Fix incorrect colour.colorimetry.sd_gaussian_fwhm definition output.

References #1171.
colour-science · Jul 22, 2023 · a2e89cf · a2e89cf
1 parent 1966033
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diff --git a/colour/colorimetry/generation.py b/colour/colorimetry/generation.py
@@ -467,14 +467,15 @@ def sd_gaussian_fwhm(
     SpectralShape(360.0, 780.0, 1.0)
     >>> sd[555]  # doctest: +ELLIPSIS
     1...
-    >>> sd[530]  # doctest: +ELLIPSIS
-    0.3678794...
+    >>> sd[530]
+    0.0625
     """
 
     settings = {"name": f"{peak_wavelength}nm - {fwhm} FWHM - Gaussian"}
     settings.update(kwargs)
 
-    values = np.exp(-(((shape.wavelengths - peak_wavelength) / fwhm) ** 2))
+    mu, sigma = peak_wavelength, fwhm / (2 * np.sqrt(2 * np.log(2)))
+    values = np.exp(-((shape.wavelengths - mu) ** 2) / (2 * sigma**2))
 
     return SpectralDistribution(values, shape.wavelengths, **settings)
 
@@ -505,7 +506,7 @@ def sd_gaussian(
         peak at.
     sigma_fwhm
         Standard deviation :math:`sigma` of the gaussian spectral distribution
-        or Full width at half maximum, i.e. width of the gaussian spectral
+        or full width at half maximum, i.e. width of the gaussian spectral
         distribution measured between those points on the *y* axis which are
         half the maximum amplitude.
     shape
@@ -544,8 +545,8 @@ def sd_gaussian(
     SpectralShape(360.0, 780.0, 1.0)
     >>> sd[555]  # doctest: +ELLIPSIS
     1...
-    >>> sd[530]  # doctest: +ELLIPSIS
-    0.3678794...
+    >>> sd[530]
+    0.0625
     """
 
     method = validate_method(method, tuple(SD_GAUSSIAN_METHODS))
@@ -557,31 +558,29 @@ def sd_gaussian(
 
 def sd_single_led_Ohno2005(
     peak_wavelength: float,
-    fwhm: float,
+    half_spectral_width: float,
     shape: SpectralShape = SPECTRAL_SHAPE_DEFAULT,
     **kwargs: Any,
 ) -> SpectralDistribution:
     """
     Return a single *LED* spectral distribution of given spectral shape at
-    given peak wavelength and full width at half maximum according to
-    *Ohno (2005)* method.
+    given peak wavelength and half spectral width :math:`\\Delta\\lambda_{0.5}`
+    according to *Ohno (2005)* method.
 
     Parameters
     ----------
     peak_wavelength
         Wavelength the single *LED* spectral distribution will peak at.
-    fwhm
-        Full width at half maximum, i.e. width of the underlying gaussian
-        spectral distribution measured between those points on the *y* axis
-        which are half the maximum amplitude.
+    half_spectral_width
+        Half spectral width :math:`\\Delta\\lambda_{0.5}`.
     shape
         Spectral shape used to create the spectral distribution.
 
     Other Parameters
     ----------------
     kwargs
-        {:func:`colour.colorimetry.sd_gaussian_fwhm`},
-        See the documentation of the previously listed definition.
+        {:class:`colour.SpectralDistribution`},
+        See the documentation of the previously listed class.
 
     Returns
     -------
@@ -606,14 +605,18 @@ def sd_single_led_Ohno2005(
     1...
     """
 
-    settings = {"name": f"{peak_wavelength}nm - {fwhm} FWHM LED - Ohno (2005)"}
+    settings = {
+        "name": f"{peak_wavelength}nm - {half_spectral_width} "
+        f"Half Spectral Width LED - Ohno (2005)"
+    }
     settings.update(kwargs)
 
-    sd = sd_gaussian_fwhm(peak_wavelength, fwhm, shape, **kwargs)
-
-    sd.values = (sd.values + 2 * sd.values**5) / 3
+    values = np.exp(
+        -(((shape.wavelengths - peak_wavelength) / half_spectral_width) ** 2)
+    )
+    values = (values + 2 * values**5) / 3
 
