Transcript Document 7208557
Short M ATLAB Tutorial
Covered by: Dan Negrut University of Wisconsin, Madison
Before getting started
…
Acknowledgement:
Almost entirely, this tutorial compiled from bits of information gathered from various internet sources It is available for download from SBEL website in PPT format for other to be able to save, edit, and distribute as they see fit Please let me know of any mistakes you find email me at my lastname @wisc.edu
The right frame of mind: You will not be able to say at the end of workshop that you know MATLAB but rather that you have been exposed to MATLAB (I don ’ t know MATLAB myself, I ’ m just using it … ) Use MATLAB ’ s “ help ” , this is your first stop Second stop: search the web for examples that come close to what you need You learn how to use MATLAB by using it, that ’ s why the start might be slow and at times frustrating
Contents – 1
1. First hour of workshop
What is Matlab?
MATLAB Components MATLAB Desktop Matrices Importing and Exporting Data Elementary math with MATLAB
Contents – 2
2. Second
hour of workshop
M-file Programming Functions vs. Scripts Variable Type/Scope Debugging MATLAB functions Flow control in MATLAB Other Tidbits Function minimization Root finding Solving ODE’s Graphics Fundamentals Data Types most likely won’t have time for it
What is MATLAB?
Integrated Development Environment (IDE) Programming Language Collection of Toolboxes Excellent Linear Algebra support
MATLAB as an IDE
Integrated development environment (IDE) Write your own code for computation Good visualization (plotting) tools Easy-to-use environment Command Window Command History Help Browser Workspace Browser Editor/Debugger
MATLAB Desktop Tools
MATLAB as Programming Language
High-level language Data types Functions Control flow statements Input/output Graphics Object-oriented programming capabilities
Toolboxes
Collections of functions to solve problems from several application fields.
DSP (Digital Signal Processing) Toolbox Image Toolbox Wavelet Toolbox Neural Network Toolbox Fuzzy Logic Toolbox Control Toolbox Multibody Simulation Toolbox And many many other http://www.tech.plym.ac.uk/spmc/links/matlab/matlab_toolbox .html
, amazing number of toolboxes available: if you need something, it ’ … ( Visit for instance s out there somewhere available for download)
MATLAB for [Linear] Algebra
Calculations at the Command Line
MATLAB as a calculator
»
-5/(4.8+5.32)^2 ans =
»
-0.0488
(3+4i)*(3-4i) ans = 25
»
cos(pi/2) ans = 6.1230e-017
»
exp(acos(0.3)) ans = 3.5470
Assigning Variables
» »
a = 2; b = 5;
»
a^b ans =
»
32 x = 5/2*pi;
»
y = sin(x) y = 1
»
z = asin(y) z = 1.5708
Semicolon suppresses screen output Results assigned to “ans” if name not specified () parentheses for function inputs A Note about Workspace: Numbers stored in double-precision floating point format
General Functions
whos : List current variables and their size clear : Clear variables and functions from memory cd : Change current working directory dir : List files in directory pwd : Tells you the current directory you work in echo : Echo commands in M-files format : Set output format (long, short, etc.) diary(foo) : Saves all the commands you type in in a file in the current directory called “ foo ”
Getting help help
command
lookfor
command Help Browser
helpwin
command Search Engine Printable Documents “ Matlabroot\help\pdf_doc\ ” Link to The MathWorks (
>>help
) (
>>lookfor
) (
>>doc
) (
>>helpwin
)
Handling Matrices in Matlab
Matrices
Entering and Generating Matrices Subscripts Scalar Expansion Concatenation Deleting Rows and Columns Array Extraction Matrix and Array Multiplication NOTE: we don ’ t have time to carefully look at all these topics. I want you to be aware that these facilities exist in MATLAB, and that you can access them when needed by first doing a “ help ” on that command
Entering Numeric Arrays
NOTE: 1) Row separator semicolon (;) 2) Column separator space OR comma (,)
»
a=[1 2;3 4] a =
»
1 2 3 4 Use square brackets [ ] b=[-2.8, sqrt(-7), (3+5+6)*3/4] b = -2.8000 0 + 2.6458i 10.5000
»
b(2,5) = 23 b = -2.8000 0 + 2.6458i 10.5000 0 0 0 0 0 0 23.0000
• Any MATLAB expression can be entered as a matrix element (internally, it is regarded as such) • In MATLAB, the arrays are always rectangular
The Matrix in MATLAB
A = Columns (n) 1 2 3 4 5 1 11 16 4 10 6 1 6 2 21 1 2 8 Rows (m) 3 7.2
3 2 1.2
7 5 8 9 7 12 13 4 1 17 18 25 11 22 23 4 5 0 4 0.5
9 4 14 23 5 83 10 13 15 A (2,4) A (17) 5 19 56 24 0 20 10 25 Rectangular Matrix: Scalar: 1-by-1 array Vector: m-by-1 array 1-by-n array Matrix: m-by-n array
Entering Numeric Arrays
Scalar expansion Creating sequences: colon operator (:) Utility functions for creating matrices.
