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Gauss-Jordan matrix inversion: Difference between revisions

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Gauss-Jordan matrix inversion (view source)

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{{trans|Kotlin}}
uses ToReducedRowEchelonForm() from [[Reduced_row_echelon_form#Phix]]
<!--<lang Phix>function inverse(sequence matphixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
integer len = length(mat)
<span style="color: #008080;">function</span> <span style="color: #000000;">ToReducedRowEchelonForm</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">M</span><span style="color: #0000FF;">)</span>
sequence aug = repeat(repeat(0,2*len),len)
<span style="color: #004080;">integer</span> <span style="color: #000000;">lead</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
for i=1 to len do
<span style="color: #000000;">rowCount</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">M</span><span style="color: #0000FF;">),</span>
if length(mat[i])!=len then ?9/0 end if -- "Not a square matrix"
<span style="color: #000000;">columnCount</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">M</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]),</span>
for j=1 to len do
<span aug[i][j] style="color: mat[#000000;">i][j]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">rowCount</span> <span style="color: #008080;">do</span>
end for
<span style="color: #008080;">if</span> <span style="color: #000000;">lead</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">columnCount</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
-- augment by identity matrix to right
<span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
aug[i][i + len] = 1
<span style="color: #008080;">while</span> <span style="color: #000000;">M</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">lead</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
end for
<span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
aug = ToReducedRowEchelonForm(aug)
<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">rowCount</span> <span style="color: #008080;">then</span>
sequence inv = repeat(repeat(0,len),len)
<span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
-- remove identity matrix to left
<span style="color: #000000;">lead</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
for i=1 to len do
<span style="color: #008080;">if</span> <span style="color: #000000;">lead</span><span style="color: #0000FF;">=</span><span style="color: #000000;">columnCount</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
for j=len+1 to 2*len do
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
inv[i][j-len] = aug[i][j]
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
end for
<span style="color: #004080;">object</span> <span style="color: #000000;">mr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">M</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">M</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">lead</span><span style="color: #0000FF;">])</span>
end for
<span style="color: #000000;">M</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;">M</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">]</span>
return inv
<span style="color: #000000;">M</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mr</span>
end function
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">rowCount</span> <span style="color: #008080;">do</span>
 
