       Re: stirring chocolate pudding backwards: identifying coordinates

• To: mathgroup at smc.vnet.net
• Subject: [mg101401] Re: stirring chocolate pudding backwards: identifying coordinates
• From: Ray Koopman <koopman at sfu.ca>
• Date: Sun, 5 Jul 2009 04:47:04 -0400 (EDT)
• References: <h2nbeg\$h80\$1@smc.vnet.net>

```On Jul 1, 3:34 am, Andreas <aa... at ix.netcom.com> wrote:
> I want to find the coordinates at each time increment of the
> weighted average of all samples with the weights in proportion to
> their performance or "values" in the time series data. Wouldn't this
> point vary, over time, across the plane from which I select the
> samples (especially as in its projected application I'll have values
> for thousands of time increments and they may have far greater
> variance than my simple example)?  Also, it seems like it wouldn't
> have to correspond to any specific point in the list of samples.

On Jul 2, 4:15 am, Ray Koopman <koopman at sfu.ca> wrote:
> Dimensions[samples] = {p,d} = {# of points, # of dimensions}. If
> each sample point has a value associated with it at each of t time
> intervals, then Dimensions[values] should be either {p,t} or {t,p}.
> Assume it's {t,p}, with each row corresponding to a time interval.
> Then values.samples/(Tr/@values) will give a matrix whose dimensions
> are {t,d}, with each row containsing the weighted average coordinates
> for a time interval.

On Jul 4, 3:38 am, Andreas <aa... at ix.netcom.com> wrote:
> I can't get values.samples/(Tr /@ values) to work.
> I get messages like the following:
>
> Dot::dotsh: "Tensors {{...}} and {{..}} have incompatible shapes.

If the analysis in my July 2 post is correct, and if you're trying to
analyze the data from your initial post, then the 'values' matrix is
the wrong size. Its dimensions are {3,3}, but they should be {3,4} or
{4,3}. Actually, things would be clearer if you used distinct values
for p, d, and t. For instance:
p = 5 sample points, d = 3 dimensions, t = 4 time intervals.

samples

{{0.35212, 0.195537, 0.452343},
{0.259074, 0.481887, 0.259039},
{0.778938, 0.00217905, 0.218883},
{0.056913, 0.266178, 0.676909},
{0.166826, 0.0516333, 0.781541}}

values

{{1.07072, 0.975643, 0.881083, 0.962515, 1.55834},
{0.411462, 0.200276, 0.823472, 1.59278, 1.31966},
{1.24984, 0.837737, 1.26199, 0.920523, 1.4315},
{1.23532, 1.81471, 0.63395, 0.0366297, 0.251216}}

values.samples/(Tr/@values)

{{0.299331, 0.186865, 0.513804},
{0.264282, 0.154305, 0.581413},
{0.338738, 0.170088, 0.491175},
{0.363291, 0.287056, 0.349653}}

```

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