Improve phasor_from_lifetime tutorial (#55)

phasorpy · Apr 15, 2024 · f4060ba · f4060ba
1 parent 94f3ccd
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diff --git a/src/phasorpy/plot.py b/src/phasorpy/plot.py
@@ -248,6 +248,7 @@ def plot(
             self._lines = ax.plot(re, im, fmt, label=lbl, **kwargs)
         if label is not None:
             ax.legend()
+        self._reset_limits()
 
     def _histogram2d(
         self,

diff --git a/tutorials/phasorpy_phasor_from_lifetime.py b/tutorials/phasorpy_phasor_from_lifetime.py
@@ -19,17 +19,24 @@
 from phasorpy.phasor import phasor_from_lifetime, phasor_to_polar
 from phasorpy.plot import PhasorPlot, plot_phasor, plot_polar_frequency
 
+rng = numpy.random.default_rng()
+
 # %%
 # Single-component lifetimes
 # --------------------------
 #
 # The phasor coordinates of single-component lifetimes are located
 # on the universal semicircle.
-# For example, 3.9788735 ns and 0.9947183 ns at a frequency of 80 MHz:
+# For example, 4.0 ns and 1.0 ns at a frequency of 80 MHz:
 
-lifetime = numpy.array([3.9788735, 0.9947183])
+frequency = 80.0
+lifetimes = [4.0, 1.0]
 
-plot_phasor(*phasor_from_lifetime(80.0, lifetime), frequency=80.0)
+plot_phasor(
+    *phasor_from_lifetime(frequency, lifetimes),
+    frequency=frequency,
+    title='Single-component lifetimes',
+)
 
 # %%
 # Multi-component lifetimes
@@ -39,12 +46,15 @@
 # fractional intensities are linear combinations of the coordinates
 # of the pure components:
 
-fraction = numpy.array(
+fractions = numpy.array(
     [[1, 0], [0.25, 0.75], [0.5, 0.5], [0.75, 0.25], [0, 1]]
 )
 
 plot_phasor(
-    *phasor_from_lifetime(80.0, lifetime, fraction), fmt='o-', frequency=80.0
+    *phasor_from_lifetime(frequency, lifetimes, fractions),
+    fmt='o-',
+    frequency=frequency,
+    title='Multi-component lifetimes',
 )
 
 # %%
@@ -55,84 +65,116 @@
 # pre-exponential amplitudes are also located on a line:
 
 plot_phasor(
-    *phasor_from_lifetime(80.0, lifetime, fraction, preexponential=True),
+    *phasor_from_lifetime(
+        frequency, lifetimes, fractions, preexponential=True
+    ),
     fmt='o-',
-    frequency=80.0,
+    frequency=frequency,
+    title='Pre-exponential amplitudes',
 )
 
+# %%
+# Average of lifetime distributions
+# ---------------------------------
+#
+# The average phasor coordinates for wider distributions of lifetimes
+# lie further inside the universal semicircle compared to the narrower
+# distributions:
+
+frequency = 80.0
+lifetime = 4.0
+standard_deviations = [0.1, 0.5, 1.0]
+samples = 100000
+
+plot = PhasorPlot(
+    frequency=frequency, title='Average of lifetime distributions'
+)
+for sigma in standard_deviations:
+    phi = numpy.sqrt(sigma * sigma / lifetime)
+    phasor_average = numpy.average(
+        phasor_from_lifetime(
+            frequency, rng.gamma(lifetime / phi, phi, samples)
+        ),
+        axis=1,
+    )
+    plot.plot(*phasor_average, label=f'{sigma=:.1f}')
+plot.show()
+
 # %%
 # Lifetime distributions at multiple frequencies
 # ----------------------------------------------
 #
 # Phasor coordinates can be calculated at once for many frequencies,
-# lifetime components, and their fractions. As an example, random distrinutions
-# of lifetimes and their fractions are plotted at three frequencies.
+# lifetime components, and their fractions. As an example, random
+# distrinutions of lifetimes and their fractions are plotted at
+# three frequencies.
 # Lifetimes are passed in units of s and frequencies in Hz, requiring to
 # specify a `unit_conversion` factor:
 
