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To use the Gekko package in Anaconda (and MATLAB), it must first be installed into the Anaconda package. The easiest way to do this is to open a new Jupyter Notebook session and install with pip package manager.

If there are not adminstrative privileges, the ---user option can be added to install locally.

$$3x+2y=1$$

$$x+2y=0$$

(:title Call Python from MATLAB:)

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MATLAB creates a new Gekko model with m = py.gekko.GEKKO(); and then initializes new variables with statements such as x = m.Var();. Equations are defined with the variables and the double equal sign as m.Equation(3*x+2*y==1);. Finally, the problem is solved with m.solve(); and the results are returned in x.VALUE{1} and y.VALUE{1}.

where k is a constant, y is the differential state, and t is time. Similar to the prior problem, MATLAB creates a new Gekko model with m = py.gekko.GEKKO(); and then initializes the y variable with y = m.Var(5.0); with an initial condition of 5. The differential equation is defined with m.Equation(k*y.dt()==-t*y); and IMODE option is changed to dynamic simulation (4). Finally, the problem is solved with m.solve(); and the results are returned in y.VALUE.value.

(:title Call Python Functions from MATLAB:) (:keywords function, Python, MATLAB, Numpy, Scipy, library, subroutine:) (:description Access Python package functions from MATLAB. Three examples show how to use Numpy and Gekko functions to compute trigonometric functions, return values, solve linear equations, and solve a differential equation.:)

There are strengths to both MATLAB and Python. Using MATLAB functions in Python and Python functions in MATLAB are both possible. This tutorial shows how to use Python functions in a MATLAB script. In order to use Python in MATLAB, a Python installation must be available and the Python paths accessible. The easiest way to do this is to install Anaconda and launch MATLAB from the Anaconda prompt.

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Exercise 1: Numpy in MATLAB

A first example uses the Numpy (Numerical Python) package in MATLAB to calculate the sine and cosine of values between 0 and 10. The values are computed with Numpy and then returned to MATLAB for plotting.

(:source lang=matlab:) clear all

x = py.numpy.linspace(0,10,101); y = py.numpy.sin(x); z = py.numpy.cos(x);

xm = cellfun(@double,cell(x.tolist())); ym = cellfun(@double,cell(y.tolist())); zm = cellfun(@double,cell(z.tolist()));

plot(xm,ym,'b-') hold on plot(xm,zm,'r--') legend('sin(x)','cos(x)') (:sourceend:)

Exercise 2: Gekko Solves Linear Equations in MATLAB

A second example is the solution of two linear equations with Python Gekko in MATLAB.

$$3x+2y==1$$

$$x+2y==0$$

To use the Gekko package in Anaconda (and MATLAB), it must first be installed into the Anaconda package. The easiest way to do this is to open a new Jupyter Notebook session and install with

  !pip install gekko

or if there are not adminstrative priviledges with:

  !pip install --user gekko

MATLAB creates a new Gekko model with **m = py.gekko.GEKKO();** and then initializes new variables with statements such as **x = m.Var();**. Equations are defined with the variables and the double equal sign as **m.Equation(3*x+2*y==1);**. Finally, the problem is solved with **m.solve();** and the results are returned in **x.VALUE{1}** and **y.VALUE{1}**.

(:source lang=matlab:) % start Matlab from Anaconda prompt close all; clear; % Solve linear equations % Initialize Model m = py.gekko.GEKKO(); % Initialize Variables x = m.Var(); % define new variable y = m.Var(); % default=0 % Define Equations m.Equation(3*x+2*y==1); m.Equation(x+2*y==0); % Solve m.solve(); % Extract values from Python lists using curly brackets disp(['x: ' num2str(x.VALUE{1})]); disp(['y: ' num2str(y.VALUE{1})]); (:sourceend:)

Exercise 3: Gekko Solves ODE in MATLAB

A third example is the solution of an ordinary differential equation (ODE) with Python Gekko in MATLAB.

$$k\frac{dy}{dt}==-t y$$

where **k** is a constant, **y** is the differential state, and **t** is time. Similar to the prior problem, MATLAB creates a new Gekko model with **m = py.gekko.GEKKO();** and then initializes the **y** variable with **y = m.Var(5.0);** with an initial condition of 5. The differential equation is defined with **m.Equation(k*y.dt()==-t*y);** and IMODE option is changed to dynamic simulation (4). Finally, the problem is solved with **m.solve();** and the results are returned in **y.VALUE.value**.

(:source lang=matlab:) % start Matlab from Anaconda prompt close all; clear;

% Solve differential equation m = py.gekko.GEKKO(pyargs('remote','False')); % Solve on local machine m.time = py.numpy.linspace(0,20,100); k = 10; y = m.Var(5.0); t = m.Param(m.time); m.Equation(k*y.dt()==-t*y); m.options.IMODE = 4; m.solve()

% retrieving the values is a little more complicated here time = cellfun(@double,cell(m.time.tolist())); y = cellfun(@double,cell(y.VALUE.value)); plot(time,y) xlabel('Time') ylabel('y') (:sourceend:)

Thanks to Abe Martin for generating the examples.