Interactive Computing with Matlab
Gerald W. Recktenwald
Department of Mechanical Engineering Portland State University
gerry@me.pdx.edu
These slides are a supplement to the book Numerical Methods with Matlab: Implementations and Applications, by Gerald W. Recktenwald,
c 2001, Prentice-Hall, Upper Saddle River, NJ. These slides are c 2001 Gerald W. Recktenwald. The PDF version of these slides may be downloaded or stored or printed only for noncommercial, educational use. The repackaging or sale of these slides in any form, without written consent of the author, is prohibited.
The latest version of this PDF file, along with other supplemental material for the book, can be found at www.prenhall.com/recktenwald.
Version 1.02 September 27, 2001
Overview
• Basic Matlab Operations
Starting Matlab
Using Matlab as a calculator
Introduction to variables and functions
• Matrices and Vectors: All variables are matrices.
Creating matrices and vectors
Subscript notation
Colon notation
• Additional Types of Variables
Complex numbers
Strings
Polynomials
• Working with Matrices and Vectors
Linear algebra
Vectorized operations
Array operators
• Managing the Interactive Environment
• Plotting
Starting Matlab
• Double click on the Matlab icon, or on unix systems type
“matlab” at the command line.
• After startup Matlab displays a command window that is used to enter commands and display text-only results.
• Enter Commands at the command prompt:
>> for full version
EDU> for educational version
• Matlab responds to commands by printing text in the command window, or by opening a figure window for graphical output.
• Toggle between windows by clicking on them with the mouse.
Matlab Windows (version 5)
Command Window Helpwin Window
Plot Window
Matlab Workspace (version 6)
Recent Directory Menu:
Used to change current working directory.
Launch Pad/Workspace:
Used to browse documentation, or view values of variables in the workspace
Command Prompt:
Enter typed commands here.
Text results are displayed here.
Command History/Current Directory:
Used to view and re-enter typed commands, or change directories
Matlab as a Calculator
Enter formulas at the command prompt
>> 2 + 6 - 4 (press return after ‘‘4’’) ans=
4
>> ans/2 ans=
2
Or, define and use variables
>> a = 5 a =
5
>> b = 6 b =
6
>> c = b/a c =
1.2000
Built-in Variables
pi (= π) and ans are a built-in variables
>> pi ans=
3.1416
>> sin(ans/4) ans=
0.7071
Note: There is no “degrees” mode. All angles are measured in radians.
Built-in Functions
Many standard mathematical functions, such as sin, cos, log, and log10, are built-in
>> log(256) ans=
5.5452
>> log10(256) ans=
2.4082
>> log2(256) ans=
8
Looking for Functions
Syntax:
lookfor string
searches first line of function descriptions for “string”.
Example:
>> lookfor cosine
produces
ACOS Inverse cosine.
ACOSH Inverse hyperbolic cosine.
COS Cosine.
COSH Hyperbolic cosine.
Ways to Get Help
• Use on-line help to request info on a specific function
>> help sqrt
• The helpwin function opens a separate window for the help browser
>> helpwin(’sqrt’)
• Use lookfor to find functions by keywords
>> lookfor functionName
On-line Help
Syntax:
help functionName
Example:
>> help log
produces
LOG Natural logarithm.
LOG(X) isthe natural logarithm of the elementsof X.
Complex results are produced if X is not positive.
See also LOG2, LOG10, EXP, LOGM.
Suppress Output with Semicolon
Results of intermediate steps can be suppressed with semicolons.
Example:
Assign values to x, y, and z, but only display the value of z in the command window:
>> x = 5;
>> y = sqrt(59);
>> z = log(y) + x^0.25 z =
3.5341
Type variable name and omit the semicolon to print the value of a variable (that is already defined)
>> y y =
7.6811 ( = log(sqrt(59)) + 5^0.25 )
Multiple Statements per Line
Use commas or semicolons to enter more than one statement at once. Commas allow multiple statements per line without
suppressing output.
