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Zen and the Art of MatLab Damian Gordon
Hard work done by : ,[object Object],[object Object]
Introduction to MatLab ,[object Object],[object Object],[object Object]
References ,[object Object],[object Object],[object Object]
Printed Circuit Board
Specific Bond Selected
Bond Shape Estimated
MATLAB Command Window To get started, type one of these: helpwin, helpdesk, or demo. For product information, type tour or visit www.mathworks.com. » » help HELP topics:
Creating Variables ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Operations + Addition - Subtraction * Multiplication ^ Power  Division /  Division ,[object Object],[object Object],[object Object],[object Object],[object Object]
Creating Complex Numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Entering Matrices (1) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Entering Matrices (2) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Entering Matrices (3) ,[object Object],[object Object],[object Object],[object Object]
Complex Matrices ,[object Object],[object Object],[object Object],[object Object]
MATLAB Command Window » who Your variables are: a  b  c   » whos Name  Size  Bytes  Class a  8x8  512  double array b  9x9  648  double array c  9x9  648  double array Grand total is 226 elements using 1808 bytes
Matrix Addition ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Matrix Subtraction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Matrix Multiplication ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Matrix - Power ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Matrix Transpose ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Matrix Division ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Matrix Operations + Addition - Subtraction * Multiplication ^ Power ‘ Conjugate  Transpose  Left Division / Right Division ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Philosophiae Naturalis  Principia  Matlab ematica Damian Gordon
Getting to Matlab
Magic Matrix ,[object Object],[object Object],[object Object],[object Object]
Identity Function ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Upper Triangle Matrix » a = ones(5) a = 1  1  1  1  1 1  1  1  1  1 1  1  1  1  1 1  1  1  1  1 1  1  1  1  1 » triu(a) ans = 1  1  1  1  1 0  1  1  1  1 0  0  1  1  1 0  0  0  1  1 0  0  0  0  1
Lower Triangle Matrix » a = ones(5) a = 1  1  1  1  1 1  1  1  1  1 1  1  1  1  1 1  1  1  1  1 1  1  1  1  1 » tril(a) ans = 1  0  0  0  0 1  1  0  0  0 1  1  1  0  0 1  1  1  1  0 1  1  1  1  1
Hilbert Matrix ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Inverse Hilbert Matrix » invhilb(4) ans = 16  -120  240  -140 -120  1200  -2700  1680 240  -2700  6480  -4200 -140  1680  -4200  2800
Toeplitz matrix. ,[object Object],[object Object],[object Object],[object Object],[object Object]
Summary of Functions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],- magic matrix - identity matrix - upper triangle - lower triangle - hilbert matrix - Inverse Hilbert matrix  - non-symmetric Toeplitz matrix
Dot Operator ,[object Object],[object Object],[object Object],[object Object]
Concatenation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Subscripts ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Colon Operator (1) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Colon Operator (2) ,[object Object],[object Object],[object Object],[object Object],[object Object]
matlABBA
The Colon Operator (1) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Colon Operator (2) ,[object Object],[object Object],[object Object],[object Object],[object Object]
Deleting Rows and Columns (1) ,[object Object],[object Object],[object Object],[object Object],[object Object]
Deleting Rows and Columns (2) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The ‘FIND’ Command (1) >> x = -3:3 x = -3 -2 -1 0 1 2 3 K = find(abs(x) > 1) K = 1 2 6 7
The ‘FIND’ Command (2) A = [ 1 2 3 ; 4 5 6 ; 7 8 9] [i, j] = find (A > 5) i = 3 3 2 3 j = 1 2 3 3
Special Variables ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],- default name for results - pi - “help eps” - count floating point ops - Infinity, e.g. 1/0 - Not a number, e.g. 0/0 - root minus one - why not ?
LOGO Command
The ‘PLOT’ Command (1)  ,[object Object],[object Object],[object Object],[object Object],[object Object]
The ‘PLOT’ Command (2) ,[object Object],[object Object],[object Object],[object Object]
 
