Plotting Functions of Two Variables:
Functions on Rectangular Grids:
Presume you wish to plot a function f(x, y) on the rectangle a ≤ x ≤ b and c ≤ y ≤ d. The graph of the function of two variables is of course a three dimensional object. Visualizing the graph is habitually very useful.
For instance presume you have a formula:
f(x, y) = x sin(xy)
And you are involved in the function on the region 0 ≤ x ≤ 5, π ≤ y ≤ 2π. A manner to plot this function in Mat lab would be the following sequence of commands
> f = inline(’x.*sin(x.*y)’,’x’,’y’)> [X,Y] = meshgrid(0:.1:5,pi:.01*pi:2*pi);> Z = f(X,Y)>mesh(X,Y,Z)
This will produce a 3-D plot that you are able to rotate by clicking on the rotate icon and then dragging with the mouse.
Instead of the command mesh you could utilize the command:
>surf(X,Y,Z)
The key command in this series is [X Y] = meshgrid(a:h:b,c:k:d) which generates matrices of x and y values in X and Y. Enter
>size(X)>size(Y)>size(Z)
to see that each one of these variables is a 101 × 51 matrix. To observe the first few entries of X enter
>X(1:6,1:6)
And to see the first several values of Y type
>Y(1:6,1:6)
You must observe that the x values in X begin at 0 on the left column and increase from left to right. The y values on the other have begun at π at the top and increase from top to bottom. Note down that this arrangement is flipped from the typical arrangement in the x-y plane.
In the command [X Y] = meshgrid(a:h:b,c:k:d) h is the increase in the x direction and k is the increment in the y direction.
Habitually we will calculate:
h = (b – a) m and k = (d − c) n
Where m is the number of intervals in the x direction as well as n is the number of intervals in the y direction. To acquire a good plot it is best if m and n can be set between 10 and 100.
For another illustration of how meshgrid works try the following and look at the output in X andY.
> [X,Y] = meshgrid(0:.5:4,1:.2:2);
Scattered Data and Triangulation:
Habitually we are interested in objects whose bases are not rectangular. For instance, data does not typically come arranged in a nice rectangular grid rather measurements are occupied where convenient.
In Mat lab we are able to produce triangles for a region by recording the coordinates of the vertices and recording which vertices belong to each triangle. The subsequent script program produces such a set of triangles:
% mytriangles% Program to produce a triangulation.% V contains vertices, which are (x,y) pairsV = [ 1/2 1/2 ; 1 1 ; 3/2 1/2 ; .5 1.5 ; 0 01 0 ; 2 0 ; 2 1 ; 1.5 1.5 ; 1 20 2 ; 0 1]% x, y are row vectors containing coordinates of verticesx = V(:,1)’;y = V(:,2)’;% Assign the trianglesT = delaunay(x,y)
You are able to plot the triangles using the following command
>trimesh(T,x,y)
You can as well prescribe values (heights) at each vertex directly (say from a survey):
> z1 = [ 2 3 2.5 2 1 1 .5 1.5 1.6 1.7 .9 .5 ];
Or by means of a function:
> f = inline(’abs(sin(x.*y)).^(3/2)’,’x’,’y’);> z2 = f(x,y);
The resulting profiles are able to be plotted:
>trimesh(T,x,y,z1)>trisurf(T,x,y,z2)
Every row of the matrix T corresponds to a triangle so T(i) gives triangle number i. The 3 corners of triangle number i are at indices T(i,1), T(i,2), and T(i,3). Therefore for example to get the y-coordinate of the second point of triangle number 5 enter
>y(T(5,2))
To see other illustration of regions defined by triangle get mywedge.m and mywasher.m from the class web site as well as run them. Every of these programs defines vectors x and y of x and y values of vertices and a matrix T. As prior to T is a list of sets of three integers. Every triple of integers indicates which vertices to connect in a triangle.
To plot a function say f(x, y) = x2 − y2 on the washer figure try
>mywasher> z = x.^2 - y.^2>trisurf(T,x,y,z)
Note again that this plot is able to be rotated using the icon and mouse.
Latest technology based Matlab Programming Online Tutoring Assistance
Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Matlab Programming help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Matlab Programming, project ideas and tutorials. We provide email based Matlab Programming help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Matlab Programming. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Matlab Programming Homework help and assignment help services. They use their experience, as they have solved thousands of the Matlab Programming assignments, which may help you to solve your complex issues of Matlab Programming. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
tutorsglobe.com systematics assignment help-homework help by online biodiversity tutors
Get 24/7 worthy insight from professional Statistical Package for the Social Science Assignment Help tutors and score A++ at fair prices.
the whole coil winding comprise one coil group per pole for each phase. total number of coils = 12/2 = 6; coils per phase = 6/3 = 2; number of coils of groups per phase = 3 x 2 = 6
tutorsglobe.com classification of wants assignment help-homework help by online characteristics of wants tutors
Metal Oxide Field Effect Transistor tutorial all along with the key concepts of MOS-FET operation, MOSFET output curves, relationship between Drain voltage and saturation in MOSFET, MOSFET device types, P-Channel Enhancement Mode
Keeping the case histories and statistical records of all installations will be extremely much helpful in trouble shooting.
Get rid of the apprehension of short deadlines and score top grades with Gender and Legal Issues Assignment Help service!
tutorsglobe.com wages assignment help-homework help by online marginal productivity theory of distribution tutors
tutorsglobe.com some early views of heredity assignment help-homework help by online heredity tutors
output devices — “how it shows you what it is doing” for instance, monitor (the screen) is how the computer sends information reverses to you, either it be surfing the web or writing a memo.
The issued share capital or allotted share capital is share capital that has been issued to shareholders.
Compounds of the Noble Gases tutorial all along with the key concepts of Compounds of Xenon, Clathrates of Noble Gases, Structure and Bonding in Xenon Compounds, Xenon Tetrafluoride, Xenon Hexafluoride and VSEPR Theory
tutorsglobe.com carrier assignment help-homework help by online antigens and antigen presentation tutors
: www.tutorsglobe.com offers nomenclature & structure of amines homework help, nomenclature & structure of amines assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
Simple Machines tutorial all along with the key concepts of Introduction to Simple machine, Force ratio or mechanical advantage, Velocity Ratio, Efficiency, Lever, Inclined plane, Pulley, Wheel and Axle, Screw and Wedge
1936987
Questions Asked
3689
Tutors
1478022
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!