Memoized forward and adjoint evaluations

This example shows how to use the pylops.MemoizeOperator operator to cache repeated applications of an operator.

import numpy as np

import pylops

Let’s start by creating a pylops.Diagonal operator and wrapping it into a pylops.MemoizeOperator operator choosing max_neval=2 (meaning that at most 4 evaluations are cached).

Op = pylops.Diagonal(np.array([2.0, 3.0, 4.0]))
MOp = pylops.MemoizeOperator(Op, max_neval=4)

Now we first apply twice the forward pass of operator (and check that only one entry is memoized), followed by one adjoint pass of operator (and check that now two entries are memoized)

x = np.array([1.0, -2.0, 0.5])
y = MOp @ x
y = MOp @ x
print("Number of evaluations: ", MOp.neval)

xadj = MOp.H @ y
print("Number of evaluations: ", MOp.neval)

Number of evaluations:  1
Number of evaluations:  2

Repeating either calculation reuses its own cached result.

print("y - ycached = ", y - MOp @ x)
print("xadj - xadjcached = ", xadj - MOp.H @ y)
print("Number of evaluations: ", MOp.neval)

y - ycached =  [0. 0. 0.]
xadj - xadjcached =  [0. 0. 0.]
Number of evaluations:  2

Finally, we can see that similar inputs are not interchangeable: any small change triggers a new memoization.

x_nearby = x.copy()
x_nearby[0] += 1e-6
y_nearby = MOp @ x_nearby
print("Number of evaluations: ", MOp.neval)

Number of evaluations:  3