# Einsum in pytensor

**URL:** <https://discourse.pymc.io/t/einsum-in-pytensor/13742>\
**Category:** v5\
**Tags:** modeling\
**Created:** [February 5, 2024, 4:02pm UTC](https://discourse.pymc.io/t/einsum-in-pytensor/13742 "2024-02-05T16:02:53Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![brandonhorsley](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/brandonhorsley/32/6693_2.png) [@brandonhorsley](https://discourse.pymc.io/u/brandonhorsley)\
**Post date:** [February 5, 2024, 4:02pm UTC](https://discourse.pymc.io/t/einsum-in-pytensor/13742/1 "2024-02-05T16:02:53Z")

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Hi all,

I’ve got a problem that I’m not quite 100% sure on how to approach (tl;dr at the bottom). The basic thing I want to do is that I have a vector of priors ‘b’ and I want to combine it with a Voltage matrix ‘Volt’ in a deterministic node so that I get the following:

![image_2024-02-05_151855062](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/1/1723ecddc35989f3e423cf294be0938bc57f13ac.png)  
so the first b multiplies across the first row, the second b in the vector multiplies across the second row and so forth. Now doing this in numpy with dummy numbers, I was able to get it done via:

```auto
res=np.transpose(np.einsum('ij,ki->jki',V,b))

```

where b was an array and V was a matrix.

But the closest parallel for einstein summation in pytensor that I could find would be either batched\_tensordot/batched\_dot (which on the website says is a subset of einstein summation), but I’m unsure on if it would work since I’m still a bit shaky regarding the dimensionality of pymc distributions and combining with pytensor. So the other alternative that i’ve seen is using pt.scan and pt.subtensor.set\_subtensor to just set the values of the resulting matrix which I believe is probably moreso the way to go but since I am uncertain I figured I’d ask in case I’m being foolish!

**tl;dr For the problem of multiplying across a vector of priors so that the i’th entry multiplies across the i’th row of a matrix, is pt.scan and pt.set\_subtensor the way to go for this problem, or can it be done more succinctly?**

Am happy to provide further context if necessary, thanks in advance!

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<div class="post-metadata">

**Author:** ![iavicenna](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/iavicenna/32/7923_2.png) [@iavicenna](https://discourse.pymc.io/u/iavicenna)\
**Post date:** [February 5, 2024, 4:27pm UTC](https://discourse.pymc.io/t/einsum-in-pytensor/13742/2 "2024-02-05T16:27:41Z")

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If I understand what you are asking for correctly then there is a simpler way to achieve it:

```auto
with pm.Model():
  
  b = pm.Normal("b", mu=0, size=5)
  V = np.random.normal(0, 1, size=(5,5))
  
  bV = pm.Deterministic("bV", b[:,None]*V)

```

This simply expands b to a matrix which has identical columns and then does the multiplication. This would also work with numpy though I am not sure why you used einstein summation (which would produce a 5x5x5 matrix in this case?).

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<div class="post-metadata">

**Author:** ![brandonhorsley](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/brandonhorsley/32/6693_2.png) [@brandonhorsley](https://discourse.pymc.io/u/brandonhorsley)\
**Post date:** [February 6, 2024, 9:21am UTC](https://discourse.pymc.io/t/einsum-in-pytensor/13742/3 "2024-02-06T09:21:23Z")

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Yep, that works perfectly. Many thanks, you just saved me a whole lot of hassle barking up the wrong tree 😂