8000 ENH: Implement most linalg operations for 0x0 matrices by eric-wieser · Pull Request #8368 · numpy/numpy · GitHub
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ENH: Implement most linalg operations for 0x0 matrices #8368

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Merged
merged 1 commit into from
Mar 4, 2017
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ENH: Implement most linalg operations for 0x0 matrices #8368

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6 changes: 6 additions & 0 deletions doc/release/1.13.0-notes.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -194,6 +194,12 @@ np.matrix with booleans elements can now be created using the string syntax
``np.matrix`` failed whenever one attempts to use it with booleans, e.g.,
``np.matrix('True')``. Now, this works as expected.

More ``linalg`` operations now accept empty vectors and matrices
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
All of the following functions in ``np.linalg`` now work when given input
arrays with a 0 in the last two dimensions: `det``, ``slogdet``, ``pinv``,
``eigvals``, ``eigvalsh``, ``eig``, ``eigh``.

Changes
=======

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38 changes: 29 additions & 9 deletions numpy/linalg/linalg.py
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Expand Up @@ -23,7 +23,7 @@
csingle, cdouble, inexact, complexfloating, newaxis, ravel, all, Inf, dot,
add, multiply, sqrt, maximum, fastCopyAndTranspose, sum, isfinite, size,
finfo, errstate, geterrobj, longdouble, rollaxis, amin, amax, product, abs,
broadcast, atleast_2d, intp, asanyarray, isscalar, object_
broadcast, atleast_2d, intp, asanyarray, isscalar, object_, ones
)
from numpy.core.multiarray import normalize_axis_index
from numpy.lib import triu, asfarray
Expand Down Expand Up @@ -217,9 +217,13 @@ def _assertFinite(*arrays):
if not (isfinite(a).all()):
raise LinAlgError("Array must not contain infs or NaNs")

def _isEmpty2d(arr):
# check size first for efficiency
return arr.size == 0 and product(arr.shape[-2:]) == 0

def _assertNoEmpty2d(*arrays):
for a in arrays:
if a.size == 0 and product(a.shape[-2:]) == 0:
if _isEmpty2d(a):
raise LinAlgError("Arrays cannot be empty")


Expand Down Expand Up @@ -898,11 +902,12 @@ def eigvals(a):

"""
a, wrap = _makearray(a)
_assertNoEmpty2d(a)
_assertRankAtLeast2(a)
_assertNdSquareness(a)
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@eric-wieser eric-wieser Dec 12, 2016 •
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eig would previously produce a cryptic ValueError: cannot remove a zero-sized axis from an iterator, since it omitted the check in other places.

It's not clear to me why NpyIter_RemoveAxis does not allow a zero-sized axis to be removed. At the very least, it should allow all but the last zero-sized axis to be removed, I think?

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I have an old PR, which would remove this error, but mostly was never merged, because it required cleaning up of all linalg functions to make sure they don't crash within lapack....

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@eric-wieser eric-wieser Dec 12, 2016 •
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Mind digging it out? Presumably it required cleaning them up C-side, so this PR is not a substitute

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Only takes a search of open PRs by me: #3861

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Eric, is my PR removing that weird error in some way useful here, or is it orthogonal. Frankly, I am not sure myself whether or not it helps here, considering that lapack probably cannot handle 0d anyway.

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My guess is rather: Once we put this one in, I can reactivate my old one....

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Lapack actually seems able to handle 0x0 (not 0d) in a lot of cases, but needs more careful argument preparation, that we are not doing. In particular, I think I can make lstsq work with it. I think your pr removing that weird error would become useful for the vectorized ops though.

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@seberg: Ok, this is in - time to revisit #3861?

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jup, and I guess we can reduce it to those deletions....

_assertFinite(a)
t, result_t = _commonType(a)
if _isEmpty2d(a):
return empty(a.shape[-1:], dtype=result_t)

extobj = get_linalg_error_extobj(
_raise_linalgerror_eigenvalues_nonconvergence)
Expand Down Expand Up @@ -1002,10 +1007,11 @@ def eigvalsh(a, UPLO='L'):
gufunc = _umath_linalg.eigvalsh_up

a, wrap = _makearray(a)
_assertNoEmpty2d(a)
_assertRankAtLeast2(a)
_assertNdSquareness(a)
t, result_t = _commonType(a)
if _isEmpty2d(a):
return empty(a.shape[-1:], dtype=result_t)
signature = 'D->d' if isComplexType(t) else 'd->d'
w = gufunc(a, signature=signature, extobj=extobj)
return w.astype(_realType(result_t), copy=False)
Expand Down Expand Up @@ -1139,11 +1145,14 @@ def eig(a):

"""
a, wrap = _makearray(a)
_assertNoEmpty2d(a)
_assertRankAtLeast2(a)
_assertNdSquareness(a)
_assertFinite(a)
t, result_t = _commonType(a)
if _isEmpty2d(a):
w = empty(a.shape[-1:], dtype=result_t)
vt = empty(a.shape, dtype=result_t)
return w, wrap(vt)

extobj = get_linalg_error_extobj(
_raise_linalgerror_eigenvalues_nonconvergence)
Expand Down Expand Up @@ -1280,8 +1289,11 @@ def eigh(a, UPLO='L'):
a, wrap = _makearray(a)
_assertRankAtLeast2(a)
_assertNdSquareness(a)
_assertNoEmpty2d(a)
t, result_t = _commonType(a)
if _isEmpty2d(a):
w = empty(a.shape[-1:], dtype=result_t)
vt = empty(a.shape, dtype=result_t)
return w, wrap(vt)

extobj = get_linalg_error_extobj(
_raise_linalgerror_eigenvalues_nonconvergence)
Expand Down Expand Up @@ -1660,7 +1672,9 @@ def pinv(a, rcond=1e-15 ):

