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nonlinear_fit.m
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nonlinear_fit.m
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clc;
clear;
close all;
exp_LTP_raw=[ 0 2.92308E-09
0.857143 6.07692E-09
1.71429 8.76923E-09
2.85714 9.92308E-09
3.71429 1.13077E-08
4.28571 1.24615E-08
5.71429 1.22308E-08
6.57143 1.30769E-08
8 1.28462E-08
9.14286 1.46923E-08
10.8571 1.43077E-08
11.7143 1.53846E-08
12.8571 1.49231E-08
13.7143 1.56923E-08
14.5714 1.63077E-08
16 1.61538E-08
16.5714 1.72308E-08
17.7143 1.76154E-08
18.8571 1.81538E-08
19.4286 1.94615E-08
20.8571 0.000000018
23.7143 2.01538E-08
24.5714 2.14615E-08
26.5714 2.09231E-08
28 2.03077E-08
28.5714 2.24615E-08
30 2.33846E-08
30.8571 2.03077E-08
31.7143 2.23846E-08
32.5714 2.33846E-08
33.4286 2.42308E-08
34.8571 2.14615E-08
37.7143 2.06154E-08
38.5714 2.21538E-08
39.4286 2.15385E-08
40.8571 0.000000022
41.7143 2.13077E-08
42.5714 2.42308E-08
43.4286 2.32308E-08
45.7143 2.46154E-08
46.5714 2.91538E-08
48 2.45385E-08
48.2857 2.41538E-08
49.4286 2.29231E-08
50.5714 2.43077E-08
51.7143 2.30769E-08
52.2857 2.49231E-08
53.7143 2.45385E-08
54.5714 2.56923E-08
55.4286 2.43077E-08
56.2857 2.59231E-08
57.4286 2.83077E-08
58.2857 2.56923E-08
59.4286 2.76154E-08
60.2857 2.86154E-08
61.4286 2.94615E-08
62.5714 2.99231E-08
63.4286 3.30769E-08
64.5714 3.17692E-08
65.4286 3.82308E-08
66.5714 0.000000031
67.4286 3.63077E-08
68.2857 3.34615E-08
69.4286 3.31538E-08
70.5714 3.29231E-08
71.1429 0.000000034
72.2857 3.61538E-08
74.5714 0.000000034
75.4286 3.25385E-08
76.2857 3.66923E-08
77.4286 3.53846E-08
78.2857 3.44615E-08
79.7143 3.51538E-08
80.2857 3.39231E-08
81.1429 3.62308E-08
82.2857 3.79231E-08
83.4286 3.21538E-08
84.2857 3.43846E-08
85.4286 3.27692E-08
86.2857 3.58462E-08
87.1429 3.66923E-08
88.2857 3.61538E-08
90 3.81538E-08
90.2857 3.90769E-08
91.1429 4.02308E-08
92.5714 3.81538E-08
93.7143 3.69231E-08
94.5714 3.78462E-08
95.4286 3.90769E-08
96.2857 4.11538E-08
97.4286 4.17692E-08];
exp_LTD_raw=[ 0 3.15385E-09
3.1424 3.53846E-09
4.0004 2.92308E-09
4.5714 4.23077E-09
6.5714 3.07692E-09
6.8574 4.15385E-09
8.0004 3.30769E-09
9.1424 4.23077E-09
10.0004 3.61538E-09
11.1424 4.07692E-09
12.0004 3.84615E-09
13.1424 4.30769E-09
15.1424 4.30769E-09
15.7144 4.23077E-09
17.1424 3.61538E-09
18.2854 0.000000003
19.1424 3.69231E-09
21.1424 4.23077E-09
22.0004 3.53846E-09
23.1424 4.07692E-09
24.2854 3.46154E-09
26.5714 3.76923E-09
28.0004 4.38462E-09
28.8574 3.30769E-09
29.7144 2.69231E-09
31.4284 3.69231E-09
32.8574 0.000000003
34.0004 3.46154E-09
35.1424 5.30769E-09
36.8574 4.69231E-09
37.4284 5.07692E-09
38.2854 5.76923E-09
39.7144 5.46154E-09
40.8574 6.07692E-09