>> a = 5; b = sin(a), c = cosh(a) b =
-0.9589 c =
74.2099
Matlab Variables Names
Legal variable names:
• Begin with one of a–z or A–Z
• Have remaining characters chosen from a–z, A–Z, 0–9, or
• Have a maximum length of 31 characters
• Should not be the name of a built-in variable, built-in function, or user-defined function
Examples:
xxxxxxxxx pipeRadius
widgets_per_baubble mySum
mysum
Note: mySum and mysum are different variables. Matlab is case sensitive.
Built-in Matlab Variables
Name Meaning
ans value of an expression when that expression is not assigned to a variable
eps floating point precision pi π, (3.141492 . . .)
realmax largest positive floating point number realmin smallest positive floating point number Inf ∞, a number larger than realmax,
the result of evaluating 1/0.
NaN not a number, the result of evaluating 0/0
Rule: Only use built-in variables on the right hand side of an expression. Reassigning the value of a built-in variable can create problems with built-in functions.
Exception: i and j are preassigned to √
−1. One or both of i or j are often reassigned as loop indices. More on this later
Matrices and Vectors
All Matlab variables are matrices
A Matlab vector is a matrix with one row or one column A Matlab scalar is a matrix with one row and one column
Overview of Working with matrices and vectors
• Creating vectors:
linspace and logspace
• Creating matrices:
ones, zeros, eye, diag, . . .
• Subscript notation
• Colon notation
• Vectorization
Creating Matlab Variables
Matlab variables are created with an assignment statement
>> x = expression
where expression is a legal combinations of numerical values, mathematical operators, variables, and function calls that
evaluates to a matrix, vector or scalar.
The expression can involve:
• Manual entry
• Built-in functions that return matrices
• Custom (user-written) functions that return matrices
• Loading matrices from text files or “mat” files
Manual Entry
For manual entry, the elements in a vector are enclosed in square brackets. When creating a row vector, separate elements with a space.
>> v = [7 3 9]
v =
7 3 9
Separate columns with a semicolon
>> w = [2; 6; 1]
w = 2 6 1
In a matrix, row elements are separated by spaces, and columns are separated by semicolons
>> A = [1 2 3; 5 7 11; 13 17 19]
A =
1 2 3
5 7 11
13 17 19
Transpose Operator
Once it is created, a variable can be transformed with other operators. The transpose operator converts a row vector to a column vector (and vice versa), and it changes the rows of a matrix to columns.
>> v = [2 4 1 7]
v =
2 4 1 7
>> v’
ans=
2 4 1 7
>> A = [1 2 3; 4 5 6; 7 8 9 ] A =
1 2 3
4 5 6
7 8 9
>> A’
ans=
1 4 7
2 5 8
3 6 9
Overwriting Variables
Once a variable has been created, it can be reassigned
>> x = 2;
>> x = x + 2 x =
4
>> y = [1 2 3 4]
y =
1 2 3 4
>> y = y’
y = 1 2 3 4
Creating vectors with linspace
The linspace function creates vectors with elements having uniform linear spacing.
Syntax:
x = linspace(startValue,endValue)
x = linspace(startValue,endValue,nelements)
Examples:
>> u = linspace(0.0,0.25,5) u =
0 0.0625 0.1250 0.1875 0.2500
>> u = linspace(0.0,0.25);
>> v = linspace(0,9,4)’
v = 0 3 6 9
Note: Column vectors are created by appending the transpose operator to linspace
Example: A Table of Trig Functions
>> x = linspace(0,2*pi,6)’; (note transpose)
>> y = sin(x);
>> z = cos(x);
>> [x y z]
ans=
0 0 1.0000
1.2566 0.9511 0.3090 2.5133 0.5878 -0.8090 3.7699 -0.5878 -0.8090 5.0265 -0.9511 0.3090
6.2832 0 1.0000
The expressions y = sin(x) and z = cos(x) take advantage of vectorization. If the input to a vectorized function is a vector or matrix, the output is often a vector or matrix having the same shape. More on this later.
Creating vectors with logspace
The logspace function creates vectors with elements having uniform logarithmic spacing.
Syntax:
x = logspace(startValue,endValue)
x = logspace(startValue,endValue,nelements)
creates nelements elements between 10startValue and 10endValue. The default value of nelements is 100.
