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Matlab Arrays

Matlab Arrays. Vectors. Initialize vectors either like : V = [1 2 3 4 5], or : V = [1,2,3,4,5] In order to create a column vector : V = [1;2;3;4;5] You can put any numeric expression for the individual elements of your vector. Accessing Vector Elements.

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Matlab Arrays

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  1. Matlab Arrays

  2. Vectors • Initialize vectors either like : • V = [1 2 3 4 5], or : • V = [1,2,3,4,5] • In order to create a column vector : • V = [1;2;3;4;5] • You can put any numeric expression for the individual elements of your vector

  3. Accessing Vector Elements • Given v = [1 2 3 4 5], or v = [1;2;3;4;5] • V(1) returns 1, • V(2)  2, … v(5)  5 • v(6)  ??? Index exceeds matrix dimensions. • v(0)  ??? Subscript indices must either be real positive integers or logicals.

  4. Changing Vector Elements >> v(3) = 8 v = 1 2 8 4 5 >> v(0) = 0 ??? Subscript indices must either be real positive integers or logicals. >> v(7) = 128 v = 1 2 8 4 5 0 128

  5. Strings are also vectors … >> st = 'abcde' st =abcde >> st(0) ??? Subscript indices must either be real positive integers or logicals. >> st(3) ans =c >> st(3) = 'X' st =abXde >> st(10) = 'O' st =abXde O

  6. Transpose Operator >> [1 2 3]' ans = 1 2 3 >> [1;2;3]' ans = 1 2 3

  7. Vector length >> length(v) ans = 7 >> length(v') ans = 7 >> v(length(v)) ans = 128 >> v(end) ans = 128

  8. Vector operations • Given vector v = [1 2 3 4 5] >> v + 10 ans = 11 12 13 14 15 >> v * 2 ans = 2 4 6 8 10 >> v' + 10 ans = 11 12 13 14 15

  9. Vector operations • Given vectors v = [1 2 3 4 5], v2 = [10 20 30 40 50] : >> v + v2 ans = 11 22 33 44 55 >> v2 -v ans = 9 18 27 36 45 >> v + v2' ??? Error using ==> + Matrix dimensions must agree.

  10. Vector Operations >> v * v2 ??? Error using ==> * Inner matrix dimensions must agree. >> v / v2 ans = 0.1000 >> v(3) = 6 v = 1 2 6 4 5 >> v / v2 ans = 0.1164

  11. Element-by-element operations >> v .* v2 ans = 10 40 90 160 250 >> v ./ v2 ans = 0.1000 0.1000 0.1000 0.1000 0.1000 >> v .+ v2 ??? v .+ v2 | Error: "identifier" expected, "+" found. >> v + v2 ans = 11 22 33 44 55

  12. Functions that Accept Vectors >> log(v) ans = 0 0.6931 1.0986 1.3863 1.6094 >> sin(v) ans = 0.8415 0.9093 0.1411 -0.7568 -0.9589 >> round(10 * log(v)) ans = 0 7 11 14 16

  13. Creating Vectors by Ranges >>v = 1:5 v = 1 2 3 4 5 >> v = 11:16 v = 11 12 13 14 15 16 >> v = 5:1 v = Empty matrix: 1-by-0 • in general : first:last  [first, first+1, first+2, … ,last-1, last]

  14. Specifying an Increment >> v = 10:10:50 v = 10 20 30 40 50 >> v = 50:-10:10 v = 50 40 30 20 10 >> v = 10:-10:50 v = Empty matrix: 1-by-0 >> v = 10:20:50 v = 10 30 50 >> v = 10:15:50 v = 10 25 40

  15. Linspace function • LINSPACE(X1, X2) generates a row vector of 100 linearly equally spaced points between X1 and X2. • LINSPACE(X1, X2, N) generates N points between X1 and X2. >> linspace(10, 20, 5) ans = 10.0000 12.5000 15.0000 17.5000 20.0000

  16. Plotting >> x = linspace(0, 4 * pi, 100); >> y = sin(x); >> y2 = (sin(x)) .^ 2; >> y3 = y + y2; >> plot(x,y);

  17. Plotting … >> plot(x,y2); >> plot(x,y3);

  18. Multiple Plots >> plot(x,y, x, y2, x, y3); >> title('An interesting plot'); >> xlabel('x'); >> ylabel('y'); >> legend('sin(x)', 'sin(x)^2', 'sin(x) + sin(x)^2');

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