numpy-discussion

[Numpy-discussion] Kronecker product

[Nils W. <nw...@is...>]

Hi,

I would appreciate it, if Numpy could handle the Kronecker-product of
two matrices X, Y.

kron(X,Y) is the Kronecker tensor product of X and Y.
The result is a large matrix formed by taking all possible products
between the elements of X and those of Y. If X is m-by-n
and Y is p-by-q, then kron(X,Y) is m*p-by-n*q.

Nils

RE: [Numpy-discussion] Kronecker product

[Paul F. D. <pa...@pf...>]

Using the outer product you get a matrix that has the right size and
contents but it is m*n by p*q
Was that a misprint in your post?
>>> x
array([1, 2, 3, 4, 5, 6])
>>> x.shape=(3,2)
>>> y = 10*transpose(x)
>>> y
array([[10, 30, 50],
       [20, 40, 60]])
>>> z = outerproduct(x.flat, y.flat)
>>> z
array([[ 10,  30,  50,  20,  40,  60],
       [ 20,  60, 100,  40,  80, 120],
       [ 30,  90, 150,  60, 120, 180],
       [ 40, 120, 200,  80, 160, 240],
       [ 50, 150, 250, 100, 200, 300],
       [ 60, 180, 300, 120, 240, 360]])
>>>

-----Original Message-----
From: num...@li...
[mailto:num...@li...]On Behalf Of Nils
Wagner
Sent: Wednesday, July 18, 2001 4:10 AM
To: num...@li...
Subject: [Numpy-discussion] Kronecker product


Hi,

I would appreciate it, if Numpy could handle the Kronecker-product of
two matrices X, Y.

kron(X,Y) is the Kronecker tensor product of X and Y.
The result is a large matrix formed by taking all possible products
between the elements of X and those of Y. If X is m-by-n
and Y is p-by-q, then kron(X,Y) is m*p-by-n*q.

Nils



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Re: [Numpy-discussion] Kronecker product

[Nils W. <nw...@is...>]

"Paul F. Dubois" schrieb:

> Using the outer product you get a matrix that has the right size and
> contents but it is m*n by p*q
> Was that a misprint in your post?
> >>> x
> array([1, 2, 3, 4, 5, 6])
> >>> x.shape=(3,2)
> >>> y = 10*transpose(x)
> >>> y
> array([[10, 30, 50],
>        [20, 40, 60]])
> >>> z = outerproduct(x.flat, y.flat)
> >>> z
> array([[ 10,  30,  50,  20,  40,  60],
>        [ 20,  60, 100,  40,  80, 120],
>        [ 30,  90, 150,  60, 120, 180],
>        [ 40, 120, 200,  80, 160, 240],
>        [ 50, 150, 250, 100, 200, 300],
>        [ 60, 180, 300, 120, 240, 360]])
> >>>
>
> -----Original Message-----
> From: num...@li...
> [mailto:num...@li...]On Behalf Of Nils
> Wagner
> Sent: Wednesday, July 18, 2001 4:10 AM
> To: num...@li...
> Subject: [Numpy-discussion] Kronecker product
>
> Hi,
>
> I would appreciate it, if Numpy could handle the Kronecker-product of
> two matrices X, Y.
>
> kron(X,Y) is the Kronecker tensor product of X and Y.
> The result is a large matrix formed by taking all possible products
> between the elements of X and those of Y. If X is m-by-n
> and Y is p-by-q, then kron(X,Y) is m*p-by-n*q.
>
> Nils
>
> _______________________________________________
> Numpy-discussion mailing list
> Num...@li...
> http://lists.sourceforge.net/lists/listinfo/numpy-discussion

>>> a

> array([[1, 2],
>              [3, 4]])

> >>> b

> array([[11, 12],
>               [13, 14]])

> >>> outerproduct(a,b)

> array([[11, 12, 13, 14],
>               [22, 24, 26, 28],
>               [33, 36, 39, 42],
>               [44, 48, 52, 56]])


The Kronecker product  applied to A,B is

kron(A,B) = array([[11,12,22,24],
                                      [13,14,26,28],
                                      [33,36,44,48],
                                      [39,42,52,56]])


How can I rearrange the result of outerproduct to the result of
Kronecker product with numpy ?

Cheers,

                  Nils

Re: [Numpy-discussion] Kronecker product

[Charles G W. <cg...@al...>]

Nils Wagner writes:
 > 
 > How can I rearrange the result of outerproduct to the result of
 > Kronecker product with numpy ?
 > 

def kron(a,b):
    o = outerproduct(a,b)
    o.shape = a.shape + b.shape
    return concatenate(concatenate(o, axis=1), axis=1)

Re: [Numpy-discussion] Kronecker product

[Konrad H. <hi...@cn...>]

> I would appreciate it, if Numpy could handle the Kronecker-product of
> two matrices X, Y.
> 
> kron(X,Y) is the Kronecker tensor product of X and Y.

import Numeric
def kron(x, y):
  return Numeric.multiply.outer(x, y)

> The result is a large matrix formed by taking all possible products
> between the elements of X and those of Y. If X is m-by-n
> and Y is p-by-q, then kron(X,Y) is m*p-by-n*q.

OK, there's one difference: the function shown about returns an array
of shape (m, n, p, q). If the input arrays are always 2D, the
following will do what you need:

import Numeric
def kron(x, y):
  z = Numeric.transpose(Numeric.multiply.outer(x, y), [0, 2, 1, 3])
  z.shape = (z.shape[0]*z.shape[1], z.shape[2]*z.shape[3])
  return z

Konrad.
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Re: [Numpy-discussion] Kronecker product

[Nils W. <nw...@is...>]

Charles G Waldman schrieb:

> Nils Wagner writes:
>  >
>  > How can I rearrange the result of outerproduct to the result of
>  > Kronecker product with numpy ?
>  >
>
> def kron(a,b):
>     o = outerproduct(a,b)
>     o.shape = a.shape + b.shape
>     return concatenate(concatenate(o, axis=1), axis=1)

What is the difference between kron(z,eye) and kron(yt,eye) ?

Nils