## Matlab Commands

The following is a brief introduction to some Matlab commands that can be used to write the computer programs in Math 373.

To start Matlab, type matlab at the unix prompt. When you see the prompt ">>", you can start entering Matlab commands. To quit Matlab, select Exit Matlab from the File menu.

Help on using Matlab commands by clicking on Help and following the links.

Matlab programs should be stored in files, called M-files, which end in the extension ".m" If your program is stored in the file program.m, then typing program at the Matlab prompt ">" will execute all the statements in the program. However, before doing so, be sure that your current directory is the one containing the file program.m. If not, click on the tab labeled Current Directory and change to that directory.

To place comments in your program, use the % sign before any line you wish as a comment. To avoid intermediate output produced by Matlab, place a semicolon at the end of any statement whose output you do NOT want Matlab to display on the screen.

### Matlab Commands:

```General Commands

diary('filename') writes a copy of all subsequent keyboard input and the
resulting output (except it does not include graphics) to the named file,
where filename is the full pathname or filename is in the current MATLAB
directory. If the file already exists, output is appended to the end of the
file.  The command diary off suspends the diary and the command diary on
resumes diary mode using the current filename.

format long -- arithmetic with 14 decimal places (the default is
format short -- 4 decimal places).

The symbols <, <=, >, >= have the obvious meanings.
* is multiplication, / is division.

sqrt(2) produces the square root of 2; log(2) gives the natural log of 2;
exp(2) gives e^2; abs(g) produces the absolute value of the expression g;
max(a,b) gives the maximium of a and b. To see the list of other elementary
functions, type help elfun

To plot a sequence of points stored in the vectors (x,y),
type plot(x,y).

Displaying output on the screen

If the variable x has been given a value (say x=2) in a
previous statement, then typing x will result in the output
x=2.

If the variables x and y have previously been assigned
values (say 2 and 3), then typing [x,y] will result in the output
ans =   2     3.

To label this displayed output, the Matlab commands disp and
sprintf may be used. The command disp(x) displays the value of x
without displaying x= first. disp('x=') can be used to display the text
(enclosed in single quotes) x=.

If we have defined x=1.23456 and y=2.34567, then the command
disp(sprintf('x=%5.4f y=%4.3f', x,y)) will produce x=1.2346 y=2.346 Note that
the text part is enclosed in single quotes, along with the format in which x
and y are displayed.  In this case, %5.4f means that x should be displayed as
a floating point number with 5 digits, 4 of which should be to the right of
the decimal point.  The final x and y are the variables whose contents are
displayed.  See the help screen for additional details.

Loops

for loops: These have the form:

for i=1:10
statements
end

if, else statements: These have the form

if a <= b
statement
else
statement
end

while loops:  These have the form:

while (abs(xnew-xold) > tolx ) & (N < Nmax)
statements
end

while (abs(xnew-xold) > tolx ) | (abs(fnew) > tolf )
statements
end

The symbol & is the logical and symbol, meaning that the loop will
continue if both statements are true.  The symbol | is the logical
or symbol, meaning that the loop will continue if either statement is
true.

Vectors and Matrices

f = zeroes(10,1)  -- defines f to a column vector with 10 rows and
places zeroes in all entries.

a = zeroes(10,10) --  defines a to be a 10 x 10 matrix and places
zeroes in all the entries.

To enter a row vector into Matlab, type
v = [1 2 3]  or v = [1,2,3]

If you wish v to be a column vector, then enter
v= [1 2 3]'   or v = [1; 2; 3]

If v = [1 2 3], then w = [v 4] gives the row vector [1 2 3 4]

To solve the linear system A x = b, where b is a row vector, type
x = A/b;   If b is a column vector, type x= A\b.
Be careful about the direction of the slash symbol.

If v is a row vector, v*v' produces a scalar, v'*v produces a matrix
and v.*v produces another row vector in which the multiplication is
performed separately on each component.  In general, placing a period
before an algebraic operation means to perform the operation on each
component of the vector.

Defining an inline function within a Matlab program

The command f=inline('x*y','x','y'); can be used to create the function
f(x,y) = xy.  Note that both the expression x*y for the function
and the function arguments x and y must be enclosed in single quotes.
Then typing f(2,3) will then give the value of this function at the point
x=2, y=3.

Defining a function in an M-file

Syntax:  function [out1, out2, ...] = funname(ini, in2, ...)

defines a function funname that accepts inputs in1, in2, etc.
and returns outputs out1, out2, etc.

Examples:

function f = fcn(x)
f = 3*x - exp(x);

In this example, the input is a number x and the output is a number
f computed by the given formula.

function b = fcnv(x)
b(1) = x(1) -  x(1)^2 - x(2)^2;
b(2) = x(2) - x(1)^2 + x(2)^2;

In this example, the input x is a vector with 2 components
and the output b is a vector with two components.  Note that b will
be returned as a row vector, when x is either a row or column vector.

function A = fcnm(x)
A(1,1) = 1 - 2*x(1);
A(1,2) = -2*x(2);
A(2,1) = -2*x(1);
A(2,2) = 1 + 2*x(2);

In this example, the input x is a vector with 2 components
and the output A is a 2 x 2 matrix.

```