MATLAB Mathematics - SERC - Index of

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4 Function Functions Function Summary Function functions are functions that call other functions as input arguments. An example of a function function is fplot, which plots the graphs of functions. You can call the function fplot with the syntax fplot(@fun, [-pi pi]) where the input argument @fun is a handle to the function you want to plot. The function fun is referred to as the called function. The function functions are located in the MATLAB funfun directory. This table provides a brief description of the functions discussed in this chapter. Related functions are grouped by category. Function Summary Category Function Description Plotting fplot Plot function Optimization and zero finding Numerical integration fminbnd fminsearch fzero quad quadl quadv dblquad triplequad Minimize function of one variable with bound constraints. Minimize function of several variables. Find zero of function of one variable. Numerically evaluate integral, adaptive Simpson quadrature. Numerically evaluate integral, adaptive Lobatto quadrature. Vectorized quadrature Numerically evaluate double integral. Numerically evaluate triple integral. 4-2
Representing Functions in MATLAB Representing Functions in MATLAB MATLAB can represent mathematical functions by expressing them as MATLAB functions in M-files or as anonymous functions. For example, consider the function 1 fx ( ) = ------------------------------------------ ( x – 0.3) 2 + 0.01 1 + ------------------------------------------ ( x – 0.9) 2 – 6 + 0.04 This function can be used as input to any of the function functions. MATLAB Functions You can find the function above in the M-file named humps.m. function y = humps(x) y = 1./((x - 0.3).^2 + 0.01) + 1./((x - 0.9).^2 + 0.04) - 6; To evaluate the function humps at 2.0, use @ to obtain a function handle for humps, and then use the function handle in the same way you would use a function name to call the function: fh = @humps; fh(2.0) ans = -4.8552 Anonymous Functions A second way to represent a mathematical function at the command line is by creating an anonymous function from a string expression. For example, you can create an anonymous function of the humps function. The value returned, fh, is a function handle: fh = @(x)1./((x-0.3).^2 + 0.01) + 1./((x-0.9).^2 + 0.04)-6; You can then evaluate fh at 2.0 in the same way that you can with a function handle for a MATLAB function: fh(2.0) ans = -4.8552 4-3
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6 Sparse Matrices Function Summary
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