»
w=[1 2;3 4] + 5 w = 6 7 8 9
»
x = 1:5 x =
»
1 2 3 4 5 y = 2:-0.5:0 y = 2.0000 1.5000 1.0000 0.5000 0
»
z = rand(2,4) z = 0.9501 0.6068 0.8913 0.4565
0.2311 0.4860 0.7621 0.0185
Numerical Array Concatenation (Tiling)
Use [ ] to combine existing arrays as matrix “elements” Row separator: semicolon (;) Column separator: space / comma (,)
»
a=[1 2;3 4] a = 1 2 3 4 Use square brackets [ ]
»
cat_a=[a, 2*a; 3*a, 4*a; 5*a, 6*a] cat_a = 1 2 2 4 3 4 6 8 3 6 4 8 9 12 12 16 5 10 6 12 15 20 18 24 4*a
Note: The resulting matrix must be rectangular
Array Subscripting / Indexing
A = 1 4 1 2 3 4 5 1 10 6 1 11 6 16 2 21 2 8 3 7.2
3 2 1.2
7 5 8 9 12 7 13 4 17 1 18 25 22 11 23 A(3,1) A(3) 4 0 4 0.5
9 4 14 5 23 5 83 10 13 15 5 19 56 24 0 20 10 25 A(1:5,5) A(1:end,end) A(:,5) A(21:25) A(:,end) A(21:end) ’ A(4:5,2:3) A([9 14;10 15])
Deleting Rows and Columns
»
A=[1 5 9;4 3 2.5; 0.1 10 3i+1] A = 1.0000 5.0000 9.0000 4.0000 3.0000 2.5000 0.1000 10.0000 1.0000+3.0000i
»
A(:,2)=[] A = “:” is a VERY important construct in MATLAB 1.0000 9.0000 4.0000 2.5000
»
0.1000 1.0000 + 3.0000i
A(2,2)=[] ??? Indexed empty matrix assignment is not allowed.
