
+def gaussian(x: np.ndarray, amp: float, width: float, x0: float) -> np.ndarray:
+    """Gaussian function of max `amp`, FWHM `width` and position `x0`"""
+    sig2 = width ** 2 / (8 * LN2)
+    return amp * np.exp(-((x - x0) ** 2) / (2 * sig2))
+
+
+def elevated_gaussian(x: np.ndarray, amp: float, width: float, x0: float, y0: float) -> np.ndarray:
+    """Gaussian function of max `amp`, FWHM `width`, position `x0` and baseline `y0`"""
+    sig2 = width ** 2 / (8 * LN2)
+    return amp * np.exp(-((x - x0) ** 2) / (2 * sig2)) + y0
+
+
+def unit_gaussian(x: np.ndarray, width: float, x0: float) -> np.ndarray:
+    """Normalized Gaussian function of FWHM `width` and position `x0`"""
+    return gaussian(x, np.sqrt(4 * LN2 / np.pi) / width, width, x0)
+
+
+def fft_gaussian(f: np.ndarray, dx: float, amp: float, width: float) -> np.ndarray:
+    """
+    Same as `gaussian` but parametrized as the fourier transform
+    of another Gaussian function of max `amp` and FWHM `width`
+    """  # exp_param =
+    freq_amp = amp * width / 2 * np.sqrt(np.pi / LN2) / dx
+    freq_width = 4 * LN2 / (width * np.pi)
+    return gaussian(f, freq_amp, freq_width, 0)
+
+
+def voigt(x: np.ndarray, gaussian_width: float, lorentzian_width: float) -> np.ndarray:
+    """Voigt profile of max 1 with specified Gaussian and Lorentzian FWHM"""
+    conv = convolve(unit_gaussian(x, gaussian_width, 0), unit_lorentzian(x, lorentzian_width, 0))
+    if conv.max() > 0:
+        return conv / conv.max()
+    return conv
+
+
+def log_voigt(x: np.ndarray, gaussian_width: float, lorentzian_width: float) -> np.ndarray:
+    """log of `voigt`"""
+    return np.log(voigt(x, gaussian_width, lorentzian_width))
+
+
+def fft_voigt(
+    f: np.ndarray, dx: float, gaussian_width: float, lorentzian_width: float
+) -> np.ndarray:
+    """
+    returns the product of a `peak_func` and a `gaussian`
+    parameterized as the Fourier transform of a Voigt profile
+    given by `gaussian_width` and `lorentzian_width`
+    """
+    profile = fft_gaussian(f, dx, 1, gaussian_width) * fft_lorentzian(f, dx, 1, lorentzian_width)
+    return profile / profile.max()
+
+
+def single_func_fit(
+    x: np.ndarray,
+    y: np.ndarray,
+    fct: Callable[[np.ndarray, float, float, float], np.ndarray],
+    force_center=False,
+    use_weights=False,
+    extra_params: int = 0,
+) -> FitResult:
+    """fits a single bell-like function (Gaussian or Lorentian, not Voigt)
+
+    Parameters
+    ----------
+    x : np.ndarray
+        x input
+    y : np.ndarray
+        corresponding y data
+    fct : Callable[[np.ndarray, float, float, float], np.ndarray]
+        function to fit
+    force_center : bool, optional
+        assume the bell is centered at x=0, by default False
+    use_weights : bool, optional
+        give more importance to higher y values, by default False
+
+    Returns
+    -------
+    FitResult
+        resuts of the fit
+    """
+    if force_center:
+
+        def _fct(_x: np.ndarray, amp: float, width: float):
+            return fct(_x, amp, width, 0)
+
+        fct = _fct
+    am = y.argmax()
+    params, cov = curve_fit(
+        fct, x, y, sigma=1 / y if use_weights else None, p0=[y[am], 1, x[am]] + [0] * extra_params
+    )
+    curve = fct(x, *params)
+    return FitResult(curve, cov, params[0], params[1], params[2], tuple(params))
