sympytensor 1.3.2

Print sympy expressions to pytensor graphs

Sympytensor

A tool for converting Sympy expressions to a Pytensor graph, with support for working with PyMC models.

Installation

pip install sympytensor

Examples

Writing expressions to pytensor

Two functions are provided to convert sympy expressions:

• as_tensor converts a sympy expression to a pytensor symbolic graph
• pytensor_function returns a compiled pytensor.function that computes the expression. Keyword arguments to pytensor.function can be provided as **kwargs

Use sympy to compute 1d splines, then convert the splines to a symbolic pytensor variable:

import pytensor
import sympy as sp
from sympytensor import as_tensor
from sympy.abc import x

x_data = [0, 1, 2, 3, 4, 5]
y_data = [3, 6, 5, 7, 9, 1]

s = sp.interpolating_spline(d=3, x=x, X=x_data, Y=y_data)
s_pt = as_tensor(s)

This generates the following function graph:

pytensor.dprint(s_pt)

>>>Out: Elemwise{switch,no_inplace} [id A]
>>>      |Elemwise{and_,no_inplace} [id B]
>>>      | |Elemwise{ge,no_inplace} [id C]
>>>      | | |x [id D]
>>>      | | |TensorConstant{0} [id E]
>>>      | |Elemwise{le,no_inplace} [id F]
>>>      |   |x [id D]
>>>      |   |TensorConstant{2} [id G]
>>>      |Elemwise{add,no_inplace} [id H]
>>>      | |TensorConstant{3} [id I]
>>>      | |Elemwise{mul,no_inplace} [id J]
>>>      | | |Elemwise{true_div,no_inplace} [id K]
>>>      | | | |TensorConstant{-33} [id L]
>>>      | | | |TensorConstant{5} [id M]
>>>      | | |Elemwise{pow,no_inplace} [id N]
>>>      | |   |x [id D]
>>>      | |   |TensorConstant{2} [id O]
>>>      | |Elemwise{mul,no_inplace} [id P]
>>>      | | |Elemwise{true_div,no_inplace} [id Q]
>>>      | | | |TensorConstant{23} [id R]
>>>      | | | |TensorConstant{15} [id S]
>>>      | | |Elemwise{pow,no_inplace} [id T]
>>>      | |   |x [id D]
>>>      | |   |TensorConstant{3} [id U]
>>>      | |Elemwise{mul,no_inplace} [id V]
>>>      |   |Elemwise{true_div,no_inplace} [id W]
>>>      |   | |TensorConstant{121} [id X]
>>>      |   | |TensorConstant{15} [id Y]
>>>      |   |x [id D]
>>>      |Elemwise{switch,no_inplace} [id Z]
>>>        |Elemwise{and_,no_inplace} [id BA]
>>>        | |Elemwise{ge,no_inplace} [id BB]
>>>        | | |x [id D]
>>>        | | |TensorConstant{2} [id BC]
>>>        | |Elemwise{le,no_inplace} [id BD]
>>>        |   |x [id D]
>>>        |   |TensorConstant{3} [id BE]
>>>        |Elemwise{add,no_inplace} [id BF]
>>>        | |Elemwise{true_div,no_inplace} [id BG]
>>>        | | |TensorConstant{103} [id BH]
>>>        | | |TensorConstant{5} [id BI]
>>>        | |Elemwise{mul,no_inplace} [id BJ]
>>>        | | |Elemwise{true_div,no_inplace} [id BK]
>>>        | | | |TensorConstant{-55} [id BL]
>>>        | | | |TensorConstant{3} [id BM]
>>>        | | |x [id D]
>>>        | |Elemwise{mul,no_inplace} [id BN]
>>>        | | |Elemwise{true_div,no_inplace} [id BO]
>>>        | | | |TensorConstant{-2} [id BP]
>>>        | | | |TensorConstant{3} [id BQ]
>>>        | | |Elemwise{pow,no_inplace} [id BR]
>>>        | |   |x [id D]
>>>        | |   |TensorConstant{3} [id BS]
>>>        | |Elemwise{mul,no_inplace} [id BT]
>>>        |   |Elemwise{true_div,no_inplace} [id BU]
>>>        |   | |TensorConstant{33} [id BV]
>>>        |   | |TensorConstant{5} [id BW]
>>>        |   |Elemwise{pow,no_inplace} [id BX]
>>>        |     |x [id D]
>>>        |     |TensorConstant{2} [id BY]
>>>        |Elemwise{switch,no_inplace} [id BZ]
>>>          |Elemwise{and_,no_inplace} [id CA]
>>>          | |Elemwise{ge,no_inplace} [id CB]
>>>          | | |x [id D]
>>>          | | |TensorConstant{3} [id CC]
>>>          | |Elemwise{le,no_inplace} [id CD]
>>>          |   |x [id D]
>>>          |   |TensorConstant{5} [id CE]
>>>          |Elemwise{add,no_inplace} [id CF]
>>>          | |TensorConstant{53} [id CG]
>>>          | |Elemwise{mul,no_inplace} [id CH]
>>>          | | |Elemwise{true_div,no_inplace} [id CI]
>>>          | | | |TensorConstant{-761} [id CJ]
>>>          | | | |TensorConstant{15} [id CK]
>>>          | | |x [id D]
>>>          | |Elemwise{mul,no_inplace} [id CL]
>>>          | | |Elemwise{true_div,no_inplace} [id CM]
>>>          | | | |TensorConstant{-28} [id CN]
>>>          | | | |TensorConstant{15} [id CO]
>>>          | | |Elemwise{pow,no_inplace} [id CP]
>>>          | |   |x [id D]
>>>          | |   |TensorConstant{3} [id CQ]
>>>          | |Elemwise{mul,no_inplace} [id CR]
>>>          |   |Elemwise{true_div,no_inplace} [id CS]
>>>          |   | |TensorConstant{87} [id CT]
>>>          |   | |TensorConstant{5} [id CU]
>>>          |   |Elemwise{pow,no_inplace} [id CV]
>>>          |     |x [id D]
>>>          |     |TensorConstant{2} [id CW]
>>>          |TensorConstant{nan} [id CX]

Inserting PyMC random variables into an expression

The SympyDeterministic function works as a drop-in replacement for pm.Deterministic, except a sympy expression is expected. It will automatically search the active model context for random variables corresponding to symbols in the expression and make substitutions.

Here is an example using sympy to symbolically compute the inverse of a matrix, which is then used in a model:

from sympytensor import SympyDeterministic
import pymc as pm
import sympy as sp
from sympy.abc import a, b, c, d

A = sp.Matrix([[a, b],
               [c, d]])
A_inv = sp.matrices.Inverse(A).doit()

with pm.Model() as m:
    a_pm = pm.Normal('a')
    b_pm = pm.Normal('b')
    c_pm = pm.Normal('c')
    c_pm = pm.Normal('d')
    A_inv_pm = SympyDeterministic('A_inv', A_inv)