solve 4 equations with some unknowns parameters.

I'm attempting to solve this problem which is attached. But I faced ERROR. Any suggestions?

[Matt J]

We can't make suggestions until you tell us what the error is.

[Skill_s]

I have attached the .m file, however the error is below:

Error in ==> equation_2_8 at 13
sol = solve([eqn1, eqn2, eqn3, eqn4], [A, B, C, D]);

>> I do not know the exact meaning of error

[Matt J]

This looks like only part of the message. The full error message should give a reason, as well as the error location.

[madhan ravi]

when I ran your code it didn't have any errors instead it returned all zeros

[Stephan]

Which Matlab Release do you use? with R2018b i got the same result as Madhan.

[Skill_s]

I use R2010b

[Skill_s]

the messages of error is: ??? Error using ==> char Conversion to char from logical is not possible.

Error in ==> solve>getEqns at 169 vc = char(v);

Error in ==> solve at 67 [eqns,vars] = getEqns(varargin{:});

Error in ==> equation_2_8 at 13 sol = solve([eqn1, eqn2, eqn3, eqn4], [A, B, C, D]);

[madhan ravi]

do you have symbolic toolbox? type ver in command window to check whether you have that toolbox

[Skill_s]

I wrote "ver" in command window, the message is:

>> ver
-------------------------------------------------------------------------------------
MATLAB Version 7.11.0.584 (R2010b)
MATLAB License Number: 
Operating System: Microsoft Windows 7 Version 6.2 (Build 9200)
Java VM Version: Java 1.6.0_17-b04 with Sun Microsystems Inc. Java HotSpot(TM) 64-Bit Server VM mixed mode
-------------------------------------------------------------------------------------
MATLAB                                                Version 7.11       (R2010b)
Simulink                                              Version 7.6        (R2010b)
Aerospace Blockset                                    Version 3.6        (R2010b)
Aerospace Toolbox                                     Version 2.6        (R2010b)
Bioinformatics Toolbox                                Version 3.6        (R2010b)
Communications Blockset                               Version 5.0        (R2010b)
Communications Toolbox                                Version 4.6        (R2010b)
Control System Toolbox                                Version 9.0        (R2010b)
Curve Fitting Toolbox                                 Version 3.0        (R2010b)
DO Qualification Kit                                  Version 1.3        (R2010b)
Database Toolbox                                      Version 3.8        (R2010b)
Datafeed Toolbox                                      Version 4.0        (R2010b)
EDA Simulator Link                                    Version 3.2        (R2010b)
Econometrics Toolbox                                  Version 1.4        (R2010b)
Filter Design HDL Coder                               Version 2.7        (R2010b)
Filter Design Toolbox                                 Version 4.7.1      (R2010b)
Financial Derivatives Toolbox                         Version 5.6        (R2010b)
Financial Toolbox                                     Version 3.8        (R2010b)
Fixed-Income Toolbox                                  Version 2.0        (R2010b)
Fixed-Point Toolbox                                   Version 3.2        (R2010b)
Fuzzy Logic Toolbox                                   Version 2.2.12     (R2010b)
Global Optimization Toolbox                           Version 3.1        (R2010b)
IEC Certification Kit                                 Version 1.3        (R2010b)
Image Acquisition Toolbox                             Version 4.0        (R2010b)
Image Processing Toolbox                              Version 7.1        (R2010b)
Instrument Control Toolbox                            Version 2.11       (R2010b)
MATLAB Builder EX                                     Version 1.3        (R2010b)
MATLAB Builder JA                                     Version 2.2        (R2010b)
MATLAB Builder NE                                     Version 3.2        (R2010b)
MATLAB Compiler                                       Version 4.14       (R2010b)
MATLAB Distributed Computing Server                   Version 5.0        (R2010b)
MATLAB Report Generator                               Version 3.9        (R2010b)
Mapping Toolbox                                       Version 3.2        (R2010b)
Model Predictive Control Toolbox                      Version 3.2.1      (R2010b)
Neural Network Toolbox                                Version 7.0        (R2010b)
Optimization Toolbox                                  Version 5.1        (R2010b)
Parallel Computing Toolbox                            Version 5.0        (R2010b)
Parallel Computing Toolbox                            Version 5.0        (R2010b)
Partial Differential Equation Toolbox                 Version 1.0.17     (R2010b)
RF Toolbox                                            Version 2.8        (R2010b)
Real-Time Workshop                                    Version 7.6        (R2010b)
Real-Time Workshop Embedded Coder                     Version 5.6        (R2010b)
Robust Control Toolbox                                Version 3.5        (R2010b)
Signal Processing Blockset                            Version 7.1        (R2010b)
Signal Processing Toolbox                             Version 6.14       (R2010b)
SimBiology                                            Version 3.3        (R2010b)
SimDriveline                                          Version 1.5.5      (R2010b)
SimElectronics                                        Version 1.5        (R2010b)
SimEvents                                             Version 3.1.1      (R2010b)
SimHydraulics                                         Version 1.8        (R2010b)
SimMechanics                                          Version 3.2.1      (R2010b)
SimPowerSystems                                       Version 5.3        (R2010b)
SimRF                                                 Version 3.0        (R2010b)
Simscape                                              Version 3.4        (R2010b)
Simulink 3D Animation                                 Version 5.2        (R2010b)
Simulink Control Design                               Version 3.2        (R2010b)
Simulink Design Optimization                          Version 1.2        (R2010b)
Simulink Design Verifier                              Version 1.7        (R2010b)
Simulink Fixed Point                                  Version 6.4        (R2010b)
Simulink Report Generator                             Version 3.9        (R2010b)
Simulink Verification and Validation                  Version 3.0        (R2010b)
Spreadsheet Link EX                                   Version 3.1.2      (R2010b)
Stateflow                                             Version 7.6        (R2010b)
Stateflow Coder                                       Version 7.6        (R2010b)
Statistics Toolbox                                    Version 7.4        (R2010b)
Symbolic Math Toolbox                                 Version 5.5        (R2010b)
System Identification Toolbox                         Version 7.4.1      (R2010b)
SystemTest                                            Version 2.6        (R2010b)
Video and Image Processing Blockset                   Version 3.1        (R2010b)
Wavelet Toolbox                                       Version 4.6        (R2010b)
>>

