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Lecture 10 Vector codes

Lecture 10 Vector codes. Matlab compiler Vector codes Hyper-plane fitting Distances between points Product of two matrices. Hanoi Tower Play Panel. PlayHanoiTower.m PlayHanoiTower.fig. mcc. Use mcc instruction to compile a matlab function. mcc –m PlayHanoiTower.m. HANOI TOWER.

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Lecture 10 Vector codes

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  1. Lecture 10 Vectorcodes • Matlab compiler • Vector codes • Hyper-plane fitting • Distances between points • Product of two matrices 軟體實作與計算實驗

  2. Hanoi Tower Play Panel PlayHanoiTower.m PlayHanoiTower.fig 軟體實作與計算實驗

  3. mcc Use mcc instruction to compile a matlab function mcc –m PlayHanoiTower.m 軟體實作與計算實驗

  4. HANOI TOWER HANOI.m 軟體實作與計算實驗

  5. Flow chart: move n disks from a to c function HANOI(n,a,b,c) n==1 %Move n-1disks from a to b HANOI(n-1,a,c,b); fprintf('%d -> %d\n',a,c); return %Move 1 disk from a to c HANOI(1,a,b,c); %Move n-1 disks from b to c HANOI(n-1,b,a,c); return 軟體實作與計算實驗

  6. Hyper-plane fitting 軟體實作與計算實驗

  7. d=5; N=1000; x=rand(N,d)*2-1; a= rand(d,1);b=rand(1,1); y=x*a+rand(N,1)*0.2-0.1; Sampling 軟體實作與計算實驗

  8. Mesh plot_2D.m 軟體實作與計算實驗

  9. Minimization 軟體實作與計算實驗

  10. Derivation of normal equations 軟體實作與計算實驗

  11. Derivation 軟體實作與計算實驗

  12. Derivation 軟體實作與計算實驗

  13. Derivation 軟體實作與計算實驗

  14. Derivation 軟體實作與計算實驗

  15. Normal equations 軟體實作與計算實驗

  16. d=3 軟體實作與計算實驗

  17. Function Ce(x,y) • Head: function C=Ce(x,y) • Body: • [N,d]=size(x); • Set C to zeros(d+1,d+1) • for m=1:d for n=1:d for i=1:N C(m,n) = C(m,n) + x(i,m)*x(i,n) • for m=1:d for i=1:N Add C(m,d+1) = C(m,d+1) + x(i,m)*y(i) • For m=1:d for i=1:N C(d+1,n) = C(d+1,n) + x(i,n) • C(d+1,d+1) = N 軟體實作與計算實驗

  18. Scalar code Ce.m 軟體實作與計算實驗

  19. Vector code I A=[x ones(N,1)]; C=A'*A;e=A'*y; u=inv(C)*e; 軟體實作與計算實驗

  20. Vector code I A=[x ones(N,1)]; C=A'*A;e=A'*y; u=C/e; 軟體實作與計算實驗

  21. Demo_hp demo_hp.m 軟體實作與計算實驗

  22. d=100; N=1000 absolute difference = 0.000 cpu time: 0.234 0.047 in sec time ratio- scalar to vector : 5.000 軟體實作與計算實驗

  23. demo_hp(500,2000) absolute difference = 0.000 cpu time: 12.391 0.656 in sec time ratio- scalar to vector : 18.881 軟體實作與計算實驗

  24. Vector code vs. sequential code • For-loop • Inefficient • Time consuming • Speed up • Vector code 軟體實作與計算實驗

  25. Distances between high dimensional data points 軟體實作與計算實驗

  26. MyDistance • Head: D=MyDisrtance(x) • Body: • [N,d]=size(x); D=zeros(N,N); • For i=1:N For j=1:N for k=1:d D(i,j)=D(i,j)+(x(i,k)-x(j,k))^2; D(i,j)=sqrt(D(i,j)); 軟體實作與計算實驗

  27. Scalar code Mydistance.m 軟體實作與計算實驗

  28. A=sum(X.^2,2)*ones(1,N); C=A'; B=X*X'; DD=A-2*B+C; 軟體實作與計算實驗

  29. Execution file demo_distance.m demo_distance.exe 軟體實作與計算實驗

  30. Example >> demo_distance Data size:1000 Dimension:20 cpu time: 14.922 0.125 in sec time ratio- scalar to vector : 119.375 Absolute difference:0.000 Press a key to return 軟體實作與計算實驗

  31. Matrix multiplication A, B denote matrices respectively with size pxq and qxr 軟體實作與計算實驗

  32. Scalar rule 軟體實作與計算實驗

  33. Matrix multiplication Head: C=myMM(A,B) Body [p,q]=size(A);[q,r]=size(B);C=zeros(p,r); for i=1:p for j=1:r for k=1:q C(i,j)=C(i,j)+ A(i,k)*B(k,j) 軟體實作與計算實驗

  34. Example: matrix multiplication p=500;q=1000;r=500; A=rand(p,q); B=rand(q,r); for i=1:p for j=1:r sv=0; for k=1:q sv=sv+A(i,k)*B(k,j); end C(i,j)=sv; end end 軟體實作與計算實驗

  35. Vector code • Matlab built-in instruction C=A*B 軟體實作與計算實驗

  36. Demo_product demo_product.m 軟體實作與計算實驗

  37. cputime • Instruction: cputime demo_cputime.m 軟體實作與計算實驗

  38. P=300 cpu time: 1.766 0.125 in sec time ratio- scalar to vector : 14.125 absolute difference:0.000000 軟體實作與計算實驗

  39. P=500 cpu time: 8.750 0.531 in sec time ratio- scalar to vector : 16.471 absolute difference:0.000000 軟體實作與計算實驗

  40. P=800 cpu time: 39.016 2.203 in sec time ratio- scalar to vector : 17.709 absolute difference:0.000000 軟體實作與計算實驗

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