MATLAB FINANCIAL DERIVATIVES TOOLBOX Instrukcja Użytkownika Pobierz pdf (Strona 66)

To find what other useful commands can be accompanied the

h and

commands, use the online help.

3.2.2.1 Examination of a Function’s Critical Points

Many times, a researcher is faced with an unconstrained optimization

problem. Than is, it has a two variable function Z=f(x,y) and wants to

examine this function in a certain area in order to locate any minimum,

maximum or saddle point(s). From the previous section, it is apparent that

in the range [-10,10] the peaks function seems to have various critical

points. In optimization theory, a critical point can be located via the use of a

contour plot. A contour plot depicts the level curves of f(x,y) for some values

V. In other words, we project the sections/incision of various heights of the

Z=f(x,y) function in the (x,y)-plane. Matlab offers such function named as:

r. Experiment with the following code to see the usefulness of contour

plots.

Matlab’s command:

>> V=-10:1:10; [c,h] = contour(x,y,Z,V); clabel(c,h), colorbar; hold

on;

>> xlabel('x'); ylabel('y'); title('Contour plot of the peaks function');

Matlab’s response:

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-4

-3

-2

-1

Contour plot of the peaks function

-6

-5

-4

-3

-2

-1

Local Minimum

Global Minimum

Local Maximum

Global Maximum

-6

-4

-2

1 2 ... 61 62 63 64 65 66 67 68 69 70 71 ... 118 119

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MATLAB FINANCIAL DERIVATIVES TOOLBOX Instrukcja Użytkownika Strona 66