Example:
>> w = logspace(1,4,4) w =
10 100 1000 10000
Functions to Create Matrices ( 1)
Name Operation(s) Performed
diag create a matrix with a specified diagonal entries, or extract diagonal entries of a matrix
eye create an identity matrix
ones create a matrix filled with ones
rand create a matrix filled with random numbers zeros create a matrix filled with zeros
linspace create a row vector of linearly spaced elements logspace create a row vector of logarithmically spaced
elements
Functions to Create Matrices ( 2)
Use ones and zeros to set intial values of a matrix or vector.
Syntax:
A = ones(nrows,ncols) A = zeros(nrows,ncols)
Examples:
>> D = ones(3,3) D =
1 1 1
1 1 1
1 1 1
>> E = ones(2,4) E =
0 0 0 0
0 0 0 0
Functions to Create Matrices ( 3)
ones and zeros are also used to create vectors. To do so, set either nrows or ncols to 1.
>> s= ones(1,4) s =
1 1 1 1
>> t = zeros(3,1) t =
0 0 0
Functions to Create Matrices ( 4)
The eye function creates identity matrices of a specified size. It can also create non-square matrices with ones on the main
diagonal.
Syntax:
A = eye(n)
A = eye(nrows,ncols)
Examples:
>> C = eye(5) C =
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
>> D = eye(3,5) D =
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
Functions to Create Matrices ( 5)
The diag function can either create a matrix with specified diagonal elements, or extract the diagonal elements from a matrix
Syntax:
A = diag(v) v = diag(A)
Example:
Use diag to create a matrix
>> v = [1 2 3];
>> A = diag(v) A =
1 0 0
0 2 0
0 0 3
Functions to Create Matrices ( 6)
Example:
Use diag to extract the diagonal of a matrix
>> B = [1:4; 5:8; 9:12]
B =
1 2 3 4
5 6 7 8
9 10 11 12
>> w = diag(B) w =
1 6 11
Note: The action of the diag function depends on the characteristics and number of the input(s). This polymorphic behavior of Matlab functions is
common. The on-line documentation (help diag) explains the possible variations.
Subscript Notation ( 1)
If A is a matrix, A(i,j) selects the element in the ith row and jth column. Subscript notation can be used on the right hand side of an expression to refer to a matrix element.
>> A = [1 2 3; 4 5 6; 7 8 9];
>> b = A(3,2) b =
8
>> c = A(1,1) c =
1
Subscript notation is also used to assign matrix elements
>> A(1,1) = c/b A =
0.2500 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000
Subscript Notation ( 2)
Referring to elements outside of current matrix dimensions resu lts in an error
>> A = [1 2 3; 4 5 6; 7 8 9];
>> A(1,4)
??? Index exceeds matrix dimensions.
Assigning an elements outside of current matrix dimensions causes the matrix to be resized!
>> A = [1 2 3; 4 5 6; 7 8 9];
A =
1 2 3
4 5 6
7 8 9
>> A(4,4) = 11 A =
1 2 3 0
4 5 6 0
7 8 9 0
0 0 0 11
Matlab automatically resizes matrices on the fly.
Colon Notation ( 1)
Colon notation is very powerful and very important in the
effective use of Matlab. The colon is used as both an operator and as a wildcard.
Use colon notation to:
• create vectors
• refer to or extract ranges of matrix elements
Syntax:
startValue:endValue
startValue:increment:endValue
Note: startValue, increment, and endValue do not need to be integers
Colon Notation ( 2)
Creating row vectors:
>> s= 1:4 s =
1 2 3 4
>> t = 0:0.1:0.4 t =
0 0.1000 0.2000 0.3000 0.4000
Creating column vectors:
>> u = (1:5)’
u = 1 2 3 4 5
>> v = 1:5’
v =
1 2 3 4 5
v is a row vector because 1:5’ creates a vector between 1 and the transpose of 5.
Colon Notation ( 3)
Use colon as a wildcard to refer to an entire column or row
>> A = [1 2 3; 4 5 6; 7 8 9];
>> A(:,1) ans=
1 4 7
>> A(2,:) ans=
4 5 6
Or use colon notation to refer to subsets of columns or rows
>> A(2:3,1) ans=
4 7
>> A(1:2,2:3) ans=
ans=
2 3
5 6
Colon Notation ( 4)
Colon notation is often used in compact expressions to obtain results that would otherwise require several steps.
