User:Grondilu

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Language	Proficiency
Perl 6	****.
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Bash	***..
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Perl 6

We're going to solve the example on the Wikipedia article using Clifford, a geometric algebra module. Optimization for large vector space does not quite work yet, so it's going to take (a lof of) time and a fair amount of memory, but it should work.

Let's create four vectors containing our input data:

${\begin{aligned}\mathbf {w} &=w^{k}\mathbf {e} _{k}\\\mathbf {h_{0}} &=(h^{k})^{0}\mathbf {e} _{k}\\\mathbf {h_{1}} &=(h^{k})^{1}\mathbf {e} _{k}\\\mathbf {h_{2}} &=(h^{k})^{2}\mathbf {e} _{k}\end{aligned}}$

Then what we're looking for are three scalars $\alpha$, $\beta$ and $\gamma$ such that:

$\alpha \mathbf {h0} +\beta \mathbf {h1} +\gamma \mathbf {h2} =\mathbf {w}$

To get for instance $\alpha$ we can first make the $\beta$ and $\gamma$ terms disappear:

$\alpha \mathbf {h0} \wedge \mathbf {h1} \wedge \mathbf {h2} =\mathbf {w} \wedge \mathbf {h1} \wedge \mathbf {h2}$

Noting $I=\mathbf {h0} \wedge \mathbf {h1} \wedge \mathbf {h2}$, we then get:

$\alpha =(\mathbf {w} \wedge \mathbf {h1} \wedge \mathbf {h2} )\cdot {\tilde {I}}/I\cdot {\tilde {I}}$

<lang perl6>use Clifford; my @height = <1.47 1.50 1.52 1.55 1.57 1.60 1.63 1.65 1.68 1.70 1.73 1.75 1.78 1.80 1.83>; my @weight = <52.21 53.12 54.48 55.84 57.20 58.57 59.93 61.29 63.11 64.47 66.28 68.10 69.92 72.19 74.46>;

my $w = [+] @weight Z* @e;

my $h0 = [+] @e[^@height]; my $h1 = [+] @height Z* @e; my $h2 = [+] (@height X** 2) Z* @e;

my $J = $h1∧$h2; my $I = $h0∧$J; say "alpha = ", ($w∧$J)·$I.reversion/($I·$I.reversion).Real;</lang>

Output:

alphas = 128.81280357844