Hi @KFrank,

Here’s an example,

```
>>> import torch
>>>
>>> A = torch.randn(3,3)
>>> M = A@A.transpose(-2,-1)
>>>
>>> M
tensor([[ 1.6559, -0.9484, 0.6780],
[-0.9484, 1.2809, -0.0119],
[ 0.6780, -0.0119, 0.5705]])
>>> torch.cholesky_inverse(M)
tensor([[ 1.0665, 0.3376, -1.2417],
[ 0.3376, 0.6097, 0.0284],
[-1.2417, 0.0284, 3.0724]])
>>> torch.inverse(M)
tensor([[ 5.9354, 4.3301, -6.9640],
[ 4.3301, 3.9398, -5.0643],
[-6.9640, -5.0643, 9.9240]])
>>>
>>> M=M.double()
>>> M
tensor([[ 1.6559, -0.9484, 0.6780],
[-0.9484, 1.2809, -0.0119],
[ 0.6780, -0.0119, 0.5705]], dtype=torch.float64)
>>> torch.cholesky_inverse(M)
tensor([[ 1.0665, 0.3376, -1.2417],
[ 0.3376, 0.6097, 0.0284],
[-1.2417, 0.0284, 3.0724]], dtype=torch.float64)
>>> torch.inverse(M)
tensor([[ 5.9354, 4.3301, -6.9640],
[ 4.3301, 3.9398, -5.0643],
[-6.9640, -5.0643, 9.9240]], dtype=torch.float64)
```

One thing I’ve just checked is multiplying the inverse by M to get back the identity matrix, but `torch.cholesky_inverse`

doesn’t give back `I`

but `torch.inverse`

does.

```
>>> iM_c = torch.cholesky_inverse(M)
>>> iM_i = torch.inverse(M)
>>>
>>> iM_c @ M
tensor([[ 6.0391e-01, -5.6433e-01, 1.0679e-02],
[ 3.1153e-17, 4.6053e-01, 2.3788e-01],
[ 4.1231e-16, 1.1777e+00, 9.1056e-01]], dtype=torch.float64)
>>> iM_i @ M
tensor([[ 1.0000e+00, 4.3730e-16, 5.4966e-16],
[-2.7408e-16, 1.0000e+00, 2.3931e-16],
[ 6.0420e-16, -6.4525e-16, 1.0000e+00]], dtype=torch.float64)
```

I assume I’m using `torch.cholesky_inverse`

incorrectly and should be using `torch.inverse`

instead?

Thank you for your help!

Edit: So, after re-reading the docs you need to apply `torch.cholesky`

before and call `torch.cholesky_inverse`

to that, rather than applying it directly! (I naively thought it was called internally, torch.cholesky_inverse — PyTorch 1.10.0 documentation )