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Re: Matrix Dot Product
*To*: mathgroup at smc.vnet.net
*Subject*: [mg52193] Re: Matrix Dot Product
*From*: Peter Pein <petsie at arcor.de>
*Date*: Sun, 14 Nov 2004 04:30:51 -0500 (EST)
*References*: <cn4lbm$13s$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
MacDonald, Calum (MAT) wrote:
> Hi
>
> I was wondering if someone could please help me with a command for
> calculating the dot product of two (NxN) matrices.
>
> For example, for two (2x2) matrices, A and B, we define the dot product
> as:
>
> A(1,1)*B(1,1) + A(2,1)*B(2,1) + A(1,2)*B(1,2) + A(2,2)*B(2,2)
>
> i.e. we multiply corresponding entries of the matrices and sum these
> values.
>
> It is easy to write this in a loop but for large matrices the
> calculation is rather slow.
>
> Is there a Mathematica function that I can call that will allow me to do
> this faster?
>
> Thanks
>
> Calum
>
>
>
In[1]:=
matrixDot[a_, b_] := Dot @@@ Transpose[{a, b}] // Tr
In[2]:=
m1 = Table[a[i, j], {i, 5}, {j, 3}];
m2 = Table[b[i, j], {i, 5}, {j, 3}];
In[4]:=
matrixDot[m1, m2]
Out[4]=
a[1, 1] b[1, 1] + a[1, 2] b[1, 2] + a[1, 3] b[1, 3] +
a[2, 1] b[2, 1] + a[2, 2] b[2, 2] + a[2, 3] b[2, 3] +
a[3, 1] b[3, 1] + a[3, 2] b[3, 2] + a[3, 3] b[3, 3] +
a[4, 1] b[4, 1] + a[4, 2] b[4, 2] + a[4, 3] b[4, 3] +
a[5, 1] b[5, 1] + a[5, 2] b[5, 2] + a[5, 3] b[5, 3]
In[5]:=
m1 = Partition[Table[Random[], {10^6}], 10^3];
m2 = Partition[Table[Random[], {10^6}], 10^3];
Timing[matrixDot[m1, m2]]
Out[7]=
{0.821 Second, 249923.}
with Mathematica 4.0 on a PII/300 Win2k
--
Peter Pein
Berlin
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