Integration for a range of values with variable limits

Question

Keelan Toal 2015-12-18

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链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/260945-integration-for-a-range-of-values-with-variable-limits

评论： Keelan Toal 2015-12-19

采纳的回答： Walter Roberson

在 MATLAB Online 中打开

Hi all,

I need to solve the following equation for each individual value of f where f=0:0.01:10:

The equation is for MSAR in the code below, with the intention of getting a range of RMSAR values for a given f.

K1=274350; C1=11040; K2=414000; C2=16000;
M=13200; L1=2.34; L2=2.885; K=2.310;
I=M*(K^2);
a1=46.85*(10^-4); b1=0.19;
syms f
w=f*2*pi;
B11=K1+K2-M*(w^2)+1i*w*(C1+C2);
B12=K2*L2-K1*L1+1i*w*(-C1*L1+C2*L2);
B13=-K1-1i*w*C1;
B21=K2*L2-K1*L1+1i*w*(-C1*L1+C2*L2);
B22=K1*(L1^2)+K2*(L2^2)-I*(w^2)+1i*w*(C1*L1^2+C2*L2^2);
B23=K1*L1+1i*w*C1*L1;
B31=0; B32=0; B33=1;
S1=K2+1i*w*C2;
S2=K2*L2+1i*w*C2*L2;
S3=0.975;
B(1,1)=B11; B(1,2)=B12; B(1,3)=B13;
B(2,1)=B21; B(2,2)=B22; B(2,3)=B23;
B(3,1)=B31; B(3,2)=B32; B(3,3)=B33;
S(1,1)=S1; S(2,1)=S2; S(3,1)=S3;
T=B\S;
hif=T(1,:)';
G1=a1*exp((-b1)*f);
MSARn=@(f)((abs(hif))^2).^(f^4)*G1;
iMSARn=int(MSARn,0.89*f,1.12*f);
MSAR=((2*pi)^4)*iMSARn;
RMSAR=MSAR.^0.5;

When I try running the code, it's incredibly slow. I left it going over night and it still wasn't done. So I need a more practical method as this is only a section of a larger code. Am I correct in thinking that only 'int' accepts variable integral limits? I've tried 'quad' in a loop but it still sees the limits as non-scalar:

for k=1:1:1001;
    f(k)=(k-1)/100;
    iMSARn(k)=quad(@PSD_Opt_int_loop,[0.89*f(k),1.21*f(k)]);
end

Thanks in advance.

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Answer 1

Walter Roberson 2015-12-18

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https://ww2.mathworks.cn/matlabcentral/answers/260945-integration-for-a-range-of-values-with-variable-limits#answer_203718

在 MATLAB Online 中打开

iMSARn(k)=quad(@PSD_Opt_int_loop, 0.89*f(k), 1.21*f(k));

Notice no []

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Keelan Toal 2015-12-19

在 MATLAB Online 中打开

That solves that problem, thanks.

However, I'm having further issues. The code runs entirely but my results are way out. Can you see any obvious issues with my code? Assuming my constants/equations are correct.

function MSARn = Func_PSD2 (f)
K1=274350; C1=11040; K2=414000; C2=16000;
M=13200; L1=2.34; L2=2.885; K=2.310;
I=M*(K^2);
a1=46.85*(10^-4); b1=0.19;
w=f*2*pi;
B11=K1+K2-M*(w.^2)+1i*w*(C1+C2);
B12=K2*L2-K1*L1+1i*w*(-C1*L1+C2*L2);
B13=-K1-1i*w*C1;
B21=K2*L2-K1*L1+1i*w*(-C1*L1+C2*L2);
B22=K1*(L1^2)+K2*(L2^2)-I*(w.^2)+1i*w*(C1*(L1^2)+C2*(L2^2));
B23=K1*L1+1i*w*C1*L1;
B31=0; B32=0; B33=1;
S1=K2+1i*w*C2;
S2=K2*L2+1i*w*C2*L2;
S3=0.975;
b11=size(B11,2);
B11p=permute(reshape(B11',1,b11,[]),[1 3 2]);
B12p=permute(reshape(B12',1,b11,[]),[1 3 2]);
B13p=permute(reshape(B13',1,b11,[]),[1 3 2]);
B21p=permute(reshape(B21',1,b11,[]),[1 3 2]);
B22p=permute(reshape(B22',1,b11,[]),[1 3 2]);
B23p=permute(reshape(B23',1,b11,[]),[1 3 2]);
S1p=permute(reshape(S1',1,b11,[]),[1 3 2]);
S2p=permute(reshape(S2',1,b11,[]),[1 3 2]);
B=zeros(3,3,b11);
B(1,1,:)=B11p; B(1,2,:)=B12p; B(1,3,:)=B13p;
B(2,1,:)=B21p; B(2,2,:)=B22p; B(2,3,:)=B23p;
B(3,1,:)=B31; B(3,2,:)=B32; B(3,3,:)=B33;
S(1,1,:)=S1p; S(2,1,:)=S2p; S(3,1,:)=S3;
T(:,:,1)=abs(B(:,:,1))\abs(S(:,:,1));
T(:,:,2)=abs(B(:,:,2))\abs(S(:,:,2));
if size(B,3)>2
    T(:,:,3)=abs(B(:,:,3))\abs(S(:,:,3));
end
if size(B,3)>3
    T(:,:,4)=abs(B(:,:,4))\abs(S(:,:,4));
end
if size(B,3)>4
    T(:,:,5)=abs(B(:,:,5))\abs(S(:,:,5));
end
if size(B,3)>5
    T(:,:,6)=abs(B(:,:,6))\abs(S(:,:,6));
end
if size(B,3)>6
    T(:,:,7)=abs(B(:,:,7))\abs(S(:,:,7));
end
hif=((squeeze(T(1,:,:)))');
G1=a1*exp((-b1)*f);
MSARn=(hif.^2).*(f.^4).*G1;
end

and

clear
clc
f=zeros(1,1001); iMSARn=zeros(1,1001);
for k=1:1:1001;
    f(k)=(k)/100;
    iMSARn(k)=quad(@Func_PSD2,0.89*f(k),1.12*f(k));
end
MSAR=((2*pi)^4)*iMSARn;
RMSAR=MSAR.^0.5;
plot(f,RMSAR)