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Handling Arrays 2/2

Handling Arrays 2/2. Numerical Computing with . MATLAB for Scientists and Engineers. You will be able to. Add, delete, permute all or sum of the vectors and matrices , Sort and search matrix elements, Change the shape of the matrix,

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Handling Arrays 2/2

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  1. Handling Arrays 2/2 Numerical Computing with . MATLAB for Scientists and Engineers

  2. You will be able to • Add, delete, permute all or sum of the vectors and matrices, • Sort and search matrix elements, • Change the shape of the matrix, • Flip, Rotate and Shift the matrix, • Manipulate 2D images

  3. Padding a Column • Inserting a column at a larger index than the size automatically fills in-betweens with zeros. a= [1 2 3; 4 5 6; 7 8 9] a(:,5)=[8 8 8]' 8 0 1 2 3 1 2 3 8 0 4 5 6 4 5 6 8 0 7 8 9 7 8 9

  4. Column Permutation • Use permuted array indexing a b=a(:,end:-1:1) c=a(:,[2 3 1]) 1 2 3 1 1 2 3 3 2 4 5 6 4 4 5 6 6 5 7 8 9 7 7 8 9 9 8

  5. Reshaping • Change matrix dimensions b=reshape(a,2,6) a 3 8 1 7 2 9 1 2 3 6 11 4 10 5 12 4 5 6 b=reshape(a,3, [ ] ) 7 8 9 6 1 10 8 10 11 12 9 4 2 11 12 7 5 3

  6. Replicate Array • Use the given matrix as the tile in order to produce a larger matrix. a b = repmat(a(2:3,:), 2, 2) 4 5 6 4 5 6 1 2 3 7 8 9 7 8 9 4 5 6 7 8 9 4 5 6 4 5 6 7 8 9 7 8 9 10 11 12

  7. Single Indexing • Looking at a matrix as a vector a sub2ind(size(a),3,2) 7 1 2 3 1 1 5 9 4 5 6 b=a(7) 8 2 6 2 10 7 8 9 3 [r c] = ind2sub(size(a),10) 7 3 11 10 11 12 4 r=2 c=3 8 4 12 1 2 3

  8. Logical Arrays a=-3:3 -3 -2 -1 0 1 2 3 1 1 0 0 0 1 1 abs(a) > 1 Logical Values -3 -2 2 3 a(abs(a) > 1) 1 -3 -1 2 3 a(logical([1010111]))

  9. Scalar Expansion • Filling matrices with a single value a=3 b=a(ones(2,3)) b(:) = 2 3 3 3 2 2 2 3 3 3 2 2 2 b=true(2,3) b(2,2:3)=false 1 1 1 1 1 1 1 1 1 1 0 0

  10. Sorting Arrays • Sort the elements in ascending or descending order. x=randperm(6) 2 3 5 4 6 1 xs = sort(x) 1 2 3 4 5 6 xs = sort(x,'descend') 6 5 4 3 2 1 [xs,idx]=sort(x) xs 1 2 3 4 5 6 idx 6 1 2 4 3 5

  11. Sorting Matrices • The default is the column-wise sorting. a=floor(10*rand(3,4)) sx=sort(a) 4 2 0 5 5 6 3 7 4 2 0 8 8 8 6 8 8 6 6 5 5 8 3 7 sx=sort(a,2) 0 2 4 8 5 6 6 8 for row-wise sorting 3 5 7 8

  12. Sort Using Pivot • Get sorting index and apply permutation. [tmp,idx]=sort(A(:,3)) A=floor(10*rand(3,4)) idx 1 4 2 0 8 3 8 6 6 5 2 5 8 3 7 As = A(idx,:) 4 2 0 8 5 8 3 7 8 6 6 5

  13. Sub-array Searching 1/2 • Substituting all elements larger than 7 to 0 [r,c] = find(A>7) r c A=floor(10*rand(3,4)) 2 1 4 2 0 8 3 2 8 6 6 5 1 4 5 8 3 7 4 2 0 0 0 6 6 5 k=find(A>7); A(k)=0 5 0 3 7

  14. Sub-array Searching 2/2 • First two or last two meeting the condition a=randperm(7) 3 4 6 2 1 7 5 2 3 6 7 find(a>3) 2 3 find(a>3,2) 6 7 find(a>3,2,'last')

  15. Minimum and Maximum • The minimum (or maximum) value and the corresponding index a 3 1 6 2 1 7 5 1 min(a) 7 max(a) 1 2 [m,i]=min(a) 7 6 [M,j]=max(a) m i M j 2 5 find(a==m) 6 find(a==M)

  16. Min / Max of a Matrix • The default is column-wise operation. a = randn(3,7); b = 10*a; c = floor(b) 1 8 4 6 3 5 8 6 8 8 8 2 7 5 3 5 8 6 3 3 3 m 1 5 4 6 2 3 3 [m,i]=min(a) 1 3 1 1 2 3 3 i 1 min(min(a))

  17. Flipping and Rotating • Matrices can be flipped, rotated and shifted. flipud(a) fliplr(a) a rot90(a) rot90(a,2) 1 2 3 4 5 6 circshift(a,1) circshift(a,-1) 7 8 9 circshift(a,[0 1]) circshift(a,[0 -1])

  18. Upper, Lower and Diagonal Matrix • Various matrices based on the original matrix d=diag(a) c=diag(d) 1 1 0 0 5 0 5 0 a 9 0 0 9 1 2 3 4 5 6 1 0 0 1 2 3 7 8 9 4 5 0 0 5 6 7 8 9 0 0 9 U=triu(a) U=tril(a)

  19. Grayscale Image 1/2 • Gray scale image is a 2-D matrix • value: 0~256 lovetriangle.m M = imread('lovetriangle.jpg'); figure(1), imshow(M); figure(2), imshow(M(5:88,215:335)); S = M; % Add photo frame S(1:5,:) = 0; S(end-5:end,:) = 0; S(:,1:5) = 0; S(:,end-5:end) = 0; figure(3), imshow(S); Black photo frame

  20. Grayscale Image 2/2 • Matrix operations apply to grayscale images M fliplr(M) triu(M) M([M<5])=250 circshift(M,[0 160]) flipud(M)

  21. Color Image • Color image is a 3-D matrix • 2x2 matrix of pixels • Each pixel is an [R G B] array • R, G, B values: 0~255 squares.m S = uint8(zeros(100,100,3)); S( 1: 50, 1: 50,1) = 255; % red S( 1: 50,51:100,2) = 255; % green S(51:100, 1: 50,3) = 255; % blue S(51:100,51:100,1:2) = 255; % yellow figure(1), imshow(S);

  22. Exercise 1 – Color Photo Frame • Choose any photo you like and add color photo frame outside of the photo. You may choose the color of the photo frame as you like.

  23. Solution 1 • Script and Screenshot photo_frame.m

  24. Exercise 2 – Photo Puzzle • Cut a photo into 2x2 pieces and put them in a random position.

  25. Solution 2 • Script and Screenshot puzzle2x2.m

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