Square root of matrix ?

[Yossi Biton]

is there a torch function which computes the square root of a matrix (not an element-wise square root)?

I have a square positive definite matrix A, and i have to compute A^(-0.5).

It's actually the inverse of A^0.5, but i can find a way to compute A^0.5.

[soumith]

Take torch.svd and then take the :sqrt on the eigen values.

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[Yossi Biton]

thanks ! 

so if anyone interested this piece of code add the powm method to Tensor class :

function torch.Tensor.powm(self, power)

   local U,D,V = torch.svd(self)

   local result = U*(D:pow(power):diag())*V:t()

   return result

end

can't guarantee it works for all kinds of matrix, but in my case when the matrix is positive definite the call A:powm(-0.5) works fine.

usage example : 

th> A = torch.randn(5,5)

                                                                      [0.0001s]

th> A = A:t()*A -- make A positive semi-definite

                                                                      [0.0000s]

th> A_sqrt = A:powm(0.5)

                                                                      [0.0001s]

th> A

  3.1788  -0.2700   3.5322   0.5113   0.4057

 -0.2700   0.5782  -0.6825   1.6945  -0.1207

  3.5322  -0.6825   5.3633   0.2835  -1.0688

  0.5113   1.6945   0.2835  11.3951  -4.5324

  0.4057  -0.1207  -1.0688  -4.5324   4.4123

[torch.DoubleTensor of dimension 5x5]

                                                                      [0.0002s]

th> A_sqrt*A_sqrt

  3.1788  -0.2700   3.5322   0.5113   0.4057

 -0.2700   0.5782  -0.6825   1.6945  -0.1207

  3.5322  -0.6825   5.3633   0.2835  -1.0688

  0.5113   1.6945   0.2835  11.3951  -4.5324

  0.4057  -0.1207  -1.0688  -4.5324   4.4123

[torch.DoubleTensor of dimension 5x5]

On Friday, March 13, 2015 at 8:49:22 PM UTC+2, smth chntla wrote:

Take torch.svd and then take the :sqrt on the eigen values.

[Ajay Talati]

Nice :)))

You should get that documented and merged?

Even for really big sparse matrices, I don't know if there's any more efficient or accurate methods better than SVD for square roots ??