![]() ![]() Using the plotting code: x = linspace(-3*pi, 3*pi, 200) Īx.XAxis.MinorTickValues = ax.XAxis.Limits(1):pi/6:ax.XAxis. ![]() Let us first define F(φ,a): function out = F(p, a) This is the code for case of γ = 0.1: hold on What I do know is that the evolution of φ(t) must be continuous. 1 Usually, when solving a 1st-order ODE, one needs 1 initial condition, without which the problem is under-defined. My problem is I don't know what inputs to give ode45 in terms of the bounds and the initial condition. Thus, piecewise mimics an if-else ladder. Here is the definition of the F(φ) function: -φ/a - π/a, if φ ∈ A piecewise expression returns the value of the first true condition and disregards any following true expressions. Recent versions include a piecewise command that lets you define the function symbolically. I need to create a program that outputs 6 plots of φ(t) for different values of γ ( γ = 0.1, 0.5, 0.95, 1.05, 2, 5), and t∈. A simple way to plot piecewise functions in MATLAB is to plot each interval separately, using the hold command between plot calls. The MATLAB provides a built-in function “piecewise” which takes the equations and conditions as an argument and returns a piecewise expression.I have a function dφ/dt = γ - F(φ) (where F(φ) - a is 2π-periodic function) and the graph of the function F(φ). Pass the plotcommand the input and output arrays. # Plotting Piecewise function using switch case statements If the ‘case’ condition is true, then that means x lies in the interval specified by that case expression and the appropriate statements will be executed. 1 Chaining equalities like that is only supported in very recent MATLAB. First of all, the case expressions check the value of x. We have separated the intervals of different sub-functions in different cases. It is almost similar to the above method but in this case, we have replaced the if-else with switch-case statements. Output: Figure 3 using switch-case statements The plot(x, result) command plots the values in variable “result” against ‘x’. The values calculated are stored into an array ‘result’ which represents the piecewise function values with respect to input (x). In this case, the body of the if statement consists of only one statement which is ” result = x.^2 “. ![]() As the value of x lies in the (0,2] interval, therefore, the x will enter into the body of the 2nd elseif condition. Here, if-else conditions are used to check the interval where the input(x) lies. Ideally, this function should be the same as the function that takes a point at the right-most point to the left-most point. ![]() The “piecewise_function” takes the value and check the conditions of if-else statements. Matlab Plotting moved here Functions In mathematics, a piecewise function (or piecewise function) is a function that computes the value of a given function at given points. Then, we have used a for loop which iterates over an array x and passes these values to the “piecewise_function”. You don't have to create piecewise linear functions by yourself. Matlab is a mathematical programming language. Matlab draws straight lines from one coordinate to the next coordinate. The array x specifies the range of values on which we want to obtain the results of the piecewise function. All plots are piecewise linear functions. We can also use “linspace” command to create an array. In this code, we have created an array “x” by using the colon operator. % create a function to plot piecewise function %iterate over the elements in x one-by-one and calculate the value of f(x) % Plotting piecewise function using if else statements. In this method, we’ll define all the sub-functions along with the constraints using if-else statements and then we will plot the piecewise function. The second method involves the use of if-else statements along with for loop. Output: Figure 2 using if-else statements The graph in fig 2 shows the output obtained as a result of the plot(x, y) command. The plot(x, y) command then plots y against x. Then, we have created an array using all the intervals i.e., ‘x’ and an array of ‘y’ representing the different equation values. In the code given above, eq1, eq2, and eq3 represent the three equations whereas x1, x2, and x3 define the intervals for their respective equations. ![]()
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