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PeakModel.m
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classdef PeakModel < handle
%PeakModel Parametric model of a single spectral peak
%
% obj = PeakModel(modelFunClass, paramLinkFuns, paramLinkFunParams, modelOptions, peakName)
%
% Input:
% modelFunClass: string, model function class: 'gaussian', 'box',
% 'harmonic', 'skewgamma', 'expdecay', 'expdoubledecay',
% 'smoothdoubledecay', 'linear'
% paramLinkFuns: 1 x numPeakParams cell array of strings of link
% function classes: 'sigmoid' (default), 'exp', 'identity', 'poly'
% paramLinkFunParams: 1 x numPeakParams cell array of
% strings of link function parameters
% modelOptions: model specific options
% peakName: string, descriptive name of peak
%
%
% PEAK FUNCTIONS:
% Gaussian ('gaussian')
% Function:
% y(x) = A * exp(-(w-F)^2 / (2*B))
% modelParams:
% F - central frequency
% A - maximum amplitude
% B - bandwidth (variance)
%
% Box Function ('box');
% Function:
% y(x) = A * exp(-(w-F)^p / (2*B))
% modelParams:
% F - central frequency
% A - maximum amplitude
% B - bandwidth (variance)
% modelOptions:
% p - polynomial order
%
% Gaussian with Harmonics ('harmonic');
% Function:
% y(x) = SUM h = 0 to H_peak: (Beta^h) * A * exp(-(w - (h+1)*F)^2 / (2*B));
% modelParams:
% F - central frequency
% A - maximum amplitude
% B - bandwidth (variance)
% Beta - harmonic ampiltude multiplier
% modelOptions:
% H_peak - number of harmonics
%
% Gamma with Skewness ('skewgamma');
% Function:
% A gamma function with fixed mode, variance, and skew
% modelParams:
% F - central frequency (mode)
% A - maximum amplitude
% B - bandwidth (variance)
% S - skewness
%
% Exponential Decay ('expdecay');
% Function:
% y(x) = BA.*(1-BR).^x +BO;
% modelParams:
% BA - maximum amplitude
% BR - decay rate
% BO - offset/baseline
%
% *****************************************
% SECOND DERIVATIVES NOT IMPLEMENTED YET
% *****************************************
% Double Exponential Decay ('expdecay');
% Function:
% y(x) = BA1.*(1-BR1).^x + BA2.*(1-BR2).^x +BO;
% modelParams:
% BA1 - maximum amplitude of first exponential
% BR1 - decay rate of first exponential
% BA2 - maximum amplitude of second exponential
% BR2 - decay rate of second exponential
% BO - offset/baseline
%
% Piecewise Exponential with Smooth Transition ('smoothdoubledecay');
% Function:
% see: Zelterman et. al, "Piecewise exponential survival curves with
% smooth transitions", Mathematical Biosciences, 1994
% modelParams:
% L1mL2 - difference between the rates of the two
% exponentials
% L2 - The rate of the second exponential
% K - maximum amplitude
% O - offset/baseline
%
% Copyright 2019 Prerau Laboratory
%
% Last modified 5/24/2019 by Michael Prerau
properties (Access = public)
modelFunClass; %Function class for peak model
modelParams = PeakObjParam; %List of state parameters
paramNames; %State variable name
paramDescriptions; %State variable description
modelOptions; %Additional variables per model
modelFun; %Handle to model function
modelDerivFuns; %Cell array of partial derivative function handles
model2ndDerivFuns; %Cell array of partial derivative function handles
peakName; %String name for peak
end
properties (SetAccess = private)
numPeakParams; %Number of peak parameters (cannot set)
end
methods (Access = public)
%-----------------------------------
% CONSTRUCTOR
%-----------------------------------
function obj = PeakModel(modelFunClass, paramLinkFuns, paramLinkFunParams, modelOptions, peakName)
%Constructor for the PeakModel class
%
% obj = PeakModel(modelFunClass, paramLinkFuns, paramLinkFunParams, modelOptions, peakName)
%
% Input:
% modelFunClass: string, model function class: 'gaussian', 'box',
% 'harmonic', 'skewgamma', 'expdecay', 'expdoubledecay',
% 'smoothdoubledecay', 'linear'
% paramLinkFuns: 1 x numPeakParams cell array of strings of link
% function classes: 'sigmoid' (default), 'exp', 'identity', 'poly'
% paramLinkFunParams: 1 x numPeakParams cell array of
% strings of link function parameters
% modelOptions: model specific options
% peakName: string, descriptive name of peak
if nargin == 0
modelFunClass = 'Gaussian';
end
if nargin < 2
paramLinkFuns = [];
end
if nargin < 3
paramLinkFunParams = [];
end
if nargin < 4
modelOptions = [];
end
if nargin < 5
peakName = [];
end
obj.modelOptions = modelOptions;
switch lower(modelFunClass)
%Sigmoid link function
case {'gaussian','normal'}
obj.modelFunClass = 'Gaussian';
%Define model function
obj.modelFun = @obj.gaussian;
obj.paramDescriptions = {'Peak Frequency', 'Amplitude', 'Bandwidth'};
%Define model partial derivative functions
obj.modelDerivFuns = {@obj.gaussian_dH_dFbar, @obj.gaussian_dH_dAbar, @obj.gaussian_dH_dBbar};
%Define model second partial derivative functions
obj.model2ndDerivFuns = ...
