# Uniroot function in Rstan

**URL:** <https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965>\
**Category:** Modeling\
**Tags:** rstan\
**Created:** [August 15, 2021, 12:17pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965 "2021-08-15T12:17:35Z")\
**Posts on this page:** 14\
**Page:** 1

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**Author:** ![evihas](https://avatars.discourse-cdn.com/v4/letter/e/9dc877/32.png) [@evihas](https://discourse.mc-stan.org/u/evihas)\
**Post date:** [August 15, 2021, 12:17pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/1 "2021-08-15T12:17:35Z")

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Hi all stan users and developers,

Does someone know how to find roots for a equation of the form CDF\_fun(x) - prob = 0 in Rstan?

Thank you

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**Author:** ![martinmodrak](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/martinmodrak/32/133_2.png) [@martinmodrak](https://discourse.mc-stan.org/u/martinmodrak)\
**Post date:** [August 25, 2021, 12:42pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/2 "2021-08-25T12:42:52Z")

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Hi,  
you are in luck - Stan has you covered via the algebraic function solver: [9.1 Algebraic equation solver | Stan Functions Reference](https://mc-stan.org/docs/2_27/functions-reference/functions-algebraic-solver.html)

Feel free to ask for clarifications if you have trouble using it - it is one of the more tricky parts of Stan language.

Best of luck with your model!

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**Author:** ![evihas](https://avatars.discourse-cdn.com/v4/letter/e/9dc877/32.png) [@evihas](https://discourse.mc-stan.org/u/evihas)\
**Post date:** [August 25, 2021, 12:57pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/3 "2021-08-25T12:57:27Z")

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Hi @martinmodrak ,

Thank you for the response. I have used `algebra_solver_newton` function in my weird code. But, I am still struggling to make my model. I am trying to do Bayesian calibration for a Microsimulation model using stan (I could develop and run the code written in R using Metropolis Algorithm, but it’s a very slow converging process). As I have several `_rng` functions in my code I tried to define them within a `user-defined _rng` function.

Please see the attached `.stan` file and then kindly help me to develop it.

Thank you

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**Author:** ![martinmodrak](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/martinmodrak/32/133_2.png) [@martinmodrak](https://discourse.mc-stan.org/u/martinmodrak)\
**Post date:** [August 26, 2021, 2:16pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/4 "2021-08-26T14:16:31Z")

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I looked at the Stan code, but I admit I have no idea on what the model represents and what it should do. Could you be a bit more specific on where you’ve encoutered problems?

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**Author:** ![evihas](https://avatars.discourse-cdn.com/v4/letter/e/9dc877/32.png) [@evihas](https://discourse.mc-stan.org/u/evihas)\
**Post date:** [August 26, 2021, 2:52pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/5 "2021-08-26T14:52:32Z")

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Hi @martinmodrak ,

Okay, sorry for my bad explanation. Simply, I am trying to use the simulation algorithm described in the below paper to do individual-level data simulations, and then it gives me a data table with information relevant to disease stages of lung cancer patients. I can easily do it in R.  
[ijm-00164.pdf](https://discourse.mc-stan.org/uploads/short-url/mBVSLenId7etRKeNMa8pWjeWZXN.pdf) (1.4 MB)

But, I need to use Bayesian calibration for parameter estimation of the model. For that, I am trying to run the simulation algorithm 10 times (say) and find the mean number of diagnosed individuals in each subgroup to feed the likelihood of my model (i.e. `data_rng` function in user-defined functions block and it returns `lambda`, that is `mean number of diagnosed individuals in each subgroup`).

My question is how to link this lambda value into the model block? Or do I have to run the simulation code in R separately to find `lambda` and then use it as data values for `cmdstan()` or `rstan()` funtions?

Thank you.

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**Author:** ![martinmodrak](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/martinmodrak/32/133_2.png) [@martinmodrak](https://discourse.mc-stan.org/u/martinmodrak)\
**Post date:** [August 26, 2021, 7:26pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/6 "2021-08-26T19:26:24Z")

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I admit I still don’t really understand what you are trying to do. What exactly do you mean by “Bayesian calibration” - the only sense in which I am familiar with this term is something like [Simulation-based calibration](https://arxiv.org/abs/1804.06788), but that appears to be different to what you are trying to do.