"""
a, wrap = _makearray(a)
_assertNoEmpty2d(a)
if _isEmpty2d(a):
res = empty(a.shape[:-2] + (a.shape[-1], a.shape[-2]), dtype=a.dtype)
return wrap(res)
a = a.conjugate()
u, s, vt = svd(a, 0)
m = u.shape[0]
Expand Down Expand Up @@ -1751,11 +1765,15 @@ def slogdet(a):

"""
a = asarray(a)
_assertNoEmpty2d(a)
_assertRankAtLeast2(a)
_assertNdSquareness(a)
t, result_t = _commonType(a)
real_t = _realType(result_t)
if _isEmpty2d(a):
# determinant of empty matrix is 1
sign = ones(a.shape[:-2], dtype=result_t)
logdet = zeros(a.shape[:-2], dtype=real_t)
return sign, logdet
signature = 'D->Dd' if isComplexType(t) else 'd->dd'
sign, logdet = _umath_linalg.slogdet(a, signature=signature)
if isscalar(sign):
Expand Down Expand Up @@ -1816,10 +1834,12 @@ def det(a):

"""
a = asarray(a)
_assertNoEmpty2d(a)
_assertRankAtLeast2(a)
_assertNdSquareness(a)
t, result_t = _commonType(a)
# 0x0 matrices have determinant 1
if _isEmpty2d(a):
return ones(a.shape[:-2], dtype=result_t)
signature = 'D->D' if isComplexType(t) else 'd->d'
r = _umath_linalg.det(a, signature=signature)
if isscalar(r):
Expand Down
25 changes: 5 additions & 20 deletions numpy/linalg/tests/test_linalg.py
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Expand Up @@ -127,7 +127,11 @@ def apply_tag(tag, cases):
array([[2. + 1j, 1. + 2j, 1 + 3j], [1 - 2j, 1 - 3j, 1 - 6j]], dtype=cdouble)),
LinalgCase("0x0",
np.empty((0, 0), dtype=double),
np.empty((0, 0), dtype=double),
np.empty((0,), dtype=double),
tags={'size-0'}),
LinalgCase("0x0_matrix",
np.empty((0, 0), dtype=double).view(np.matrix),
np.empty((0, 1), dtype=double).view(np.matrix),
tags={'size-0'}),
LinalgCase("8x8",
np.random.rand(8, 8),
Expand Down Expand Up @@ -549,9 +553,6 @@ class ArraySubclass(np.ndarray):
class TestEigvals(LinalgSquareTestCase, LinalgGeneralizedSquareTestCase):

def do(self, a, b, tags):
if 'size-0' in tags:
assert_raises(LinAlgError, linalg.eigvals, a)
return
ev = linalg.eigvals(a)
evalues, evectors = linalg.eig(a)
assert_almost_equal(ev, evalues)
Expand All @@ -569,10 +570,6 @@ def check(dtype):
class TestEig(LinalgSquareTestCase, LinalgGeneralizedSquareTestCase):

def do(self, a, b, tags):
if 'size-0' in tags:
assert_raises(LinAlgError, linalg.eig, a)
return

evalues, evectors = linalg.eig(a)
assert_allclose(dot_generalized(a, evectors),
np.asarray(evectors) * np.asarray(evalues)[..., None, :],
Expand Down Expand Up @@ -667,9 +664,6 @@ def test(self):
class TestPinv(LinalgSquareTestCase, LinalgNonsquareTestCase):

def do(self, a, b, tags):
if 'size-0' in tags:
assert_raises(LinAlgError, linalg.pinv, a)
return
a_ginv = linalg.pinv(a)
# `a @ a_ginv == I` does not hold if a is singular
assert_almost_equal(dot(a, a_ginv).dot(a), a, single_decimal=5, double_decimal=11)
Expand All @@ -679,9 +673,6 @@ def do(self, a, b, tags):
class TestDet(LinalgSquareTestCase, LinalgGeneralizedSquareTestCase):

def do(self, a, b, tags):
if 'size-0' in tags:
assert_raises(LinAlgError, linalg.det, a)
return
d = linalg.det(a)
(s, ld) = linalg.slogdet(a)
if asarray(a).dtype.type in (single, double):
Expand Down Expand Up @@ -820,9 +811,6 @@ def test_square(self):
class TestEigvalsh(HermitianTestCase, HermitianGeneralizedTestCase):

def do(self, a, b, tags):
if 'size-0' in tags:
assert_raises(LinAlgError, linalg.eigvalsh, a, 'L')
return
# note that eigenvalue arrays returned by eig must be sorted since
# their order isn't guaranteed.
ev = linalg.eigvalsh(a, 'L')
Expand Down Expand Up @@ -873,9 +861,6 @@ def test_UPLO(self):
class TestEigh(HermitianTestCase, HermitianGeneralizedTestCase):

def do(self, a, b, tags):
if 'size-0' in tags:
assert_raises(LinAlgError, linalg.eigh, a)
return
# note that eigenvalue arrays returned by eig must be sorted since
# their order isn't guaranteed.
ev, evc = linalg.eigh(a)
Expand Down
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