[Numpy-discussion] help with applying a transform

Gary Ruben gruben@bigpond.net...
Sat Apr 18 06:17:01 CDT 2009


I think I've answered my own question - I remembered tensordot, and the 
following seems to work:

def transform(tx_matrix, psi1, psi2):
     psi = np.tensordot(tx_matrix,
           np.concatenate((psi1[newaxis],psi2[newaxis])),axes=1))
     return psi[0], psi[1]

sorry for the noise,
Gary

Gary Ruben wrote:
> I'm trying to work out how to apply a 2x2 transform matrix to a spinor, e.g.
> 
> [psi1']   [a  b][psi1]
> [     ] = [    ][    ]
> [psi2']   [c  d][psi2]
> 
> where [[a,b],[c,d]] is a transform matrix and psi1 and psi2 are
> i x j x k complex arrays representing complex scalar field data. I 
> worked that one way to do it with 2D fields (psi1 and psi2 being 2D,
> i x j arrays) is
> 
> def transform(tx_matrix, psi1, psi2):
>      psi = np.dot(tx_matrix, np.rollaxis(np.dstack((psi1,psi2)),2,1))
>      return psi[0], psi[1]
> 
> or, equivalently
> 
> def transform(tx_matrix, psi1, psi2):
>      psi = np.dot(tx_matrix, np.rollaxis(
>              np.concatenate((psi1[newaxis],psi2[newaxis])),1))
>      return psi[0], psi[1]
> 
> but, as seems usual for me, I'm confused with trying to extend this to 
> the next higher dimension; 3D in this case. It seems to me that there 
> might be a neater way to do this, i.e. some built-in feature of an 
> existing numpy function. How do I extend this for 3D psi1 and psi2 
> arrays? Are there any general tips or guides for helping to minimise 
> confusion when it comes to manipulating axes like this, such as standard 
> ways to extend 2D recipes to 3D?
> 
> Gary R.
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> 


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