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

軟體實作與計算實驗 2 Nonlinear system

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

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

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))

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

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

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

軟體實作與計算實驗 9

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

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

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

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')

軟體實作與計算實驗 14 Demo_lsq_2c source code

軟體實作與計算實驗 15

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

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')

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

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

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

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

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

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

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

軟體實作與計算實驗 25 Constrained optimization

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

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

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 = 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

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

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

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.

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

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

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

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

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;

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

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

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

軟體實作與計算實驗 40 Transition probability