- File names for .m files
- The exponential function and the number e
- The natural logarithm ln
- The quadl command
- Error messages from solve
- Plotting a constant function with ezplot
- New figures (plot windows)
- Preventing MATLAB from putting a new plot on top of an old one
- Plotting surfaces
- Plotting more than one surface
- Setting the range on the axes
- Solving a system of equations
- A command for rotating a 3 dimensional plot
- Error messages in viewSolid
- Fixing a bad pagebreak in your html file
- Suppressing warnings
- Suppressing steps of simple
Do not have a space or a hyphen in the names of your .m files. If you have a space or hyphen, when you publish to html MATLAB will give an error message when it tries to execute the first command and won't try to execute any later commands.
MATLAB (and most mathematical software) knows the exponential function as exp(x) so the number e in MATLAB is exp(1).
MATLAB (and most mathematical software) knows the natural logarithm as log(x).
If MATLAB doesn't recognize the quadl command, make sure that you have typed it correctly. It ends with the letter el. You probably typed the number 1.
The solve command takes as its input a symbolic expression, not an equation and assumes that the expression is equal to 0. Suppose you want to solve the equation x^2-5*x=6. The command solve(x^2-5*x=-6) gives the error message
Error: The expression to the left of the equals sign is not a valid target for an assignment.
and solve(x^2-5*x+6=0) gives a similar error message. To solve the equation, give the command:
Or you can give the solve command an equation enclosed in single quotes:
ezplot requires a variable in a symbolic expression. So, for example, to use it to plot the constant function 5, you can write 5 as 5+0*x and plot that.
syms x ezplot(5+0*x)
Alternatively, you can create an anonymous constant function and plot that.
f = @(x) 5 ezplot(f)
f = @(x)5
You can get a new figure window by giving the command
Here is the new blank (and invisible) figure.
Give the command before giving the command for the plot you want to appear in the new window.
The first thing is to try is the command hold off before the new plot command. If MATLAB ignores hold off (which it does occasionally), give the command
to clear the plot window. Give the command before giving the command for the plot you want to appear in the new window.
To plot a surface, you may want to think of the surface as parametrized. Since it is two dimensional, there will be two parameters. To parametrize the surface given by the equation f(x,y,z)=0, you need functions x(s,t), y(s,t) and z(s,t) so that f(x(s,t),y(s,t),z(s,t))=0. For example, for the ellipsoid I can use with
(This is just spherical coordinates, calling the angles s and t, which are shorter to type than theta and phi.) One way to plot this is to use ezsurf or ezmesh. You can do this with the commands
syms s t ezsurf(3*cos(s)*sin(t),2*sin(s)*sin(t),cos(t))
which gets you a solid shaded surface or with
syms s t ezmesh(3*cos(s)*sin(t),2*sin(s)*sin(t),cos(t))
which gets you a shaded mesh surface.
Another way to plot this surface is to use surf or mesh, which gives you more control over the plot. You start by creating a grid of points (the parameter values which will be used for plotting).
You can then plot it with surf or mesh
Notice that since I am using a grid, I am effectively working with matrices; I need to multiply two of them component by component (not using ordinary matrix multiplication), so I need a period after the first one.
To plot more than one surface you have to use the mesh or surf commands - you can't use ezsurf or ezmesh for the first surface because it will undo the effect of a hold on command. For example, to plot the ellipsoid above and the cylinder parametrized by you can use the following commands:
surf(3*cos(s).*sin(t),2*sin(s).*sin(t),cos(t)), axis equal, hold on surf(cos(u),sin(u),v), hold off
mesh(3*cos(s).*sin(t),2*sin(s).*sin(t),cos(t)), axis equal, hold on mesh(cos(u),sin(u),v), hold off
or use mesh for one surface and surf for the other, so here's my favorite version of the plot:
mesh(3*cos(s).*sin(t),2*sin(s).*sin(t),cos(t)), axis equal, hold on surf(cos(u),sin(u),v), hold off
The axis equal command makes the scaling the same on all of the axes. If you leave it out, the right circular cylinder would appear to be elliptical instead of circular.
In 2 dimensions, you can give the command axis([xmin xmax ymin ymax]) and in 3 dimensions, you can give the command axis([xmin xmax ymin ymax zmin zmax]) to set the range on the axes.
You can use solve to solve a system of equations. For example, to solve
you can enter the commands:
syms x y [x,y] = solve('x^2-y=0','y-3*x=7')
x = 37^(1/2)/2 + 3/2 3/2 - 37^(1/2)/2 y = (3*37^(1/2))/2 + 23/2 23/2 - (3*37^(1/2))/2
Notice that you get two values for each variable. There are two solutions to this system, (x(1),y(1)) and (x(2),y(2)).
This can be done This can be done with the command view. If you rotate the plot using the tool for rotating, you will see the new azimuth and elevation in the lower left corner of the plot window. For example, if you see Az: -30 El: 28, the command view([-30 28]) will give you the same view. For example, here is a rotated view of the last plot above.
mesh(3*cos(s).*sin(t),2*sin(s).*sin(t),cos(t)), axis equal, hold on surf(cos(u),sin(u),v), hold off view([-56 68])
If you get the following error messages from viewSolid
??? Attempted to access f(-1);
index must be a positive integer or logical. Error in ==>
viewSolid>oldviewSolid at 44 YY = f(xx)*ones(1,
Error in ==> viewSolid at 37 oldviewSolid(char(xvar), double(a), double(b), ...
they are probably the result of using a constant as the lower y limit. The code for viewSolid treats the lower y limit as an inline function of x, and the independent variable in an inline function has to appear explicitly. You can fix this by adding 0*x to the lower y limit, so, for example, if the solid is a cube with 1 or -1 as each coordinate of the vertices, the command viewSolid(z,-1,1,y,-1,1,x,-1,1) produces the error messages above, but
syms x y z viewSolid(z,-1,1,y,-1+0*x,1,x,-1,1)
If you have a bad pagebreak in your html file and want to fix it by making sure there's a pagebreak at a particular place, insert the following lines in your m-file where you would like a pagebreak:
% <p style="page-break-before: always">
You may want to do this before printing a published m-file, but I don't recommend suppressing warnings at other times, because they might warn you about something you should pay attention to.
The command warning off will suppress warnings. The command warning on will turn warnings back on.
If you just want to see the final output from applying the command simple to the expression x^3+3*x^2+3*x+1 and not all the ways MATLAB attempted the simplification, give the result a name, say A and then give the commands
If you would also like to know how MATLAB did the simplification, give the command