# How to write complicated Deterministic?

**URL:** <https://discourse.pymc.io/t/how-to-write-complicated-deterministic/11195>\
**Category:** v5\
**Created:** [January 15, 2023, 3:27am UTC](https://discourse.pymc.io/t/how-to-write-complicated-deterministic/11195 "2023-01-15T03:27:19Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![drshenlei](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/drshenlei/32/6016_2.png) [@drshenlei](https://discourse.pymc.io/u/drshenlei)\
**Post date:** [January 15, 2023, 3:27am UTC](https://discourse.pymc.io/t/how-to-write-complicated-deterministic/11195/1 "2023-01-15T03:27:19Z")

</div>

I’m trying to translate examples in “Bayesian methods for hackers” into pyMC v5. Actually it is really painful since many documents from google are mixed with v2, v3, v4. Even I have read the migration guide of v4, there’s still a lot I don’t understand.

To be specific, in the SMS frequency example, how can I construct `lambda_` that involves array index manipulation?

```auto
lambda_1 = pm.Exponential("lambda_1", alpha)
lambda_2 = pm.Exponential("lambda_2", alpha)
tau = pm.DiscreteUniform("tau", lower=0, upper=n_count_data)

@pm.deterministic
def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):
    out = np.zeros(n_count_data)
    out[:tau] = lambda_1 # lambda before tau is lambda1
    out[tau:] = lambda_2 # lambda after tau is lambda2
    return out

observation = pm.Poisson("obs", lambda_, value=count_data, observed=True)
model = pm.Model([observation, lambda_1, lambda_2, tau])

```

I tried the following:

```auto
def mixed_lambda(lambda1=lambda1, lambda2=lambda2, tau=tau):
    out = np.zeros(len(real_pv))
    t = tau.eval()
    out[:t] = lambda1.eval()
    out[t:] = lambda2.eval()
    return out

with model:
    mixed_lambda = pm.Deterministic("mixed_lambda", mixed_lambda())

```

However pyMC blames incompatible between `np.array` and `aesara.tensor`. Could you tell me the right way to do it? Any related tip and best practice are welcome. Thank you in advance.

---

<div class="post-metadata">

**Author:** ![ricardoV94](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/ricardov94/32/5775_2.png) [@ricardoV94](https://discourse.pymc.io/u/ricardoV94)\
**Post date:** [January 15, 2023, 9:00am UTC](https://discourse.pymc.io/t/how-to-write-complicated-deterministic/11195/2 "2023-01-15T09:00:01Z")

</div>

The book has an official PyMC3 version: [GitHub - CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers: aka "Bayesian Methods for Hackers": An introduction to Bayesian methods + probabilistic programming with a computation/understanding-first, mathematics-second point of view. All in pure Python ;)](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers#pymc3)

That API should be much more similar to V4/V5.

In general you can write complex deterministics just like you would write Numpy (replacing `np` by `pt` or `at`), except for some special operations like branching, looping and writing to arrays (as you are doing with indexing). Writing to arrays is supported via `set_subtensor`, but it’s probably easier to use `where` which works just like in numpy.

You should not use `eval`. That’s for debugging only, as it tries to evaluate the expression you have. You should always give PyMC an unevaluated expression.

```python
import pytensor.tensor as pt

with pm.Model() as m:
  lambda_1 = pm.Exponential("lambda_1", alpha)
  lambda_2 = pm.Exponential("lambda_2", alpha)
  tau = pm.DiscreteUniform("tau", lower=0, upper=n_count_data)

  lambda_ = pt.where(tau <= pt.arange(len(count_data)), lambda_1, lambda_2)
  observation = pm.Poisson("obs", lambda_, observed=count_data)

```

---

<div class="post-metadata">

**Author:** ![drshenlei](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/drshenlei/32/6016_2.png) [@drshenlei](https://discourse.pymc.io/u/drshenlei)\
**Post date:** [January 15, 2023, 10:33am UTC](https://discourse.pymc.io/t/how-to-write-complicated-deterministic/11195/3 "2023-01-15T10:33:22Z")

</div>

Thank you for the reply, it works! `pt.where` and `.eval` concepts helps me a lot.

However, when I change `pytensor` to `aesara`, it blames at `tau <= at.arange(len(real_pv))` part for:

```auto
NotImplementedError: Cannot convert ARange{dtype='int64'}.0 to a tensor variable.

File ~/pyenv/lib/python3.10/site-packages/pytensor/tensor/var.py:45, in _tensor_py_operators. __le__ (self, other)
     44 def __le__ (self, other):
---> 45 rval = at.math.le(self, other)
     46 rval._is_nonzero = False
     47 return rval

File ~/pyenv/lib/python3.10/site-packages/pytensor/graph/op.py:296, in Op. __call__ (self, *inputs, **kwargs)
    254 r"""Construct an `Apply` node using :meth:`Op.make_node` and return its outputs.
    255 
    256 This method is just a wrapper around :meth:`Op.make_node`.
   (...)
    293 
    294 """
    295 return_list = kwargs.pop("return_list", False)
--> 296 node = self.make_node(*inputs, **kwargs)
    298 if config.compute_test_value != "off":
    299 compute_test_value(node)
...

```

It seems the `tensor` in `pytensor` and `aesara` are slightly different. The backend of pyMC changes a lot and really complicated. Why does pyMC mix two or more tensor structure? Is there any preference or idiom about tensor types for daily usage?

---

<div class="post-metadata">

**Author:** ![ricardoV94](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/ricardov94/32/5775_2.png) [@ricardoV94](https://discourse.pymc.io/u/ricardoV94)\
**Post date:** [January 15, 2023, 10:47am UTC](https://discourse.pymc.io/t/how-to-write-complicated-deterministic/11195/4 "2023-01-15T10:47:18Z")

</div>

You cannot mix Aesara and Pytensor!!!

PyMC 4.x uses Aesara  
PyMC 5.x uses PyTensor

Otherwise they work the same (PyTensor is a fork of the Aesara project maintained by the PyMC developers)