Are you trying to estimate the parameters of the simulator? Or are you estimating something else?

> [@evihas](#):
>
> For that, I am trying to run the simulation algorithm 10 times (say) and find the mean number of diagnosed individuals in each subgroup to feed the likelihood of my model (i.e. `data_rng` function in user-defined functions block and it returns `lambda` , that is `mean number of diagnosed individuals in each subgroup` ).
> 
> My question is how to link this lambda value into the model block? Or do I have to run the simulation code in R separately to find `lambda` and then use it as data values for `cmdstan()` or `rstan()` funtions?

Stan needs the likelihood to be completely deterministic. If you only need to generate `lambda` once and then use the same value in all likelihood evaluations, you can do that in `transformed data` block (that would be equivalent to running the code in R and passing it as data). However, within the `model` block, everything needs to be deterministic, so you cannot use a stochastic simulator there.

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<div class="post-metadata">

**Author:** ![evihas](https://avatars.discourse-cdn.com/v4/letter/e/9dc877/32.png) [@evihas](https://discourse.mc-stan.org/u/evihas)\
**Post date:** [August 27, 2021, 12:26pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/7 "2021-08-27T12:26:35Z")

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Hi @martinmodrak ,

I am trying to figure out the CDF function of the following function using stan.  
h(t) = \dfrac{\nu \mu X[exp(\gamma+2B).t - 1]}{\gamma+B[exp(\gamma+2B).t +1]}

Here, I defined CDF as  
CDF = 1 - exp(-\int\_0^{t}h(u)du  
and then need to find t values when CDF has a uniform distribution.  
Can I use `algebraic_solver` and` integrate_1d` within a same user defined function in order to pass into the model block in stan?

Can someone help me to write stan code here?

Thank you

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<div class="post-metadata">

**Author:** ![martinmodrak](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/martinmodrak/32/133_2.png) [@martinmodrak](https://discourse.mc-stan.org/u/martinmodrak)\
**Post date:** [September 1, 2021, 4:17pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/8 "2021-09-01T16:17:14Z")

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> [@evihas](#):
>
> Can I use `algebraic_solver` and ` integrate_1d` within a same user defined function in order to pass into the model block in stan?

Yes you can, but it will likely be very slow.

> [@evihas](#):
>
> Can someone help me to write stan code here?

We did our best general explanations in the Stan documentation for those functions and the relevant chapters of Stan User’s guide. If you feel like you have a more specific issue, feel free to ask for additional advice.

Best of luck with your model!

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<div class="post-metadata">

**Author:** ![evihas](https://avatars.discourse-cdn.com/v4/letter/e/9dc877/32.png) [@evihas](https://discourse.mc-stan.org/u/evihas)\
**Post date:** [September 1, 2021, 11:05pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/9 "2021-09-01T23:05:31Z")

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Hi Martin,

Thank you for the response. I am very keen to see more examples and techniques for Rstan as I am planning to use Rstan in my whole project. How can I collect specific Rstan issues?

I have a question, is it possible to call **integrator** within another user-defined function instead of in the `model block`?  
Something like that…

```
functions{
  real ht_func(real x, real xc, real[] theta, real[] x_r, int[] x_i){
    real NC = theta[1];
    real mu = theta[2];
    real nu = theta[2]; 
    real alpha1 = theta[3];
    real alpha2 = theta[4];
    real gamma_ns = theta[5];
    real alpha_ns = theta[6];
    real q = theta[7]; 
    real ht;
    real alpha = alpha_ns * (1 + alpha1* pow(q,alpha2));
    real gamma = gamma_ns * (1 + alpha1* pow(q,alpha2)); 
    real B = (-gamma + sqrt(gamma^2 + 4 * alpha * mu))/2;
    ht = (nu * mu * NC * (exp(gamma + 2* B) * x -1))/(gamma + (B *(exp(gamma + 2* B) * x + 1)));
    return ht;
  }
  
  vector HT_func(vector x, vector theta, real[] x1_r, int[] x1_i){
    real NC = theta[1];
    real mu = theta[2];
    real nu = theta[2]; 
    real alpha1 = theta[3];
    real alpha2 = theta[4];
    real gamma_ns = theta[5];
    real alpha_ns = theta[6];
    real q = theta[7];
    real t;
    vector[1] Ht;
    Ht = intrgrate_1d(ht_func, 0, t, {NC, mu, nu, alpha1, alpha2, gamma_ns, alpha_ns, q}, {0.0}, {0}, 1e-8);
    return Ht;
  }
}

