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Element-wise product of matrices

asked 2017-03-25 07:48:47 -0500

dmital gravatar image

I am trying to calculate Hadamard product of two matrices.


def elementwise(M, N):
    assert(M.parent() == N.parent())
    nc, nr = M.ncols(), M.nrows()
    A = copy(M.parent().zero_element())
    for r in xrange(nr):
        for c in xrange(nc):
            A[r,c] = M[r,c] * N[r,c]
    return A

ring = PolynomialRing(QQ, 1, 'x') T = Matrix(ring, [ [1,-x,-x,0], [-x,1,0,-x], [0,-x,1,0], [-x,0,0,1]])

R = Matrix(QQ, [ [1,1,0,1], [1,1,1,0], [1,0,0,1], [0,1,1,0]])

B = ~T elementwise(B,R)

I get a following mistake

Error in lines 21-21
Traceback (most recent call last):
  File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 982, in execute
    exec compile(block+'\n', '', 'single') in namespace, locals
  File "", line 1, in <module>
  File "", line 2, in elementwise
AssertionError

Although elementwise(B,R) does not work, the program calculates elementwise(B,B) and elementwise(R,R) without any mistakes. Probably that's because matrices B and R have different types (B is a dense matrix over general ring and R is a rational dense matrix). What should I do?

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answered 2017-03-25 16:36:24 -0500

dan_fulea gravatar image

The following works:

def elementwise( M, N ):
    print "M parent is: %s" % M.parent()
    print "N parent is: %s" % N.parent()

    assert( M.parent() == N.parent() )

    nc, nr = M.ncols(), M.nrows()
    A = copy( M.parent().zero() )

    for r in xrange(nr):
        for c in xrange(nc):
            A[r,c] = M[r,c] * N[r,c]
    return A

ring  = PolynomialRing( QQ, 1, 'x' )
field = ring.fraction_field()

T = Matrix( ring, [
    [ 1, -x, -x,  0] ,
    [-x,  1,  0, -x] ,
    [ 0, -x,  1,  0] ,
    [-x,  0,  0,  1] ] )

R = Matrix( field, [
    [ 1, 1, 0, 1 ] ,
    [ 1, 1, 1, 0 ] ,
    [ 1, 0, 0, 1 ] ,
    [ 0, 1, 1, 0 ] ] )

B = ~T

elementwise( B, R )

(I only took care that the assertion does not fail. So i replaced the definition ring / field QQ from R, made it the field of fraction of the polynomial ring ring. While computing B, its parent is no longer the ring, as in T, but the field.)

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answered 2017-03-25 17:20:29 -0500

tmonteil gravatar image

updated 2017-03-25 17:23:54 -0500

The assertion error comes from the line

assert(M.parent() == N.parent())

because:

sage: B.parent()
Full MatrixSpace of 4 by 4 dense matrices over Fraction Field of Multivariate Polynomial Ring in x over Rational Field
sage: R.parent()
Full MatrixSpace of 4 by 4 dense matrices over Rational Field

Just remove that line and you will get:

sage: elementwise(B,R)    # with the assertion removed
[        (-1)/(x^4 + 2*x^3 + x^2 - 1)   (-x^2 - x)/(x^4 + 2*x^3 + x^2 - 1)                                    0 (-x^3 - x^2)/(x^4 + 2*x^3 + x^2 - 1)]
[  (-x^2 - x)/(x^4 + 2*x^3 + x^2 - 1)         (-1)/(x^4 + 2*x^3 + x^2 - 1) (-x^3 - x^2)/(x^4 + 2*x^3 + x^2 - 1)                                    0]
[(-x^3 - x^2)/(x^4 + 2*x^3 + x^2 - 1)                                    0                                    0       (-x^2)/(x^4 + 2*x^3 + x^2 - 1)]
[                                   0 (-x^3 - x^2)/(x^4 + 2*x^3 + x^2 - 1)       (-x^2)/(x^4 + 2*x^3 + x^2 - 1)                                    0]

Alternatively, if you want to keep your function intact, you can define both matrices on the same ring:

sage: elementwise(B,R.change_ring(B.base_ring()))   # without removing the assertion
[        (-1)/(x^4 + 2*x^3 + x^2 - 1)   (-x^2 - x)/(x^4 + 2*x^3 + x^2 - 1)                                    0 (-x^3 - x^2)/(x^4 + 2*x^3 + x^2 - 1)]
[  (-x^2 - x)/(x^4 + 2*x^3 + x^2 - 1)         (-1)/(x^4 + 2*x^3 + x^2 - 1) (-x^3 - x^2)/(x^4 + 2*x^3 + x^2 - 1)                                    0]
[(-x^3 - x^2)/(x^4 + 2*x^3 + x^2 - 1)                                    0                                    0       (-x^2)/(x^4 + 2*x^3 + x^2 - 1)]
[                                   0 (-x^3 - x^2)/(x^4 + 2*x^3 + x^2 - 1)       (-x^2)/(x^4 + 2*x^3 + x^2 - 1)                                    0]

Alternatively, the elementwise_product method doesthe job, see R.elementwise_product? for the documentation:

sage: R.elementwise_product(B)
[        (-1)/(x^4 + 2*x^3 + x^2 - 1)   (-x^2 - x)/(x^4 + 2*x^3 + x^2 - 1)                                    0 (-x^3 - x^2)/(x^4 + 2*x^3 + x^2 - 1)]
[  (-x^2 - x)/(x^4 + 2*x^3 + x^2 - 1)         (-1)/(x^4 + 2*x^3 + x^2 - 1) (-x^3 - x^2)/(x^4 + 2*x^3 + x^2 - 1)                                    0]
[(-x^3 - x^2)/(x^4 + 2*x^3 + x^2 - 1)                                    0                                    0       (-x^2)/(x^4 + 2*x^3 + x^2 - 1)]
[                                   0 (-x^3 - x^2)/(x^4 + 2*x^3 + x^2 - 1)       (-x^2)/(x^4 + 2*x^3 + x^2 - 1)                                    0]
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Asked: 2017-03-25 07:48:47 -0500

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Last updated: Mar 25