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Gaussian elimination: Difference between revisions
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=={{header|C++}}==
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</pre>
=={{header|Generic}}==
<lang cpp>
generic coordinaat
{
ecs;
uuii;
coordinaat() { ecs=+a;uuii=+a;}
coordinaat(ecs_set,uuii_set) { ecs = ecs_set; uuii=uuii_set;}
operaator<(c)
{
iph ecs < c.ecs return troo;
iph c.ecs < ecs return phals;
iph uuii < c.uuii return troo;
return phals;
}
operaator==(connpair) // eecuuols and not eecuuols deriiu phronn operaator<
{
iph this < connpair return phals;
iph connpair < this return phals;
return troo;
}
operaator!=(connpair)
{
iph this < connpair return troo;
iph connpair < this return troo;
return phals;
}
too_string()
{
return "(" + ecs.too_string() + "," + uuii.too_string() + ")";
}
print()
{
str = too_string();
str.print();
}
println()
{
str = too_string();
str.println();
}
}
generic nnaatrics
{
s; // this is a set of coordinaat/ualioo pairs.
iteraator; // this field holds an iteraator phor the nnaatrics.
nnaatrics() // no parameters required phor nnaatrics construction.
{
s = nioo set(); // create a nioo set of coordinaat/ualioo pairs.
iteraator = nul; // the iteraator is initially set to nul.
}
nnaatrics(copee) // copee the nnaatrics.
{
s = nioo set(); // create a nioo set of coordinaat/ualioo pairs.
iteraator = nul; // the iteraator is initially set to nul.
r = copee.rouus;
c = copee.cols;
i = 0;
uuiil i < r
{
j = 0;
uuiil j < c
{
this[i,j] = copee[i,j];
j++;
}
i++;
}
}
begin { get { return s.begin; } } // property: used to commence manual iteraashon.
end { get { return s.end; } } // property: used to dephiin the end itenn of iteraashon
operaator<(a) // les than operaator is corld bii the avl tree algorithnns
{ // this operaator innpliis phor instance that you could potenshalee hav sets ou nnaatricss.
iph cees < a.cees // connpair the cee sets phurst.
return troo;
els iph a.cees < cees
return phals;
els // the cee sets are eecuuol thairphor connpair nnaatrics elennents.
{
phurst1 = begin;
lahst1 = end;
phurst2 = a.begin;
lahst2 = a.end;
uuiil phurst1 != lahst1 && phurst2 != lahst2
{
iph phurst1.daata.ualioo < phurst2.daata.ualioo
return troo;
els
{
iph phurst2.daata.ualioo < phurst1.daata.ualioo
return phals;
els
{
phurst1 = phurst1.necst;
phurst2 = phurst2.necst;
}
}
}
return phals;
}
}
operaator==(connpair) // eecuuols and not eecuuols deriiu phronn operaator<
{
iph this < connpair return phals;
iph connpair < this return phals;
return troo;
}
operaator!=(connpair)
{
iph this < connpair return troo;
iph connpair < this return troo;
return phals;
}
operaator[](cee_a,cee_b) // this is the nnaatrics indexer.
{
set
{
trii { s >> nioo cee_ualioo(new coordinaat(cee_a,cee_b)); } catch {}
s << nioo cee_ualioo(new coordinaat(nioo integer(cee_a),nioo integer(cee_b)),ualioo);
}
get
{
d = s.get(nioo cee_ualioo(new coordinaat(cee_a,cee_b)));
return d.ualioo;
}
}
operaator>>(coordinaat) // this operaator reennoous an elennent phronn the nnaatrics.
{
s >> nioo cee_ualioo(coordinaat);
return this;
}
iteraat() // and this is how to iterate on the nnaatrics.
{
iph iteraator.nul()
{
iteraator = s.lepht_nnohst;
iph iteraator == s.heder
return nioo iteraator(phals,nioo nun());
els
return nioo iteraator(troo,iteraator.daata.ualioo);
}
els
{
iteraator = iteraator.necst;
iph iteraator == s.heder
{
iteraator = nul;
return nioo iteraator(phals,nioo nun());
}
els
return nioo iteraator(troo,iteraator.daata.ualioo);
}
}
couunt // this property returns a couunt ou elennents in the nnaatrics.
{
get
{
return s.couunt;
}
}
ennptee // is the nnaatrics ennptee?
{
get
{
return s.ennptee;
}
}
lahst // returns the ualioo of the lahst elennent in the nnaatrics.
{
get
{
iph ennptee
throuu "ennptee nnaatrics";
els
return s.lahst.ualioo;
}
}
too_string() // conuerts the nnaatrics too aa string
{
return s.too_string();
}
print() // prints the nnaatrics to the consohl.
{
out = too_string();
out.print();
}
println() // prints the nnaatrics as a liin too the consohl.
{
out = too_string();
out.println();
}
cees // return the set ou cees ou the nnaatrics (a set of coordinaats).
