pymc-devs/pytensor

import pytensor
from pytensor import tensor as pt

# Declare two symbolic floating-point scalars
a = pt.dscalar("a")
b = pt.dscalar("b")

# Create a simple example expression
c = a + b

# Convert the expression into a callable object that takes `(a, b)`
# values as input and computes the value of `c`.
f_c = pytensor.function([a, b], c)

assert f_c(1.5, 2.5) == 4.0

# Compute the gradient of the example expression with respect to `a`
dc = pytensor.grad(c, a)

f_dc = pytensor.function([a, b], dc)

assert f_dc(1.5, 2.5) == 1.0

# Compiling functions with `pytensor.function` also optimizes
# expression graphs by removing unnecessary operations and
# replacing computations with more efficient ones.

v = pt.vector("v")
M = pt.matrix("M")

d = a/a + (M + a).dot(v)

pytensor.dprint(d)
#  Add [id A]
#  ├─ ExpandDims{axis=0} [id B]
#  │  └─ True_div [id C]
#  │     ├─ a [id D]
#  │     └─ a [id D]
#  └─ dot [id E]
#     ├─ Add [id F]
#     │  ├─ M [id G]
#     │  └─ ExpandDims{axes=[0, 1]} [id H]
#     │     └─ a [id D]
#     └─ v [id I]

f_d = pytensor.function([a, v, M], d)

# `a/a` -> `1` and the dot product is replaced with a BLAS function
# (i.e. CGemv)
pytensor.dprint(f_d)
# Add [id A] 5
#  ├─ [1.] [id B]
#  └─ CGemv{inplace} [id C] 4
#     ├─ AllocEmpty{dtype='float64'} [id D] 3
#     │  └─ Shape_i{0} [id E] 2
#     │     └─ M [id F]
#     ├─ 1.0 [id G]
#     ├─ Add [id H] 1
#     │  ├─ M [id F]
#     │  └─ ExpandDims{axes=[0, 1]} [id I] 0
#     │     └─ a [id J]
#     ├─ v [id K]
#     └─ 0.0 [id L]