Fundamental of Matlab

Special Variables

ans

dafault variable name for the rsult

pi

π : 3.1415926..

eps

ε : 2.2204e-16, smallest value by which two numbers can differ

inf

∞, Infinity

NAN or nan

not-a-number

Command involving variables

who

list the names of the defined variables

whos

list the names and sizes of defined variables

clear

clears all variables

clear [name]

clears the variable [name]

clc

clear the command window

clf

clears the current figure and the graph window

Vectors

The colon notation may be used to address a block of elements

(start:increment:end)

Example

>> x=[0 .25*pi .5*pi .75*pi pi]

x =

         0    0.7854    1.5708    2.3562    3.1416

>> (1:2:5)

ans =

         0    1.5708    3.1416

start:end

Create row vector x starting with start, counting 1, ending at end

start:increment:end

Create row vector x starting with start, counting by increment, ending at end

linspace(start,end,number)

Create linearly spaced row vector x starting with start, ending at end, having number elements

logspace(start,end,number)

Create logarithmically spaced row vector x starting with start, ending at end, having number elements

length(x)

Returns the length of vector x

x'

Transpose of vector x

dot(x,y), cross(x,y)

Returns the scalar dot and vector cross product of the vector x and y

Array Operations

Element-by-Element Array-Array Mathematics

Addition

a + b

Subtraction

a - b

Multiplication

a .* b

Division

a ./ b

Exponentiation

a .^ b

Matrices

Matrix Addressing

Matrix name(row, column)

Colon may be used in place of a row or column reference to select the entire row or column.

Some useful commands

zeros(n)

Returns a n X n matrix of zeros

zeros(m, n)

Returns a m X n matrix of zeros

ones(n)

Returns a n X n matrix of ones

ones(m, n)

Returns a m X n matrix of ones

size(A)

For a m X n matrix A, returns the row vector [m,n] containing the number of rows and columns in matrix

length(A)

Returns the larger of the number of rows or columns in A

More commands

Transpose

A'

Identity Matrix

eye(n)

returns an n X n identity matrix

eye(m, n)

returns an m X n matrix with ones on the main diagonal and zeros elsewhere

Additional and Subtraction

C = A + B

C = A - B

Scalar Multiplication

B = α A, where α is a scalar

Matrix Multiplication

A * B

Matrix Division

A \ B, Same as inv(A) * B

Matrix Inverse

inv(A), A must be a square matrix in this case

Matrix Powers

B = A * A, A must be a square matrix

Determinant

det(A), A must be a square matrix

Polynomials

The polynomials are represented by their coefficients in MATLAB

Consider the following polynomial:

A(x) = s³ + 3s² + 3s + 1

For s is scalar:

use scalar operations

A = S ^ 3 + 3 * s ^ 2 + 3 * s + 1;

For s is a vector or a matrix:

use array or element by element operation

A = S .^ 3 + 3 * s .^ 2 + 3 * s + 1;

Function polyval(a,s):

evaluate a polynomial with coefficients in vector a for the values in s

Operation

Addition

A + B

Sum of polynomial A and B, the coefficient vectors must have the same length.

Scalar Multiple

3 * A

Multiply the polynomial A by 3.

Polynomial Multiplication

conv(A, B)

Returns the coefficient vector for the resulting from the product of polynomial A and B.

Polynomial Division

[q, r] = deconv(A, B)

Returns the long division of A and B. q is the quotient polynomial coefficient, and r is the remainder polynomial coefficient.

Derivatives

polyder(A)

Returns the coefficients of the derivative of the polynomial A.

polyder(A, B)

Returns the coefficients of the derivative of the product of A and B.

[N, D] = polyder(B, A)

Returns the derivative of ratio B / A, represented as N / D.

Find Roots

roots(A)

Returns the roots of the polynomial A in column vector form.

Find Polynomials

Poly(r)

Returns the coefficient vector of the polynomial having roots r.

Plotting

For more information on 2-D plotting, type help graph2d

Plotting a point:

pot(variablename, 'symbol')

Commands for axes

axis([xmin xmax ymin ymax])

Define minimum and maximum values of the axes

axis square

Produce a square plot

axis equal

Equal scaling factors for both axes

axis normal

Turn off axis square, equal

axis auto

Return the axis to defaults

Plotting curves

plot(x, y)

generate a linear plot of the values of x (horizontal axis) and y (vertical axis)

semilogx(x, y)

generate a plot of the values of x (logarithmic scale) and y (linear scale)

semilogy(x, y)

loglog(x, y)

generate a plot of the values of x and y (both logarithmic scale)