{@obj.gaussian_d2H_dFbar2, @obj.gaussian_d2H_dFbar_dAbar, @obj.gaussian_d2H_dFbar_dBbar; ...
@obj.gaussian_d2H_dFbar_dAbar, @obj.gaussian_d2H_dAbar2, @obj.gaussian_d2H_dAbar_dBbar; ...
@obj.gaussian_d2H_dFbar_dBbar, @obj.gaussian_d2H_dAbar_dBbar, @obj.gaussian_d2H_dBbar2};
%Set default model link functions
if isempty(paramLinkFuns)
paramLinkFuns = {'Sigmoid', 'Sigmoid', 'Sigmoid'};
end
%Set default model link function parameters
if isempty(paramLinkFunParams)
paramLinkFunParams = {[0 1], [0 1], [0 1]};
end
%Create the parameters
obj.modelParams(1) = PeakObjParam('F', paramLinkFuns{1}, paramLinkFunParams{1});
obj.modelParams(2) = PeakObjParam('A', paramLinkFuns{2}, paramLinkFunParams{2});
obj.modelParams(3) = PeakObjParam('B', paramLinkFuns{3}, paramLinkFunParams{3});
case {'gaussian harmonic','harmonic', 'gaussian_harmonic', 'normal harmonic','normal_harmonic'}
obj.modelFunClass = 'Gaussian Harmonic';
%Define model function
obj.modelFun = @obj.gaussian_harmonic;
obj.paramDescriptions = {'Peak Frequency', 'Amplitude', 'Bandwidth', 'Harmonic Ratio'};
%Set two harmonics by default
if isempty(obj.modelOptions)
obj.modelOptions = 2;
end
%Define model partial derivative functions
obj.modelDerivFuns = {@obj.gaussian_harmonic_dH_dFbar, @obj.gaussian_harmonic_dH_dAbar, @obj.gaussian_harmonic_dH_dBbar , @obj.gaussian_harmonic_dH_dBetabar};
%Define model second partial derivative functions
obj.model2ndDerivFuns = ...
{@obj.gaussian_harmonic_d2H_dFbar2, @obj.gaussian_harmonic_d2H_dFbar_dAbar, @obj.gaussian_harmonic_d2H_dFbar_dBbar, @obj.gaussian_harmonic_d2H_dFbar_dBetabar; ...
@obj.gaussian_harmonic_d2H_dFbar_dAbar, @obj.gaussian_harmonic_d2H_dAbar2, @obj.gaussian_harmonic_d2H_dAbar_dBbar, @obj.gaussian_harmonic_d2H_dAbar_dBetabar; ...
@obj.gaussian_harmonic_d2H_dFbar_dBbar, @obj.gaussian_harmonic_d2H_dAbar_dBbar, @obj.gaussian_harmonic_d2H_dBbar2, @obj.gaussian_harmonic_d2H_dBbar_dBetabar; ...
@obj.gaussian_harmonic_d2H_dFbar_dBetabar, @obj.gaussian_harmonic_d2H_dAbar_dBetabar, @obj.gaussian_harmonic_d2H_dBbar_dBetabar, @obj.gaussian_harmonic_d2H_dBetabar2};
%Set default model link functions
if isempty(paramLinkFuns)
paramLinkFuns = {'Sigmoid', 'Sigmoid', 'Sigmoid', 'Sigmoid'};
end
%Set default model link function parameters
if isempty(paramLinkFunParams)
paramLinkFunParams = {[0 1], [0 1], [0 1], [0 1]};
end
%Create the parameters
obj.modelParams(1) = PeakObjParam('F',paramLinkFuns{1},paramLinkFunParams{1});
obj.modelParams(2) = PeakObjParam('A',paramLinkFuns{2},paramLinkFunParams{2});
obj.modelParams(3) = PeakObjParam('B',paramLinkFuns{3},paramLinkFunParams{3});
obj.modelParams(4) = PeakObjParam('Beta',paramLinkFuns{4},paramLinkFunParams{4});
case {'box', 'smoothed box'}
obj.modelFunClass = 'Box';
%Define model function
obj.modelFun = @obj.boxfun;
obj.paramDescriptions = {'Peak Frequency', 'Amplitude', 'Bandwidth'};
%Set default for p
if isempty(obj.modelOptions)
obj.modelOptions = 16;
end
%Define model partial derivative functions
obj.modelDerivFuns = {@obj.boxfun_dH_dFbar, @obj.boxfun_dH_dAbar, @obj.boxfun_dH_dBbar};
%Define model second partial derivative functions
obj.model2ndDerivFuns = ...
{@obj.box_d2H_dFbar2, @obj.box_d2H_dFbar_dAbar, @obj.box_d2H_dFbar_dBbar; ...
@obj.box_d2H_dFbar_dAbar, @obj.box_d2H_dAbar2, @obj.box_d2H_dAbar_dBbar; ...