Matrix Multiplication
» »
a = [1 2 3 4; 5 6 7 8]; b = ones(4,3);
»
c = a*b c = 10 10 10 26 26 26 [2x4] [4x3] [2x4]*[4x3] [2x3] a(2nd row).b(3rd column)
Array Multiplication (componentwise operation) » »
a = [1 2 3 4; 5 6 7 8]; b = [1:4; 1:4];
»
c = a.*b c = 1 4 9 16 5 12 21 32 c(2,4) = a(2,4)*b(2,4)
Matrix Manipulation Functions
• • • • • • • • • zeros : Create an array of all zeros ones : Create an array of all ones eye : Identity Matrix rand : Uniformly distributed random numbers diag : Diagonal matrices and diagonal of a matrix size : Return array dimensions fliplr : Flip matrices left-right flipud : Flip matrices up and down repmat : Replicate and tile a matrix
Matrix Manipulation Functions
• • • • • • • • • • transpose (
’
) : Transpose matrix rot90 : rotate matrix 90 tril : Lower triangular part of a matrix triu : Upper triangular part of a matrix cross : Vector cross product dot : Vector dot product det : Matrix determinant inv : Matrix inverse eig : Evaluate eigenvalues and eigenvectors rank: Rank of matrix
Exercise 1 (10 minutes)
Define a matrix A of dimension 2 by 4 whose (i,j) entry is A(i,j)=i+j Extract two 2 by 2 matrices A1 and A2 out of the matrix A. A1 contains the first two columns of A, A2 contains the last two columns of A Compute the matrix B to be the sum of A1 and A2 Compute the eigenvalues and eigenvectors of B Solve the linear system Bx=b, where b has all the entries equal to 1 Compute the determinant of B Compute the inverse of B Compute the condition number of B NOTE: Use only MATLAB native functions for all operations
Elementary Math
Elementary Math Logical Operators Math Functions Polynomial and Interpolation
Logical Operations
= = equal to > greater than < less than >= Greater or equal <= less or equal ~ not & and | or isfinite(), etc. . . .
all(), any() find
» »
Mass = [-2 10 NaN 30 -11 Inf 31]; each_pos = Mass>=0 each_pos = 0 1 0 1 0 1 1
»
all_pos = all(Mass>=0) all_pos = 0
»
all_pos = any(Mass>=0) all_pos = 1
»
pos_fin = (Mass>=0)&(isfinite(Mass)) pos_fin = 0 1 0 1 0 0 1
Note: • 1 = TRUE • 0 = FALSE
Elementary Math Function
• • • • • abs , sign : Absolute value and Signum Function sin , cos , asin , acos …: Triangular functions exp , log , log10 : Exponential, Natural and Common (base 10) logarithm ceil , floor : Round to integer, toward +/-infinity fix : Round to integer, toward zero
Elementary Math Function
round : Round to the nearest integer gcd : Greatest common divisor lcm : Least common multiple sqrt : Square root function real , imag : Real and Image part of complex rem : Remainder after division
Elementary Math Function Operating on Arrays
• • • • • • • • max , min : Maximum and Minimum of arrays mean , median : Average and Median of arrays std , var : Standard deviation and variance sort: Sort elements in ascending order sum , prod: Summation & Product of Elements trapz : Trapezoidal numerical integration cumsum , cumprod: Cumulative sum, product diff , gradient : Gradient Differences and Numerical
Polynomials and Interpolation
Polynomials Representing Roots (
>> roots
) Evaluation Derivatives Curve Fitting (
>> polyval
) (
>> polyder
) (
>> polyfit
) Partial Fraction Expansion (>>
residue
) Interpolation One-Dimensional (
interp1
) Two-Dimensional (
interp2
)
Example
polysam=[1 0 0 8]; roots(polysam) ans = -2.0000 1.0000 + 1.7321i
1.0000 - 1.7321i
polyval(polysam,[0 1 2.5 4 6.5]) ans = 8.0000 9.0000 23.6250 72.0000 282.6250
polyder(polysam) ans = 3 0 0 [r p k]=residue(polysam,[1 4 3]) r = 9.5 3.5
p = -3 -1 k = 1 -4
Curve fitting
polyfit(X,Y,N) - finds the coefficients of a polynomial P(X) of degree N that over the points X fits the data Y best in a least-squares sense
x = [0: 0.1: 2.5]; y = erf(x); p = polyfit(x,y,6) p = 0.0084 -0.0983 0.4217 -0.7435 0.1471 1.1064 0.0004
interp1(x,y,[0.45 0.95 2.2 3.0]) ans = 0.4744 0.8198 0.9981 NaN
Exercise 2 (10 minutes)
Let x be an array of values from 0 to 2, equally spaced by 0.01
