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Introduction to MATLAB for Biomedical Engineering BME 1008 Introduction to Biomedical Engineering FIU, Spring 2015 Lesson 2: Element-wise vs. matrix operations save(), load(), matlab script plot(x,y)

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Creating Vectors (1D arrays) Explicit list of elements >> x1 = [-2 -1 0 1 2 3 4 5] x = -2 -1 0 1 2 3 4 5 Using colon (:) notation >> x2 = -2 : 5 x2 = -2 -1 0 1 2 3 4 5

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General colon (:) syntax: initial value : increment : final value >> x3 = 1:1.5:6 x3 = 1.0 2.5 4.0 5.5 >> x4 = 1:6 %default increment 1 x4 = 1.0 2.0 3.0 4.0 5.0 6.0

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In matrix algebra In MATLAB A*B means matrix product A.* B means element-by-element multiplication '. ' (dot) - indicates element-by-element operation Matrix product C = AB

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Element-wise (array) operators: +, -,.*,./,.^ '+ ' - addition always element wise >> x1 = [1 2 3]; x2 = [4 5 6]; >> x1 + x2 ans = 5 7 9 >> x1 + 10 ans = 11 12 13

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>> x1 + [10 20] ??? Error using ==> plus Matrix dimensions must agree. '- ' - subtraction always element wise >> x1 = [1 2 3]; x2 = [4 5 6]; >> x1 - x2 ans = -3 -3 -3 >> 3 - x1 ans = 2 1 0

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'.* ' - element-wise multiplication >> x1 = [1 2 3]; x2 = [4 5 6]; >> x1.* x2 ans = 4 10 18 >> x1 * 10 ans = 11 12 13 >> x1*x2 ??? Error using ==> mtimes Inner matrix dimensions must agree.

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'./ ' - element-wise multiplication >> x1 = [1 2 3]; x2 = [4 5 6]; >> x1./ x2 ans = 0.25 0.4 0.5 >> 1./x1 ans = 1.0 0.5 0.33 >> 1/x1 ??? Error using ==> mrdivide Matrix dimensions must agree.

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'.^ ' - element-wise power >> A = [5 1 -2]; >> A.^ 3 ans = 125 1 -8 >> A ^ 3 ??? Error using ==> mpower Matrix must be square.

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Matrix operators *, ^ >> x1 = [1 2 3]; %row vector x1 = 123 >> x2 = [4 5 6]'; %column vector x2 = 4 5 6 >> x1*x2 %matrix multiplication ans = 32

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>> x1 = [1 2; 3 4] % 2-by-2 matrix x1 = 12 34 >> x1^2 % or x1*x1 ans = 7 10 15 22 %matrix product

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Quiz 1 1) What is the average of: 1 3, 1.5 3, 2 3, 2.5 3..., 11.5 3, 12 3 ? Hint: First create vector, then cube. 2) What is the maximum element of C, where Hint: Use max() two times.

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Answers to Quiz 1 1) >> x = [1:0.5:12]; y = x.^3; >> average = mean(y) average = 489.1250

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2) >> A=[30 5.5; 2 -7]; B=[-3 6; 8 12]; >> C = A*B C = -46 246 -62 -72 >> max(C) %returns max. element from each column ans = -46 246 >> max(max(C)) %returns max. element from C ans = 246

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Matlab Scalar functions sin(), cos(), exp(), log(), log10() operate element-wise >> t = [0 : pi/2: 2*pi ] % pi = 3.14 Matlab constant t = 0 1.573.144.716.28 >> y = sin(t) y = 0 1 0 -1 0 >> e = exp([0 1 -1]) %exponential function e = 1.00 2.71 0.36

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SAVE & LOAD Commands save('filename') saves all workspace variables to disk in current directory in the file 'filename.mat' '.mat' - default extension for Matlab binary file (MAT-file) save('filename','var1','var2') saves only variables 'var1' and 'var2' load('filename') loads workspace variables from disk from the file 'filename.mat'

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>> clear %removes variables from workspace >> x = [0: 0.1 : 1000]; >> y = exp(-x/500); % x, y vectors with 10000 elements >> save('myResults') >> save('myResults_y','y') >> clear >> whos >> load('myResults') >> whos

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Manual Loading & Saving

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Importing data from other file formats (.txt,.xls,.jpg,...)

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Matlab script text file with a series of Matlab commands Matlab program with no input and output arguments has extension '.m' (M-file) (1) New or Open (2) Edit in Matlab editor (4) Run(3) Save

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plot(x,y) command % Moore's Law -transistor count double every two years transistors= [50 100 200 400 800 1600... 3200 6400 12800]; years=[2000:1.5:2012]; plot(years, transistors)

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plot(years, transistors,'r*--') %'r*--' red, star, dashed line ylabel('transistor count (million)') % y-axis label xlabel('year') % x-axis label title('Moore''s law')

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Figure editing (1) Edit plot (3) Change properties (2) Select object (line, axis, label)

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Saving figures '.fig' file, Matlab format, figure can be edited as image file, e.g. '.bmp'

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Copy & Paste figure to Word or PPT

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Quiz 2 Given y = sin(x) × e -x/15 and x = [0:0.2:10*pi] hint: exp() max() plot y vs. x find maximum y

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Answer to Quiz 2 >> x = [0:0.2:10*pi]; >> y = sin(x).*exp(-x/15); >> figure %opens new figure window >> plot(x,y) >> y_max = max(y) y_max = 0.8984

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