Need to fit a curve to some data points

I am new to matlab, and I have a problem.

I have the data points:

x = [1 2 100]

y = [55 22 0]

I need to generate a curve that goes through these values. I thought some version of polyfit would work, but I also can't have the y values go below 0. I am looking for something like the upper half of the function 1/x. What should I use

[the cyclist]

Here is a plot of your data:

x = [1 2 100];
y = [55 22 0];

scatter(x,y,64)

Are you saying you want a smooth curve that passes through these points and never goes below zero? Doesn't go below zero for any x, or just x in [1,100]?

Out of curiosity, what's the purpose?

[ISh]

I would like a smooth curve that goes through or at least close to these points. I can't have it ever go below 0 for any positive x values. I cannot go into details of the purpose.

Answer 1

[Sam Chak]

Here's another candidate. An exponential decay function model should align with the description you provided.

Try learning how to fit it into the data.

%% Data
x   = [ 1  2 100];
y   = [55 22   0];

%% Exponential decay function
xx  = linspace(x(1), x(end));
f   = 137.5*exp(-0.9163*xx);

%% Plot results
plot(x, y, 'o', 'markersize', 10, 'linewidth', 2), hold on
plot(xx, f, 'linewidth', 1.5), grid on
xlabel x, ylabel y

[Alexander]

Where do you get 137.5 and -0.91629 from?

[Sam Chak]

From the fitting app. But I didn't use lsqcurvefit().

dXdata = [1 2 100];
dYdata = [55 22 0];
x      = linspace(0,100,1000);
% y = a*exp(-b*x);
fun2   = @(w,xdata)(w(1)*exp(dXdata*(w(2))));
x02    = [0,0];
xFit2  = lsqcurvefit(fun2,x02,dXdata,dYdata)

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.

xFit2 = 1×2

137.5000 -0.9163

yAsy2  = xFit2(1).*exp(x*(xFit2(2)));
plot(x,yAsy2,dXdata,dYdata,'o'); grid;

Answer 2

[Matt J]

This uses the fminspleas downloadable,

x = [1 2 100];
y = [55 22 0];

flist={@(p,x)1./(x-p(1)).^p(2)};

[p,A]=fminspleas(flist,[0,1], x,y, [-inf,0])

p = 1x2

0.0005 1.3219

A = 54.9679

f=@(x) A./(x-p(1)).^p(2); %The fitted function

xs=linspace(x(1),x(end));
plot(x,y,'or',xs,f(xs),'b--');

Answer 3

[Alexander]

Seems to be an exponetial behavior. Use lsqcurvefit to approximate a curve according your needs. My code:

dXdata = [1 2 100]

dYdata = [55 22 0]

x = linspace(0,100,1000);

% y = a*exp(-b*x);

fun2 = @(w,xdata)(w(1)*exp(dXdata*(w(2))));

x02 = [0,0];

xFit2 = lsqcurvefit(fun2,x02,dXdata,dYdata);

yAsy2 = xFit2(1).*exp(x*(xFit2(2)));

plot(x,yAsy2,dXdata,dYdata,'o'); grid;

Answer 4

[Matt J]

x = [1 2 100];
y = [55 22 0];

ylog=log(y+eps);

p=polyfit(x,ylog,2);

f=@(x) exp(polyval(p,x));  %The fitted function

fitError=abs(f(x)-y)

fitError = 1x3

1.0e-12 * 0.8669 0.0355 0.0002

xs=linspace(x(1),x(end));
plot(x,y,'or',xs,f(xs),'b--');

Answer 5

[Sam Chak]

Hi @ISh

This Rational function model (Rat11) precisely fits the three data points.

format long g

%% Data
xdat = [ 1  2 100];
ydat = [55 22   0];

%% A Rational function model (Rat11) with coefficients {p1, p2, p3} is proposed
yfit = @(p, xdat) (p(1)*xdat + 1)./(p(2)*xdat + p(3));

%% Initial guess of coefficients {p1, p2, p3}
p0   = [1, 2, 3];

%% Call lsqcurvefit to fit the model
[psol, resnorm] = lsqcurvefit(yfit, p0, xdat, ydat)

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.

psol = 1×3

-0.00999999999999777 0.0265454545454659 -0.00854545454549746

resnorm = 
      9.40049033638573e-21

%% Plot fitting result
xq   = linspace(xdat(1), xdat(end), 1000);
plot(xdat, ydat, 'o', 'markersize', 10, 'linewidth', 2), hold on
plot(xq, yfit(psol, xq), 'linewidth', 1.5), grid on
legend('Data points', 'Fitted curve', 'location', 'best', 'fontsize', 12)
xlabel('x'), ylabel('y')
title({'$y(t) = \frac{-0.01 x + 1}{\frac{73}{2750} x - \frac{47}{5500}}$'}, 'interpreter', 'latex', 'fontsize', 16)

%% Test
p     = [-0.01, 73/2750, -47/5500];     % <-- True values of the coefficients
ytest = yfit(p, xdat)

ytest = 1×3

55 22 0