Compute the array of exponentials corresponding to the values stored in x Find the polynomial p of degree 5 that is the best least square approximation to y on the given interval [0,2] Evaluate the polynomial p at the values of x, and compute the error z with respect to the array y Interpolate the (x,z) data to approximate the value of the error in interpolation at the point .9995
END MATLAB for [Linear] Algebra
Programming and Application Development
Topics discussed …
The concept of m-file in MATLAB Script versus function files The concept of workspace Variables in MATLAB Type of a variable Scope of a variable Flow control in MATLAB The Editor/Debugger
Before Getting Lost in Details
… Obtaining User Input “ input ” - Prompting the user for input >> apls = input( ‘ How many apples? ‘ ) “ keyboard ” - Pausing During Execution (when in M-file) Shell Escape Functions ( ! Operator ) Optimizing MATLAB Code Vectorizing loops Preallocating Arrays
Function M-file
function r = ourrank(X,tol) % rank of a matrix s = svd(X); if (nargin == 1) tol = max(size(X)) * s(1)* eps; end r = sum(s > tol); Multiple Input Arguments use ( )
»
r=ourrank(rand(5),.1); Multiple Output Arguments, use [ ]
»
[m std]=ourstat(1:9); function [mean,stdev] = ourstat(x) [m,n] = size(x); if m == 1 m = n; end mean = sum(x)/m; stdev = sqrt(sum(x.^2)/m – mean.^2);
Basic Parts of a Function M-File
Output Arguments Function Name Input Arguments Online Help Function Code function y = mean (x) % MEAN Average or mean value.
% For vectors, MEAN(x) returns the mean value.
% For matrices, MEAN(x) is a row vector % containing the mean value of each column.
[m,n] = size(x); if m == 1 m = n; end y = sum(x)/m;
Script and Function Files
• Script Files • Work as though you typed commands into MATLAB prompt • Variable are stored in MATLAB workspace • Function Files • Let you make your own MATLAB Functions • All variables within a function are
local
• All information must be passed to functions as parameters • Subfunctions are supported
The concept of
Workspace
• At any time in a MATLAB session, the code has a workspace associated with it • The workspace is like a sandbox in which you find yourself at a certain point of executing MATLAB • The “Base Workspace”: the workspace in which you live when you execute commands from prompt • Remarks: • Each MATLAB function has its own workspace (its own sandbox) • A function invoked from a calling function has its own and separate workspace (sandbox) • A script does not lead to a new workspace (
unlike
a function), but lives in the workspace from which it was invoked
Variable Types in MATLAB
• Local Variables • In general, a variable in MATLAB has
local
scope, that is, it’s only available in its workspace • The variable disappears when the workspace ceases to exist • Recall that a script does not define a new workspace – be careful, otherwise you can step on variables defined at the level where the script is invoked • Since a function defines its own workspace, a variable defined in a function is local to that function • Variables defined outside the function should be passed to function as arguments.
Furthermore
, the arguments are passed by value • Every variable defined in the subroutine, if to be used outside the body of the function, should be returned back to the calling workspace
Variable Types in MATLAB
• Global Variables • These are variables that are available in multiple workspaces • They have to be explicitly declared as being global • Not going to expand on this, since using global variables is a bad programming practice • A note on returning values from a function • Since all variables are local and input arguments are passed by value, when returning from a function a variable that is modified inside that function will not appear as modified in the calling workspace
unless
the variable is either global, or declared a return variable for that function
Flow Control Statements
if
Statement
if ((attendance >= 0.90) & (grade_average >= 60)) pass = 1; end;
while
Loops
eps = 1; while (1+eps) > 1 eps = eps/2; end eps
Flow Control Statements
for
Loop:
switch
Statement:
a = zeros(k,k) % Preallocate matrix for m = 1:k for n = 1:k a(m,n) = 1/(m+n -1); end end method = 'Bilinear'; ... (some code here)...
