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.
The sole proprietorship is in which an individual is the sole owner of a business. These businesses are quite small in terms of size.
Theory and lecture notes of Pumping Lemma for CFLs all along with the key concepts of Pumping Lemma for CFLs. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Pumping Lemma for CFLs.
Switched Mode Power Supply tutorial all along with the key concepts of Switched-mode power supply operation, Rectifier, filter and inverter, Converter and output rectifier, Drawbacks of switched mode power supplies, switched-mode power supply
www.tutorsglobe.com offers Checklist Guide to Better Budgeting homework help, assignment help, case study, writing homework help, online tutoring assistance by accounting tutors.
Whatever be the method employed, the drying-out operation should be carried on until the transformer oil samples from the top and bottom of the tank depict high di-electric strength and the windings high insulation resistance.
tutorsglobe.com artificial technique of vegetative propagation assignment help-homework help by online reproduction in angiosperms tutors
tutorsglobe.com significance of financial management assignment help-homework help by online financial management tutors
tutorsglobe.com criticism of lionel definition assignment help-homework help by online lionel robbins definition tutors
Theory and lecture notes of Combinations of Functions all along with the key concepts of Arithmetic Combinations of Functions, Composition of Functions, Domains on Composition of Functions, Polynomial Functions and Radical Functions. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Combinations of Functions.
an mp3 cd is a compact disc (generally a cd-r or cd-rw) which consist of digital audio in the mp3 file format.
tutorsglobe.com point method assignment help-homework help by online measurement of price elasticity of demand tutors
to find the fault that occurred in radio receiver. there are two type of fault in radio receiver. live fault, dead fault
The transfer prices might be fixed on the basis of 'Negotiated Prices' that are fixed by negotiations among the selling and the buying division.
while the finishing end of the first coil is connected to the starting end of the next coil that starts from similar pole
tutorsglobe.com conditions of perfect competition assignment help-homework help by online perfect competition tutors
1934519
Questions Asked
3689
Tutors
1448790
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!