[ENH] - Add formula to Mode

README.rst

@@ -41,7 +41,7 @@ Overview
 
 The power spectrum model conceives of a model of the power spectrum as a combination of two distinct functional processes:
 
-- An aperiodic component, reflecting 1/f like characteristics, with
+- An aperiodic component, with power across all frequencies (e.g. 1/f-like characteristics), with
 - A variable number of periodic components (putative oscillations), as peaks rising above the aperiodic component
 
 This model driven approach can be used to measure periodic and aperiodic properties of electrophysiological data,

specparam/modes/definitions.py

@@ -5,56 +5,58 @@
 
 from specparam.modes.mode import Mode
 from specparam.modes.params import ParamDefinition
-from specparam.modes.funcs import (expo_function, expo_nk_function, double_expo_function,
+from specparam.modes.funcs import (powerlaw_function, lorentzian_function, double_expo_function,
                                    gaussian_function, skewed_gaussian_function, cauchy_function)
 from specparam.modes.jacobians import jacobian_gauss
 from specparam.utils.checks import check_selection
 
 ###################################################################################################
 ## APERIODIC MODES
 
-## AP - Fixed Mode
+## AP - Powerlaw (1/f) Mode ('fixed')
 
-params_fixed = ParamDefinition(OrderedDict({
+params_powerlaw = ParamDefinition(OrderedDict({
     'offset' : 'Offset of the aperiodic component.',
     'exponent' : 'Exponent of the aperiodic component.',
 }))
 
-ap_fixed = Mode(
+ap_powerlaw = Mode(
     name='fixed',
     component='aperiodic',
-    description='Fit an exponential, with no knee.',
-    func=expo_nk_function,
+    description='One-over-f (powerlaw) function.',
+    formula=r'A(F) = 10^b * \frac{1}{F^\chi}',
+    func=powerlaw_function,
     jacobian=None,
-    params=params_fixed,
+    params=params_powerlaw,
     ndim=1,
     freq_space='linear',
     powers_space='log10',
 )
 
 
-## AP - Knee Mode
+## AP - Lorentzian Mode ('knee')
 
-params_knee = ParamDefinition(OrderedDict({
+params_lorentzian = ParamDefinition(OrderedDict({
     'offset' : 'Offset of the aperiodic component.',
     'knee' : 'Knee of the aperiodic component.',
     'exponent' : 'Exponent of the aperiodic component.',
 }))
 
-ap_knee = Mode(
+ap_lorentzian = Mode(
     name='knee',
     component='aperiodic',
-    description='Fit an exponential, with a knee.',
-    func=expo_function,
+    description='Lorentzian function, with a powerlaw exponent and a knee.',
+    formula=r'A(F) = 10^b * \frac{1}{(k + F^\chi)}',
+    func=lorentzian_function,
     jacobian=None,
-    params=params_knee,
+    params=params_lorentzian,
     ndim=1,
     freq_space='linear',
     powers_space='log10',
 )
 
 
-## AP - Double Exponent Mode
+## AP - Double Exponent Mode ('doublexp')
 
 params_doublexp = ParamDefinition(OrderedDict({
     'offset' : 'Offset of the aperiodic component.',
@@ -66,7 +68,8 @@
 ap_doublexp = Mode(
     name='doublexp',
     component='aperiodic',
-    description='Fit an function with 2 exponents and a knee.',
+    description='Multi-fractal powerlaw function with 2 exponents and a knee.',
+    formula=r'A(F) = 10^b * \frac{1}{F^{\chi_{0}} * (k + F^{\chi_{1}})}',
     func=double_expo_function,
     jacobian=None,
     params=params_doublexp,
@@ -78,8 +81,8 @@
 
 # Collect available aperiodic modes
 AP_MODES = {
-    'fixed' : ap_fixed,
-    'knee' : ap_knee,
+    'fixed' : ap_powerlaw,
+    'knee' : ap_lorentzian,
     'doublexp' : ap_doublexp,
 }
 
@@ -98,6 +101,7 @@
     name='gaussian',
     component='periodic',
     description='Gaussian peak fit function.',
+    formula=r'P(F)_n = a * exp (\frac{- (F - c)^2}{2 * w^2})',
     func=gaussian_function,
     jacobian=jacobian_gauss,
     params=params_gauss,
@@ -120,6 +124,7 @@
     name='skewed_gaussian',
     component='periodic',
     description='Skewed Gaussian peak fit function.',
+    formula=r'P(F)_n = \frac{2}{w\sqrt{2\pi}} e^{\frac{(F - \epsilon)^2} {2w^2}}',
     func=skewed_gaussian_function,
     jacobian=None,
     params=params_skewed_gaussian,
@@ -141,6 +146,7 @@
     name='cauchy',
     component='periodic',
     description='Cauchy peak fit function.',
+    formula=r'P(F)_n = a * \frac {w^2} {(F - c)^2 + w^2}',
     func=cauchy_function,
     jacobian=None,
     params=params_cauchy,