#Polyfit matlab how to#
'Linear fit at 1.5', 'Linear fit at 6.0' . See 'testpolyfit.cpp' for an example of how to call the polyfit() routine if you are not interested in the CppUTest portions. 'Location', 'Best' ) grid on title ( '1st Order Interpolations' ) axis () subplot ( 2, 1, 2 ) %% Plot original data plot ( x, y, 'ko' ) %% Calculate model across entire domain and plot xm = linspace ( x ( 1 ), x ( end ), 100 ) ym = polyval ( polyfit ( x, y, 1 ), xm ) hold on plot ( xm, ym, 'g-' ) % Calculate and plot estimate using fit yFit1p5 = polyval ( polyfit ( x, y, 1 ), 1.5 ) yFit6p0 = polyval ( polyfit ( x, y, 1 ), 6 ) plot ( 1.5, yFit1p5, 'ms', 6, yFit6p0, 'm*' ) %% Extra legend ( 'Original', 'Fit model'. 'Interpolation at 1.5', 'Interpolation at 6.0'. In this case, the goal is to find two different values - one at x=1.5 and one at x=6.Ĭlear format short e x = y = figure ( 1 ) clf subplot ( 2, 1, 1 ) %% Plot original data plot ( x, y, 'ko' ) hold on %% Plot segment of closest basis points plot ( x ( 1 : 2 ), y ( 1 : 2 ), 'r-' ) plot ( x ( 3 : 4 ), y ( 3 : 4 ), 'b-' ) %% Calculate and plot interpolated values yInterp1p5 = polyval ( polyfit ( x ( 1 : 2 ), y ( 1 : 2 ), 1 ), 1.5 ) yInterp6p0 = polyval ( polyfit ( x ( 3 : 4 ), y ( 3 : 4 ), 1 ), 6 ) plot ( 1.5, yInterp1p5, 'ms', 6, yInterp6p0, 'm*' ) %% Extra legend ( 'Original', 'Segment for 1.5', 'Segment for 6.0'. Polyfit generates the coefficients of the polynomial, which can be used to model a curve to fit the data.
#Polyfit matlab code#
The code and graph below will show the differences between the code for and meaning of polynomial interpolation (top) and fitting (bottom). Polyfit is a Matlab function that computes a least squares polynomial for a given set of data. A second order polynomial interpolation will always use the quadratic that interpolates among the nearest three points - depending on spacing, there may be two different but equally valid sets of points to you.
For instance, a first order polynomial interpolation will always use the straight line between the two closes points in the data set. Polynomial interpolation will always be of an order one less than the number of points used it will always go through the basis points you use to create the interpolation. Polynomial fitting seeks to take a single polynomial - generally of a low order - and finds the coefficients which gets the polynomial collectively as close to all the points as possible, but which may not actually hit any of the points. Polynomial interpolation is different from polynomial fitting. Give this a try and let us know what you think here or leave a comment for Are.Your code for the Minilab will be *much simpler* than the demo below since you do not need to make graphs and do not need to calculate fits at all.
If you need other sophisticated constraints, you would want to check out Optimization Toolbox. norm(x_lsqlin2-x_polyfix')Īre's polyfit is great for performing polynomial fits with constraints around passing points. If we compare this result with that from lsqlin, we see that it's essentially identical. Set(gca, 'XTick',0:0.5:2) % Adjust tick marks to show points of interest x_polyfix =
Let's solve the same problem using polyfix, 7th order polynomial to fit through (0,0), (2,0), (0.5,1), (1.5,-1) and derivative of zero at $t$ = 0.5 and $t$ = 1.5. This entry achieves the goal of performing a polynomial fit with constraints to pass through specific points with specific derivatives. In the MATLAB Answers post I mentioned above, Are actually posted a response mentioning polyfix. Set(gca, 'XTick',0:0.5:2) % Adjust tick marks to show points of interest Warning: The trust-region-reflective algorithm can handle bound constraints Legend( 'data', 'lsqlin (with derivative constraint)') Let's fit and see if we've accomplished our goal. lsqlin solves the following least-squares curve fitting problem. There are several ways to deal with this, and one of them is to use a function like lsqlin from Optimization Toolbox. But first, let me talk about a different method. This is where Are's entry comes into play. Perhaps, you want the curve to cross (0, 0) and (2, 0). What if you want this polynomial to go through certain points. We'll fit a 3rd order polynomial to the data. The function polyfit lets you fit a polynomial to your data.