@obj.box_d2H_dFbar_dBbar, @obj.box_d2H_dAbar_dBbar, @obj.box_d2H_dBbar2};
%Set default model link functions
if isempty(paramLinkFuns)
paramLinkFuns = {'Sigmoid', 'Sigmoid', 'Sigmoid'};
end
%Set default model link function parameters
if isempty(paramLinkFunParams)
paramLinkFunParams = {[0 1], [0 1], [0 1]};
end
%Create the parameters
obj.modelParams(1) = PeakObjParam('F',paramLinkFuns{1},paramLinkFunParams{1});
obj.modelParams(2) = PeakObjParam('A',paramLinkFuns{2},paramLinkFunParams{2});
obj.modelParams(3) = PeakObjParam('B',paramLinkFuns{3},paramLinkFunParams{3});
case {'gamma', 'skewgamma','skew_gamma','skew gamma', 'skewed gamma', 'skewed_gamma'}
obj.modelFunClass = 'Skewed Gamma';
%Define model function
obj.modelFun = @obj.skewgamma;
obj.paramDescriptions = {'Peak Frequency', 'Amplitude', 'Bandwidth', 'Skewness'};
%Define model partial derivative functions
obj.modelDerivFuns = {@obj.skewgamma_dH_dFbar, @obj.skewgamma_dH_dAbar, @obj.skewgamma_dH_dBbar , @obj.skewgamma_dH_dSbar};
%Define model second partial derivative functions
obj.model2ndDerivFuns = ...
{@obj.skewgamma_d2H_dFbar2, @obj.skewgamma_d2H_dFbar_dAbar, @obj.skewgamma_d2H_dFbar_dBbar, @obj.skewgamma_d2H_dFbar_dSbar; ...
@obj.skewgamma_d2H_dFbar_dAbar, @obj.skewgamma_d2H_dAbar2, @obj.skewgamma_d2H_dAbar_dBbar, @obj.skewgamma_d2H_dAbar_dSbar; ...
@obj.skewgamma_d2H_dFbar_dBbar, @obj.skewgamma_d2H_dAbar_dBbar, @obj.skewgamma_d2H_dBbar2, @obj.skewgamma_d2H_dBbar_dSbar; ...
@obj.skewgamma_d2H_dFbar_dSbar, @obj.skewgamma_d2H_dAbar_dSbar, @obj.skewgamma_d2H_dBbar_dSbar, @obj.skewgamma_d2H_dSbar2};
%Set default model link functions
if isempty(paramLinkFuns)
paramLinkFuns = {'Sigmoid', 'Sigmoid', 'Sigmoid', 'Sigmoid'};
end
%Set default model link function parameters
if isempty(paramLinkFunParams)
paramLinkFunParams = {[0 1], [0 1], [0 1], [.5 1]};
end
%Create the parameters
obj.modelParams(1) = PeakObjParam('F',paramLinkFuns{1},paramLinkFunParams{1});
obj.modelParams(2) = PeakObjParam('A',paramLinkFuns{2},paramLinkFunParams{2});
obj.modelParams(3) = PeakObjParam('B',paramLinkFuns{3},paramLinkFunParams{3});
obj.modelParams(4) = PeakObjParam('S',paramLinkFuns{4},paramLinkFunParams{4});
case {'expdecay', 'decay','exponential decay', 'exponential_decay'}
obj.modelFunClass = 'Exponential Decay';
%Define model function
obj.modelFun = @obj.expdecay;
obj.paramDescriptions = {'Y-Intercept', 'Rate', 'Offset'};
%Define model partial derivative functions
obj.modelDerivFuns = {@obj.expdecay_dHdBA_bar, @obj.expdecay_dHdBR_bar, @obj.expdecay_dHdBO_bar};
%Define model second partial derivative functions
obj.model2ndDerivFuns = ...
{@obj.expdecay_d2H_dBAbar2, @obj.expdecay_d2H_dBAbar_dBRbar, @obj.expdecay_d2H_dBAbar_dBObar; ...
@obj.expdecay_d2H_dBAbar_dBRbar, @obj.expdecay_d2H_dBRbar2, @obj.expdecay_d2H_dBRbar_dBObar; ...