Example:
>> A = ones(8,8);
>> A(3:6,3:6) = zeros(4,4) A =
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 0 0 0 0 1 1
1 1 0 0 0 0 1 1
1 1 0 0 0 0 1 1
1 1 0 0 0 0 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
Colon Notation ( 5)
Finally, colon notation is used to convert any vector or matrix to a column vector.
Examples:
>> x = 1:4;
>> y = x(:) y =
1 2 3 4
>> A = rand(2,3);
>> v = A(:) v =
0.9501 0.2311 0.6068 0.4860 0.8913 0.7621 0.4565
Note: The rand function generates random elements between zero and one. Repeating the preceding statements will, in all likelihood, produce different numerical values for the elements of v.
Additional Types of Variables
The basic Matlab variable is a matrix — a two dimensional array of values. The elements of a matrix variable can either be numeric values or characters. If the elements are numeric values they can either be real or complex (imaginary).
More general variable types are available: n-dimensional arrays (where n > 2), structs, cell arrays, and objects. Numeric (real and complex) and string arrays of dimension two or less will be sufficient for our purposes.
We now consider some simple variations on numeric and string matrices:
• Complex Numbers
• Strings
• Polynomials
Complex Numbers
Matlab automatically performs complex arithmetic
>> sqrt(-4) ans=
0 + 2.0000i
>> x = 1 + 2*i (or, x = 1 + 2*j) x =
1.0000 + 2.0000i
>> y = 1 - 2*i y =
1.0000 - 2.0000i
>> z = x*y z =
5
Unit Imaginary Numbers
i and j are ordinary Matlab variables that have be preassigned the value √
−1.
>> i^2 ans=
-1
Both or either i and j can be reassigned
>> i = 5;
>> t = 8;
>> u = sqrt(i-t) (i-t = -3, not -8+i) u =
0 + 1.7321i
>> u*u ans=
-3.0000
>> A = [1 2; 3 4];
>> i = 2;
>> A(i,i) = 1 A =
1 2
3 1
Euler Notation ( 1)
Euler notation represents a complex number by a phaser z = ζeiθ
x = Re(z) = |z| cos(θ) = ζ cos(θ) y = iIm(z) = i|z| sin(θ) = iζ sin(θ)
θ ζ
real imaginary
x
iy z = ζeiθ
Functions for Complex Arithmetic ( 1)
Function Operation
abs Compute the magnitude of a number abs(z) is equivalent to
to sqrt( real(z)^2 + imag(z)^2 ) angle Angle of complex number in Euler notation exp If x is real,
exp(x) = ex If z is complex,
exp(z) = eRe(z)(cos(Im(z) + i sin(Im(z)) conj Complex conjugate of a number
imag Extract the imaginary part of a complex number real Extract the real part of a complex number
Note: When working with complex numbers, it is a good idea to reserve either i or j for the unit imaginary value √
−1.
Functions for Complex Arithmetic ( 2)
Examples:
>> zeta = 5; theta = pi/3;
>> z = zeta*exp(i*theta) z =
2.5000 + 4.3301i
>> abs(z) ans=
5
>> sqrt(z*conj(z)) ans=
5
>> x = real(z) x =
2.5000
>> y = imag(z) y =
4.3301
>> angle(z)*180/pi ans=
60.0000
Remember: There is no “degrees” mode in Matlab. All angles are measured in radians.
Strings
• Strings are matrices with character elements.