Multiple curves

plot(x, y, w, z)

multiple curves can be plotted on the same graph: y vs. x and z vs. w

legend('string1', 'string2', ...)

used to distinguish between plots on the same graph

Multiple figures

figure(n)

use in creation of multiple plot windows before the command plot()

close

closes the figure n window

close all

closes all the plot windows

Sublplots

subplot(m, n, p)

m by n grid of windows, with p specifying the current plot as the pth window

Example: (polynomial function)

Plot the polynomial using linear/linear, log/linear, linear/log, log/log scale

y = 2x² + 7x + 9

>> % generate the polynomial:

>> x=linspace(0, 10, 100);

>> y=2*x.^2+7*x-9;

>> figure(1);

>> subplot(2,2,1), plot(x,y)

>> title('polynomial, linear/linear scale');

>> ylabel('y'),grid;

>> subplot(2,2,2), semilogx(x,y);

>> title('polynomial, log/linear scale');

>> ylabel('y'),grid;

>> subplot(2,2,3), semilogy(x,y);

>> title('polynomial, linear/log scale');

>> ylabel('y'), grid;

>> subplot(2,2,4), loglog(x,y);

>> title('polynomial, log/log scale');

>> ylabel('y'),grid;

Adding new curves to the existing graph, use the hold command to add lines/points to an existing plot

hold on

retain existing axes, add new curves to current axes.

hold off

release the current figure windows for new plots.

Grid and labels

grid on

Add dashed grids lines at the tick marks

grid off

Removes grid lines (default)

grid

Toggles grid statues (off to on or on to off)

title('text')

Labels top of plot with text

xlabel('text')

Labels horizontal (x) axis with text

ylabel('text')

Labels vertical (x) axis with test

text(x, y, 'text')

Adds text to location (x, y) on the current axes, where (x, y) is in units from the current plot

Programming

Flow control and loops

Simple if statement:

if logical expression

  commands

end

Example: (Nested)

if d < 50

  count = count + 1;

  disp(d);

  if b > d

    b = 0;

  end

end

Example: (else and elseif clauses)

if temperature > 100

  disp('Too hot - equipment malfunctioning.');

elseif temperature > 90

  disp('Normal operating range.');

elseif temperature > 75

  disp('Below desired operating range.');

else

  disp('Too cold - Turn off equipment.');

end

The switch statement:

switch expression

  case test expression 1

    commands

  case test expression 2

    commands

  otherwise

    commands

end

Example: (switch interval)

case 1

  xinc = interval / 10;

case 0

  xinc = 0.1;

otherwise

  disp('wrong value');

end

Loops

for loop

for variable = expression

  commands

end

while loop

while expression

  command

end

Example: (for loop)

for t = 1 : 5000

  y(t) = sin( 2 * pi * t / 10 );

end

Example: (while loop)

while EPS > 1

  EPS = EPS / 2

end

the break statement

break - is used to terminate the execution of the loop

M-Files

Before, we have executed the commands in the command window. The more general way is to create a M-file

The M-file is a text file that consists a group of MATLAB commands.

MATLAB can open and execute the commands exactly as if they were entered at the MATLAB command window.

To run the M-files, just type the file name in the command window. (make sure the current working directory is set correctly)

User-Defined Function

Add the following command in the beginning of your m-file:

function [output variables] = function_name (input variables);

Note: the function_name should be the same as your file name to avoid confusion.

Calling your function

A user-defined function is called by the name of the m-file, not the name given in the function definition.

Type in the m-file name like other pre-defined commands.

Comments:

The first few lines should be comments, as they will be displayed if help is requested for the function name. the first comment line is reference by the lookfor command.

Example: ( circle1.m )  // 이거 디버깅하느라 고생함 ㅠㅠ

function y = circle1(center, radius, nop, style)

% circle1 draws a circle with center defined as a vector 'center'

% radius as a scalar 'radius'. 'nop'is the number of points on the circle

% 'style' is the style of the point

% Example to use: circle1([1 3], 4, 500, ':');

[m, n] = size( center );

if( ~( ( m == 1 ) || ( n == 1 ) ) || ( m == 1 && n == 1 ) )

  error('Input must be a vector')

end

close all

x0 = center(1);

y0 = center(2);

t0 = 2 * pi / nop;

axis equal

axis([x0-radius-1 x0+radius+1 y0-radius-1 y0+radius+1])

hold on

for i = 1 : nop + 1

  pos1 = radius * cos( t0 * ( i - 1 ) ) + x0;

  pos2 = radius * sin( t0 * ( i - 1 ) ) + y0;

  plot( pos1, pos2, style );

end