```

Thank you

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<div class="post-metadata">

**Author:** ![martinmodrak](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/martinmodrak/32/133_2.png) [@martinmodrak](https://discourse.mc-stan.org/u/martinmodrak)\
**Post date:** [September 3, 2021, 10:52am UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/10 "2021-09-03T10:52:33Z")

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> [@evihas](#):
>
> I have a question, is it possible to call **integrator** within another user-defined function instead of in the `model block` ?  
> Something like that…

Yes, that should definitely be possible.

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<div class="post-metadata">

**Author:** ![evihas](https://avatars.discourse-cdn.com/v4/letter/e/9dc877/32.png) [@evihas](https://discourse.mc-stan.org/u/evihas)\
**Post date:** [September 6, 2021, 10:26pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/11 "2021-09-06T22:26:01Z")

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Hi @martinmodrak ,

There is another weird thing for me to understand when applying `Algebraic equation solver` . In my case, `algebra_solver_newton` doesn’t recognize the function (i.e. function does not exit) but `algebra_solver` does for the same argumunets.

Do you know why does it happen and any solutions ?

Also, are there any extra references with examples related to `algebraic equation solver` ?

Thank you.

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<div class="post-metadata">

**Author:** ![martinmodrak](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/martinmodrak/32/133_2.png) [@martinmodrak](https://discourse.mc-stan.org/u/martinmodrak)\
**Post date:** [September 7, 2021, 7:10am UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/12 "2021-09-07T07:10:50Z")

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Most likely, this is because you are using an older version of Stan, `algebra_solver_newton` was AFAIK introduced around Stan 2.26 (not sure exactly). If you are using `rstan`, you may need to use [Repository for distributing (some) stan-dev R packages | r-packages](https://mc-stan.org/r-packages/) as the version on CRAN is not updated currently (for stupid reasons, we are trying to resolve).

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<div class="post-metadata">

**Author:** ![evihas](https://avatars.discourse-cdn.com/v4/letter/e/9dc877/32.png) [@evihas](https://discourse.mc-stan.org/u/evihas)\
**Post date:** [September 7, 2021, 4:09pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/13 "2021-09-07T16:09:43Z")

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> [@martinmodrak](#):
>
> Most likely, this is because you are using an older version of Stan, `algebra_solver_newton` was AFAIK introduced around Stan 2.26 (not sure exactly).

The latest `rstan` version is `2.21.2`, isn’t it? (which is available in CRAN and mine as well). Are there other new versions which compatible with `algebra_solver_newton ` because version `2.21.2` didn’t help me to find roots.

Thank you

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<div class="post-metadata">

**Author:** ![martinmodrak](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/martinmodrak/32/133_2.png) [@martinmodrak](https://discourse.mc-stan.org/u/martinmodrak)\
**Post date:** [September 14, 2021, 1:14pm UTC](https://discourse.mc-stan.org/t/uniroot-function-in-rstan/23965/14 "2021-09-14T13:14:10Z")

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Sorry, forgot about this thread.

The latest r-stan version is 2.27 and it is available at [Repository for distributing (some) stan-dev R packages | r-packages](https://mc-stan.org/r-packages/) Unfortunately, the latest CRAN version is still 2.21.2 due to somewhat stupid reasons).