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赵小夭annie

铁虫 (初入文坛)

应助: 0 (幼儿园)
金币: 20
帖子: 15
在线: 3.9小时
虫号: 5708409
注册: 2017-02-23
性别: MM
专业: 机械动力学

[求助] 怎样在fsolve中对初值进行循环并缩短运行时间？

本人在解四个非线性方程，每一个非线性方程需要给定对应初值才能解，本人给初值写了四个循环，分别对应的是t0i,t1i0,t2i0,t3i0。要求是当非线性方程解出的结果满足一定条件时则这组初值可选，问题在于四个for循环计算时间很长，请问大家有何方法可以改进？我用了fsolve解初值，把初值设置成了变量。以下为可运行程序，但是运行时间很长。

% Find the initial condition
clc
clear
tic
global t1i C1 C2 a d d1 d2 omega w yi t0i t2i t3i t4i t1i0 t2i0 t3i0 t4i0 j d3 d4 C3 C4

a=20;
c=100;
d=0.5;
w=sqrt(c-d^2);
j=0;
m=0;
n=1;
A=zeros(10,n);
omega=4.8;
T=2*pi/omega;
t4i0=t0i+T;
d1=(c-omega^2)/((c-omega^2)^2+(2*d*omega)^2);
d2=(2*d*omega)/((c-omega^2)^2+(2*d*omega)^2);
d3=(-1)/(omega^2+4*d^2);
d4=(2*d)/((omega)*(omega^2+4*d^2));

% 以下为循环

for yi=5:0.1:13
for t0i=0

(2*pi/omega)/500)

2*pi/omega)
for t1i0=(1/5)*T+t0i:1

1/4)*T+t0i
for t2i0=(2/5)*T+t0i:1

1/2)*T+t0i
for t3i0=(3/5)*T+t0i:1

4/5)*T+t0i




C1=-a*(d1*cos(omega*t0i)+d2*sin(omega*t0i));
C2=(1/w)*(yi-a*((d2*d-d1*omega)*sin(omega*t0i)+(d1*d+d2*omega)*cos(omega*t0i)));

t1i=fsolve(@(t1i) (C1*cos(w*(t1i-t0i))+C2*sin(w*(t1i-t0i)))*exp(-d*(t1i-t0i))+a*(d1*cos(omega*t1i)+d2*sin(omega*t1i)),t1i0);
x2=((C2*w-C1*d)*cos(w*(t1i-t0i))-(C1*w+C2*d)*sin(w*(t1i-t0i)))*exp((-d)*(t1i-t0i))-a*omega*(d1*sin(omega*t1i)-d2*cos(omega*t1i));

C3=(1/(-2*d))*(x2+(a*omega)*(d3*sin(omega*t1i)-d4*cos(omega*t1i)));
C4=(1/(2*d))*(x2+2*d*1-(a/omega)*sin(omega*t1i));

t2i=fsolve(@(t2i) C3*exp(-2*d*(t2i-t1i))+C4+a*(d3*cos(omega*t2i)+d4*sin(omega*t2i))+1,t2i0);
x4=-2*d*C3*exp(-2*d*(t2i-t1i))-a*omega*(d3*sin(omega*t2i)-d4*cos(omega*t2i));

C1=-a*(d1*cos(omega*t2i)+d2*sin(omega*t2i));
C2=(1/w)*(x4-a*((d2*d-d1*omega)*sin(omega*t2i)+(d1*d+d2*omega)*cos(omega*t2i)));

t3i=fsolve(@(t3i) (C1*cos(w*(t3i-t2i))+C2*sin(w*(t3i-t2i)))*exp(-d*(t3i-t2i))+a*(d1*cos(omega*t3i)+d2*sin(omega*t3i)),t3i0);
x6=((C2*w-C1*d)*cos(w*(t3i-t2i))-(C1*w+C2*d)*sin(w*(t3i-t2i)))*exp((-d)*(t3i-t2i))-a*omega*(d1*sin(omega*t3i)-d2*cos(omega*t3i));

C3=(1/(-2*d))*(x6+(a*omega)*(d3*sin(omega*t3i)-d4*cos(omega*t3i)));
C4=(1/(2*d))*(x6-2*d-(a/omega)*sin(omega*t3i));

t4i=fsolve(@(t4i) C3*exp(-2*d*(t4i-t3i))+C4+a*(d3*cos(omega*t4i)+d4*sin(omega*t4i))-1,t0i+T);
x8=-2*d*C3*exp(-2*d*(t4i-t3i))-a*omega*(d3*sin(omega*t4i)-d4*cos(omega*t4i));

%选初值的条件

  if  abs(t4i-T-t0i)<0.1 && abs(x8-yi)<0.1 && t4i>t3i && t3i>t2i && t2i>t1i && x2<0 && x4<0 && x6>0 && x8>0
   figure(1)
   hold on
   axis([0 8 0 20])
   plot(omega,yi,'o')
   A(:,n)=[t0i;yi;t1i;x2;t2i;x4;t3i;x6;t4i;x8];
   n=n+1;
  end
  j=j+1;
  j
                  end
            end
         end
end
end

toc
load chirp
sound(y,Fs)

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