Matlab Chapter6.pdf

The matrix a is 30 × 30. The element in the middle a(15, 15) is 1, all the elements in row 7
are 0.1, and all the remaining elements in column 15 are 0.2. mesh(a) then interprets the rows
and columns of a as an x-y coordinate grid, with the values a(i, j) forming the mesh surface
above the points (i, j).
2.2.1 Contour plots
If you managed to draw a plot try the command
≫ contour(u)
You should get a contour plot of the heat distribution for example. Here’s the code:
≫ [x, y] = meshgrid(−2.1 : 0.15 : 2.1, −6 : 0.15 : 6);
≫ u = 80 ∗ y. ∧ 2. ∗ exp(−x. ∧ 2 − 0.3 ∗ y. ∧ 2);
≫ contour(u)
Remark 2.2 The function contour can take a second input variable. It can be a scalar specifying
how many contour levels to plot, or it can be a vector specifying the values at which to
plot the contour levels.
Remark 2.3 A simple contour plotting facility is provided by ezcontour. ezcontour in the
following example produces contours for the function sin(3y − x 2 + 1) + cos(2y 2 − 2x) over the
range −2 ≤ x ≤ 2 and −1 ≤ y ≤ 1;
subplot(211)
ezcontour( ′ sin(3 ∗ y − x ∧ 2 + 1) + cos(2 ∗ y ∧ 2 − 2 ∗ x) ′ , [−2 2 − 1 1]);
x = −2 : .01 : 2; y = −1 : .01 : 1;
[X, Y]=meshgrid(x, y);
Z = sin(3 ∗ Y − X. ∧ 2 + 1) + cos(2 ∗ Y. ∧ 2 − 2 ∗ X);
subplot(212)
contour(x, y, Z, 20)
Example 2.2 (meshc) A 3-D contour may be drawn under a surface as follows:
≫ [x y] = meshgrid(−2 : .2 : 2);
≫ z = x. ∗ exp(−x. ∧ 2 − y. ∧ 2);
≫ meshc(z)
Example 2.3 (Cropping a surface with NaNs) If a matrix for a surface plot contains a
data of type NaNs, these elements are not plotted. This enables you to cut away (crop) parts
of a surface.
[x y] = meshgrid(−2 : .2 : 2, −2 : .2 : 2);
z = x. ∗ exp(−x. ∧ 2 − y. ∧ 2);
c = z; % preserve the original surface
c(1 : 11, 1 : 21) = nan ∗ c(1 : 11, 1 : 21);
mesh(c), xlabel(x-axis), ylabel(y-axis)
Example 2.4 Consider the scalar function of two variables V = x 2 + y. The gradient of V is
defined as the vector field
( ∂V
∇V =
∂x , ∂V )
= (2x, 1).
∂y
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