@obj.expdecay_d2H_dBAbar_dBObar, @obj.expdecay_d2H_dBRbar_dBObar, @obj.expdecay_d2H_dBObar2};
%Set default model link functions
if isempty(paramLinkFuns)
paramLinkFuns = {'Sigmoid', 'Sigmoid', 'Identity'};
end
%Set default model link function parameters
if isempty(paramLinkFunParams)
paramLinkFunParams = {[0 10], [0 1], [ ]};
end
%Create the parameters
obj.modelParams(1) = PeakObjParam('BA',paramLinkFuns{1},paramLinkFunParams{1});
obj.modelParams(2) = PeakObjParam('BR',paramLinkFuns{2},paramLinkFunParams{2});
obj.modelParams(3) = PeakObjParam('BO',paramLinkFuns{3},paramLinkFunParams{3});
case {'doubleexpdecay', 'doubledecay', 'double decay', 'double_decay','double exponential decay', 'double_exponential_decay'}
obj.modelFunClass = 'Exponential Decay';
%Define model function
obj.modelFun = @obj.doubledecay;
obj.paramDescriptions = {'Y-Intercept 1', 'Rate 1', 'Y-Intercept 2', 'Rate 2', 'Offset'};
%Define model partial derivative functions
obj.modelDerivFuns = {@obj.doubledecay_dHdBA1_bar, @obj.doubledecay_dHdBR1_bar,@obj.doubledecay_dHdBA2_bar, @obj.doubledecay_dHdBR2_bar,@obj.doubledecay_dHdBO_bar};
%Set default model link functions
if isempty(paramLinkFuns)
paramLinkFuns = {'Sigmoid', 'Sigmoid', 'Sigmoid', 'Sigmoid', 'Identity'};
end
%Set default model link function parameters
if isempty(paramLinkFunParams)
paramLinkFunParams = {[0 10], [0 1], [0 10], [0 1], [ ]};
end
%Create the parameters
obj.modelParams(1) = PeakObjParam('BA1',paramLinkFuns{1},paramLinkFunParams{1});
obj.modelParams(2) = PeakObjParam('BR1',paramLinkFuns{2},paramLinkFunParams{2});
obj.modelParams(3) = PeakObjParam('BA2',paramLinkFuns{3},paramLinkFunParams{3});
obj.modelParams(4) = PeakObjParam('BR2',paramLinkFuns{4},paramLinkFunParams{4});
obj.modelParams(5) = PeakObjParam('BO',paramLinkFuns{5},paramLinkFunParams{5});
case {'gamma double decay', 'smooth double decay', 'gamma_double_decay', 'gamma_double', 'smoothdoubledecay','gammadoubledecay'}
obj.modelFunClass = 'Double Exponential Decay with Gamma Transition';
%Define model function
obj.modelFun = @obj.smoothdoubledecay;
obj.paramDescriptions = {'L1 minus L2', 'L2', 'K', 'Offset'};
%Define model partial derivative functions
obj.modelDerivFuns = {@obj.smoothdoubledecay_dHdL1mL2t_bar, @obj.smoothdoubledecay_dHdL2_bar, ...
@obj.smoothdoubledecay_dHdK_bar, @obj.smoothdoubledecay_dHdO_bar};
%Set default model link functions
if isempty(paramLinkFuns)
paramLinkFuns = {'Sigmoid', 'Sigmoid', 'Sigmoid', 'Identity'};
end
%Set default model link function parameters
if isempty(paramLinkFunParams)
paramLinkFunParams = {[0 10], [0 1], [0 10], [0 1], [ ]};
end
%Create the parameters
obj.modelParams(1) = PeakObjParam('L1mL2',paramLinkFuns{1},paramLinkFunParams{1});
obj.modelParams(2) = PeakObjParam('L2',paramLinkFuns{2},paramLinkFunParams{2});
obj.modelParams(3) = PeakObjParam('K',paramLinkFuns{3},paramLinkFunParams{3});
obj.modelParams(4) = PeakObjParam('O',paramLinkFuns{4},paramLinkFunParams{4});
%Set default for p
if isempty(obj.modelOptions)
obj.modelOptions = [1 2];
end
case {'oof'}
obj.modelFunClass = 'One-Over-F';
%Define model function
obj.modelFun = @obj.oof;
obj.paramDescriptions = {'Knee', 'Rate', 'Baseline Offset'};
%Define model partial derivative functions
obj.modelDerivFuns = {@obj.oof_dHdK_bar, @obj.oof_dHdR_bar, @obj.oof_dHdB_bar};
%Define model second partial derivative functions
obj.model2ndDerivFuns = ...
{@obj.oof_d2H_dKbar2, @obj.oof_d2H_dKbar_dRbar, @obj.oof_d2H_dKbar_dBbar; ...
@obj.oof_d2H_dKbar_dRbar, @obj.oof_d2H_dRbar2, @obj.oof_d2H_dRbar_dBbar; ...
@obj.oof_d2H_dKbar_dBbar, @obj.oof_d2H_dRbar_dBbar, @obj.oof_d2H_dBbar2};
%Set default model link functions
if isempty(paramLinkFuns)
paramLinkFuns = {'Sigmoid', 'Sigmoid', 'Identity'};
end
%Set default model link function parameters
if isempty(paramLinkFunParams)
paramLinkFunParams = {[0 10], [0 1], [ ]};
end
%Create the parameters
obj.modelParams(1) = PeakObjParam('K',paramLinkFuns{1},paramLinkFunParams{1});
obj.modelParams(2) = PeakObjParam('R',paramLinkFuns{2},paramLinkFunParams{2});
obj.modelParams(3) = PeakObjParam('B',paramLinkFuns{3},paramLinkFunParams{3});
case {'linear'}
obj.modelFunClass = 'Linear';
%Define model function
obj.modelFun = @obj.linear;
obj.paramDescriptions = {'Slope', 'Y-Intercept'};
%Define model partial derivative functions
obj.modelDerivFuns = {@obj.linear_dH_dMbar, @obj.linear_dH_dBbar};
%Define model second partial derivative functions
obj.model2ndDerivFuns = ...
{@obj.linear_dH_dMbar2, @obj.linear_dH_dMbar_dBbar; ...