switch lower(method) case {'linear','bilinear'} disp('Method is linear') case 'cubic' disp('Method is cubic') otherwise disp('Unknown method.') end Method is linear
Editing and Debugging M-Files
The Editor/Debugger Debugging M-Files Types of Errors ( Syntax Error and Runtime Error ) Using
keyboard
and “
;
” statement Setting Breakpoints Stepping Through Continue, Go Until Cursor, Step, Step In, Step Out Examining Values Selecting the Workspace Viewing
Datatips
in the Editor/Debugger Evaluating a Selection
Debugging
Select Workspace Set Auto Breakpoints tips
Importing and Exporting Data
Using the Import Wizard Using
Save
and
Load
command
save fname save fname x y z save fname -ascii save fname -mat load fname load fname x y z load fname -ascii load fname -mat
Input/Output for Text File
•Read formatted data, reusing the format string N times.
»
[A1…An]=textread(filename,format,N)
Suppose the text file stars.dat contains data in the following form: Jack Nicholson 71 No Yes 1.77
Helen Hunt 45 No No 1.73
Read each column into a variable [firstname, lastname, age, married, kids, height] = textread('stars.dat','%s%s%d%s%s%f'); •Import and Exporting
Numeric
Data with General ASCII delimited files »
M = dlmread(filename,delimiter,range)
Input/Output for Binary File
fopen : Open a file for input/output fclose : Close one or more open files fread : Read binary data from file fwrite : Write binary data to a file fseek : Set file position indicator » » » » » »
fid= fopen( ' mydata.bin
' , ' wb ' ); fwrite (fid,eye(5) , ' int32 ' ); fclose (fid); fid= fopen( ' mydata.bin
' , ' rb ' ); M= fread(fid, [5 5], ' int32 ') fclose (fid);
Exercise 3: A debug session (10 minutes)
Use the function demoBisect provided on the next slide to run a debug session Save the MATLAB function to a file called demoBisect.m in the current directory Call once the demoBisect.m from the MATLAB prompt to see how it works >>help demoBisect >>demoBisect(0, 5, 30) Place some breakpoints and run a debug session Step through the code, and check the values of variables Use the MATLAB prompt to echo variables Use dbstep, dbcont, dbquit commands
function xm = demoBisect(xleft,xright,n) % demoBisect Use bisection to find the root of x - x^(1/3) - 2 % % Synopsis: x = demoBisect(xleft,xright) % x = demoBisect(xleft,xright,n) % % Input: xleft,xright = left and right brackets of the root % n = (optional) number of iterations; default: n = 15 % % Output: x = estimate of the root if nargin<3, n=15; end % Default number of iterations a = xleft; b = xright; % Copy original bracket to local variables fa = a - a^(1/3) - 2; % Initial values of f(a) and f(b) fb = b - b^(1/3) - 2; fprintf(' k a xmid b f(xmid)\n'); for k=1:n xm = a + 0.5*(b-a); % Minimize roundoff in computing the midpoint fm = xm - xm^(1/3) - 2; % f(x) at midpoint fprintf('%3d %12.8f %12.8f %12.8f %12.3e\n',k,a,xm,b,fm); if sign(fm)==sign(fa) % Root lies in interval [xm,b], replace a a = xm; fa = fm; else % Root lies in interval [a,xm], replace b b = xm; fb = fm; end end
Other Tidbits
The “inline” Utility
•
inline
function Use
char
function to convert
inline
object to
string
»
f = inline(' 3*sin(2*x.^2) ',' x ') f = Inline function: f(x) = 3*sin(2*x.^2)
»
f(2) ans = 2.9681
• Numerical Integration using
quad
» » » »
Q = quad('1./(x.^3-2*x-5)',0,2); F = inline('1./(x.^3-2*x-5)'); Q = quad(F,0,2); Q = quad(' myfun ',0,2)
Note :
quad
function use adaptive
function y = myfun(x)
Simpson quadrature
y = 1./(x.^3-2*x-5);
Root Finding, Optimization …
fzero
finds a zero of a single variable function
[x,fval]= fzero(fun,x0,options)
fun is inline function or m-function