-rng = numpy.random.default_rng()
-
 samples = 100
-lifetime_distribution = (
+lifetimes = [4.0, 2.0, 1.0]
+
+lifetime_distributions = (
     numpy.column_stack(
-        (
-            rng.normal(3.9788735, 0.05, samples),
-            rng.normal(1.9894368, 0.05, samples),
-            rng.normal(0.9947183, 0.05, samples),
-        )
+        [rng.gamma(lifetime / 0.01, 0.01, samples) for lifetime in lifetimes]
     )
     * 1e-9
 )
-fraction_distribution = numpy.column_stack(
-    (rng.random(samples), rng.random(samples), rng.random(samples))
+fraction_distributions = numpy.column_stack(
+    [rng.random(samples) for lifetime in lifetimes]
 )
 
 plot_phasor(
     *phasor_from_lifetime(
         frequency=[40e6, 80e6, 160e6],
-        lifetime=lifetime_distribution,
-        fraction=fraction_distribution,
+        lifetime=lifetime_distributions,
+        fraction=fraction_distributions,
         unit_conversion=1.0,
     ),
     fmt='.',
     label=('40 MHz', '80 MHz', '160 MHz'),
+    title='Lifetime distributions at multiple frequencies',
 )
 
 # %%
 # FRET efficiency
 # ---------------
 #
 # The phasor coordinates of a fluorescence energy transfer donor
-# with a single lifetime component of 4.2 ns as a function of FRET efficiency
+# with a single lifetime component of 4.0 ns as a function of FRET efficiency
 # at a frequency of 80 MHz, with some background signal and about 90 %
 # of the donors participating in energy transfer, are on a curved trajectory.
 # For comparison, when 100% donors participate in FRET and there is no
 # background signal, the phasor coordinates lie on the universal semicircle:
 
+frequency = 80.0
 samples = 25
+lifetime = 4.0
 efficiency = numpy.linspace(0.0, 1.0, samples)
 
-plot = PhasorPlot(frequency=80.0)
+lifetime_quenched = lifetime * (1.0 - efficiency)
+
+plot = PhasorPlot(frequency=frequency, title='FRET efficiency')
 plot.plot(
-    *phasor_from_lifetime(80.0, 4.2 * (1.0 - efficiency)),
+    *phasor_from_lifetime(frequency, lifetime_quenched),
     label='100% Donor in FRET',
     fmt='k.',
 )
 plot.plot(
     *phasor_from_lifetime(
-        80.0,
+        frequency,
         lifetime=numpy.column_stack(
             (
-                numpy.full(samples, 4.2),  # donor-only lifetime
-                4.2 * (1.0 - efficiency),  # donor lifetime with FRET
+                numpy.full(samples, lifetime),  # donor-only lifetime
+                lifetime_quenched,  # donor lifetime with FRET
                 numpy.full(samples, 1e9),  # background with long lifetime
             )
         ),
         fraction=[0.1, 0.9, 0.1 / 1e9],
         preexponential=True,
     ),
-    label='90% Donor in FRET',
     fmt='o-',
+    label='90% Donor in FRET',
 )
 plot.show()
 
@@ -143,14 +185,14 @@
 # Phase shift and demodulation of multi-component lifetimes can be calculated
 # as a function of the excitation light frequency and fractional intensities:
 
-frequency = numpy.logspace(-1, 4, 32)
-fraction = numpy.array([[1, 0], [0.5, 0.5], [0, 1]])
+frequencies = numpy.logspace(-1, 4, 32)
+lifetimes = [4.0, 1.0]
+fractions = numpy.array([[1, 0], [0.5, 0.5], [0, 1]])
 
 plot_polar_frequency(
-    frequency,
-    *phasor_to_polar(
-        *phasor_from_lifetime(frequency, [3.9788735, 0.9947183], fraction)
-    ),
+    frequencies,
+    *phasor_to_polar(*phasor_from_lifetime(frequencies, lifetimes, fractions)),
+    title='Multi-frequency plot',
 )
 
 # %%