sklearn/covariance/tests/test_covariance.py::test_covariance FAILED [ 9%]
=================================================== FAILURES ===================================================
_______________________________________________ test_covariance ________________________________________________
def test_covariance():
# Tests Covariance module on a simple dataset.
# test covariance fit from data
cov = EmpiricalCovariance()
cov.fit(X)
emp_cov = empirical_covariance(X)
assert_array_almost_equal(emp_cov, cov.covariance_, 4)
assert_almost_equal(cov.error_norm(emp_cov), 0)
assert_almost_equal(cov.error_norm(emp_cov, norm="spectral"), 0)
assert_almost_equal(cov.error_norm(emp_cov, norm="frobenius"), 0)
assert_almost_equal(cov.error_norm(emp_cov, scaling=False), 0)
assert_almost_equal(cov.error_norm(emp_cov, squared=False), 0)
with pytest.raises(NotImplementedError):
cov.error_norm(emp_cov, norm="foo")
# Mahalanobis distances computation test
mahal_dist = cov.mahalanobis(X)
assert np.amin(mahal_dist) > 0
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
cov = EmpiricalCovariance()
> cov.fit(X_1d)
sklearn/covariance/tests/test_covariance.py:58:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
sklearn/base.py:1151: in wrapper
return fit_method(estimator, *args, **kwargs)
sklearn/covariance/_empirical_covariance.py:247: in fit
self._set_covariance(covariance)
sklearn/covariance/_empirical_covariance.py:205: in _set_covariance
self.precision_ = linalg.pinvh(covariance, check_finite=False)
/usr/lib64/python3.11/site-packages/scipy/linalg/_basic.py:1536: in pinvh
s, u = _decomp.eigh(a, lower=lower, check_finite=False)
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
a = array([[0.00226244]]), b = None, lower = True, eigvals_only = False, overwrite_a = False
overwrite_b = False, turbo = False, eigvals = None, type = 1, check_finite = False, subset_by_index = None
subset_by_value = None, driver = 'evr'
def eigh(a, b=None, lower=True, eigvals_only=False, overwrite_a=False,
overwrite_b=False, turbo=False, eigvals=None, type=1,
check_finite=True, subset_by_index=None, subset_by_value=None,
driver=None):
"""
Solve a standard or generalized eigenvalue problem for a complex
Hermitian or real symmetric matrix.
Find eigenvalues array ``w`` and optionally eigenvectors array ``v`` of
array ``a``, where ``b`` is positive definite such that for every
eigenvalue λ (i-th entry of w) and its eigenvector ``vi`` (i-th column of
``v``) satisfies::
a @ vi = λ * b @ vi
vi.conj().T @ a @ vi = λ
vi.conj().T @ b @ vi = 1
In the standard problem, ``b`` is assumed to be the identity matrix.
Parameters
----------
a : (M, M) array_like
A complex Hermitian or real symmetric matrix whose eigenvalues and
eigenvectors will be computed.
b : (M, M) array_like, optional
A complex Hermitian or real symmetric definite positive matrix in.
If omitted, identity matrix is assumed.
lower : bool, optional
Whether the pertinent array data is taken from the lower or upper
triangle of ``a`` and, if applicable, ``b``. (Default: lower)
eigvals_only : bool, optional
Whether to calculate only eigenvalues and no eigenvectors.
(Default: both are calculated)
subset_by_index : iterable, optional
If provided, this two-element iterable defines the start and the end
indices of the desired eigenvalues (ascending order and 0-indexed).
To return only the second smallest to fifth smallest eigenvalues,
``[1, 4]`` is used. ``[n-3, n-1]`` returns the largest three. Only
available with "evr", "evx", and "gvx" drivers. The entries are
directly converted to integers via ``int()``.
subset_by_value : iterable, optional
If provided, this two-element iterable defines the half-open interval
``(a, b]`` that, if any, only the eigenvalues between these values
are returned. Only available with "evr", "evx", and "gvx" drivers. Use
``np.inf`` for the unconstrained ends.
driver : str, optional
Defines which LAPACK driver should be used. Valid options are "ev",
"evd", "evr", "evx" for standard problems and "gv", "gvd", "gvx" for
generalized (where b is not None) problems. See the Notes section.
The default for standard problems is "evr". For generalized problems,
"gvd" is used for full set, and "gvx" for subset requested cases.
type : int, optional
For the generalized problems, this keyword specifies the problem type
to be solved for ``w`` and ``v`` (only takes 1, 2, 3 as possible
inputs)::
1 => a @ v = w @ b @ v
2 => a @ b @ v = w @ v
3 => b @ a @ v = w @ v
This keyword is ignored for standard problems.
overwrite_a : bool, optional
Whether to overwrite data in ``a`` (may improve performance). Default
is False.
overwrite_b : bool, optional
Whether to overwrite data in ``b`` (may improve performance). Default
is False.
check_finite : bool, optional
Whether to check that the input matrices contain only finite numbers.