[Skill_s]

Thnks all the version of my windows is 10. Is it related to the version of windows?

[Star Strider]

The ver output disagrees with you:

MATLAB Version 7.11.0.584 (R2010b) 
Operating System: Microsoft Windows 7 Version 6.2 (Build 9200)
    ...
Symbolic Math Toolbox Version 5.5 (R2010b)
    ...

[Skill_s]

Thanks a lot. So, what should I do? Should I run another version of MATLAB?

Answer 1

[Bruno Luong]

Your problem looks like you find the EM field with 3 layers and 2 interfaces. The coefficients A, B, C, D gives the strength of different field components, they are linearly related because EM is linear. In order to solve with without getting trivial solution

A=B=C=D=0

You must for example fix one of them arbitrary, e.g.

A = 1

That left you with 4 linear equations and 3 unknowns. Then in order such system to have solution, you must have the linear system to have dependent equation, meaning determinant of the matrix is 0.

Write it down this probably gives the equation you looks for.

I don't have symbolic tbx to do this kind of calculation to confirm, it would be possible to carry out numerically me think.

[Skill_s]

Yes @ Bruno Luong . Thanks. The EM field with 3 layers. yeah you are right.

[Walter Roberson]

If you solve the first three equations for B, C, D, then you are left with

-A*(-(eps1*k3+eps3*k1)*(eps1*k2+eps2*k1)*exp(a*(2*k1-k3))+exp(-a*(2*k1+k3))*(-eps1*k3+eps3*k1)*(-eps1*k2+eps2*k1))/(2*eps3*k1*eps2*eps1) == 0

The obvious solution is A == 0, which then causes B, C, D to all be 0. If, on the other hand, (-(eps1*k3+eps3*k1)*(eps1*k2+eps2*k1)*exp(a*(2*k1-k3))+exp(-a*(2*k1+k3))*(-eps1*k3+eps3*k1)*(-eps1*k2+eps2*k1))/(2*eps3*k1*eps2*eps1) can be 0, then the equations would hold for all finite A, in which case there would be a family of solutions

B = A*((eps1*k3+eps3*k1)*exp(4*a*k1)+eps3*k1-eps1*k3)*exp(-a*(2*k1-k2+k3))/(2*eps3*k1)
C = -A*(eps1*k3-eps3*k1)*exp(-a*(k1+k3))/(2*eps3*k1)
D = A*(eps1*k3+eps3*k1)*exp(a*(k1-k3))/(2*eps3*k1)

which are linear in A.

