User:Grondilu: Difference between revisions
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{{mylang|Raku|<nowiki>****.</nowiki>}} |
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{{mylang|Perl|<nowiki>**...</nowiki>}} |
{{mylang|Perl|<nowiki>**...</nowiki>}} |
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{{mylang|Bash|<nowiki>***..</nowiki>}} |
{{mylang|Bash|<nowiki>***..</nowiki>}} |
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{{mylang|Octave|<nowiki>*....</nowiki>}} |
{{mylang|Octave|<nowiki>*....</nowiki>}} |
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{{mylang|Wolfram Language|<nowiki>*....</nowiki>}} |
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=={{header|Perl 6}}== |
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We're going to solve the example on the Wikipedia article using [https://github.com/grondilu/clifford Clifford], a [https://en.wikipedia.org/wiki/Geometric_algebra 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. |
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Let's create four vectors containing our input data: |
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<math>\begin{align} |
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\mathbf{w} & = w^k\mathbf{e}_k\\ |
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\mathbf{h_0} & = (h^k)^0\mathbf{e}_k\\ |
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\mathbf{h_1} & = (h^k)^1\mathbf{e}_k\\ |
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\mathbf{h_2} & = (h^k)^2\mathbf{e}_k |
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\end{align}</math> |
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Then what we're looking for are three scalars <math>\alpha</math>, <math>\beta</math> and <math>\gamma</math> such that: |
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<math>\alpha\mathbf{h0} + \beta\mathbf{h1} + \gamma\mathbf{h2} = \mathbf{w}</math> |
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To get for instance <math>\alpha</math> we can first make the <math>\beta</math> and <math>\gamma</math> terms disappear: |
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<math>\alpha\mathbf{h0}\wedge\mathbf{h1}\wedge\mathbf{h2} = \mathbf{w}\wedge\mathbf{h1}\wedge\mathbf{h2}</math> |
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Noting <math>I = \mathbf{h0}\wedge\mathbf{h1}\wedge\mathbf{h2}</math>, we then get: |
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<math>\alpha = (\mathbf{w}\wedge\mathbf{h1}\wedge\mathbf{h2})\cdot\tilde{I}/I\cdot\tilde{I}</math> |
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<lang perl6>use Clifford; |
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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>; |
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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>; |
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my $w = [+] @weight Z* @e; |
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my $h0 = [+] @e[^@height]; |
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my $h1 = [+] @height Z* @e; |
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my $h2 = [+] (@height X** 2) Z* @e; |
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my $J = $h1∧$h2; |
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my $I = $h0∧$J; |
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say "alpha = ", ($w∧$J)·$I.reversion/($I·$I.reversion).Real;</lang> |
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{{out}} |
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<pre>alphas = 128.81280357844</pre> |
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Latest revision as of 13:15, 10 September 2022
| My Favorite Languages | |
| Language | Proficiency |
| Raku | ****. |
| Perl | **... |
| Bash | ***.. |
| Octave | *.... |
| Wolfram Language | *.... |