MATLAB: Finding mathematical function of set of points

functionmathematicalpoints

There are some points on X-Y coordinates. Is it possible in MATLAB to find mathematical function between X and Y?

for example for X=1,3,5,7,8,9,23,25,30 respectively Y is equals to Y=1,3,5,7,9,12,13,17,20

now how MATLAB could find relation between X and Y in mathematical function form? ( finding Y=f(X) )

mathematical function must be algebra in this form: y=a+bx^2+cx^3+dx^4+…nx^K (Not sinusoidal and etc)

that a,b,…,n and K are unknown. Is it possible in MATLAB to find this parameters?

Best Answer

There are literally an infinite number of mathematical functions that fit any finite set of (X,Y) pairs exactly. Unless you have some prior information as to what the form of the mathematical function "should be", there is no way of distinguishing which of those infinite number of functions is the "right" one.

Related Solutions

MATLAB: Uniform point interpolation along a line described by non-uniform distributed points

See this demo:

% Code to plot data, plus points interpolated in between the data.
clc;    % Clear the command window.
clearvars;
close all;  % Close all figures (except those of imtool.)
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 22;
% Make up sample data.
numOriginalPoints = 20;
xOriginal = sort(100 * rand(1, numOriginalPoints), 'ascend');
yOriginal = 30 * rand(1, numOriginalPoints) - 10;
% Plot them
subplot(3, 1, 1);
plot(xOriginal, yOriginal, 'ro-', 'LineWidth', 2);
grid on;
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
title('Training Points', 'FontSize', fontSize);
% Interpolate points in between, linearly from the min to the max.
numNewPoints = 100;
xInterpolated = linspace(min(xOriginal), max(xOriginal), numNewPoints);
yInterpolated = interp1(xOriginal, yOriginal, xInterpolated);
% Plot interpolated points.

subplot(3, 1, 2);
plot(xInterpolated, yInterpolated, 'bo-', 'LineWidth', 2);
% Plot training points over them so we can see where they are in relation to the new points.

hold on;
plot(xOriginal, yOriginal, 'ro', 'LineWidth', 2);
grid on;
title('Interpolated Points without Including Training Points', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
legend('Interpolated', 'Training');
% Enlarge figure to full screen.

set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% Note, if you want the original points included in the set of new, interpolated points, 
% Add them to xInterpolated list.
subplot(3, 1, 3);
xInterpolated = sort([xInterpolated, xOriginal], 'ascend');
yInterpolated = interp1(xOriginal, yOriginal, xInterpolated);
% Plot interpolated points.
plot(xInterpolated, yInterpolated, 'bo-', 'LineWidth', 2);
% Plot training points over them so we can see where they are in relation to the new points.
hold on;
plot(xOriginal, yOriginal, 'ro', 'LineWidth', 2);
grid on;
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
title('Interpolated Points Including Training Points', 'FontSize', fontSize);
legend('Interpolated', 'Training');
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);

MATLAB: Getting a plot to wrap from right to left

Hi Bill,

You have six points whose real starting point is evidently at x = -65. The idea here is to take the two leftmost x points and put them to the right by adding 360 degrees. Then do the spline. That's shown in figure 1. To get a plot like the example you have to cut out a part of that curve and move it back to the left. That's the process for figure 2.

x = [-65.0600; -0.5310; 71.5820; 137.4960; -153.9860; -87.7790];
y = [0.1000; 18.9260; 11.4630; -12.4760; -18.9610; 1.5900];
% move two x points to the right
x1 = x;
x1(x1<-75) = x1(x1<-75) + 360;
interpolatedX = linspace(min(x1), max(x1), 500);
interpolatedY = spline(x1,y,interpolatedX);
figure(1)
plot(x1,y,'ro',interpolatedX,interpolatedY,'b')
% cut out the part greater than 160 degrees, move it to the left
ind = interpolatedX > 160;
piece1X = interpolatedX(ind)-360;
piece1Y = interpolatedY(ind);
piece2X = interpolatedX(~ind);
piece2Y = interpolatedY(~ind);
figure(2)
plot(piece1X,piece1Y,'b',piece2X,piece2Y,'b','LineWidth', 3)
hold on
plot(x,y,'ro','MarkerSize', 10)
hold off

Best Answer

Related Solutions

MATLAB: Uniform point interpolation along a line described by non-uniform distributed points

MATLAB: Getting a plot to wrap from right to left

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