@obj.linear_dH_dMbar_dBbar, @obj.linear_dH_dBbar2};
%Set default model link functions
if isempty(paramLinkFuns)
paramLinkFuns = {'Sigmoid', 'Identity'};
end
%Set default model link function parameters
if isempty(paramLinkFunParams)
paramLinkFunParams = {[0 10], [ ]};
end
%Create the parameters
obj.modelParams(1) = PeakObjParam('M',paramLinkFuns{1},paramLinkFunParams{1});
obj.modelParams(2) = PeakObjParam('B',paramLinkFuns{2},paramLinkFunParams{2});
otherwise
error('Invalid model class');
end
%Number of parameters
obj.numPeakParams = length(obj.modelParams);
obj.paramNames = {obj.modelParams.paramName};
obj.peakName = peakName;
end
%-----------------------------------
% PLOT PEAK FUNCTION
%-----------------------------------
function plot(obj, X, w)
%Plot function for PeakModel class
%
% plot(obj, X, w, <plot function arguments>)
%
% Input:
% X: 1 x totalPeakParams double, state vector (default: zeros)
% w: 1 x W double, frequency vector
if nargin < 3 || isempty(X)
X=zeros(1, obj.numPeakParams);
end
if nargin < 2 || isempty(w)
%Figure out the range of frequencies the covers the peak
freq_idx = find(strcmpi({obj.modelParams.paramName},'F'));
bw_idx = find(strcmpi({obj.modelParams.paramName},'B'));
%Set the range with a default of 0-100Hz for non-peak functions
if ~isempty(freq_idx) && ~isempty(bw_idx)
F = obj.modelParams(freq_idx).linkFun(X(freq_idx));
B = obj.modelParams(bw_idx).linkFun(X(freq_idx));
if strcmpi(obj.modelFunClass, 'gaussian harmonic')
w=linspace(F - 4*B, F*obj.modelOptions + 4*B, 10000);
else
w=linspace(F - 4*B, F + 4*B, 10000);
end
else
w=linspace(0, 100, 10000);
end
end
H_peak = obj.modelFun(w,X);
plot(w, H_peak);
end
%-----------------------------------
% NUMERICAL DERIVATIVES
%-----------------------------------
function testDerivs(obj, X, dX)
%Test to see if the derivatives are correct against numerical approximation
%
% testDerivs(dX)
%
% Input:
% dX: double, size of state difference (default: 1e-3)
%Set default for dX
if nargin<3
dX =[];
end
if nargin<2
X = [];
end
if isempty(dX)
dX=1e-3;
end
if isempty(X)
X=zeros(obj.numPeakParams, 1);
end
%Figure out the range of frequencies the covers the peak
freq_idx = find(strcmpi({obj.modelParams.paramName},'F'));
bw_idx = find(strcmpi({obj.modelParams.paramName},'B'));
%Set the range with a default of 0-100Hz for non-peak functions
if ~isempty(freq_idx) && ~isempty(bw_idx)
F = obj.modelParams(freq_idx).linkFun(0);
B = obj.modelParams(bw_idx).linkFun(0);
if strcmpi(obj.modelFunClass, 'gaussian harmonic')
w=linspace(F - 4*B, F*obj.modelOptions + 4*B, 10000);
else
w=linspace(F - 4*B, F + 4*B, 10000);
end
else
w=linspace(0, 100, 10000);
end
%Loop over each parameter an plot comparison with numerical difference
for ii = 1:obj.numPeakParams
%Create X and adjusted X
Xdp = X;
Xdp(ii) = Xdp(ii)+dX;
%Compute both H_peak functions and take difference
H_peak = obj.modelFun(w,X);
H_peak_2 = obj.modelFun(w,Xdp);
emp_deriv = (H_peak_2-H_peak)/dX;
analytic_deriv = obj.modelDerivFuns{ii}(w,X, H_peak);
%Plot results
figure
hold all
plot(w, H_peak, 'linewidth',2)
plot(w, analytic_deriv, 'linewidth',2);
plot(w, emp_deriv, '--', 'linewidth',2);
legend('Function', 'Analytic', 'Numerical');
title(obj.modelParams(ii).paramName);
end
end
function test2ndDerivs(obj,X,dX)
%Test to see if the derivatives are correct against numerical approximation
%
% test2ndDerivs(dX)
%
% Input:
% dX: double, size of state difference (default: 1e-3)
%Set default for dX
if nargin<3
dX = [];
end
if nargin<2
X = [];
end
if isempty(dX)
dX=1e-5;
end
if isempty(X)
X=zeros(obj.numPeakParams, 1);
end
%Figure out the range of frequencies the covers the peak
freq_idx = find(strcmpi({obj.modelParams.paramName},'F'));
bw_idx = find(strcmpi({obj.modelParams.paramName},'B'));
%Set the range with a default of 0-100Hz for non-peak functions
if ~isempty(freq_idx) && ~isempty(bw_idx)