fminbnd
minimize a single variable function on a fixed interval. x 1 [x,fval]= fminbnd(fun,x1,x2,options) fminsearch minimize function w/ several variables [x,fval]= fminsearch(fun,x0,options) Use optimset to determine options parameter. options = optimset('param1',value1,...) An explicit ODE with initial value: Using ode45 for non-stiff functions and for stiff functions. ode23t [t,y] = solver(odefun,tspan,y0,options) function dydt = odefun(t,y) Initialvlue [initialtime finaltime] • Use odeset to define options parameter function dydt=myfunc(t,y) dydt=zeros(2,1); dydt(1)=y(2); dydt(2)=(1-y(1)^2)*y(2)-y(1); » [t,y]=ode45(' myfunc ',[0 20],[2;0]) 3 Note: Help on odeset to set options for more accuracy and other useful utilities like drawing results during solving. 2 -1 -2 1 0 -3 0 2 4 6 8 10 12 14 16 18 20 Use the example on the previous page to solve the slightly different IVP on the interval [0,20] seconds: y y 1 1 (0) 2 y 1 (0) 0 y 1 2 ) y 1 y 1 0 Basic Plotting plot, title, xlabel, grid, legend, hold, axis Editing Plots Property Editor Mesh and Surface Plots meshgrid, mesh, surf, colorbar, patch, hidden Handle Graphics color line marker Syntax: plot(x1, y1, 'clm1', x2, y2, 'clm2', ...) Example: x=[0:0.1:2*pi]; y=sin(x); z=cos(x); plot(x,y,x,z, 'linewidth' ,2) title('Sample Plot', 'fontsize' ,14); xlabel( 'X values' , 'fontsize' ,14); ylabel( 'Y values' , 'fontsize' ,14); legend( 'Y data' , 'Z data' ) grid on Ylabel Legend Xlabel Title Grid Nomenclature: Figure window – the window in which MATLAB displays plots Plot – a region of a window in which a curve (or surface) is displayed Three typical ways to display multiple curves in MATLAB (other combinations are possible … ) One figure contains one plot that contains multiple curves Requires the use of the command “ hold ” (see MATLAB help) One figure contains multiple plots, each plot containing one curve Requires the use of the command “ subplot ” Multiple figures, each containing one or more plots, each containing one or more curves Requires the use of the command “ figure ” and possibly “ subplot ” Syntax: subplot(rows,cols,index) » subplot(2,2,1); » … » subplot(2,2,2) » ... » subplot(2,2,3) » ... » subplot(2,2,4) » ... “ ” Use if you want to have several figures open for plotting The command by itself creates a new figure window and returns its handle >> figure If you have 20 figures open and want to make figure 9 the default one (this is where the next plot command will display a curve) do >> figure(9) >> plot( … ) Use the command close(9) if you want to close figure 9 in case you don ’ t need it anymore x = 0:0.1:2; y = 0:0.1:2; [xx, yy] = meshgrid(x,y); zz=sin(xx.^2+yy.^2); surf(xx,yy,zz) xlabel('X axes') ylabel('Y axes') contourf-colorbar-plot3-waterfall-contour3-mesh-surf bar-bar3h-hist-area-pie3-rose Graphics in MATLAB consist of root, figure, axes, image, line, patch, rectangle, surface, text, light Creating Objects Setting Object Properties Upon Creation Obtaining an Object ’ s Handles Knowing Object Properties Modifying Object Properties Using Using Command Line Property Editor Surface object Line objects Text objects Root object 1. Upon Creation h_line = plot(x_data, y_data, ...) 