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2-D Arrays (Matrices)

2-D Arrays (Matrices). Creating 2-D Arrays. m = [ 11 12 13 21 22 23 31 32 33]; or >> m = [11 12 13; 21 22 23; 31 32 33] m = 11 12 13 21 22 23 31 32 33. Accessing Elements. >> m(2, 1) ans = 21 >> m(2, 3) ans = 23 >> m(4, 1)

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2-D Arrays (Matrices)

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  1. 2-D Arrays (Matrices)

  2. Creating 2-D Arrays m = [ 11 12 13 21 22 23 31 32 33]; or >> m = [11 12 13; 21 22 23; 31 32 33] m = 11 12 13 21 22 23 31 32 33

  3. Accessing Elements >> m(2, 1) ans = 21 >> m(2, 3) ans = 23 >> m(4, 1) ??? Index exceeds matrix dimensions.

  4. Modifying Elements >> m(1, 3) = 1133 m = 11 12 1133 21 22 23 31 32 33 >> m(5, 6) = 56 m = 11 12 1133 0 0 0 21 22 23 0 0 0 31 32 33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 56

  5. zeros function >> z = zeros(3) z = 0 0 0 0 0 0 0 0 0 >> z = zeros(2, 4) z = 0 0 0 0 0 0 0 0 >> zeros(1, 5) + (1:5) ans = 1 2 3 4 5

  6. ones function >> ones(3) ans = 1 1 1 1 1 1 1 1 1 >> ones(1, 5) + (10:14) ans = 11 12 13 14 15

  7. Getting Columns and Rows >> m = [11 12 13; 21 22 23; 31 32 33] m = 11 12 13 21 22 23 31 32 33 >> m(1, :) ans = 11 12 13 >> m(3, :) ans = 31 32 33 >> m(:, 2) ans = 12 22 32

  8. size function >> m = ones(4, 7); >> size(m) ans = 4 7 >> [rsize csize] = size(m) rsize = 4 csize = 7 >> size(m(1, :)) ans = 1 7 >> length( m(1, :)) ans = 7 >> length( m(:, 1)) ans = 4

  9. Programming Example : max function max=x(v) max = -inf; for i = 1:length(v(1, :)) for j = 1:length(v(:, 1)) if (v(i, j) > max) max = v(i, j); end end end

  10. Adding two matrices • Add corresponding elements of two matrices • Allow matrices to be of any sizes • Assume that the missing elements are 0. • Example: for [1;2] and [10, 20], produce: 11 20 2 0

  11. Adding Matrices Example >> v1 = ones(2,3) v1 = 1 1 1 1 1 1 >> v2 = ones(4, 2) v2 = 1 1 1 1 1 1 1 1 >> x(v1, v2) ans = 2 2 1 2 2 1 1 1 0 1 1 0

  12. function sum=sum_matrices(v1, v2) nrows1 = length(v1(:, 1)); nrows2 = length(v2(:, 1)); ncols1 = length(v1(1, :)); ncols2 = length(v2(1, :)); nrows = max([ nrows1 nrows2 ]); ncols = max([ ncols1 ncols2 ]); sum = zeros(nrows, ncols); for i = 1: nrows for j = 1: ncols n1 = 0; n2 = 0; if ( i <= nrows1 && j <=ncols1) n1 = v1(i, j); end if ( i <= nrows2 && j <=ncols2) n2 = v2(i, j); end sum(i, j) = n1 + n2; end end

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