F = obj.modelParams(freq_idx).linkFun(0);
B = obj.modelParams(bw_idx).linkFun(0);
if strcmpi(obj.modelFunClass, 'gaussian harmonic')
w=linspace(F - 4*B, F*obj.modelOptions + 4*B, 10000);
else
w=linspace(F - 4*B, F + 4*B, 10000);
end
else
w=linspace(0, 100, 10000);
end
H_peak = obj.modelFun(w,X);
%Loop over each parameter an plot comparison with numerical difference
for zz1 = 1:obj.numPeakParams
for zz2 = zz1:obj.numPeakParams
analytic_2nd_deriv = obj.model2ndDerivFuns{zz1,zz2}(w,X, H_peak);
dx1 = zeros(size(X));
dx1(zz1) = dX;
dx2 = zeros(size(X));
dx2(zz2) = dX;
if zz1~=zz2
hx1px2p = obj.modelFun(w,X+dx1+dx2);
hx1px2m = obj.modelFun(w,X+dx1-dx2);
hx1mx2p = obj.modelFun(w,X-dx1+dx2);
hx1mx2m = obj.modelFun(w,X-dx1-dx2);
emp_2nd_deriv = (hx1px2p - hx1px2m - hx1mx2p + hx1mx2m)/(4*dX*dX);
else
hx1px2 = obj.modelFun(w,X+dx1);
hx1mx2 = obj.modelFun(w,X-dx1);
emp_2nd_deriv = (hx1px2 - 2*H_peak + hx1mx2)/(dX*dX);
end
%Plot results
figure
hold all
plot(w, H_peak, 'linewidth',2)
plot(w, analytic_2nd_deriv, 'linewidth',2);
plot(w, emp_2nd_deriv, '--', 'linewidth',2);
legend('Function', 'Analytic', 'Numerical');
title([obj.modelFunClass ': d/d' obj.modelParams(zz1).paramName ' d/d' obj.modelParams(zz2).paramName]);
end
end
end
end
methods (Access = private)
%% GAUSSIAN MODEL
%-----------------------------------
% GAUSSIAN PEAK MODEL
%-----------------------------------
function H_peak = gaussian(obj, w, X)
if size(X,1) ~= 3
error('Gaussian model requires 3 parameters: F, A, and B');
end
%Get param values through link functions
F=obj.modelParams(1).linkFun(X(1,:));
A=obj.modelParams(2).linkFun(X(2,:));
B=obj.modelParams(3).linkFun(X(3,:));
H_peak=A.*exp(-(w-F).^2./(2*B));
end
%-----------------------------------
% GAUSSIAN PEAK MODEL DERIVAIVES
%-----------------------------------
function out = gaussian_dH_dFbar(obj, w, X, H_peak)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
B = obj.modelParams(3).linkFun(X(3,:));
%Get derivatives of link functions
dF_dFbar = obj.modelParams(1).linkDerivFun(X(1,:));
out = H_peak.*(w-F)/(B).*dF_dFbar;
end
function out = gaussian_dH_dAbar(obj, ~, X, H_peak)
%Get param values through link functions
A = obj.modelParams(2).linkFun(X(2,:));
%Get derivatives of link functions
dA_dAbar = obj.modelParams(2).linkDerivFun(X(2,:));
out = H_peak./A.*dA_dAbar;
end
function out = gaussian_dH_dBbar(obj, w, X, H_peak)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
B = obj.modelParams(3).linkFun(X(3,:));
%Get derivatives of link functions
dB_dBbar = obj.modelParams(3).linkDerivFun(X(3,:));
out = H_peak.*(w-F).^2./(2*B.^2).*dB_dBbar;
end
%-----------------------------------
% GAUSSIAN PEAK MODEL 2nd DERIVAIVES
%-----------------------------------
function out = gaussian_d2H_dFbar2(obj, w, X, H_peak)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
A = obj.modelParams(2).linkFun(X(2,:));
B = obj.modelParams(3).linkFun(X(3,:));
%Get derivatives of link functions
dF_dFbar = obj.modelParams(1).linkDerivFun(X(1,:));
dA_dAbar = obj.modelParams(2).linkDerivFun(X(2,:));
dB_dBbar = obj.modelParams(3).linkDerivFun(X(3,:));
%Get 2nd derivatives of link functions
d2F_dFbar2 = obj.modelParams(1).linkDeriv2Fun(X(1,:));
d2A_dAbar2 = obj.modelParams(2).linkDeriv2Fun(X(2,:));
d2B_dBbar2 = obj.modelParams(3).linkDeriv2Fun(X(3,:));
Z = (w-F)./B;
dZ_dF = -1/B;
out = H_peak.*( (Z.^2 + dZ_dF).*(dF_dFbar.^2) + Z.*d2F_dFbar2);
end
function out = gaussian_d2H_dFbar_dAbar(obj, w, X, H_peak)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
A = obj.modelParams(2).linkFun(X(2,:));
B = obj.modelParams(3).linkFun(X(3,:));
%Get derivatives of link functions
dF_dFbar = obj.modelParams(1).linkDerivFun(X(1,:));
dA_dAbar = obj.modelParams(2).linkDerivFun(X(2,:));
dB_dBbar = obj.modelParams(3).linkDerivFun(X(3,:));
%Get 2nd derivatives of link functions
d2F_dFbar2 = obj.modelParams(1).linkDeriv2Fun(X(1,:));