• String constants are enclosed in single quotes
• Colon notation and subscript operations apply
Examples:
>> first = ’John’;
>> last = ’Coltrane’;
>> name = [first,’ ’,last]
name =
John Coltrane
>> length(name) ans=
13
>> name(9:13) ans=
trane
Functions for String Manipulation ( 1)
Function Operation
char convert an integer to the character using ASCII codes, or combine characters into a character matrix
findstr finds one string in another string
length returns the number of characters in a string num2str converts a number to string
str2num converts a string to a number strcmp compares two strings
strmatch identifies rows of a character array that begin with a string
strncmp compares the first n elements of two strings sprintf converts strings and numeric values to a string
Functions for String Manipulation ( 2)
Examples:
>> msg1 = [’There are ’,num2str(100/2.54),’ inches in a meter’]
message1 =
There are 39.3701 inchesin a meter
>> msg2 = sprintf(’There are %5.2f cubic inches in a liter’,1000/2.54^3) message2 =
There are 61.02 cubic inchesin a liter
>> both = char(msg1,msg2) both =
There are 39.3701 inchesin a meter There are 61.02 cubic inchesin a liter
>> strcmp(msg1,msg2) ans=
0
>> strncmp(msg1,msg2,9) ans=
1
>> findstr(’in’,msg1) ans=
19 26
Polynomials
Matlab polynomials are stored as vectors of coefficients. The polynomial coefficients are stored in decreasing powers of x
Pn(x) = c1xn + c2xn−1 + . . . + cnx + cn+1
Example:
Evaluate x3 − 2x + 12 at x = −1.5
>> c = [1 0 -2 12];
>> polyval(c,1.5) ans=
12.3750
Functions for Manipulating Polynomials
Function Operations performed
conv product (convolution) of two polynomials deconv division (deconvolution) of two polynomials poly Create a polynomial having specified roots polyder Differentiate a polynomial
polyval Evaluate a polynomial polyfit Polynomial curve fit
roots Find roots of a polynomial
Manipulation of Matrices and Vectors
The name “Matlab” evolved as an abbreviation of “MATrix LABoratory”. The data types and syntax used by Matlab
make it easy to perform the standard operations of linear algebra including addition and subtraction, multiplication of vectors and matrices, and solving linear systems of equations.
Chapter 7 provides a detailed review of linear algebra. Here we provide a simple introduction to some operations that are
necessary for routine calculation.
• Vector addition and subtraction
• Inner and outer products
• Vectorization
• Array operators
Vector Addition and Subtraction
Vector and addition and subtraction are element-by-element operations.
Example:
>> u = [10 9 8]; (u and v are row vectors)
>> v = [1 2 3];
>> u+v ans=
11 11 11
>> u-v ans=
9 7 5
Vector Inner and Outer Products
The inner product combines two vectors to form a scalar σ = u · v = u vT ⇐⇒ σ =
ui vi
The outer product combines two vectors to form a matrix A = uTv ⇐⇒ ai,j = ui vj
Inner and Outer Products in Matlab
Inner and outer products are supported in Matlab as natural extensions of the multiplication operator
>> u = [10 9 8]; (u and v are row vectors)
>> v = [1 2 3];
>> u*v’ (inner product) ans=
52
>> u’*v (outer product) ans=
10 20 30
9 18 27
8 16 24
Vectorization
• Vectorization is the use of single, compact expressions that operate on all elements of a vector without explicitly
executing a loop. The loop is executed by the Matlab kernel, which is much more efficient at looping than interpreted Matlab code.
• Vectorization allows calculations to be expressed succintly so that programmers get a high level (as opposed to detailed) view of the operations being performed.
• Vectorization is important to make Matlab operate efficiently.
Vectorization of Built-in Functions
Most built-in function support vectorized operations. If the input is a scalar the result is a scalar. If the input is a vector or matrix, the output is a vector or matrix with the same number of rows and columns as the input.
Example:
>> x = 0:pi/4:pi (define a row vector) x =
0 0.7854 1.5708 2.3562 3.1416
>> y = cos(x) (evaluate cosine of each x(i) y =
1.0000 0.7071 0 -0.7071 -1.0000
Contrast with Fortran implementation:
real x(5),y(5) pi = 3.14159624 dx = pi/4.0 do 10 i=1,5
x(i) = (i-1)*dx y(i) = sin(x(i)) 10 continue
No explicit loop is necessary in Matlab.
