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Cholesky decomposition: Difference between revisions

Cholesky decomposition (view source)

Revision as of 12:57, 4 January 2022

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→‎{{header|Phix}}: added syntax colouring, marked p2js compatible
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=={{header|Phix}}==
{{trans|Sidef}}
<!--<lang Phix>function cholesky(sequence matrixphixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
integer l = length(matrix)
<span style="color: #008080;">function</span> <span style="color: #000000;">cholesky</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">)</span>
sequence chol = repeat(repeat(0,l),l)
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">)</span>
for row=1 to l do
<span style="color: #004080;">sequence</span> <span style="color: #000000;">chol</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">),</span><span style="color: #000000;">l</span><span style="color: #0000FF;">)</span>
for col=1 to row do
<span style="color: #008080;">for</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
atom x = matrix[row][col]
<span style="color: #008080;">for</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">row</span> <span style="color: #008080;">do</span>
for i=1 to col do
<span style="color: #004080;">atom</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">row</span><span style="color: #0000FF;">][</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]</span>
x -= chol[row][i] * chol[col][i]
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">col</span> <span style="color: #008080;">do</span>
end for
<span style="color: #000000;">x</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">chol</span><span style="color: #0000FF;">[</span><span style="color: #000000;">row</span><span style="color: #0000FF;">][</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">chol</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">][</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
chol[row][col] = iff(row == col ? sqrt(x) : x/chol[col][col])
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end for
<span style="color: #000000;">chol</span><span style="color: #0000FF;">[</span><span style="color: #000000;">row</span><span style="color: #0000FF;">][</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">row</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">col</span> <span style="color: #0000FF;">?</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">:</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">/</span><span style="color: #000000;">chol</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">][</span><span style="color: #000000;">col</span><span style="color: #0000FF;">])</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
return chol
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">chol</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
ppOpt({pp_Nest,1})
pp(cholesky({{ 25, 15, -5 },
<span style="color: #7060A8;">ppOpt</span><span style="color: #0000FF;">({</span><span style="color: #004600;">pp_Nest</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span>
{ 15, 18, 0 },
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cholesky</span><span style="color: #0000FF;">({{</span> <span style="color: #000000;">25</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">15</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">5</span> <span style="color: #0000FF;">},</span>
{ -5, 0, 11 }}))
<span style="color: #0000FF;">{</span> <span style="color: #000000;">15</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span> <span style="color: #0000FF;">},</span>
pp(cholesky({{ 18, 22, 54, 42},
<span style="color: #0000FF;">{</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">11</span> <span style="color: #0000FF;">}}))</span>
{ 22, 70, 86, 62},
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cholesky</span><span style="color: #0000FF;">({{</span> <span style="color: #000000;">18</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">54</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">42</span><span style="color: #0000FF;">},</span>
{ 54, 86, 174, 134},
<span style="color: #0000FF;">{</span> <span style="color: #000000;">22</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">70</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">86</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">62</span><span style="color: #0000FF;">},</span>
{ 42, 62, 134, 106}}))</lang>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">54</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">86</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">174</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">134</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">42</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">62</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">134</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">106</span><span style="color: #0000FF;">}}))</span>
<!--</lang>-->
{{out}}
<pre>
Petelomax
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