+
+
+def linear_direct_voigt_fit(x: np.ndarray, y: np.ndarray, use_weights=False) -> VoigtFitResult:
+    params, cov = curve_fit(voigt, x, y, sigma=1 / y if use_weights else None)
+    curve = voigt(x, *params)
+    return VoigtFitResult("Linear direct fit", curve, cov, *params)
+
+
+def log_direct_voigt_fit(x: np.ndarray, y: np.ndarray) -> VoigtFitResult:
+    ind = y > 0
+    y_fit = np.log(y[ind])
+    x_fit = x[ind]
+    params, cov = curve_fit(log_voigt, x_fit, y_fit, bounds=[1e-12, np.inf])
+    curve = np.exp(log_voigt(x, *params))
+    return VoigtFitResult("Log direct fit", curve, cov, *params)
+
+
+def linear_fft_voigt_fit(f: np.ndarray, A: np.ndarray, x: np.ndarray, dx: float) -> VoigtFitResult:
+    params, cov = curve_fit(
+        lambda _f, _g, _l: fft_voigt(_f, dx, _g, _l), f, A, bounds=[1e-12, np.inf]
+    )
+    curve = voigt(x, *params)
+    return VoigtFitResult("Linear FFT fit", curve, cov, *params)
+
+
+def convolve(gau: np.ndarray, lor: np.ndarray) -> np.ndarray:
+    return np.convolve(gau, lor, mode="same")
+
+
+def add_noise(arr: np.ndarray, abs_fac: float, rel_fac: float):
+    return (
+        arr + abs_fac * np.random.rand(len(arr)) + rel_fac * arr * (np.random.rand(len(arr)) - 0.5)
+    )
+
+
+@main.command(help="fit a lorentzian with a gaussian")
+def demo1():
+    x = np.linspace(-10, 10, 501)
+    with PlotApp(
+        FWHM=np.geomspace(0.1, 10),
+        relative_noise=np.linspace(0, 2),
+        absolute_noise=[0, *np.geomspace(0.001, 1)],
+    ) as app:
+        app.set_antialiasing(True)
+        app.params["FWHM"].value = 3.7
+
+        @app.update
+        def draw(FWHM, relative_noise, absolute_noise):
+            lo = lorentzian(x, 1, FWHM, 0)
+            lo = add_noise(lo, absolute_noise, relative_noise * 0.04)
+            fit = single_func_fit(x, lo, gaussian)
+            app[0].set_line_data("Lorentzian", x, lo, width=2)
+            app[0].set_line_data(
+                "gaus fit", x, fit.curve, width=2, label=f"Gaussian fit : FWHM = {fit.width}"
+            )
+
+
+@main.command(name="default", help="illustrate the influence of noises and fit a voigt profile")
+def demo2():
+    with PlotApp(
+        n=np.arange(256, 2046),
+        lorentz_fwhm=np.geomspace(0.1, 1),
+        gauss_fwhm=np.linspace(1, 10),
+        relative_noise=np.linspace(0, 2),
+        absolute_noise=[0, *np.geomspace(1e-6, 1, 201)],
+    ) as app:
+        app.set_antialiasing(True)
+        ax = app["Main Plot"]
+
+        app.params["gauss_fwhm"].value = 5
+        app.params["n"].value = 1024
+        app.params_layout.setSpacing(0)
+
+        @app.update
+        def draw(n, lorentz_fwhm, gauss_fwhm, absolute_noise, relative_noise):
+            x, dx, f, df = setup_axes(n, (-20, 20))
+            gaus = gaussian(x, 1, gauss_fwhm, 0)
+            lore = lorentzian(x, 1, lorentz_fwhm, 0)
+            ax.set_line_data("Gaussian", x, gaus / gaus.max(), width=2)
+            ax.set_line_data("Lorentz", x, lore / lore.max(), width=2)
+
+            conv = convolve(gaus, lore)
+            conv /= conv.max()
+            conv_noise = add_noise(conv, absolute_noise, relative_noise * 0.1)
+            gaus_noise = add_noise(gaus, absolute_noise, relative_noise * 0.1)
+            ax.set_line_data("Voigt", x, conv, width=2)