Vector Calculations ( 3)
More examples
>> A = pi*[ 1 2; 3 4]
A =
3.1416 6.2832 9.4248 12.5664
>> S = sin(A) S =
0 0
0 0
>> B = A/2 B =
1.5708 3.1416 4.7124 6.2832
>> T = sin(B) T =
1 0
-1 0
Array Operators
Array operators support element-by-element operations that are not defined by the rules of linear algebra
Array operators are designated by a period prepended to the standard operator
Symbol Operation
.* element-by-element multiplication ./ element-by-element “right” division .\ element-by-element “left” division .^ element-by-element exponentiation
Array operators are a very important tool for writing vectorized code.
Using Array Operators ( 1)
Examples:
Element-by-element multiplication and division
>> u = [1 2 3];
>> v = [4 5 6];
>> w = u.*v (element-by-element product) w =
4 10 18
>> x = u./v (element-by-element division) x =
0.2500 0.4000 0.5000
>> y = sin(pi*u/2) .* cos(pi*v/2) y =
1 0 1
>> z = sin(pi*u/2) ./ cos(pi*v/2) Warning: Divide by zero.
z =
1 NaN 1
Using Array Operators ( 2)
Examples:
Application to matrices
>> A = [1 2 3 4; 5 6 7 8];
>> B = [8 7 6 5; 4 3 2 1];
>> A.*B ans=
8 14 18 20
20 18 14 8
>> A*B
??? Error using ==> *
Inner matrix dimensions must agree.
>> A*B’
ans=
60 20
164 60
>> A.^2 ans=
1 4 9 16
25 36 49 64
The Matlab Workspace (1)
All variables defined as the result of entering statements in the command window, exist in the Matlab workspace.
At the beginning of a Matlab session, the workspace is empty.
Being aware of the workspace allows youto
• Create, assign, and delete variables
• Load data from external files
• Manipulate the Matlab path
The Matlab Workspace (2)
The clear command deletes variables from the workspace. The who command lists the names of variables in the workspace
>> clear (Delete all variables from the workspace)
>> who
(No response, no variables are defined after ‘clear’)
>> a = 5; b = 2; c = 1;
>> d(1) = sqrt(b^2 - 4*a*c);
>> d(2) = -d(1);
>> who
Your variablesare:
a b c d
The Matlab Workspace (3)
The whos command lists the name, size, memory allocation, and the class of each variables defined in the workspace.
>> whos
Name Size BytesClass
a 1x1 8 double array
b 1x1 8 double array
c 1x1 8 double array
d 1x2 32 double array (complex)
Grand total is5 elementsusing 56 bytes
Built-in variable classes are double, char, sparse, struct, and cell. The class of a variable determines the type of data that can be stored in it. We will be dealing primarily with numeric data, which is the double class, and occasionally with string data, which is in the char class.
Working with External Data Files
Write data to a file
save fileName
save fileName variable1 variable2 ...
save fileName variable1 variable2 ... -ascii
Read in data stored in matrices
load fileName
load fileName matrixVariable
Loading Data from External File
Example:
Load data from a file and plot the data
>> load wolfSun.dat;
>> xdata = wolfSun(:,1);
>> ydata = wolfSun(:,2);
>> plot(xdata,ydata)
The Matlab Path
Matlab will only use those functions and data files that are in its path.
To add N:\IMAUSER\ME352\PS2 to the path, type
>> p = path;
>> path(p,’N:\IMAUSER\ME352\PS2’);
Matlab version 5 and later has an interactive path editor that makes it easy to adjust the path.
The path specification string depends on the operating system.
On a Unix/Linux computer a path setting operation might look like:
>> p = path;
>> path(p,’~/matlab/ME352/ps2’);
Plotting
• Plotting (x, y) data
• Axis scaling and annotation
• 2D (contour) and 3D (surface) plotting
Plotting (x, y) Data (1)
Two dimensional plots are created with the plot function Syntax:
plot(x,y)
plot(xdata,ydata,symbol) plot(x1,y1,x2,y2,...)
plot(x1,y1,symbol1,x2,y2,symbol2,...)
Note: x and y must have the same shape, x1 and y1 must have the same shape, x2 and y2 must have the same shape, etc.