-    return sd
+    return SpectralDistribution(values, shape.wavelengths, **settings)
 
 
 SD_SINGLE_LED_METHODS: CanonicalMapping = CanonicalMapping(
@@ -628,24 +631,18 @@ def sd_single_led_Ohno2005(
 
 def sd_single_led(
     peak_wavelength: float,
-    fwhm: float,
     shape: SpectralShape = SPECTRAL_SHAPE_DEFAULT,
     method: Literal["Ohno 2005"] | str = "Ohno 2005",
     **kwargs: Any,
 ) -> SpectralDistribution:
     """
     Return a single *LED* spectral distribution of given spectral shape at
-    given peak wavelength and full width at half maximum according to given
-    method.
+    given peak wavelength according to given method.
 
     Parameters
     ----------
     peak_wavelength
         Wavelength the single *LED* spectral distribution will peak at.
-    fwhm
-        Full width at half maximum, i.e. width of the underlying gaussian
-        spectral distribution measured between those points on the *y*
-        axis which are half the maximum amplitude.
     shape
         Spectral shape used to create the spectral distribution.
     method
@@ -673,31 +670,30 @@ def sd_single_led(
 
     Examples
     --------
-    >>> sd = sd_single_led(555, 25)
+    >>> sd = sd_single_led(555, half_spectral_width=25)
     >>> sd.shape
     SpectralShape(360.0, 780.0, 1.0)
     >>> sd[555]  # doctest: +ELLIPSIS
     1...
     """
 
     method = validate_method(method, tuple(SD_SINGLE_LED_METHODS))
+    kwargs["shape"] = shape
 
-    return SD_SINGLE_LED_METHODS[method](
-        peak_wavelength, fwhm, shape, **kwargs
-    )
+    return SD_SINGLE_LED_METHODS[method](peak_wavelength, **kwargs)
 
 
 def sd_multi_leds_Ohno2005(
     peak_wavelengths: ArrayLike,
-    fwhm: ArrayLike,
+    half_spectral_widths: ArrayLike,
     peak_power_ratios: ArrayLike | None = None,
     shape: SpectralShape = SPECTRAL_SHAPE_DEFAULT,
     **kwargs: Any,
 ) -> SpectralDistribution:
     """
     Return a multi *LED* spectral distribution of given spectral shape at
-    given peak wavelengths and full widths at half maximum according to
-    *Ohno (2005)* method.
+    given peak wavelengths, half spectral widths :math:`\\Delta\\lambda_{0.5}`
+    and peak power ratios according to *Ohno (2005)* method.
 
     The multi *LED* spectral distribution is generated using many single *LED*
     spectral distributions generated with :func:`colour.sd_single_led_Ohno2005`
@@ -708,10 +704,8 @@ def sd_multi_leds_Ohno2005(
     peak_wavelengths
         Wavelengths the multi *LED* spectral distribution will peak at, i.e.
         the peaks for each generated single *LED* spectral distributions.
-    fwhm
-        Full widths at half maximum, i.e. widths of the underlying gaussian
-        spectral distributions measured between those points on the *y* axis
-        which are half the maximum amplitude.
+    half_spectral_widths
+        Half spectral widths :math:`\\Delta\\lambda_{0.5}`.
     peak_power_ratios
         Peak power ratios for each generated single *LED* spectral
         distributions.
@@ -752,7 +746,9 @@ def sd_multi_leds_Ohno2005(
     """
 
     peak_wavelengths = as_float_array(peak_wavelengths)
-    fwhm = np.resize(fwhm, peak_wavelengths.shape)
+    half_spectral_widths = np.resize(
+        half_spectral_widths, peak_wavelengths.shape
+    )
     if peak_power_ratios is None:
         peak_power_ratios = ones(peak_wavelengths.shape)
     else:
@@ -762,11 +758,13 @@ def sd_multi_leds_Ohno2005(
 
     sd = sd_zeros(shape)
 
