There are many reasons to do this, for example, if the theoretical model agrees with the observed data values, the theory is likely to be right and hopefully you have gained new insight into the. This function can represent either an empirical or a theoretical model. You can extend 'h' to contain one constraint for every data point in your set (see doc). In many areas of science, you want to fit a function to data. Notice that the constraint function 'h' ensures that the polynomial will lie above (x1,y1), and the objective function 'phi' will try to keep it as close as possible. Note that 'x' would be the polynomial coefficients you want to fit and h(x) is the polynomial evaluated at a specific data point.įor example: phi = delta_mod (P, x, y) % mod: Don't increase the importance of negative residuals!!
the h(x)>=0 (see doc).Īs objective function phi you could use a square norm error, as in your example, and add constraints of the form h(x)>=0 for every data point. You could try to use the non-linear inequality constraint options that Octave's 'sqp' offers, i.e.
This may fail for different data sets, especially if they are larger, i.e. You may want to avoid multiplying the error by an arbitrary number (1000 in your example) when it is negative. Please explain why if you think it can't be used. Your method seems fine, and I see no reason it can't be used for higher-order polynomials actually. Plot(x, y, xi, yi, " initial guess ", xi, yio, " optimized ") īut as you can see, the optimized and evaluated poly has points < the orginal point which isn't allowed. The easies way would be to just use polyfit and then calculate max(y-yi) and add this as offset but this wouldn't be optimal.ĮDIT: I want to use GNU OCtave but added "matlab" as tag because the language and functions are similiar.ĮDIT: based on tvo's answer and real data: x = Is there a better way/method which also works with higher order polynomials? Of the current figure with the "tag" set to "legend".I want to fit a polynomial to noisy data so that the approximated polynomial is always >= the original data. Implementation Note: A legend is implemented as an additional axes object Labels or DisplayNames are available, then the label text is simply Is taken from the DisplayName property of graphics objects. The legend label text is either provided in the call to legend or Graphics handles to the plot objects which were used in making the legend.Ī cell array of strings of the labels in the legend. Graphics handles to the text and line objects which make up the legend. The graphics handle of the legend object. Place label text to the right of the keys (default) Toggles between "hide" and "show" "boxon" The following customizations are available using option: The optional parameter orient determines if the key elements are s : indicates not to evaluate the entered expression. The optional parameter pos specifies the location of the legend Syntax : input (prompt, s)Parameters : prompt : the text prompted on the terminal. A plot must exist before legend is called. legend works on line graphs,īar graphs, etc. Hobjs, are not specified then the legend’s strings will be associated Rather than the current axes returned by gca. If the first argument hax is an axes handle, then plot into this axis, Legend entries may be specified as individual character string arguments,Ī character array, or a cell array of character strings. : legend ( str1, str2, …) : legend ( matstr) : legend ( cellstr) : legend (…, "location", pos) : legend (…, "orientation", orient) : legend ( hax, …) : legend ( hobjs, …) : legend ( hax, hobjs, …) : legend (" option") : = legend (…)ĭisplay a legend for the current axes using the specified strings as labels.