d2A_dAbar2 = obj.modelParams(2).linkDeriv2Fun(X(2,:));
d2B_dBbar2 = obj.modelParams(3).linkDeriv2Fun(X(3,:));
out = H_peak.*((w-F)./B).*(1/A).*dF_dFbar.*dA_dAbar;
end
function out = gaussian_d2H_dFbar_dBbar(obj, w, X, H_peak)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
A = obj.modelParams(2).linkFun(X(2,:));
B = obj.modelParams(3).linkFun(X(3,:));
%Get derivatives of link functions
dF_dFbar = obj.modelParams(1).linkDerivFun(X(1,:));
dA_dAbar = obj.modelParams(2).linkDerivFun(X(2,:));
dB_dBbar = obj.modelParams(3).linkDerivFun(X(3,:));
%Get 2nd derivatives of link functions
d2F_dFbar2 = obj.modelParams(1).linkDeriv2Fun(X(1,:));
d2A_dAbar2 = obj.modelParams(2).linkDeriv2Fun(X(2,:));
d2B_dBbar2 = obj.modelParams(3).linkDeriv2Fun(X(3,:));
out = H_peak.*(((w-F).^3)./(2*B.^3)-(w-F)./(B.^2)).*dF_dFbar.*dB_dBbar;
end
function out = gaussian_d2H_dAbar2(obj, w, X, H_peak)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
A = obj.modelParams(2).linkFun(X(2,:));
B = obj.modelParams(3).linkFun(X(3,:));
%Get derivatives of link functions
dF_dFbar = obj.modelParams(1).linkDerivFun(X(1,:));
dA_dAbar = obj.modelParams(2).linkDerivFun(X(2,:));
dB_dBbar = obj.modelParams(3).linkDerivFun(X(3,:));
%Get 2nd derivatives of link functions
d2F_dFbar2 = obj.modelParams(1).linkDeriv2Fun(X(1,:));
d2A_dAbar2 = obj.modelParams(2).linkDeriv2Fun(X(2,:));
d2B_dBbar2 = obj.modelParams(3).linkDeriv2Fun(X(3,:));
out = H_peak.*(1/A).*d2A_dAbar2;
end
function out = gaussian_d2H_dAbar_dBbar(obj, w, X, H_peak)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
A = obj.modelParams(2).linkFun(X(2,:));
B = obj.modelParams(3).linkFun(X(3,:));
%Get derivatives of link functions
dF_dFbar = obj.modelParams(1).linkDerivFun(X(1,:));
dA_dAbar = obj.modelParams(2).linkDerivFun(X(2,:));
dB_dBbar = obj.modelParams(3).linkDerivFun(X(3,:));
%Get 2nd derivatives of link functions
d2F_dFbar2 = obj.modelParams(1).linkDeriv2Fun(X(1,:));
d2A_dAbar2 = obj.modelParams(2).linkDeriv2Fun(X(2,:));
d2B_dBbar2 = obj.modelParams(3).linkDeriv2Fun(X(3,:));
out = H_peak.*( ((w-F).^2)./(2*B.^2) .* (1/A) ) .* dA_dAbar .* dB_dBbar;
end
function out = gaussian_d2H_dBbar2(obj, w, X, H_peak)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
A = obj.modelParams(2).linkFun(X(2,:));
B = obj.modelParams(3).linkFun(X(3,:));
%Get derivatives of link functions
dF_dFbar = obj.modelParams(1).linkDerivFun(X(1,:));
dA_dAbar = obj.modelParams(2).linkDerivFun(X(2,:));
dB_dBbar = obj.modelParams(3).linkDerivFun(X(3,:));
%Get 2nd derivatives of link functions
d2F_dFbar2 = obj.modelParams(1).linkDeriv2Fun(X(1,:));
d2A_dAbar2 = obj.modelParams(2).linkDeriv2Fun(X(2,:));
d2B_dBbar2 = obj.modelParams(3).linkDeriv2Fun(X(3,:));
Z = ((w-F).^2)./(2*B.^2);
dZ_dB = -((w-F).^2)./(B.^3);
out = H_peak.*((Z.^2 + dZ_dB).*(dB_dBbar.^2) + Z.*d2B_dBbar2);
end
%% GAUSSIAN HARMONIC MODEL
%-----------------------------------
% GAUSSIAN HARMONIC PEAK MODEL
%-----------------------------------
function H_peak = gaussian_harmonic(obj, w, X)
if size(X,1) ~= 4
error('Gaussian harmonic model requires 4 parameters: F, A, B and Beta');
end
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
A = obj.modelParams(2).linkFun(X(2,:));
B = obj.modelParams(3).linkFun(X(3,:));
Beta = obj.modelParams(4).linkFun(X(4,:));
%Get number of harmonics
N = obj.modelOptions;
%No weighting on the fundamental
H_peak = zeros(size(w));
for harmonic_num=0:N
H_peak = H_peak + (Beta.^harmonic_num).*A.*exp(-(w-(harmonic_num+1)*F).^2./(2*B));
end
end
%---------------------------------------------
% GAUSSIAN HARMONIC PEAK MODEL DERIVAIVES
%---------------------------------------------
function out=gaussian_harmonic_dH_dFbar(obj, w, X, ~)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
A = obj.modelParams(2).linkFun(X(2,:));
B = obj.modelParams(3).linkFun(X(3,:));
Beta = obj.modelParams(4).linkFun(X(4,:));
%Get derivatives of link functions
