import numpy as np
from pylops.utils.backend import get_module, to_numpy
[docs]def dottest(Op, nr=None, nc=None, tol=1e-6, complexflag=0, raiseerror=True, verb=False,
backend='numpy'):
r"""Dot test.
Generate random vectors :math:`\mathbf{u}` and :math:`\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.
Parameters
----------
Op : :obj:`pylops.LinearOperator`
Linear operator to test.
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)
tol : :obj:`float`, optional
Dottest tolerance
complexflag : :obj:`bool`, optional
generate random vectors with real (0) or complex numbers
(1: only model, 2: only data, 3:both)
raiseerror : :obj:`bool`, optional
Raise error or simply return ``False`` when dottest fails
verb : :obj:`bool`, optional
Verbosity
backend : :obj:`str`, optional
Backend used for dot test computations (``numpy`` or ``cupy``). This
parameter will be used to choose how to create the random vectors.
Raises
------
ValueError
If dot-test is not verified within chosen tolerance.
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})
"""
ncp = get_module(backend)
if nr is None:
nr = Op.shape[0]
if nc is None:
nc = Op.shape[1]
assert (nr, nc) == Op.shape, 'Provided nr and nc do not match operator shape'
# make u and v vectors
if complexflag != 0:
rdtype = np.real(np.ones(1, Op.dtype)).dtype
if complexflag in (0, 2):
u = ncp.random.randn(nc).astype(Op.dtype)
else:
u = ncp.random.randn(nc).astype(rdtype) + \
1j * ncp.random.randn( nc).astype(rdtype)
if complexflag in (0, 1):
v = ncp.random.randn(nr).astype(Op.dtype)
else:
v = ncp.random.randn(nr).astype(rdtype) + \
1j * ncp.random.randn(nr).astype(rdtype)
y = Op.matvec(u) # Op * u
x = Op.rmatvec(v) # Op'* v
if getattr(Op, 'clinear', True):
yy = ncp.vdot(y, v) # (Op * u)' * v
xx = ncp.vdot(u, x) # u' * (Op' * v)
else:
# Op is only R-linear, so treat complex numbers as elements of R^2
yy = ncp.dot(y.real, v.real) + ncp.dot(y.imag, v.imag)
xx = ncp.dot(u.real, x.real) + ncp.dot(u.imag, x.imag)
# 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]
# evaluate if dot test is passed
if complexflag == 0:
if np.abs((yy - xx) / ((yy + xx + 1e-15) / 2)) < tol:
if verb: print('Dot test passed, v^T(Opu)=%f - u^T(Op^Tv)=%f'
% (yy, xx))
return True
else:
if raiseerror:
raise ValueError('Dot test failed, v^T(Opu)=%f - u^T(Op^Tv)=%f'
% (yy, xx))
if verb: print('Dot test failed, v^T(Opu)=%f - u^T(Op^Tv)=%f'
% (yy, xx))
return False
else:
checkreal = np.abs((np.real(yy) - np.real(xx)) /
((np.real(yy) + np.real(xx)+1e-15) / 2)) < tol
checkimag = np.abs((np.imag(yy) - np.imag(xx)) /
((np.imag(yy) + np.imag(xx)+1e-15) / 2)) < tol
if checkreal and checkimag:
if verb:
print('Dot test passed, v^T(Opu)=%f%+fi - u^T(Op^Tv)=%f%+fi'
% (yy.real, yy.imag, xx.real, xx.imag))
return True
else:
if raiseerror:
raise ValueError('Dot test failed, v^H(Opu)=%f%+fi '
'- u^H(Op^Hv)=%f%+fi'
% (yy.real, yy.imag, xx.real, xx.imag))
if verb:
print('Dot test failed, v^H(Opu)=%f%+fi - u^H(Op^Hv)=%f%+fi'
% (yy.real, yy.imag, xx.real, xx.imag))
return False