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# problems about solve exponential function

Asked by xueqi on 13 Feb 2013

Hi,

please have a look at a part of my code in the function maxmin0. The general idea is that I use solve to get the solution for a exponential function funcion, and then assign the solution to a variable called pf5, which is the output for maxmin0. The function runs well itself. But when I call this function in another function, it always show a error message . I am doubting it is the way I write the this function is not smart and so there is problem when it is being called...Could you help to check that?

Here is the code

```    if true
%  p1=1-lb2-lb3;
p2=lb2;
p3=lb3;
if (d2(i,3)==d2(i,1))
pf5(2,i)=[0;0];
eu(i)=-Inf;
else
coef1=d1(i,1)+(d1(i,1)-d1(i,3))*d2(i,1)/(d2(i,3)-d2(i,1));
coef2=d1(i,2)+(d1(i,1)-d1(i,3))*d2(i,2)/(d2(i,3)-d2(i,1));
coef3=d1(i,3)+(d1(i,1)-d1(i,3))*d2(i,3)/(d2(i,3)-d2(i,1));
syms x
f5=simplify(p1*coef1*exp(-r*coef1*x)+p2*coef2*exp(-r*coef2*x)+p3*coef3*exp(-r*coef3*x));
y5(i)=solve(f5,x);
pf5(1,i)=double(y5(i));
end```

and here is the error message

```Warning: Explicit solution could not be found.
> In solve at 169
In maxmin0 at 138
In maxmin at 15
In beta at 18
In C:\Program Files\MATLAB\R2012a\toolbox\shared\optimlib\finDiffEvalAndChkErr.p>finDiffEvalAndChkErr at 26
In C:\Program Files\MATLAB\R2012a\toolbox\shared\optimlib\finitedifferences.p>finitedifferences at 128
In C:\Program Files\MATLAB\R2012a\toolbox\optim\optim\barrier.p>barrier at 135
In fmincon at 841
In main at 6
Error in MuPAD command: Subscripted assignment dimension mismatch
```
```Error in sym/subsasgn (line 1638)
```
```Error in maxmin0 (line 138)
y5(i)=solve(f5,x);
```
```Error in maxmin (line 15)
[PF0,eu0]=maxmin0(sub,DD);
```
```Error in beta (line 18)
mu = maxmin(sub,DD);
```
```Error in C:\Program Files\MATLAB\R2012a\toolbox\shared\optimlib\finDiffEvalAndChkErr.p>finDiffEvalAndChkErr (line 26)
```
```Error in C:\Program Files\MATLAB\R2012a\toolbox\shared\optimlib\finitedifferences.p>finitedifferences (line 128)
```
```Error in C:\Program Files\MATLAB\R2012a\toolbox\optim\optim\private\computeFinDiffGradAndJac.p>computeFinDiffGradAndJac (line 28)
```
```Error in C:\Program Files\MATLAB\R2012a\toolbox\optim\optim\barrier.p>barrier (line 135)
```
```Error in fmincon (line 841)
```
```Error in main (line 6)
```

xueqi on 13 Feb 2013

and it is also weird that I dont have this error (but the whole program still doesn't work )showing when I run the program in matlab 2010 but in 2012 there shows this error. So I think it might be the reason that the whole program doesn't work...

Walter Roberson on 15 Feb 2013

At the point of the solve(), could you show us what f5 is? I want to check for solutions myself.

xueqi on 16 Feb 2013

Hi do you mean the explicit expression for f5? The expression depends on the input of the function, and this error shows when the function in called in an optimization routine. So I cant know the exact input either... PS I have made the imrovement that add in if (isempty(y)==1) PF(i,1)=0; else PF(i,1)=double(y); end But this similar error still show!!!And this time it is 2010 shows this message...

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Answer by Carlos on 14 Feb 2013
Edited by Walter Roberson on 14 Feb 2013

When you execute this code in Matlab

```>> syms x;
>> f=-10*exp(-x);
>> solve(f,x)
>> isempty(a)
```
```ans =
```
`       1`

Whereas if you execute this code

```>> syms x;
>> f=x^2-4
>> solve(f,x)
>> isempty(a)
```
```ans =
```
`       0`

You can use the isempty command. If isempty returns true (1), it means your roots array is empty because there are no roots.

Carlos on 18 Feb 2013
`    yes a=solve(f,x),just to find out if the string is empty (which means matlab is unable to solve because the equation cannot be solved)`
xueqi on 18 Feb 2013

Hi, I have add in this bit in my code, it still shows me the same message. Can you think of the reason? Also can you go to my question here http://www.mathworks.com/matlabcentral/answers/63963-problems-about-solve-exponential-function

Carlos on 19 Feb 2013

Sorry, I cannot figure out the reason for different behaivours in different versions.

Answer by Carlos on 13 Feb 2013
Edited by Walter Roberson on 14 Feb 2013

In the warning message displayed by Matlab it says no solution has been found(just as it happens if the function has no roots), and exp(-ax) has no roots, this is what happens when I try the following code in Matlab

```>> syms x;
>> f=-10*exp(-x);
>> solve(f,x)
Warning: Explicit solution could not be found.
> In solve at 81
```
```ans =
```
```[ empty sym ]
```

However if there is no problem with Matlab 2010 this might not be the case, I just wanted you to consider the possibility the function has no roots.

## 1 Comment

xueqi on 13 Feb 2013

Yes I begin to think it may be the problems. So I think it would be better if I modify the code so that pf=0 if there is no solution. Could you offer any advice how to say 'if there is no solution' into matlab lauguage?