dF_dFbar = obj.modelParams(1).linkDerivFun(X(1,:));
%Get number of harmonics
N = obj.modelOptions;
out= zeros(size(w));
for harmonic_num = 0:N
Hh = A.* Beta.^harmonic_num .* exp(-(w-(harmonic_num+1).*F).^2./(2*B));
out = out+Hh.*((harmonic_num+1).*(w-F.*(harmonic_num+1)))./B;
end
out=out.*dF_dFbar;
end
function out=gaussian_harmonic_dH_dAbar(obj, ~, X, H_peak)
%Get param values through link functions
A = obj.modelParams(2).linkFun(X(2,:));
%Get derivatives of link functions
dA_dAbar = obj.modelParams(2).linkDerivFun(X(2,:));
out=H_peak./A.*dA_dAbar;
end
function out=gaussian_harmonic_dH_dBbar(obj, w, X, ~)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
A = obj.modelParams(2).linkFun(X(2,:));
B = obj.modelParams(3).linkFun(X(3,:));
Beta = obj.modelParams(4).linkFun(X(4,:));
%Get derivatives of link functions
dB_dBbar = obj.modelParams(3).linkDerivFun(X(3,:));
%Get number of harmonics
N = obj.modelOptions;
%No weighting on the fundamental
H0=A.*exp(-(w-F).^2./(2*B));
out= H0.*((w-F).^2)/(2*B.^2);
for harmonic_num=1:N
Hh=A.* Beta.^harmonic_num .* exp(-(w-(harmonic_num+1).*F).^2./(2*B));
out=out+Hh.*(w-F.*(harmonic_num+1)).^2./(2*B.^2);
end
out=out.*dB_dBbar;
end
function out=gaussian_harmonic_dH_dBetabar(obj, w, X, ~)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
A = obj.modelParams(2).linkFun(X(2,:));
B = obj.modelParams(3).linkFun(X(3,:));
Beta = obj.modelParams(4).linkFun(X(4,:));
%Get derivatives of link functions
dBetAdBetA_bar = obj.modelParams(4).linkDerivFun(X(4,:));
%Get number of harmonics
N = obj.modelOptions;
out=0;
for harmonic_num=1:N
Hh=A.* Beta.^harmonic_num .* exp(-(w-(harmonic_num+1).*F).^2./(2*B));
out=out+Hh.*(harmonic_num./Beta);
end
out=out.*dBetAdBetA_bar;
end
%---------------------------------------------
% GAUSSIAN HARMONIC PEAK MODEL 2nd DERIVAIVES
%---------------------------------------------
function out=gaussian_harmonic_d2H_dFbar2(obj, w, X, ~)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
A = obj.modelParams(2).linkFun(X(2,:));
B = obj.modelParams(3).linkFun(X(3,:));
Beta = obj.modelParams(4).linkFun(X(4,:));
%Get derivatives of link functions
dF_dFbar = obj.modelParams(1).linkDerivFun(X(1,:));
dA_dAbar = obj.modelParams(2).linkDerivFun(X(2,:));
dB_dBbar = obj.modelParams(3).linkDerivFun(X(3,:));
dBeta_dBetabar = obj.modelParams(4).linkDerivFun(X(4,:));
%Get 2nd derivatives of link functions
d2F_dFbar2 = obj.modelParams(1).linkDeriv2Fun(X(1,:));
d2A_dAbar2 = obj.modelParams(2).linkDeriv2Fun(X(2,:));
d2B_dBbar2 = obj.modelParams(3).linkDeriv2Fun(X(3,:));
d2Beta_dBetabar2 = obj.modelParams(4).linkDeriv2Fun(X(4,:));
%Get number of harmonics
N = obj.modelOptions;
H0 = A.*exp(-(w-F).^2./(2*B));
out = H0.*(((w-F)./B).^2-1/B);
first_deriv = H0.*((w-F)./B);
for nn = 1:N
Hn = A.* Beta.^nn .* exp(-(w-(nn+1).*F).^2./(2*B));
out = out + Hn.*(((nn+1).*(w-(nn+1).*F)./B).^2-((nn+1)^2)/B);
first_deriv = first_deriv + Hn.*((nn+1).*(w-(nn+1).*F)./B);
end
out = out.*(dF_dFbar.^2) + first_deriv.*d2F_dFbar2;
end
function out=gaussian_harmonic_d2H_dFbar_dAbar(obj, w, X, ~)
%Get param values through link functions
F = obj.modelParams(1).linkFun(X(1,:));
A = obj.modelParams(2).linkFun(X(2,:));
B = obj.modelParams(3).linkFun(X(3,:));
Beta = obj.modelParams(4).linkFun(X(4,:));
%Get derivatives of link functions
dF_dFbar = obj.modelParams(1).linkDerivFun(X(1,:));
dA_dAbar = obj.modelParams(2).linkDerivFun(X(2,:));
dB_dBbar = obj.modelParams(3).linkDerivFun(X(3,:));
dBeta_dBetabar = obj.modelParams(4).linkDerivFun(X(4,:));
%Get 2nd derivatives of link functions
d2F_dFbar2 = obj.modelParams(1).linkDeriv2Fun(X(1,:));
d2A_dAbar2 = obj.modelParams(2).linkDeriv2Fun(X(2,:));
d2B_dBbar2 = obj.modelParams(3).linkDeriv2Fun(X(3,:));
d2Beta_dBetabar2 = obj.modelParams(4).linkDeriv2Fun(X(4,:));
%Get number of harmonics
N = obj.modelOptions;
H0 = A.*exp(-(w-F).^2./(2*B));