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Generic Programming

- Matlab Cookbook I -

This section includes several examples of generic programming. These programs perform a variety of common, practical tasks.

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Remarks or comments are included in the examples to help Matlab learners understand how each program works.

Roots of Quadratic Equations
We are going to create now a Matlab program that calculates the quadratic  roots (roots of a quadratic equation). The equation must be in the following form: ax2 + bx + c = 0, where a, b, and c are real coefficients...

Polygon Area
This program calculates the area of a polygon, using Matlab . You must supply the x and y coordinates of all vertices. Coordinates must be entered in order of successive vertices...

Trigonometry (finding parts of a triangle)
This program calculates three unknown parts of a triangle when three parts are given (basic trigonometry is used). At least one part given must be the length of a side. As in a generic programming way to do it, we show in this code four possibilities for data entry...

Matrix decomposition
Matlab includes several functions for matrix decomposition or factorization. LU, QR, Cholesky, and SVD built-in functions are explored...

Geometric Mean and Geometric deviation
This program computes the geometric mean and geometric deviation of a set of data. We obtain the results in two ways, using iterations and available vectorized operations in...

Interpolation
This page shows the most usual and common interpolation concept, as if we were using generic programming techniques (Matlab has its own function for this purpose). This code calculates the y-coordinates of points on a line given their x-coordinates. It is necessary to know coordinates of two points on the same line...

Curvilinear (Lagrange) interpolation
An improvement over the linear interpolation...

Linear Regression
This program fits a straight line to a given set of coordinates using the method of least squares (linear regression). The coefficients of the line, coefficient of determination...

Numerical approximation of a Derivative
We are going to develop a Matlab function to calculate the numerical derivative of any unidimensional scalar function fun(x) at a point x0. The function is going to have the following usage: D = Derivative(fun, x0) ...

Numerical approximation of a Gradient
We are going to include the concepts in our Derivative function created before, to develop a Matlab function to calculate the gradient of a multidimensional scalar function. The function is going to have the following usage: g = Grad(fun, x0)...

Integration - Trapezoidal Rule
This code approximates the definite integral of a function. The integral is calculated using the trapezoidal rule. Parameters of the function are the limits of integration and the number of intervals within the limits...

Integration - Simpson's Rule
This code approximates the definite integral of a function. The integral is calculated using Simpsons rule. You must supply the limits of integration, the increment between points within the limits, and the function of the curve to be integrated...

Prime Numbers
It is well known that prime factors of a positive integer are the prime numbers that divide into that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization. Here’s the full Matlab script...

Euclidean Algorithm
This program calculates the Greatest Common Denominator (GCD) of two integers (see flow-chart). It is based on the Euclidean algorithm for finding the GCD...

Coordinate Conversion
As another example of generic programming, this couple of Matlab functions convert the coordinates of a point given in Cartesian coordinates to Polar coordinates, and vice versa. When we use the polar-to-cartesian function, we enter a magnitude and an angle in degrees as parameters. The function returns a real number (x) and a complex number (y value)...

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