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Matrix square root for a not-perfectly PSD matrix #8

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Matrix square root for a not-perfectly PSD matrix #8

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15 changes: 15 additions & 0 deletions tensorcircuit/backends/abstract_backend.py
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Original file line number Diff line number Diff line change
Expand Up @@ -60,6 +60,21 @@
e = self.sqrt(e)
return v @ self.diagflat(e) @ self.adjoint(v)

def sqrtmhpos(self: Any, a: Tensor) -> Tensor:
"""
Return the sqrtm of a known-to-be PSD Hermitian matrix ``a``.
:param a: tensor in matrix form
:type a: Tensor
:return: sqrtm of ``a`` after setting the negative eigenvalues (if they exist) to zero
:rtype: Tensor
"""
# maybe friendly for AD and also cosidering that several backend has no support for native sqrtm
e, v = self.eigh(a)
e = self.relu(e)
e = self.sqrt(e)
return v @ self.diagflat(e) @ self.adjoint(v)

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@refraction-ray refraction-ray Jan 18, 2025

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what about directly including relu line in sqrtmh function implementation as non-PSD matrix has no well defined sqrtm anyway?

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@abhinavd abhinavd Jan 18, 2025

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That should also work, although hopefully no one relies on the current behaviour of sqrtmh. That's why I thought it might be safest to have a different function itself. Or maybe add an optional keyword in sqrtmh to enforce PSD-ness.

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@refraction-ray refraction-ray Jan 18, 2025

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@abhinavd , ah, yes, sqrt can return complex values if the input is of negative value and in complex dtype. Then I think the better way is to add an optional keyword in sqrtmh, default as psd=False.


def eigvalsh(self: Any, a: Tensor) -> Tensor:
"""
Get the eigenvalues of matrix ``a``.
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