How do I perform a sin^2 or a cos^2 fit for my data?

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Akshay Arvind 2024-5-23

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评论： Star Strider 2024-5-23

采纳的回答： Star Strider

I have the following x data and y data:

x = [0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180]

y = [880,1200,1900,2700,3300,3600,3000,2100,1300,860,1200,1900,2700,3150,3300,2900,2100,1300,860]

How do I perform a cos^2 (x) or a sin^2 (x) fit for the above data?

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Answer 1

Star Strider 2024-5-23

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2121841-how-do-i-perform-a-sin-2-or-a-cos-2-fit-for-my-data#answer_1462306

在 MATLAB Online 中打开

Perhaps this —

x = [0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180];

y = [880,1200,1900,2700,3300,3600,3000,2100,1300,860,1200,1900,2700,3150,3300,2900,2100,1300,860];

LvLocs = islocalmax(y, 'MinProminence',mean(y));

xlocs = x(LvLocs)

xlocs = 1x2

50 140

freq = 1/mean(diff(xlocs))

freq = 0.0111

[lb,ub] = bounds(y)

lb = 860

ub = 3600

fcn = @(b,x) b(1).*sin(2*pi*x*b(2)).^2 + b(3);

[B,fv] = fminsearch(@(b)norm(y - fcn(b,x)), rand(3,1))

B = 3x1

1.0e+03 * 2.5314 0.0006 0.9046

fv = 371.2053

txt = sprintf('$f(x) = %.2f \\cdot sin(2 \\pi x %.3f)^2 %+.3f$', B)

txt = '$f(x) = 2531.45 \cdot sin(2 \pi x 0.595)^2 +904.574$'

figure

plot(x, y)

hold on

plot(x, fcn(B,x), '-r')

hold off

grid

xlabel('X')

ylabel('Y')

text(50, 3750, txt, 'Interpreter','LaTeX')

.

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Star Strider 2024-5-23

在 MATLAB Online 中打开

Sure!

That only requires creating a smoother ‘x’ vector with higher resolution. I also added a phase term, and tweaked the initial parameter estimates to make the fit a bit more reliable.

x = [0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180];

y = [880,1200,1900,2700,3300,3600,3000,2100,1300,860,1200,1900,2700,3150,3300,2900,2100,1300,860];

LvLocs = islocalmax(y, 'MinProminence',mean(y));

xlocs = x(LvLocs);

freq = 1/(2*mean(diff(xlocs)));

[lb,ub] = bounds(y);

% fcn = @(b,x) b(1).*sin(2*pi*x*b(2)).^2 + b(3);

fcn = @(b,x) b(1).*sin(2*pi*x*b(2) + b(3)).^2 + b(4);

B0 = [ub-lb; freq; rand; lb];

[B,fv] = fminsearch(@(b)norm(y - fcn(b,x)), B0)

B = 4x1

1.0e+03 * 2.5246 0.0000 -0.0000 0.9213

fv = 332.3104

mdl = fitnlm(x, y, fcn, B) % Calculate Statistics (Nor Required)

mdl =

Nonlinear regression model: y ~ b1*sin(2*pi*x*b2 + b3)^2 + b4 Estimated Coefficients: Estimate SE tStat pValue _________ __________ _______ __________ b1 2524.6 54.67 46.18 1.3773e-17 b2 0.0055511 3.8132e-05 145.58 4.7733e-25 b3 -0.046424 0.024564 -1.8899 0.078249 b4 921.31 34.028 27.075 3.7727e-14 Number of observations: 19, Error degrees of freedom: 15 Root Mean Squared Error: 85.8 R-Squared: 0.993, Adjusted R-Squared 0.992 F-statistic vs. constant model: 717, p-value = 2.06e-16

% txt = sprintf('$f(x) = %.2f \\cdot sin(2 \\pi x %.3f)^2 %+.3f$', B);

txt = sprintf('$f(x) = %.2f \\cdot sin(2 \\pi \\cdot %.5f \\cdot x %+.3f)^2 %+.3f$', B);

xv = linspace(min(x), max(x), 250);

figure

plot(x, y, '.:b', 'DisplayName','Data')

hold on

plot(xv, fcn(B,xv), '-r', 'DisplayName','Regression')

hold off

grid

xlabel('X')

ylabel('Y')

legend('Location','best')

title(txt, 'Interpreter','LaTeX')

The fit is better statistically as well.

.

Akshay Arvind 2024-5-23

I see, thanks very much! I appreciate the help.

Star Strider 2024-5-23

As always, my pleasure!

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How do I perform a sin^2 or a cos^2 fit for my data?

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