The ‘PLOT’ Command (1)  ,[object Object],[object Object],[object Object],[object Object],[object Object]
The ‘PLOT’ Command (2) ,[object Object],[object Object],[object Object],[object Object]
PLOT Options ,[object Object],[object Object],[object Object],[object Object]
PLOT Options ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
SUBPLOT Command ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Specialised matrices ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Polynomials ,[object Object],[object Object],[object Object],[object Object],[object Object]
Polynomials ,[object Object],[object Object],[object Object]
Polynomials ,[object Object],[object Object],[object Object],[object Object]
Polynomial Addition/Sub ,[object Object],[object Object],[object Object],[object Object]
Polynomial Addition/Sub ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Polynomial Multiplication ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Polynomial Division ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Polynomial Differentiation ,[object Object],[object Object],[object Object],[object Object]
Polynomial Evaluation ,[object Object],[object Object],[object Object],[object Object]
Rational Polynomials ,[object Object],[object Object],[object Object],[object Object]
An Anthropologist on Matlab
Data Analysis Functions (1) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Data Analysis Functions (2) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Symbolic Math Toolbox
Symbolic Expressions ,[object Object],[object Object],[object Object],[object Object]
Symbolic Expressions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Symbolic Functions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Advanced Operations ,[object Object],[object Object],[object Object],[object Object],[object Object]
Advanced Operations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Symbolic Differentiation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Symbolic Integration ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Comments &Punctuation (1) ,[object Object],[object Object],[object Object],[object Object]
Comments &Punctuation (2) ,[object Object],[object Object],[object Object],[object Object],[object Object]
SAVE Command (1) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
SAVE Command (2) ,[object Object],[object Object],[object Object],[object Object]
Load Command ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
M-Files ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
IF Condition if condition {commands} end If x = 2 output = ‘x is even’ end
WHILE Loop while condition {commands} end X = 10; count = 0; while x > 2 x = x / 2; count = count + 1; end
FOR Loop for  x=array {commands} end for n = 1:10 x(n) = sin(n); end A = zeros(5,5); % prealloc for n = 1:5 for m = 5:-1:1 A(n,m) = n^2 + m^2; end disp(n) end
Creating a function ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Quick Exercise (!) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Flash Gordon   and the Mud Men of Matlab
Quick Exercise (!) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Creating Programs ,[object Object],function out = program(inputs) % PROGRAM <code> C:
Know Thyself ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Quick Answer (!) function  c = mypoly(a,b) % MYPOLY  Add two polynomials of variable lengths  %  mypoly(a,b) add the polynomial A to the polynomial  %  B, even if they are of different length % %  Author: Damian Gordon %  Date  : 3/5/2001 %  Mod'd : x/x/2001 % c = [zeros(1,length(b) - length(a)) a] + [zeros(1, length(a) - length(b)) b];
Recursion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Curve Fitting ,[object Object],[object Object],[object Object],[object Object]
POLYFIT : Curve Fitting ,[object Object],[object Object],[object Object],[object Object],[object Object]
Curve Fitting Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Curve Fitting Example ,[object Object],[object Object],[object Object]
Interpolation - 1D ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Interpolation - 2D ,[object Object],TYPE = 'nearest' - nearest neighbor interpolation 'linear'  - bilinear interpolation 'cubic'  - bicubic interpolation 'spline'  - spline interpolation
Fourier Functions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Tensors ,[object Object],[object Object],[object Object]
3D Graphics ,[object Object],[object Object]
3D Graphics ,[object Object],[object Object],[object Object]
3D Graphics ,[object Object],[object Object],[object Object]

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Introduction to MatLab programming

  • 1. Zen and the Art of MatLab Damian Gordon
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  • 8. MATLAB Command Window To get started, type one of these: helpwin, helpdesk, or demo. For product information, type tour or visit www.mathworks.com. » » help HELP topics:
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  • 16. MATLAB Command Window » who Your variables are: a b c » whos Name Size Bytes Class a 8x8 512 double array b 9x9 648 double array c 9x9 648 double array Grand total is 226 elements using 1808 bytes
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  • 24. Philosophiae Naturalis Principia Matlab ematica Damian Gordon
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  • 28. Upper Triangle Matrix » a = ones(5) a = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 » triu(a) ans = 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1
  • 29. Lower Triangle Matrix » a = ones(5) a = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 » tril(a) ans = 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1
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  • 31. Inverse Hilbert Matrix » invhilb(4) ans = 16 -120 240 -140 -120 1200 -2700 1680 240 -2700 6480 -4200 -140 1680 -4200 2800
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  • 44. The ‘FIND’ Command (1) >> x = -3:3 x = -3 -2 -1 0 1 2 3 K = find(abs(x) > 1) K = 1 2 6 7
  • 45. The ‘FIND’ Command (2) A = [ 1 2 3 ; 4 5 6 ; 7 8 9] [i, j] = find (A > 5) i = 3 3 2 3 j = 1 2 3 3
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  • 84. IF Condition if condition {commands} end If x = 2 output = ‘x is even’ end
  • 85. WHILE Loop while condition {commands} end X = 10; count = 0; while x > 2 x = x / 2; count = count + 1; end
  • 86. FOR Loop for x=array {commands} end for n = 1:10 x(n) = sin(n); end A = zeros(5,5); % prealloc for n = 1:5 for m = 5:-1:1 A(n,m) = n^2 + m^2; end disp(n) end
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  • 89. Flash Gordon and the Mud Men of Matlab
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  • 93. Quick Answer (!) function c = mypoly(a,b) % MYPOLY Add two polynomials of variable lengths % mypoly(a,b) add the polynomial A to the polynomial % B, even if they are of different length % % Author: Damian Gordon % Date : 3/5/2001 % Mod'd : x/x/2001 % c = [zeros(1,length(b) - length(a)) a] + [zeros(1, length(a) - length(b)) b];
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