42.5714 5.23077E-09
44.0004 0.000000006
44.8574 5.30769E-09
46.8574 6.69231E-09
48.0004 7.46154E-09
49.1424 0.000000007
49.7144 6.38462E-09
50.5714 7.23077E-09
52.5714 8.46154E-09
54.5714 7.76923E-09
56.8574 8.76923E-09
57.4284 8.30769E-09
60.2854 9.76923E-09
61.4284 9.38462E-09
63.7144 0.000000011
64.2854 1.04615E-08
65.7144 1.21538E-08
67.7144 0.000000011
68.0004 1.13077E-08
69.7144 1.26923E-08
70.5714 1.35385E-08
71.7144 1.41538E-08
73.1424 1.56154E-08
74.5714 1.77692E-08
76.0004 1.87692E-08
76.5714 1.95385E-08
79.4284 2.04615E-08
80.2854 2.16923E-08
80.8574 2.07692E-08
82.5714 2.35385E-08
83.7144 2.36923E-08
85.4284 2.67692E-08
87.1424 2.71538E-08
87.4284 3.18462E-08
89.4284 3.26923E-08
91.4284 0.000000034
91.7144 0.000000036
93.7144 3.47692E-08
94.0004 3.83846E-08
96.0004 3.93077E-08
96.2854 3.93846E-08
97.7144 3.63846E-08
98.8574 4.10769E-08
100.5714 4.17692E-08];
xf_ltp = floor(max(exp_LTP_raw(:,1)));
xf_ltd = floor(max(exp_LTD_raw(:,1)));
x_step_ltp = 1/xf_ltp;
x_step_ltd = 1/xf_ltd;
yf_ltp = max(exp_LTP_raw(:,2));
yf_ltd = max(exp_LTD_raw(:,2));
yi_ltp = min(exp_LTP_raw(:,2));
yi_ltd = min(exp_LTD_raw(:,2));
exp_LTP(:,1) = exp_LTP_raw(:,1)/xf_ltp;
exp_LTD(:,1) = exp_LTD_raw(:,1)/xf_ltd;
exp_LTP(:,2) = (exp_LTP_raw(:,2)-yi_ltp)/(yf_ltp-yi_ltp);
exp_LTD(:,2) = (exp_LTD_raw(:,2)-yi_ltd)/(yf_ltd-yi_ltd);
plot(exp_LTP(:,1), exp_LTP(:,2), 'bo', 'LineWidth', 1);
hold on;
plot(exp_LTD(:,1), exp_LTD(:,2), 'ro', 'LineWidth', 1);
xf = 1;
A_LTP = 0.5;
B_LTP = 1./(1-exp(-1./A_LTP));
A_LTD = -0.2;
B_LTD = 1./(1-exp(-1./A_LTD));
% LTP fitting
var_amp = 0.035; % LTP cycle-to-cycle variation
rng(103);
x_ltp(1) = 0;
y_ltp(1) = 0;
for n=1:1/x_step_ltp+1
x_ltp(n+1) = x_ltp(n)+x_step_ltp;
y_ltp(n+1) = B_LTP(1)*(1-exp(-x_ltp(n+1)/A_LTP(1)));
delta_y = (y_ltp(n+1)-y_ltp(n)) + randn*var_amp;
y_ltp(n+1) = y_ltp(n) + delta_y;
if y_ltp(n+1)>=1
y_ltp(n+1)=1;
elseif y_ltp(n+1)<=0
y_ltp(n+1)=0;
end
x_ltp(n+1) = -A_LTP(1)*log(1-(y_ltp(n+1))/B_LTP(1));
end
plot((0:n-1)/(n-1), y_ltp(1:n), 'b', 'linewidth', 2);
% LTD fitting
var_amp = 0.025; % LTD cycle-to-cycle variation
rng(898);
x_ltd(1) = 1;
y_ltd(1) = 1;
for n=1:1/x_step_ltd+1
x_ltd(n+1) = x_ltd(n)-x_step_ltd;
y_ltd(n+1) = B_LTD(1)*(1-exp(-x_ltd(n+1)/A_LTD(1)));
delta_y = (y_ltd(n+1)-y_ltd(n)) + randn*var_amp;
y_ltd(n+1) = y_ltd(n) + delta_y;
if y_ltd(n+1)>=1
y_ltd(n+1)=1;
elseif y_ltd(n+1)<=0
y_ltd(n+1)=0;
end
x_ltd(n+1) = -A_LTD(1)*log(1-(y_ltd(n+1))/B_LTD(1));
end
x_start = numel(x_ltd(:));
x_end = numel(x_ltd(:)) - n;
plot((n-1:-1:0)/(n-1), y_ltd(1:n), 'r', 'linewidth', 2);
xlabel('Normalized Pulse #');
ylabel('Normalized Conductance');
legend('Exp data (LTP)','Exp data (LTD)', 'Fit (LTP)', 'Fit (LTD)', 'location', 'southeast');