<span style="color: #008080;">if</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">r</span> <span style="color: #008080;">then</span>
constant test = {{ 2, -1, 0},
<span style="color: #000000;">M</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: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">M</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">M</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">lead</span><span style="color: #0000FF;">],</span><span style="color: #000000;">M</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">]))</span>
{-1, 2, -1},
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
{ 0, -1, 2}}
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
pp(inverse(test),{pp_Nest,1})</lang>
<span style="color: #000000;">lead</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">M</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #000080;font-style:italic;">--&lt;/end of copy&gt;</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">inverse</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">mat</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">len</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mat</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">aug</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;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">len</span><span style="color: #0000FF;">),</span><span style="color: #000000;">len</span><span style="color: #0000FF;">)</span>
<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;">len</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mat</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])!=</span><span style="color: #000000;">len</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- "Not a square matrix"</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">len</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">aug</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;">mat</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: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000080;font-style:italic;">-- augment by identity matrix to right</span>
<span style="color: #000000;">aug</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">i</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">len</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">aug</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ToReducedRowEchelonForm</span><span style="color: #0000FF;">(</span><span style="color: #000000;">aug</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">inv</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;">len</span><span style="color: #0000FF;">),</span><span style="color: #000000;">len</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- remove identity matrix to left</span>
<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;">len</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">len</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">len</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">inv</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: #000000;">len</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">aug</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: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">inv</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">test</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">}}</span>
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">inverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">test</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>
<!--</lang>-->
{{out}}
<pre>
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===alternate===
{{trans|PowerShell}}
<!--<lang Phix>function gauss_jordan_inv(sequence aphixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
integer n = length(a)
<span style="color: #008080;">function</span> <span style="color: #000000;">gauss_jordan_inv</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
sequence b = repeat(repeat(0,n),n)
<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;">a</span><span style="color: #0000FF;">)</span>
for i=1 to n do b[i,i] = 1 end for
<span style="color: #004080;">sequence</span> <span style="color: #000000;">b</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;">n</span><span style="color: #0000FF;">),</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
for k=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;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span> <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: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
integer lmax = k
<span style="color: #008080;">for</span> <span style="color: #000000;">k</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>
atom amax = abs(a[k][k])
<span style="color: #004080;">integer</span> <span style="color: #000000;">lmax</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">k</span>
for l=k+1 to n do
<span style="color: #004080;">atom</span> <span style="color: #000000;">amax</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;">k</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">])</span>
atom tmp = abs(a[l][k])
<span style="color: #008080;">for</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">=</span><span style="color: #000000;">k</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>
if amax<tmp then
<span style="color: #004080;">atom</span> <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;">l</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">])</span>
{amax,lmax} = {tmp,l}
<span style="color: #008080;">if</span> <span style="color: #000000;">amax</span><span style="color: #0000FF;"><</span><span style="color: #000000;">tmp</span> <span style="color: #008080;">then</span>
end if
<span style="color: #0000FF;">{</span><span style="color: #000000;">amax</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lmax</span><span style="color: #0000FF;">}</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;">l</span><span style="color: #0000FF;">}</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if k!=lmax then
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
{a[k], a[lmax]} = {a[lmax], a[k]}
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">lmax</span> <span style="color: #008080;">then</span>
{b[k], b[lmax]} = {b[lmax], b[k]}
<span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">lmax</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;">lmax</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]}</span>
end if
<span style="color: #0000FF;">{</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">lmax</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;">lmax</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]}</span>
atom akk = a[k][k]
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if akk=0 then throw("Irregular matrix") end if
<span style="color: #004080;">atom</span> <span style="color: #000000;">akk</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
for j=1 to n do
<span style="color: #008080;">if</span> <span style="color: #000000;">akk</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">throw</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"Irregular matrix"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
a[k][j] /= akk
<span style="color: #008080;">for</span> <span style="color: #000000;">j</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>
b[k][j] /= akk
<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</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;">akk</span>
end for
<span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</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;">akk</span>
for i=1 to n do
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
if i!=k then
<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;">n</span> <span style="color: #008080;">do</span>
atom aik = a[i][k]
<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">k</span> <span style="color: #008080;">then</span>
for j=1 to n do
<span style="color: #004080;">atom</span> <span style="color: #000000;">aik</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;">k</span><span style="color: #0000FF;">]</span>
a[i][j] -= a[k][j]*aik
<span style="color: #008080;">for</span> <span style="color: #000000;">j</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>
b[i][j] -= b[k][j]*aik
<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;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">aik</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: #000000;">j</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;">k</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">aik</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
return b
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">b</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
sequence a = {{ 2, -1, 0},
{-1, 2, -1},
<span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>
{ 0, -1, 2}},
<span style="color: #0000FF;">{-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span>
inva = gauss_jordan_inv(a)
<span style="color: #0000FF;">{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">}},</span>
puts(1,"a = ")
<span style="color: #000000;">inva</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">gauss_jordan_inv</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>
pp(a,{pp_Nest,1,pp_Indent,4,pp_IntFmt,"%2d"})
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"a = "</span><span style="color: #0000FF;">)</span>
puts(1,"inv(a) = ")
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</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><span style="color: #004600;">pp_Indent</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_IntFmt</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d"</span><span style="color: #0000FF;">})</span>
pp(inva,{pp_Nest,1,pp_Indent,9,pp_FltFmt,"%4.2f"})</lang>
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"inv(a) = "</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">inva</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><span style="color: #004600;">pp_Indent</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_FltFmt</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%4.2f"</span><span style="color: #0000FF;">})</span>
<!--</lang>-->
{{out}}
<pre>
Petelomax
7,820

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/279841"