Re: Can I speed up a matrix * tensor calculation?

• To: mathgroup at smc.vnet.net
• Subject: [mg111364] Re: Can I speed up a matrix * tensor calculation?
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Thu, 29 Jul 2010 06:42:25 -0400 (EDT)
• References: <i2m4je\$o1h\$1@smc.vnet.net>

```On 27/07/10 09:15, Jagra wrote:
> I have a tensor and a matrix. Both pretty large.  Both have real
> numbers with machine precision:
>
>      Dimensions[matrix]
>      {10000, 5000}
>
>      Dimensions[tensor]
>      {5000, 7, 10000}
>
> I need to do the following:
>
>      Total[matrix]* Transpose[tensor {2, 3, 1}]];
>
> but this runs very slowly.  I've thought I needed to transpose the
> tensor to multiply it properly.
> The result should give me a vector of 5000 elements.
>
> Any suggestions that can speed this up?
>
> Thanks.
>
> J
>
The square brackets are not matched in your expression, so it is hard to
know exactly what calculation you need to do. Also, is the '*' meant to
be a matrix multiplication, and there seems to be a camma missing inside
the Transpose operation! It would be best if you posted some slow but
working code, with some idea of the speedup you are hoping to achieve.

Nevertheless, there are a few general points to make here:

1)  If your tensors are sparse, you may be better off to use SparseArray
objects.

2)  Check if your arrays are stored as packed arrays, testing with
Developer`PackedArrayQ and converting if necessary. Note that real
arrays containing the odd integer (such as 0 !) will not pack, and you
may want to apply N to such an array prior to packing with
Developer`ToPackedArray.

The difference between working with packed and unpacked arrays of this
size will be substantial.

David Bailey

http://www.dbaileyconsultancy.co.uk

```

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