How to find the value from equations?

Question

Chuanjung Lin 2022-8-5

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1774370-how-to-find-the-value-from-equations

评论： Walter Roberson 2022-8-8

采纳的回答： Walter Roberson

在 MATLAB Online 中打开

Hi all,

I have a dataset (Ids) and equestion as the attachment.

Ids = [6.35E-06
18E-06
01E-06
84E-06
68E-06
52E-06
36E-06
20E-06
05E-06
89E-06
75E-06
60E-06
45E-06
31E-06
17E-06
03E-06
90E-06
76E-06
63E-06
50E-06
38E-06
25E-06
13E-06
01E-06
90E-06
78E-06
67E-06
56E-06
45E-06
35E-06
25E-06
15E-06
05E-06
95E-06
86E-06
77E-06
68E-06
60E-06
51E-06
43E-06
35E-06
28E-06
20E-06
13E-06
06E-06
95E-07
30E-07
68E-07
08E-07
50E-07
95E-07
41E-07
90E-07
41E-07
95E-07
51E-07
09E-07
69E-07
31E-07
95E-07
62E-07
31E-07
02E-07
75E-07
50E-07
27E-07
06E-07
77E-08
09E-08
60E-08
31E-08
20E-08
28E-08
52E-08
39E-09
11E-09
28E-09
14E-10
12E-10
28E-12
10E-13
54E-15
27E-16
-2.03E-16
-2.06E-16
78E-16
29E-16
-3.03E-16
10E-16];

where, the Wg = 6; Lg = 2.3;

may I know how to obtain the Ids'?

Here, I set Ids' = a , and code as following:

Wg = 6;
Lg = 2.3;
syms a
eqn = (1*10^(-5)).*(Wg./Lg)* log10( 1 + exp(a./5)) ./ ( 1 + exp(a./5))==Ids
S = solve(eqn);
S

when I click the run, it seems no response. Does this approach is correct?

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Answer 1

Walter Roberson 2022-8-5

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1774370-how-to-find-the-value-from-equations#answer_1021465

在 MATLAB Online 中打开

eqn = (1*10^(-5)).*(Wg./Lg)* log10( 1 + exp(a./5)) ./ ( 1 + exp(a./5))==Ids

IDS is a vector, so eqn is a vector. But syms a is a scalar symbolic variable.

S = solve(eqn);

You are asking to solve the vector of equations for the single scalar value for a that solves all of the equations simultaneously. That is not going to exist.

Are you looking for "best fit" or are you looking to solve each of the equations independently ?

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Walter Roberson 2022-8-5

编辑：Walter Roberson 2022-8-5

在 MATLAB Online 中打开

Ids = [6.35E-06

6.18E-06

6.01E-06

5.84E-06

5.68E-06

5.52E-06

5.36E-06

5.20E-06

5.05E-06

4.89E-06

4.75E-06

4.60E-06

4.45E-06

4.31E-06

4.17E-06

4.03E-06

3.90E-06

3.76E-06

3.63E-06

3.50E-06

3.38E-06

3.25E-06

3.13E-06

3.01E-06

2.90E-06

2.78E-06

2.67E-06

2.56E-06

2.45E-06

2.35E-06

2.25E-06

2.15E-06

2.05E-06

1.95E-06

1.86E-06

1.77E-06

1.68E-06

1.60E-06

1.51E-06

1.43E-06

1.35E-06

1.28E-06

1.20E-06

1.13E-06

1.06E-06

9.95E-07

9.30E-07

8.68E-07

8.08E-07

7.50E-07

6.95E-07

6.41E-07

5.90E-07

5.41E-07

4.95E-07

4.51E-07

4.09E-07

3.69E-07

3.31E-07

2.95E-07

2.62E-07

2.31E-07

2.02E-07

1.75E-07

1.50E-07

1.27E-07

1.06E-07

8.77E-08

7.09E-08

5.60E-08

4.31E-08

3.20E-08

2.28E-08

1.52E-08

9.39E-09

5.11E-09

2.28E-09

7.14E-10

1.12E-10

6.28E-12

2.10E-13

6.54E-15

3.27E-16

-2.03E-16

-2.06E-16

4.78E-16

3.29E-16

-3.03E-16

4.10E-16];

Wg = 6;

Lg = 2.3;

syms a

eqn = (1*10^(-5)).*(Wg./Lg)* log10( 1 + exp(a./5)) ./ ( 1 + exp(a./5))==Ids

eqn =

residue = sum((lhs(eqn)-rhs(eqn)).^2);

besta = vpasolve(diff(residue,a),a)

besta =

2.7066242730645905448917817746634

eqn2 = (1*10^(-5)).*(Wg./Lg)* log10( 1 + exp(a./5)) ./ ( 1 + exp(a./5)) == mean(Ids)

eqn2 =

besta2 = vpasolve(eqn2)

besta2 =

okay, so just taking the mean wasn't good enough ;-)

Chuanjung Lin 2022-8-5

Hi Roberson,

First of all, thank you for your feedback quickly. Acutally, I'm doing the ANN modeling. Because the Ids has large dynamic range from 4.1E-16 to 6.35E-6. So, I've to preproecess the Ids data for accurancy improvment. And I plan used the preproecess that paper mentioned. But, I don't know how to conduct it (Transfer the measurement Ids to Ids'). Thank you.

Walter Roberson 2022-8-8

Are you looking for "best fit" or are you looking to solve each of the equations independently ? The code I posted shows the best fit in a least-squares sense. If you want to solve each individually then loop or use arrayfun.

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