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Gaussian elimination: Difference between revisions

Gaussian elimination (view source)

Revision as of 10:06, 25 December 2021

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→‎{{header|Phix}}: added syntax colouring, made p2js compatible
m (→‎version 3: added whitespace to the REXX section header wording.)
m (→‎{{header|Phix}}: added syntax colouring, made p2js compatible)
Line 4,166:
=={{header|Phix}}==
{{trans|PHP}}
<!--<lang Phix>function gauss_eliminate(sequence a, bphixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
integer n = length(b)
<span style="color: #008080;">function</span> <span style="color: #000000;">gauss_eliminate</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
atom tmp
<span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">({</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">})</span>
for col=1 to n do
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
integer m = col
<span style="color: #004080;">atom</span> <span style="color: #000000;">tmp</span>
atom mx = a[m][m]
<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;">n</span> <span style="color: #008080;">do</span>
for i=col+1 to n do
<span style="color: #004080;">integer</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">col</span>
tmp = abs(a[i][col])
<span style="color: #004080;">atom</span> <span style="color: #000000;">mx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">][</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]</span>
if tmp>mx then
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</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;">n</span> <span style="color: #008080;">do</span>
{m,mx} = {i,tmp}
<span style="color: #000000;">tmp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">col</span><span style="color: #0000FF;">])</span>
end if
<span style="color: #008080;">if</span> <span style="color: #000000;">tmp</span><span style="color: #0000FF;">></span><span style="color: #000000;">mx</span> <span style="color: #008080;">then</span>
end for
<span style="color: #0000FF;">{</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mx</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmp</span><span style="color: #0000FF;">}</span>
if col!=m then
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
{a[col],a[m]} = {a[m],a[col]}
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
{b[col],b[m]} = {b[m],b[col]}
<span style="color: #008080;">if</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">m</span> <span style="color: #008080;">then</span>
end if
<span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">],</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">],</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]}</span>
for i=col+1 to n do
<span style="color: #0000FF;">{</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">],</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">],</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]}</span>
tmp = a[i][col]/a[col][col]
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
for j=col+1 to n do
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</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;">n</span> <span style="color: #008080;">do</span>
a[i][j] -= tmp*a[col][j]
<span style="color: #000000;">tmp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]/</span><span style="color: #000000;">a</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;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</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;">n</span> <span style="color: #008080;">do</span>
a[i][col] = 0
<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">tmp</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
b[i] -= tmp*b[col]
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end for
<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</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: #000000;">0</span>
end for
<span style="color: #000000;">b</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;">tmp</span><span style="color: #0000FF;">*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]</span>
sequence x = repeat(0,n)
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
for col=n to 1 by -1 do
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
tmp = b[col]
<span style="color: #004080;">sequence</span> <span style="color: #000000;">x</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;">n</span><span style="color: #0000FF;">)</span>
for j=n to col+1 by -1 do
<span style="color: #008080;">for</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">=</span><span style="color: #000000;">n</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
tmp -= x[j]*a[col][j]
<span style="color: #000000;">tmp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]</span>
end for
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">n</span> <span style="color: #008080;">to</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
x[col] = tmp/a[col][col]
<span style="color: #000000;">tmp</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
return x
<span style="color: #000000;">x</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: #000000;">tmp</span><span style="color: #0000FF;">/</span><span style="color: #000000;">a</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 function
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">x</span>
constant a = {{1.00, 0.00, 0.00, 0.00, 0.00, 0.00},
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
{1.00, 0.63, 0.39, 0.25, 0.16, 0.10},
{1.00, 1.26, 1.58, 1.98, 2.49, 3.13},
<span style="color: #008080;">constant</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.00</span><span style="color: #0000FF;">},</span>
{1.00, 1.88, 3.55, 6.70, 12.62, 23.80},
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.63</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.39</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.25</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.16</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.10</span><span style="color: #0000FF;">},</span>
{1.00, 2.51, 6.32, 15.88, 39.90, 100.28},
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.26</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.58</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.98</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.49</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.13</span><span style="color: #0000FF;">},</span>
{1.00, 3.14, 9.87, 31.01, 97.41, 306.02}},
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.88</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.55</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.70</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">12.62</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.80</span><span style="color: #0000FF;">},</span>
b = {-0.01, 0.61, 0.91, 0.99, 0.60, 0.02}
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.51</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.32</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">15.88</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">39.90</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">100.28</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.14</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.87</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">31.01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">97.41</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">306.02</span><span style="color: #0000FF;">}},</span>
pp(gauss_eliminate(a, b))</lang>
<span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">0.01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.61</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.91</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.99</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.60</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.02</span><span style="color: #0000FF;">}</span>
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">gauss_eliminate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">))</span>
<!--</lang>-->
{{out}}
<pre>
Petelomax
7,805

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