1. 軟體實作與計算實驗 1  Roots of nonlinear functions  Nested FOR loops Lecture 5II

2. 軟體實作與計算實驗 2 Nonlinear system

3. 軟體實作與計算實驗 3 A set of nonlinear functions

4. 軟體實作與計算實驗 4 function F = myfun(x) F(1) = x(1).^2 + x(2)^2-4; F(2) = x(1) - x(2); return Function evaluation

5. 軟體實作與計算實驗 5 x=linspace(-2,2); plot(x,x); hold on; plot(x,sqrt(4-x.^2)) plot(x,-sqrt(4-x.^2))

6. 軟體實作與計算實驗 6 Least square of nonlinear functions

7. 軟體實作與計算實驗 7 x0= ones(1,2)*2; x = lsqnonlin(@myfun,x0) Find a zero y=myfun(x); sum(y.^2) CHECKING

8. 軟體實作與計算實驗 8 Multiple roots x0= ones(1,2)*2; x = lsqnonlin(@myfun,x0) v=[v;x]; plot(x(1),x(2),'o'); v=[] for i=1:n demo_lsq.m

9. 軟體實作與計算實驗 9

10. 10 function F = myfun2(x) F(1) = 2*x(1).^2 + x(2)^2-24; F(2) = x(1).^2 - x(2).^2+12; return Function evaluation

11. 軟體實作與計算實驗 11 x0= ones(1,2)*2; x = lsqnonlin(@myfun2,x0) Find a zero y=myfun2(x); sum(y.^2) CHECKING

12. 軟體實作與計算實驗 12 Multiple roots x0= ones(1,2)*2; x = lsqnonlin(@myfun2,x0) v=[v;x]; plot(x(1),x(2),'o'); v=[] for i=1:n

13. 軟體實作與計算實驗 13 x=linspace(-5,5); plot(x,sqrt(24-2*x.^2),'r');hold on; plot(x,-sqrt(24-2*x.^2),'r') plot(x,sqrt(12+x.^2),'b') plot(x,-sqrt(12+x.^2),'b')

14. 軟體實作與計算實驗 14 Demo_lsq_2c source code

15. 軟體實作與計算實驗 15

16. 軟體實作與計算實驗 16 function F = myfun3(x) F(1) = x(1).^2 -2* x(2)^2-2; F(2) = x(1).*x(2) -2; return Function evaluation

17. 軟體實作與計算實驗 17 x=linspace(-3,3); x=x(find(abs(x) > 0.1)); plot(x,sqrt((x.^2-2)/2),'r');hold on; plot(x,-sqrt((x.^2-2)/),'r') x=linspace(0.5,3); plot(x,2./x,'b'); x=linspace(-0.5,-3); plot(x,2./x,'b')

18. 軟體實作與計算實驗 18 x0= ones(1,2)*2; x = lsqnonlin(@myfun3,x0) Find a zero y=myfun3(x); sum(y.^2) CHECKING

19. 軟體實作與計算實驗 19 Multiple roots x0= ones(1,2)*2; x = lsqnonlin(@myfun3,x0) v=[v;x]; plot(x(1),x(2),'o'); v=[] for i=1:n

20. 軟體實作與計算實驗 20 demo_lsq_hyperbola.txt two_hyperbola.txt

21. 軟體實作與計算實驗 21 Matrix Multiplication C=A*B C(i,j)=A(i,:) *B(:,j) for all i,j

22. 軟體實作與計算實驗 22 Nested FOR Loops C(i,j)=A(i,:) *B(:,j) [n,d1]=size(A);[d2,m]=size(B) for i=1:n for j=1:m

23. 軟體實作與計算實驗 23 [n,d1]=size(A);[d2,m]=size(B); for i=1:n for j=1:m C(i,j)=A(i, :) *B(:,j); end

24. 軟體實作與計算實驗 24 Constrained optimization Inequality constraint Nonlinear equality

25. 軟體實作與計算實驗 25 Constrained optimization

26. 軟體實作與計算實驗 26 Constraints Lower bound and upper bound Equality constraint Inequality constraint

27. 軟體實作與計算實驗 27 Constraints Lower bound Upper bound Inequality constraints

28. 軟體實作與計算實驗 28 Demo_conop2 function demo_conop2() lb =[-2 0]; ub =[10,10]; Aeq=[-1 1];beq=[0]; A=[];b=[]; x = fmincon(@fun,[1 1],A,b,Aeq,beq,lb,ub) x(1).^2+x(2).^2 return function y = fun(x) y = (x(1).^2+x(2).^2-13).^2; return demo_conop2.m

29. 軟體實作與計算實驗 29 function y = fun(x) y = (x(1).^2+x(2).^2-13).^2; return Objective function

30. 軟體實作與計算實驗 30 Calling fmincon x = fmincon(@fun,[1 1],A,b,Aeq,beq,lb,ub) objective function initial guess linear equality inequality Lower and upper bound

31. 軟體實作與計算實驗 31 Random variable Sample space S={A,T,C,G} X is a discrete random variable with sample space S.

32. 軟體實作與計算實驗 32 Generative model papa ptpt pcpc pgpg A TCG Flip-flop gatcacaggt

33. 軟體實作與計算實驗 33 Partition 0 1 Knots partition [0,1] into four intervals respectively with lengths,

34. 軟體實作與計算實驗 34 r=rand; Tag= (r c(1))+3*(r c(2))+4*(r c(3)) switch Tag case 1 s=[s 'A']; case 2 s=[s 'T']; case 3 s=[s 'C']; case 4 s=[s 'G']; end

35. 軟體實作與計算實驗 35 Sequence generation Emulation of a generative model for creation of an atcg sequence

36. 軟體實作與計算實驗 36 FOR Loops r=rand; switch r … end input p,m n=length(p) p_sum=0;s=[]; for i=1:n for j=1:m p_sum=p_sum+p(i); c(i)=p_sum;

37. 軟體實作與計算實驗 37 Mixture model papa ptpt pcpc pgpg A TCG Flip-flop papa ptpt pcpc pgpg A TCG

38. 軟體實作與計算實驗 38 Mixture model According to probabilities, and each time one of two joined models is selected to generate a character Created characters are collected to form an atcg sequence

39. 軟體實作與計算實驗 39 Hidden Markov model 12 papa ptpt pcpc pgpg A TCG papa ptpt pcpc pgpg A TCG

40. 軟體實作與計算實驗 40 Transition probability