2. Utility Functions 0 - root object handle gcf - current figure handle gca- current axis handle gco- current object handle What is the current object? • Last object created • OR Last object clicked 3. FINDOBJ h_obj = findobj(h_parent, 'Property', 'Value', ...) Default = 0 (root object) • Obtaining a list of current properties: get(h_object) • Obtaining a list of settable properties: set(h_object) • Modifying an object’s properties Using Command Line set(h_object,'PropertyName','New_Value',...) Using Property Editor What is GUI? What is Using and *.fig file? command GUI controls GUI menus Axes static text Checkbox Radio Buttons Push Buttons Frames Slider Edit text Guide Editor Property Inspector Result Figure Created using single quote delimiter (') » str = 'Hi there,' str = Hi there, » str2 = 'Isn''t MATLAB great?' str2 = Isn't MATLAB great? Each character is a separate matrix element (16 bits of memory per character) str = H i t h e r e , 1x9 vector Indexing same as for numeric arrays Using [ ] operator: Each row must be same length Row separator: semicolon (;) Column separator: space / comma (,) » » » str ='Hi there,'; str1='Everyone!'; 1x9 vectors new_str=[str, ' ', str1] new_str = Hi there, Everyone! » 1x19 vectors str2 = 'Isn''t MATLAB great?'; » new_str2=[new_str; str2] new_str2 = Hi there, Everyone! Isn't MATLAB great? 2x19 matrix • • For strings of different length: STRVCAT char » new_str3 = strvcat(str, str2) new_str3 = Hi there, Isn't MATLAB great? 2x19 matrix (zero padded) String Comparisons strcmp : compare whole strings strncmp : compare first ‘ N ’ characters findstr : finds substring within a larger string Converting between numeric & string arrays: num2str : convert from numeric to string array str2num : convert from string to numeric array Numeric Arrays Multidimensional Arrays Structures and Cell Arrays The first references array dimension 1, the row. The second references dimension 2, the column. The third references dimension 3, The page. 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 1 3 6 10 1 4 10 20 Page N » » A = pascal(4); A(:,:,2) = magic(4) A(:,:,1) = 1 1 1 1 1 2 3 4 1 3 6 10 1 4 10 20 A(:,:,2) = 16 2 3 13 5 11 10 8 » 9 7 6 12 4 14 15 1 A(:,:,9) = diag(ones(1,4)); Page 1 • Arrays with named data containers called fields . » » » patient.name= 'John Doe' ; patient.billing = 127.00; patient.test= [79 75 73; 180 178 177.5; 220 210 205]; • Also, Build structure arrays using the struct function. • Array of structures » » » patient(2).name= 'Katty Thomson' ; Patient(2).billing = 100.00; Patient(2).test= [69 25 33; 120 128 177.5; 220 210 205]; • Array for which the elements are cell s and can hold other MATLAB arrays of different types. » A(1,1) = {[1 4 3; 0 5 8; 7 2 9]}; » A(1,2) = { 'Anne Smith' }; » » A(2,1) = {3+7i}; A(2,2) = {-pi:pi/10:pi}; • Using braces {} to point to elements of cell array • Using celldisp function to display cell array Matlab is a language of technical computing. Matlab, a high performance software, a high level language Matlab supports GUI, API, and … Matlab Toolboxes best fits different applications Matlab … • Contact http://www.mathworks.com/support • You can find more help and FAQ about mathworks products on this page. • Contact comp.soft-sys.matlab Newsgroup • Use google to find more information (like the content of this presentation, in the first place) ?Ordinary Differential Equations (Solving Initial Value Problem)
ODE Example:
Example 4: Using ODE45 (5 minutes)
Graphics Fundamentals
Graphics and Plotting in MATLAB
2-D Plotting
Sample Plot
Displaying Multiple Plots
Subplots
The
figure
Command
Surface Plot Example
3-D Surface Plotting
Specialized Plotting Routines
Advanced Topics
Handle Graphics
objects:
Graphics Objects
Obtaining an Object’s Handle
Modifying Object Properties
Graphical User Interface
figure
guide
Character String Manipulation
Character Arrays (Strings)
String Array Concatenation
Working with String Arrays
Data Types
Data Types
Multidimensional Arrays
Structures
Cell Arrays
Conclusion
Getting more help