-    for peak_wavelength, fwhm_s, peak_power_ratio in zip(
-        peak_wavelengths, fwhm, peak_power_ratios
+    for peak_wavelength, half_spectral_width, peak_power_ratio in zip(
+        peak_wavelengths, half_spectral_widths, peak_power_ratios
     ):
         sd += (
-            sd_single_led_Ohno2005(peak_wavelength, fwhm_s, **kwargs)
+            sd_single_led_Ohno2005(
+                peak_wavelength, half_spectral_width, **kwargs
+            )
             * peak_power_ratio
         )
 
@@ -777,7 +775,7 @@ def _format_array(a: NDArrayFloat) -> str:
 
     sd.name = (
         f"{_format_array(peak_wavelengths)}nm - "
-        f"{_format_array(fwhm)} FWHM - "
+        f"{_format_array(half_spectral_widths)} FWHM - "
         f"{_format_array(peak_power_ratios)} Peak Power Ratios - "
         f"LED - Ohno (2005)"
     )
@@ -797,29 +795,19 @@ def _format_array(a: NDArrayFloat) -> str:
 
 def sd_multi_leds(
     peak_wavelengths: ArrayLike,
-    fwhm: ArrayLike,
-    peak_power_ratios: ArrayLike | None = None,
     shape: SpectralShape = SPECTRAL_SHAPE_DEFAULT,
     method: Literal["Ohno 2005"] | str = "Ohno 2005",
     **kwargs: Any,
 ) -> SpectralDistribution:
     """
     Return a multi *LED* spectral distribution of given spectral shape at
-    given peak wavelengths and full widths at half maximum according to given
-    method.
+    given peak wavelengths.
 
     Parameters
     ----------
     peak_wavelengths
         Wavelengths the multi *LED* spectral distribution will peak at, i.e.
         the peaks for each generated single *LED* spectral distributions.
-    fwhm
-        Full widths at half maximum, i.e. widths of the underlying gaussian
-        spectral distributions measured between those points on the *y* axis
-        which are half the maximum amplitude.
-    peak_power_ratios
-        Peak power ratios for each generated single *LED* spectral
-        distributions.
     shape
         Spectral shape used to create the spectral distribution.
     method
@@ -849,8 +837,8 @@ def sd_multi_leds(
     --------
     >>> sd = sd_multi_leds(
     ...     np.array([457, 530, 615]),
-    ...     np.array([20, 30, 20]),
-    ...     np.array([0.731, 1.000, 1.660]),
+    ...     half_spectral_widths=np.array([20, 30, 20]),
+    ...     peak_power_ratios=np.array([0.731, 1.000, 1.660]),
     ... )
     >>> sd.shape
     SpectralShape(360.0, 780.0, 1.0)
@@ -859,7 +847,6 @@ def sd_multi_leds(
     """
 
     method = validate_method(method, tuple(SD_MULTI_LEDS_METHODS))
+    kwargs["shape"] = shape
 
-    return SD_MULTI_LEDS_METHODS[method](
-        peak_wavelengths, fwhm, peak_power_ratios, shape, **kwargs
-    )
+    return SD_MULTI_LEDS_METHODS[method](peak_wavelengths, **kwargs)
diff --git a/colour/colorimetry/tests/test_generation.py b/colour/colorimetry/tests/test_generation.py
@@ -187,17 +187,18 @@ class TestSdGaussianFwhm(unittest.TestCase):
 
     def test_sd_gaussian_fwhm(self):
         """
-        Test :func:`colour.colorimetry.generation.sd_gaussian_fwhm`
-        definition.
+        Test :func:`colour.colorimetry.generation.sd_gaussian_fwhm` definition.
         """
 
         sd = sd_gaussian_fwhm(555, 25)
 
-        self.assertAlmostEqual(sd[530], 0.367879441171443, places=7)
+        self.assertAlmostEqual(sd[530], 0.0625, places=7)
 
         self.assertAlmostEqual(sd[555], 1, places=7)
 
-        self.assertAlmostEqual(sd[580], 0.367879441171443, places=7)
+        self.assertAlmostEqual(sd[580], 0.062499999999999, places=7)
+
+        self.assertAlmostEqual(sd[555 - 25 / 2], 0.5, places=7)
 
 
 class TestSdSingleLedOhno2005(unittest.TestCase):