## solve equation without fsolve

### Max Bernstein (view profile)

on 18 Oct 2011

Hello,

I have the following equation that I'm trying to solve. I need to solve for T for a very long array of known RT

```function RT=RTD(T)
a=0.003925;
b=0.110361;
d=1.492690;
R0=100;
RT=R0*(1+a*(1+d/100)*T-a*d/100^2*T^2+a*b/100^3*T^3-a*b/100^4*T^4);
```

I dont think I have fsolve or symbolic toolbox installed. Is there anyway to automate this without using those?

Thanks

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### Naz (view profile)

on 19 Oct 2011

Assuming that each RT will yield four roots:

```a=0.003925;
```
```b=0.110361;
```
```d=1.492690;
```
```R0=100;
```
```T=zeros(4,length(RT));
```
```for n=1:length(RT)
```
`   T(:,n)=roots(-a*b/100^4*R0 a*b/100^3*R0 -a*d/100^2*R0 a*(1+d/100)*R0 (1-RT(n))*R0);`
```end
```

If you want to create an actual function, go to file->new->script and paste the following:

```function [T]=RTD(RT)
```
```a=0.003925;
```
```b=0.110361;
```
```d=1.492690;
```
```R0=100;
```
```T=zeros(4,length(RT));
```
```for n=1:length(RT)
```
`   T(:,n)=roots(-a*b/100^4*R0 a*b/100^3*R0 -a*d/100^2*R0 a*(1+d/100)*R0 (1-RT(n))*R0);`
```end
```
```end
```

Then you can call this function and pass your array of RT. The function will return you an array of T.

```T=RTD(RT)
```

P.S. Make sure there is enough parenthesis in the equation so the coefficients are calculated properly. I recommend to calculate the coefficients prior sending them to roots function. This also will save some time, since the coefficients will be calculated only once instead of each loop.

Walter Roberson

### Walter Roberson (view profile)

on 19 Oct 2011

You left out the [] in that roots() call, so this code will end up taking roots() of a scalar.

### Andrei Bobrov (view profile)

on 19 Oct 2011
```a=0.003925;
b=0.110361;
d=1.492690;
R0=100;
syms k T
cf = coeffs(k-R0*(1+a*(1+d/100)*T-a*d/100^2*T^2+a*b/100^3*T^3-a*b/100^4*T^4),T)
fcf = matlabFunction(cf(end:-1:1))
RTD = @(RT)cell2mat(arrayfun(@(x)roots(fcf(x)),RT,'un',0))
```

use function RTD

```T = RTD(RT)
```

Valerio

### Valerio (view profile)

on 18 Jul 2013

I have used your proposed solution, but the output variable of Temp = RTD(RT) is the sym T. What is the problem? Can you help me?

Thanks

### Walter Roberson (view profile)

on 18 Oct 2011
```roots( [R0*a*b, -100*R0*a*b, 10000*R0*a*d, -100000000*R0*a-1000000*R0*a*d, -100000000*R0+100000000*RT] )
```

Note that roots() can only process one set of coefficients at a time: it is not vectorized.