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Added a .pinv() method to MultiVectors plus tests #367

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Added a .pinv() method to MultiVectors plus tests #367

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edce4c4
Added a .pinv() method to MultiVectors plus tests
tBuLi Oct 9, 2020
9f50083
PEP8 my comments
tBuLi Oct 9, 2020
e929b9e
Added docstring to .pinv()
tBuLi Oct 9, 2020
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23 changes: 23 additions & 0 deletions clifford/_layout.py
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Original file line number Diff line number Diff line change
Expand Up @@ -690,6 +690,29 @@ def leftLaInvJIT(value):

return leftLaInvJIT

@_cached_property
def pinv_func(self):
"""
Get a function that returns left-pseudoinverse using a computational
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Is the left pseudo-inverse equal to the right pseudo-inverse (i.e., can you find a counterexample where it isn't?)

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@tBuLi tBuLi Oct 9, 2020 •
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Good question. I can't come up with a counter example. Something interesting and perhaps related I noticed is that if I replace the original np.linalg.solve with np.linalg.lstsq I get for the test example

Expected :0.5 + (3002399751580329.5^e2) - (0.5^e3) - (0.75^e13) - (3002399751580329.5^e23)
Actual   :0.5 - (0.5^e3)

I think it is save to say that this is undesired behavior. The pinv function clearly behaves much gentler. And in the numpy docs I see no mention of left and right actually, so perhaps we should leave that distinction altogether? Since it seems to return the input element anyway in case of singular behavior I don't see how that could be different left and right.

linear algebra method proposed by Christian Perwass. Identical to
`inv_func` except the inverse has been replaced by a pseudo inverse.
"""
mult_table = self.gmt
k_list, l_list, m_list = mult_table.coords
mult_table_vals = mult_table.data
n_dims = mult_table.shape[1]

identity = np.zeros((n_dims,))
identity[self._basis_blade_order.bitmap_to_index[0]] = 1

@_numba_utils.njit
def leftLaPInvJIT(value):
intermed = _numba_val_get_left_gmt_matrix(value, k_list, l_list, m_list, mult_table_vals, n_dims)
sol = np.linalg.pinv(intermed) @ identity
return sol

return leftLaPInvJIT

def get_left_gmt_matrix(self, x):
"""
This produces the matrix X that performs left multiplication with x
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7 changes: 7 additions & 0 deletions clifford/_multivector.py
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Expand Up @@ -773,6 +773,13 @@ def inv(self) -> 'MultiVector':
leftInv = leftLaInv
rightInv = leftLaInv

def pinv(self) -> 'MultiVector':
"""Returns the pseudoinverse using a computational
linear algebra method proposed by Christian Perwass. Identical to
`inv` when an inverse exists.
"""
return self._newMV(self.layout.pinv_func(self.value))
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def dual(self, I=None) -> 'MultiVector':
r"""The dual of the multivector against the given subspace I, :math:`\tilde M = MI^{-1}`

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11 changes: 11 additions & 0 deletions clifford/test/test_clifford.py
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Expand Up @@ -184,6 +184,17 @@ def test_indexing(self, g3):
e12[1 + e12]
assert e12[(2, 1)] == -1

def test_pinv(self, g3):
layout, blades = g3, g3.blades
e2 = blades['e2']
e3 = blades['e3']
x = 0.5*(1-e3) # Singular
y = 2*e2 + 5*e3 # invertible
with pytest.raises(ValueError):
x.leftLaInv()
assert x == x.pinv()
assert y.pinv() == y.leftLaInv()

def test_add_float64(self, g3):
'''
test array_wrap method to take control addition from numpy array
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