Disabling may give a performance gain, but may result in problems
(crashes, non-termination) if the inputs do contain infinities or NaNs.
turbo : bool, optional, deprecated
.. deprecated:: 1.5.0
`eigh` keyword argument `turbo` is deprecated in favour of
``driver=gvd`` keyword instead and will be removed in SciPy
1.12.0.
eigvals : tuple (lo, hi), optional, deprecated
.. deprecated:: 1.5.0
`eigh` keyword argument `eigvals` is deprecated in favour of
`subset_by_index` keyword instead and will be removed in SciPy
1.12.0.
Returns
-------
w : (N,) ndarray
The N (1<=N<=M) selected eigenvalues, in ascending order, each
repeated according to its multiplicity.
v : (M, N) ndarray
(if ``eigvals_only == False``)
Raises
------
LinAlgError
If eigenvalue computation does not converge, an error occurred, or
b matrix is not definite positive. Note that if input matrices are
not symmetric or Hermitian, no error will be reported but results will
be wrong.
See Also
--------
eigvalsh : eigenvalues of symmetric or Hermitian arrays
eig : eigenvalues and right eigenvectors for non-symmetric arrays
eigh_tridiagonal : eigenvalues and right eiegenvectors for
symmetric/Hermitian tridiagonal matrices
Notes
-----
This function does not check the input array for being Hermitian/symmetric
in order to allow for representing arrays with only their upper/lower
triangular parts. Also, note that even though not taken into account,
finiteness check applies to the whole array and unaffected by "lower"
keyword.
This function uses LAPACK drivers for computations in all possible keyword
combinations, prefixed with ``sy`` if arrays are real and ``he`` if
complex, e.g., a float array with "evr" driver is solved via
"syevr", complex arrays with "gvx" driver problem is solved via "hegvx"
etc.
As a brief summary, the slowest and the most robust driver is the
classical ``<sy/he>ev`` which uses symmetric QR. ``<sy/he>evr`` is seen as
the optimal choice for the most general cases. However, there are certain
occasions that ``<sy/he>evd`` computes faster at the expense of more
memory usage. ``<sy/he>evx``, while still being faster than ``<sy/he>ev``,
often performs worse than the rest except when very few eigenvalues are
requested for large arrays though there is still no performance guarantee.
For the generalized problem, normalization with respect to the given
type argument::
type 1 and 3 : v.conj().T @ a @ v = w
type 2 : inv(v).conj().T @ a @ inv(v) = w
type 1 or 2 : v.conj().T @ b @ v = I
type 3 : v.conj().T @ inv(b) @ v = I
Examples
--------
>>> import numpy as np
>>> from scipy.linalg import eigh
>>> A = np.array([[6, 3, 1, 5], [3, 0, 5, 1], [1, 5, 6, 2], [5, 1, 2, 2]])
>>> w, v = eigh(A)
>>> np.allclose(A @ v - v @ np.diag(w), np.zeros((4, 4)))
True
Request only the eigenvalues
>>> w = eigh(A, eigvals_only=True)
Request eigenvalues that are less than 10.
>>> A = np.array([[34, -4, -10, -7, 2],
... [-4, 7, 2, 12, 0],
... [-10, 2, 44, 2, -19],
... [-7, 12, 2, 79, -34],
... [2, 0, -19, -34, 29]])
>>> eigh(A, eigvals_only=True, subset_by_value=[-np.inf, 10])
array([6.69199443e-07, 9.11938152e+00])
Request the second smallest eigenvalue and its eigenvector
>>> w, v = eigh(A, subset_by_index=[1, 1])
>>> w
array([9.11938152])
>>> v.shape # only a single column is returned
(5, 1)
"""
if turbo:
warnings.warn("Keyword argument 'turbo' is deprecated in favour of '"
"driver=gvd' keyword instead and will be removed in "
"SciPy 1.12.0.",
DeprecationWarning, stacklevel=2)
if eigvals:
warnings.warn("Keyword argument 'eigvals' is deprecated in favour of "
"'subset_by_index' keyword instead and will be removed "
"in SciPy 1.12.0.",
DeprecationWarning, stacklevel=2)
# set lower
uplo = 'L' if lower else 'U'
# Set job for Fortran routines
_job = 'N' if eigvals_only else 'V'
drv_str = [None, "ev", "evd", "evr", "evx", "gv", "gvd", "gvx"]
if driver not in drv_str:
raise ValueError('"{}" is unknown. Possible values are "None", "{}".'
