MATLAB FINANCIAL DERIVATIVES TOOLBOX Uživatelský manuál stáhnout pdf (Strana 61)

functional expression, z=f(x,y), is evaluated. Usually, we evaluate the z

behavior in a certain area of the (x,y)-plane in which z has some interesting

properties (e.g. it presents a minimum, a maximum or a saddle point).

Suppose that a

x vector that defines the x-axis (abscissa) and a

y vector that

defines the y-axis (ordinate) exist and define the (x,y)-plane on which we

would like to create the 3D surface of z=f(x,y). To plot the surface, it is

needed to create a grid of sample points (most preferable with high density

and this is defined by the difference between the elements of

x and

y) that

covers the rectangular domain of the (x,y) plane in order to generate

X and

matrices consisting of repeated rows and columns of

x and

y, respectively,

over the domain of the function. Then these matrices will be used to

evaluate and graph the function.

The

d function transforms the domain specified by two vectors,

and

y, into matrices,

X and

Y. You then use these matrices to evaluate the

z=f(x,y). The rows of

X are copies of the vector

x and the columns of

Y are

copies of the vector

We will see how we can plot a 3D surface via an example. Let say that we

need a graph of the well know peaks function that has the following

functional form:

222222

15312

1013

y)x(yx)y(x

ee)yx

(e)x()y,x(fZ

−+−−−+−−

−−−−−==

We want to examine this function in the rectangular space of (x,y)-plane

defined as:

≤≤−

≤

−

Since Matlab understands combinations of (x,y,z) pairs only, it is needed to

evaluate

Z at various points (the number of these points defines the surface

smoothness) that lay in the above rectangular space.

d can be used

to create the desired grid of points. The following code lead to the generation

of the grid:

1 2 ... 56 57 58 59 60 61 62 63 64 65 66 ... 118 119

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