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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,2 @@ | ||
| # isort: skip_file | ||
| from .dottest import * |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,107 @@ | ||
| __all__ = ["dottest"] | ||
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| from typing import Optional | ||
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| import numpy as np | ||
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| from pylops_mpi.DistributedArray import DistributedArray | ||
| from pylops.utils.backend import to_numpy | ||
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| def dottest( | ||
| Op, | ||
| u: DistributedArray, | ||
| v: DistributedArray, | ||
| nr: Optional[int] = None, | ||
| nc: Optional[int] = None, | ||
| rtol: float = 1e-6, | ||
| atol: float = 1e-21, | ||
| raiseerror: bool = True, | ||
| verb: bool = False, | ||
| ) -> bool: | ||
| r"""Dot test. | ||
| Perform dot-test to verify the validity of forward and adjoint | ||
| operators using user-provided random vectors :math:`\mathbf{u}` | ||
| and :math:`\mathbf{v}` (whose Partition must be consistent with | ||
| the operator being tested). This test can help to detect errors | ||
| in the operator ximplementation. | ||
| Parameters | ||
| ---------- | ||
| Op : :obj:`pylops_mpi.LinearOperator` | ||
| Linear operator to test. | ||
| u : :obj:`pylops_mpi.DistributedArray` | ||
| Distributed array of size equal to the number of columns of operator | ||
| v : :obj:`pylops_mpi.DistributedArray` | ||
| Distributed array of size equal to the number of rows of operator | ||
| nr : :obj:`int` | ||
| Number of rows of operator (i.e., elements in data) | ||
| nc : :obj:`int` | ||
| Number of columns of operator (i.e., elements in model) | ||
| rtol : :obj:`float`, optional | ||
| Relative dottest tolerance | ||
| atol : :obj:`float`, optional | ||
| Absolute dottest tolerance | ||
| .. versionadded:: 2.0.0 | ||
| raiseerror : :obj:`bool`, optional | ||
| Raise error or simply return ``False`` when dottest fails | ||
| verb : :obj:`bool`, optional | ||
| Verbosity | ||
| Returns | ||
| ------- | ||
| passed : :obj:`bool` | ||
| Passed flag. | ||
| Raises | ||
| ------ | ||
| AssertionError | ||
| If dot-test is not verified within chosen tolerances. | ||
| Notes | ||
| ----- | ||
| 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: | ||
| .. math:: | ||
| (\mathbf{Op}\,\mathbf{u})^H\mathbf{v} = | ||
| \mathbf{u}^H(\mathbf{Op}^H\mathbf{v}) | ||
| """ | ||
| if nr is None: | ||
| nr = Op.shape[0] | ||
| if nc is None: | ||
| nc = Op.shape[1] | ||
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| if (nr, nc) != Op.shape: | ||
| raise AssertionError("Provided nr and nc do not match operator shape") | ||
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| y = Op.matvec(u) # Op * u | ||
| x = Op.rmatvec(v) # Op'* v | ||
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| yy = np.vdot(y.asarray(), v.asarray()) # (Op * u)' * v | ||
| xx = np.vdot(u.asarray(), x.asarray()) # u' * (Op' * v) | ||
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| # convert back to numpy (in case cupy arrays were used), make into a numpy | ||
| # array and extract the first element. This is ugly but allows to handle | ||
| # complex numbers in subsequent prints also when using cupy arrays. | ||
| xx, yy = np.array([to_numpy(xx)])[0], np.array([to_numpy(yy)])[0] | ||
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| # evaluate if dot test passed | ||
| passed = np.isclose(xx, yy, rtol, atol) | ||
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| # verbosity or error raising | ||
| if (not passed and raiseerror) or verb: | ||
| passed_status = "passed" if passed else "failed" | ||
| msg = f"Dot test {passed_status}, v^H(Opu)={yy} - u^H(Op^Hv)={xx}" | ||
| if not passed and raiseerror: | ||
| raise AssertionError(msg) | ||
| else: | ||
| print(msg) | ||
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| return passed |
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