improve Lognormal docstring + add unit tests (#1319)

thanks @crocicc for feedback

PySDM/initialisation/spectra/lognormal.py

@@ -12,6 +12,9 @@
 
 class Lognormal(Spectrum):
     def __init__(self, norm_factor: float, m_mode: float, s_geom: float):
+        """`norm_factor=1` corresponds to standard normalised probability density,
+        other settings allow to express, e.g., size or mass distributions;
+        `m_mode` is the median value, `s_geom` is the geometric standard deviation"""
         super().__init__(lognorm, (math.log(s_geom), 0, m_mode), norm_factor)
 
     @property

tests/unit_tests/initialisation/test_spectra_lognormal.py

@@ -0,0 +1,52 @@
+""" tests for lognormal probability distribution """
+
+import numpy as np
+import pytest
+from PySDM.initialisation.spectra import Lognormal
+
+
+class TestSpectraLognormal:
+    """checks ctor args against computed values"""
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        "m_mode, s_geom",
+        (
+            (0.01, 1.5),
+            (0.1, 1.1),
+            (1, 1.01),
+        ),
+    )
+    def test_median(m_mode, s_geom):
+        # arrange
+        sut = Lognormal(m_mode=m_mode, norm_factor=1, s_geom=s_geom)
+
+        # act
+        median = sut.percentiles(0.5)
+
+        # assert
+        assert median == m_mode
+
+    @staticmethod
+    @pytest.mark.parametrize(
+        "m_mode, s_geom",
+        (
+            (0.01, 3.5),
+            (0.1, 2.1),
+            (1, 1.5),
+        ),
+    )
+    def test_mean(m_mode, s_geom):
+        # arrange
+        sut = Lognormal(m_mode=m_mode, norm_factor=1, s_geom=s_geom)
+        x = np.linspace(m_mode / 1000, m_mode * 1000, num=10000)
+
+        # act
+        mean = np.sum(sut.pdf(x) * x) / np.sum(sut.pdf(x))
+
+        # assert
+        np.testing.assert_approx_equal(
+            actual=np.log(m_mode) + 0.5 * np.log(s_geom) ** 2,
+            desired=np.log(mean),
+            significant=3,
+        )