Plotting (x, y) Data (2)
Example:
A simple line plot
>> x = linspace(0,2*pi);
>> y = sin(x);
>> plot(x,y);
0 2 4 6 8
-1 -0.5 0 0.5 1
Line and Symbol Types ( 1)
The curves for a data set are drawn from combinations of the color, symbol, and line types in the following table.
Color Symbol Line
y yellow . point - solid
m magenta o circle : dotted
c cyan x x-mark -. dashdot
r red + plus -- dashed
g green * star
b blue s square
w white d diamond
k black v triangle
(down)
^ triangle (up)
< triangle (left)
> triangle (right) p pentagram h hexagram
To choose a color/symbol/line style, chose one entry from each column.
Line and Symbol Types ( 2)
Examples:
Put yellow circles at the data points:
plot(x,y,’yo’)
Plot a red dashed line with no symbols:
plot(x,y,’r--’)
Put black diamonds at each data point and connect the diamonds with black dashed lines:
plot(x,y,’kd--’)
Alternative Axis Scaling ( 1)
Combinations of linear and logarithmic scaling are obtained with functions that, other than their name, have the same syntax as the plot function.
Name Axis scaling
loglog log10(y) versus log10(x) plot linear y versus x
semilogx linear y versus log10(x) semilogy log10(y) versus linear x
Note: As expected, use of logarithmic axis scaling for data sets with negative or zero values results in a error.
Matlab will complain and then plot only the positive (nonzero) data.
Alternative Axis Scaling ( 2)
Example:
>> x = linspace(0,3);
>> y = 10*exp(-2*x);
>> plot(x,y);
0 1 2 3
0 2 4 6 8 10
>> semilogy(x,y);
-2
10-1 100 101
Multiple plots per figure window ( 1)
The subplot function is used to create a matrix of plots in a single figure window.
Syntax:
subplot(nrows,ncols,thisPlot)
Repeat the values of nrows and ncols for all plots in a single figure window. Increment thisPlot for each plot
Example:
>> x = linspace(0,2*pi);
>> subplot(2,2,1);
>> plot(x,sin(x)); axis([0 2*pi -1.5 1.5]); title(’sin(x)’);
>> subplot(2,2,2);
>> plot(x,sin(2*x)); axis([0 2*pi -1.5 1.5]); title(’sin(2x)’);
>> subplot(2,2,3);
>> plot(x,sin(3*x)); axis([0 2*pi -1.5 1.5]); title(’sin(3x)’);
>> subplot(2,2,4);
>> plot(x,sin(4*x)); axis([0 2*pi -1.5 1.5]); title(’sin(4x)’);
(See next slide for the plot.)
Multiple plots per figure window ( 2)
0 2 4 6
-1.5 -1 -0.5 0 0.5 1 1.5
sin(x)
0 2 4 6
-1.5 -1 -0.5 0 0.5 1 1.5
sin(2x)
0 2 4 6
-1.5 -1 -0.5 0 0.5 1 1.5
sin(3x)
0 2 4 6
-1.5 -1 -0.5 0 0.5 1 1.5
sin(4x)
Plot Annotation
Name Operation(s) performed axis Reset axis limits
grid Draw grid lines corresponding to the major major ticks on the x and y axes
gtext Add text to a location determined by a mouse click
legend Create a legend to identify symbols and line types when multiple curves are drawn on the same plot
text Add text to a specified (x, y) location xlabel Label the x-axis
ylabel Label the y-axis
title Add a title above the plot
Plot Annotation Example
>> D = load(’pdxTemp.dat’); m = D(:,1); T = D(:,2:4);
>> plot(m,t(:,1),’ro’,m,T(:,2),’k+’,m,T(:,3),’b-’);
>> xlabel(’Month’);
>> ylabel(’Temperature ({}^\circ F)’);
>> title(’Monthly average temperature at PDX’);
>> axis([1 12 20 100]);
>> legend(’High’,’Low’,’Average’,2);
2 4 6 8 10 12
20 30 40 50 60 70 80 90 100
Month Temperature (° F)
Monthly average temperatures at PDX High
Low Average
Note: The pdxTemp.dat file is in the data directory of the NMM toolbox. Make sure the toolbox is installed and is included in the Matlab path.