+            ax.set_line_data("Noisy Voigt", x, conv_noise, width=2)
+            ax.set_line_data("Noisy Gaussian", x, gaus_noise, width=2)
+
+            lin_fit = linear_direct_voigt_fit(x, conv_noise)
+            log_fit = log_direct_voigt_fit(x, conv_noise)
+            transfo = np.fft.fft(np.fft.fftshift(conv_noise)).real
+            fft_fit = linear_fft_voigt_fit(f, transfo / transfo.max(), x, dx)
+            for fit in lin_fit, log_fit, fft_fit:
+                display_fit(x, fit)
+
+        def display_fit(x: np.ndarray, fit: VoigtFitResult):
+            ax.set_line_data(fit.name, x, fit.curve)
+            ax.set_line_data(
+                fit.name + "gauss",
+                x,
+                gaussian(x, 1, fit.gaussian_width, 0),
+                label=f"{fit.name} - Gaussian {fit.gaussian_width:.2f}",
+                width=1.5,
+            )
+            ax.set_line_data(
+                fit.name + "loren",
+                x,
+                lorentzian(x, 1, fit.lorentzian_width, 0),
+                label=f"{fit.name} - Lorentzian {fit.lorentzian_width:.2f}",
+                width=1.5,
+            )
+
+
+@main.command(help="Explore fft fitting")
+def demo3():
+    x, dx, f, df = setup_axes(1001, (-20, 20))
+    with PlotApp(
+        lorentz_fwhm=np.geomspace(0.1, 1),
+        gauss_fwhm=np.linspace(1, 10),
+        relative_noise=np.linspace(0, 2),
+        absolute_noise=[0, *np.geomspace(1e-6, 1, 201)],
+    ) as app:
+        app.set_antialiasing(True)
+
+        ax = app[0]
+        ind = np.argsort(f)
+
+        @app.update
+        def draw(lorentz_fwhm, gauss_fwhm, absolute_noise, relative_noise):
+            gaus_clean = gaussian(x, 1, gauss_fwhm, 0)
+            lore_clean = lorentzian(x, 1, lorentz_fwhm, 0)
+            voig_clean = convolve(gaus_clean, lore_clean)
+
+            gaus = add_noise(gaus_clean, absolute_noise, relative_noise * 0.1)
+            lore = add_noise(lore_clean, absolute_noise, relative_noise * 0.1)
+            voig = add_noise(voig_clean, absolute_noise, relative_noise * 0.1)
+
+            gaus_f = np.fft.fft(np.fft.fftshift(gaus)).real
+            lore_f = np.fft.fft(np.fft.fftshift(lore)).real
+            voig_f = np.fft.fft(np.fft.fftshift(voig)).real
+
+            ax.set_line_data("Transformed Gaussian", f[ind], gaus_f[ind])
+            ax.set_line_data("Transformed Lorentz", f[ind], lore_f[ind])
+            ax.set_line_data("Transformed Voigt", f[ind], voig_f[ind])
+
+            gaus_ff = fft_gaussian(f, dx, 1, gauss_fwhm)
+            lore_ff = fft_lorentzian(f, dx, 1, lorentz_fwhm)
+            voig_ff = fft_voigt(f, dx, gauss_fwhm, lorentz_fwhm) * voig_clean.sum()
+
+            ax.set_line_data("Expected Gaussian", f[ind], gaus_ff[ind], width=1)
+            ax.set_line_data("Expected Lorentz", f[ind], lore_ff[ind], width=1)
+            ax.set_line_data("Expected Voigt", f[ind], voig_ff[ind], width=1)
+
+
+@click.argument("file", type=click.Path(True, dir_okay=False))
+@main.command(name="fit")
+def fit_measurement(file):
+    wl, intens = lab.osa.load_osa_spectrum(file)
+    wl *= 1e9
+    gauss_fit = single_func_fit(wl, intens, elevated_gaussian, extra_params=1)
+    wl0 = gauss_fit.x0
+    baseline = gauss_fit.params[-1]
+    intens -= baseline
+    gauss_fit.curve -= baseline