''.format(driver, '", "'.join(drv_str[1:])))
a1 = _asarray_validated(a, check_finite=check_finite)
if len(a1.shape) != 2 or a1.shape[0] != a1.shape[1]:
raise ValueError('expected square "a" matrix')
overwrite_a = overwrite_a or (_datacopied(a1, a))
cplx = True if iscomplexobj(a1) else False
n = a1.shape[0]
drv_args = {'overwrite_a': overwrite_a}
if b is not None:
b1 = _asarray_validated(b, check_finite=check_finite)
overwrite_b = overwrite_b or _datacopied(b1, b)
if len(b1.shape) != 2 or b1.shape[0] != b1.shape[1]:
raise ValueError('expected square "b" matrix')
if b1.shape != a1.shape:
raise ValueError("wrong b dimensions {}, should "
"be {}".format(b1.shape, a1.shape))
if type not in [1, 2, 3]:
raise ValueError('"type" keyword only accepts 1, 2, and 3.')
cplx = True if iscomplexobj(b1) else (cplx or False)
drv_args.update({'overwrite_b': overwrite_b, 'itype': type})
# backwards-compatibility handling
subset_by_index = subset_by_index if (eigvals is None) else eigvals
subset = (subset_by_index is not None) or (subset_by_value is not None)
# Both subsets can't be given
if subset_by_index and subset_by_value:
raise ValueError('Either index or value subset can be requested.')
# Take turbo into account if all conditions are met otherwise ignore
if turbo and b is not None:
driver = 'gvx' if subset else 'gvd'
# Check indices if given
if subset_by_index:
lo, hi = (int(x) for x in subset_by_index)
if not (0 <= lo <= hi < n):
raise ValueError('Requested eigenvalue indices are not valid. '
'Valid range is [0, {}] and start <= end, but '
'start={}, end={} is given'.format(n-1, lo, hi))
# fortran is 1-indexed
drv_args.update({'range': 'I', 'il': lo + 1, 'iu': hi + 1})
if subset_by_value:
lo, hi = subset_by_value
if not (-inf <= lo < hi <= inf):
raise ValueError('Requested eigenvalue bounds are not valid. '
'Valid range is (-inf, inf) and low < high, but '
'low={}, high={} is given'.format(lo, hi))
drv_args.update({'range': 'V', 'vl': lo, 'vu': hi})
# fix prefix for lapack routines
pfx = 'he' if cplx else 'sy'
# decide on the driver if not given
# first early exit on incompatible choice
if driver:
if b is None and (driver in ["gv", "gvd", "gvx"]):
raise ValueError('{} requires input b array to be supplied '
'for generalized eigenvalue problems.'
''.format(driver))
if (b is not None) and (driver in ['ev', 'evd', 'evr', 'evx']):
raise ValueError('"{}" does not accept input b array '
'for standard eigenvalue problems.'
''.format(driver))
if subset and (driver in ["ev", "evd", "gv", "gvd"]):
raise ValueError('"{}" cannot compute subsets of eigenvalues'
''.format(driver))
# Default driver is evr and gvd
else:
driver = "evr" if b is None else ("gvx" if subset else "gvd")
lwork_spec = {
'syevd': ['lwork', 'liwork'],
'syevr': ['lwork', 'liwork'],
'heevd': ['lwork', 'liwork', 'lrwork'],
'heevr': ['lwork', 'lrwork', 'liwork'],
}
if b is None: # Standard problem
drv, drvlw = get_lapack_funcs((pfx + driver, pfx+driver+'_lwork'),
[a1])
clw_args = {'n': n, 'lower': lower}
if driver == 'evd':
clw_args.update({'compute_v': 0 if _job == "N" else 1})
lw = _compute_lwork(drvlw, **clw_args)
# Multiple lwork vars
if isinstance(lw, tuple):
lwork_args = dict(zip(lwork_spec[pfx+driver], lw))
else:
lwork_args = {'lwork': lw}
drv_args.update({'lower': lower, 'compute_v': 0 if _job == "N" else 1})
> w, v, *other_args, info = drv(a=a1, **drv_args, **lwork_args)
E _flapack.error: (liwork>=max(1,10*n)||liwork==-1) failed for 10th keyword liwork: dsyevr:liwork=1
/usr/lib64/python3.11/site-packages/scipy/linalg/_decomp.py:560: error
I build 1.3.0 and 1.3.1 and get this error: