![]() If you want to get deep into Matlab's symbolic math, you can create piecewise functions using MuPAD, which are accessible from Matlab – e.g., see my example here. In your case, x is obviously not "always" on one side or the other of zero, but you may still find this useful in other cases. To add to comment, you should convert the output of any logical comparison to symbolic before using isAlways: isAlways(sym(x<0)) Set the value of a piecewise function when no condition is true (called otherwise value) by specifying an additional input argument. In Matlab R2012a+, you can take advantage of assumptions in addition to the normal relational operators. This MATLAB function returns the piecewise expression or function pw whose value is val1 when condition cond1 is true, is val2 when cond2 is true, and so on. ![]() In this other multiple functions are used to apply on specific intervals of. You can shift it to compare values other than zero. A piecewise function is a function, which is defined by various multiple functions. Piecewise is a term also used to describe any property of a piecewise function that is true for each piece but may not be true for the whole domain of the function. Yes, the Heaviside function is 0.5 at zero – this gives it the appropriate mathematical properties. A function f of a variable x (noted f(x)) is a relationship whose definition is given differently on different subsets of its domain. (You could keep f in a separate file called f.m, but I'd go with one file for both functions. So the first code sample needs to be saved in a file named myode.m. You can also take advantage of the heaviside function, which is available in much older versions. The 'regular' function approach gives you the most flexibility in describing your ODEs, but MATLAB requires that functions be stored in function files. Finally, the third piece adds in another offset in above x 1. Then we add in a piece that takes effect above zero. The first term is what happens for x below the first break point. P (x) -1 + H (x)3 + H (x-1) (-1) See that there are three pieces to P (x). In such an old version of Matlab, you may want to break up your piecewise function into separate continuous functions and solve them separately: syms x Our piecewise function is now derived from H (x). A symbolic method is only needed if, for example, you want a formula or if you need to ensure precision. For example, let’s define a simple piecewise function. You can also set the value which will be true when no condition is true. Look at fzero and fsolve amongst many others. To define a piecewise function, you have to put the condition and its value inside the piecewise () function and then the second condition and its value, and so on. First, make sure symbolic math is even the appropriate solution method for your problem.
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