[Skill_s]

Thanks a lot. @ Walter Roberson. thnks

[Bruno Luong]

Actually solving linear system is not what Skill interested, what he is interested is the the condition under which the 4 linear equation is dependent thus solvable.

This boils down to single equation of determinant. I shows here the solution he gives makes DET(M) = 0.

% Fake k, epsilon 1,2,3
k = rand(1,3);
eps = rand(1,3);
p = k./eps;

% compute solution a
r = ((p(1)+p(2))*(p(1)+p(3)))/((p(1)-p(2))*(p(1)-p(3)));
a = log(r)/(-4*k(1))

% Forming linear matrix
ep = exp(k*a);
em = exp(-k*a);

M = [em(3)      0           -ep(1)        -em(1);
     p(3)*em(3) 0           p(1)*ep(1)  -p(1)*em(1);
     0          em(2)       -em(1)        -ep(1);
     0          -p(2)*em(2)  p(1)*em(1)  -p(1)*ep(1)];

% verifies the 4 x  4 system is rank 3

rank(M)  
det(M)

Now if Walter who has access to Symb Tbx can show the opposite, started from

det(M) = 0

shows the solution of it is

r = ((p(1)+p(2))*(p(1)+p(3)))/((p(1)-p(2))*(p(1)-p(3)));
a = log(r)/(-4*k(1))

Then the problem is completely solved.

Answer 2

[Florian Augustin]

Hi,

I think you are using a modern syntax to call 'solve' that was not supported in R2010b. The equivalent call in R2010b would be

syms a A B C D eps1 eps2 eps3 k1 k2 k3;

eqn1 = (C*exp(k1*a))+(D*exp(-k1*a))-(A*exp(-k3*a));
eqn2 = ((-(C*k1)/eps1)*exp(k1*a))+(((D*k1)/eps1)*exp(-k1*a))-(((A*k3)/eps3)*exp(-k3*a));
eqn3 = (C*exp(-k1*a))+(D*exp(k1*a))-(B*exp(-k2*a));
eqn4 = ((-(C*k1)/eps1)*exp(-k1*a))+(((D*k1)/eps1)*exp(k1*a))+(((B*k2)/eps2)*exp(-k2*a));

sol = solve(eqn1, eqn2, eqn3, eqn4, A, B, C, D);

ASol = sol.A
BSol = sol.B
CSol = sol.C
DSol = sol.D

You can access the documentation for your release of MATLAB by typing 'doc solve' in the MATLAB interface.

Hope this helps,

-Florian

[Skill_s]

Thanks a lot for your guidance.

[Matt J]

@Skill93,

If Florian's answer was what you were looking for, then you should Accept-click it.

[Walter Roberson]

If I recall correctly, in R2010b, the syntax used for solve() was available but not clearly documented.

The problem was elsewhere: before R2011b, using relational expressions with symbolic expressions caused the expressions to be evaluated as a logical immediately. So the line

eqn1 = (C*exp(k1*a))+(D*exp(-k1*a))-(A*exp(-k3*a))==0;

built the expression on the left side, and immediately compared it to 0, found it was not identical, and immediately returned false into eqn1.

The workaround in those days was to not do the ==0 part on the equations: convert

eqn = A == B

to

eqn = (A) - (B)

And in those days, if you had an inequality such as

 eqn1 = (C*exp(k1*a))+(D*exp(-k1*a))-(A*exp(-k3*a)) > 3

then you would have to build it using character vectors,

 eqn1 = '(C*exp(k1*a))+(D*exp(-k1*a))-(A*exp(-k3*a)) > 3'

This would pretty much force you to use separate entries in the solve() command, like the

sol = solve(eqn1, eqn2, eqn3, eqn4, A, B, C, D);

that Florian shows, since [eqn1, eqn2, eqn3, eqn4] with character vectors would result in a single long character vector instead of multiple equations.

So, Florian's suggested code should work for the purpose, just not for exactly the reason that Florian indicated.

[Skill_s]

Yes @Walter Roberson said correctly. and the guidance of @ Florian Augustin , gives zero output. the purpose is to solve parametric solutions not numerically. May be I should change to higher version of MATLAB

[Stephan]

Executing your code in 2018b gives the same result. So you need a better approach.

[Walter Roberson]

MATLAB gives all 0.

If you work through the equations one by one doing stepwise elimination, then all 0 is the only solution.

[Skill_s]

Thanks all...