pylops.utils.dottest(Op, nr=None, nc=None, rtol=1e-06, atol=1e-21, complexflag=0, raiseerror=True, verb=False, backend='numpy')[source]

Dot test.

Generate random vectors \(\mathbf{u}\) and \(\mathbf{v}\) and perform dot-test to verify the validity of forward and adjoint operators. This test can help to detect errors in the operator implementation.

Op : pylops.LinearOperator

Linear operator to test.

nr : int

Number of rows of operator (i.e., elements in data)

nc : int

Number of columns of operator (i.e., elements in model)

rtol : float, optional

Relative dottest tolerance

atol : float, optional

Absolute dottest tolerance .. versionadded:: 2.0.0

complexflag : bool, optional

Generate random vectors with

  • 0: Real entries for model and data
  • 1: Complex entries for model and real entries for data
  • 2: Real entries for model and complex entries for data
  • 3: Complex entries for model and data
raiseerror : bool, optional

Raise error or simply return False when dottest fails

verb : bool, optional


backend : str, optional

Backend used for dot test computations (numpy or cupy). This parameter will be used to choose how to create the random vectors.


If dot-test is not verified within chosen tolerances.


A dot-test is mathematical tool used in the development of numerical linear operators.

More specifically, a correct implementation of forward and adjoint for a linear operator should verify the following equality within a numerical tolerance:

\[(\mathbf{Op}\,\mathbf{u})^H\mathbf{v} = \mathbf{u}^H(\mathbf{Op}^H\mathbf{v})\]