+    intens[intens < 0] = 0
+    wl -= wl0
+    with PlotApp(n=np.arange(len(wl) // 2)[1:]) as app:
+        app.set_antialiasing(True)
+
+        ax1 = app["Measurement"]
+        ax2 = app["Fourier domain"]
+        ax1.set_line_data("Measured spectrum", wl, intens, width=2, color="red")
+        ax1.set_line_data("Initial Guassian fit", wl, gauss_fit.curve, width=2, color="blue")
+        ax1.plot_widget.plotItem.setLogMode(y=True)
+
+        @app.update
+        def draw(n):
+            s = slice(n, -n) if n else slice(None)
+
+            wl_fit = wl[s]
+            intens_fit = intens[s] - intens[s].min()
+            f, ind, dwl = freq_axis(wl_fit)
+
+            ax1.set_line_data("Fitted spectrum", wl_fit, intens_fit)
+
+            trans = np.abs(np.fft.fft(intens_fit))[ind]
+            m = trans.max()
+            ax2.set_line_data("Transformed", f, trans)
+
+            fft_fit = linear_fft_voigt_fit(f, trans / m, wl_fit, dwl)
+            lin_fit = linear_direct_voigt_fit(wl_fit, intens_fit)
+            log_fit = log_direct_voigt_fit(wl_fit, intens_fit)
+            for fit in fft_fit, lin_fit, log_fit:
+                display_fit(wl_fit, dwl, f, fit, m)
+
+        def display_fit(x: np.ndarray, dx: float, f: np.ndarray, fit: VoigtFitResult, amp: float):
+            ax2.set_line_data(
+                fit.name, f, amp * fft_voigt(f, dx, fit.gaussian_width, fit.lorentzian_width)
+            )
+            ax1.set_line_data(fit.name, x, fit.curve)
+            ax1.set_line_data(
+                fit.name + "gauss",
+                x,
+                gaussian(x, 1, fit.gaussian_width, 0),
+                label=f"{fit.name} - Gaussian {fit.gaussian_width:.2f}",
+                width=1.5,
+            )
+            ax1.set_line_data(
+                fit.name + "lorentz",
+                x,
+                lorentzian(x, 1, fit.lorentzian_width, 0),
+                label=f"{fit.name} - Lorentzian {fit.lorentzian_width:.2f}",
+                width=1.5,
+            )
+
+
+if __name__ == "__main__":
+    main()

test_scaling.py

@@ -0,0 +1,46 @@
+"""test what the scaling factore of numpy's fft is"""
+import numpy as np
+from customfunc.app import PlotApp
+
+
+def setup_axes(n: int, lims=(-10, 10)) -> tuple[np.ndarray, float, np.ndarray, float]:
+    x, dx = np.linspace(*lims, n, retstep=True)
+    f = np.fft.fftfreq(n, dx)
+    return x, dx, f, f[1] - f[0]
+
+
+def abs2(z):
+    return z.real ** 2 + z.imag ** 2
+
+
+def g(x, w):
+    return np.exp(-w * x ** 2)
+
+
+def main():
+
+    with PlotApp(exp_param=np.linspace(1, 50), n=np.arange(32, 1024)) as app:
+
+        app.set_antialiasing(True)
+        fax = app["Frequency"]
+
+        @app.update
+        def draw(exp_param, n):
+            x, dx, f, df = setup_axes(n)
+            ind = np.argsort(f)
+            time_amp = 1
+
+            freq_amp = np.sqrt(np.pi / exp_param) * time_amp / dx
+            freq_w = np.pi ** 2 / exp_param
+
+            signal = g(x, exp_param) * time_amp
+
+            transformed = np.fft.fft(np.fft.fftshift(signal))
+            fax.set_line_data("transformed", f[ind], transformed[ind].real)
+
+            modeled = g(f, freq_w) * freq_amp
+            fax.set_line_data("expected", f[ind], modeled[ind])
+
+
+if __name__ == "__main__":
+    main()