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Fast evaluation of modified dot product

• To: mathgroup at smc.vnet.net
• Subject: [mg86720] Fast evaluation of modified dot product
• From: Art <grenander at gmail.com>
• Date: Wed, 19 Mar 2008 05:26:00 -0500 (EST)

I have (below) a vector x and matrix y and would like to compute z
efficiently:

{n, m, b} = {10000, 100, 10};  (* n >> m > b *)
x = RandomReal[{-1.,1.}, n - b +1]
y = RandomChoice[{-1,1}, {n, m}];

w = Partition[y, b, 1];
z = Dot[x, w];

I have to compute z for many different x with w fixed. For large n, w
becomes prohibitively big.

Doing the below is much slower but doesn't require large memory
allocation:

z2 = Fold[(#1 + x[[#2]] y[[#2;;#2+b-1]]) &, 0., Range[Length[x]] ];

I was wondering if there is a good way to compute z that doesn't
require a lot of memory.

Thanks,
Art.

• Follow-Ups:
  • Re: Fast evaluation of modified dot product
    • From: Carl Woll <carlw@wolfram.com>
  • Re: Fast evaluation of modified dot product
    • From: Daniel Lichtblau <danl@wolfram.com>