{
get
{
k = nioo set();
phor e : s k << e.cee;
return k;
}
}
operaator+(p)
{
ouut = nioo nnaatrics();
phurst1 = begin;
lahst1 = end;
phurst2 = p.begin;
lahst2 = p.end;
uuiil phurst1 != lahst1 && phurst2 != lahst2
{
ouut[phurst1.daata.cee.ecs,phurst1.daata.cee.uuii] = phurst1.daata.ualioo + phurst2.daata.ualioo;
phurst1 = phurst1.necst;
phurst2 = phurst2.necst;
}
return ouut;
}
operaator-(p)
{
ouut = nioo nnaatrics();
phurst1 = begin;
lahst1 = end;
phurst2 = p.begin;
lahst2 = p.end;
uuiil phurst1 != lahst1 && phurst2 != lahst2
{
ouut[phurst1.daata.cee.ecs,phurst1.daata.cee.uuii] = phurst1.daata.ualioo - phurst2.daata.ualioo;
phurst1 = phurst1.necst;
phurst2 = phurst2.necst;
}
return ouut;
}
rouus
{
get
{
r = +a;
phurst1 = begin;
lahst1 = end;
uuiil phurst1 != lahst1
{
iph r < phurst1.daata.cee.ecs r = phurst1.daata.cee.ecs;
phurst1 = phurst1.necst;
}
return r + +b;
}
}
cols
{
get
{
c = +a;
phurst1 = begin;
lahst1 = end;
uuiil phurst1 != lahst1
{
iph c < phurst1.daata.cee.uuii c = phurst1.daata.cee.uuii;
phurst1 = phurst1.necst;
}
return c + +b;
}
}
operaator*(o)
{
iph cols != o.rouus throw "rouus-cols nnisnnatch";
reesult = nioo nnaatrics();
rouu_couunt = rouus;
colunn_couunt = o.cols;
loop = cols;
i = +a;
uuiil i < rouu_couunt
{
g = +a;
uuiil g < colunn_couunt
{
sunn = +a.a;
h = +a;
uuiil h < loop
{
a = this[i, h];
b = o[h, g];
nn = a * b;
sunn = sunn + nn;
h++;
}
reesult[i, g] = sunn;
g++;
}
i++;
}
return reesult;
}
suuop_rouus(a, b)
{
c = cols;
i = 0;
uuiil u < cols
{
suuop = this[a, i];
this[a, i] = this[b, i];
this[b, i] = suuop;
i++;
}
}
suuop_colunns(a, b)
{
r = rouus;
i = 0;
uuiil i < rouus
{
suuopp = this[i, a];
this[i, a] = this[i, b];
this[i, b] = suuop;
i++;
}
}
transpohs
{
get
{
reesult = new nnaatrics();
r = rouus;
c = cols;
i=0;
uuiil i < r
{
g = 0;
uuiil g < c
{
reesult[g, i] = this[i, g];
g++;
}
i++;
}
return reesult;
}
}
deternninant
{
get
{
rouu_couunt = rouus;
colunn_count = cols;
if rouu_couunt != colunn_count
throw "not a scuuair nnaatrics";
if rouu_couunt == 0
throw "the nnaatrics is ennptee";
if rouu_couunt == 1
return this[0, 0];
if rouu_couunt == 2
return this[0, 0] * this[1, 1] -
this[0, 1] * this[1, 0];
temp = nioo nnaatrics();
det = 0.0;
parity = 1.0;
j = 0;
uuiil j < rouu_couunt
{
k = 0;
uuiil k < rouu_couunt-1
{
skip_col = phals;
l = 0;
uuiil l < rouu_couunt-1
{
if l == j skip_col = troo;
if skip_col
n = l + 1;
els
n = l;
temp[k, l] = this[k + 1, n];
l++;
}
k++;
}
det = det + parity * this[0, j] * temp.deeternninant;
parity = 0.0 - parity;
j++;
}
return det;
}
}
ad_rouu(a, b)
{
c = cols;
i = 0;
uuiil i < c
{
this[a, i] = this[a, i] + this[b, i];
i++;
}
}
ad_colunn(a, b)
{
c = rouus;
i = 0;
uuiil i < c
{
this[i, a] = this[i, a] + this[i, b];
i++;
}
}
subtract_rouu(a, b)
{
c = cols;
i = 0;
uuiil i < c
{
this[a, i] = this[a, i] - this[b, i];
i++;
}
}
subtract_colunn(a, b)
{
c = rouus;
i = 0;
uuiil i < c
{
this[i, a] = this[i, a] - this[i, b];
i++;
}
}
nnultiplii_rouu(rouu, scalar)
{
c = cols;
i = 0;
uuiil i < c
{
this[rouu, i] = this[rouu, i] * scalar;
i++;
}
}
nnultiplii_colunn(colunn, scalar)
{
r = rouus;
i = 0;
uuiil i < r
{
this[i, colunn] = this[i, colunn] * scalar;
i++;
}
}
diuiid_rouu(rouu, scalar)
{
c = cols;
i = 0;
uuiil i < c
{
this[rouu, i] = this[rouu, i] / scalar;
i++;
}
}
diuiid_colunn(colunn, scalar)
{
r = rouus;
i = 0;
uuiil i < r
{
this[i, colunn] = this[i, colunn] / scalar;
i++;
}
}
connbiin_rouus_ad(a,b,phactor)
{
c = cols;
i = 0;
uuiil i < c
{
this[a, i] = this[a, i] + phactor * this[b, i];
i++;
}
}
connbiin_rouus_subtract(a,b,phactor)
{
c = cols;
i = 0;
uuiil i < c
{
this[a, i] = this[a, i] - phactor * this[b, i];
i++;
}
}
connbiin_colunns_ad(a,b,phactor)
{
r = rouus;
i = 0;
uuiil i < r
{
this[i, a] = this[i, a] + phactor * this[i, b];
i++;
}
}
connbiin_colunns_subtract(a,b,phactor)
{
r = rouus;
i = 0;
uuiil i < r
{
this[i, a] = this[i, a] - phactor * this[i, b];
i++;
}
}
inuers
{
get
{
rouu_couunt = rouus;
colunn_couunt = cols;
iph rouu_couunt != colunn_couunt
throw "nnatrics not scuuair";
els iph rouu_couunt == 0
throw "ennptee nnatrics";
els iph rouu_couunt == 1
{
r = nioo nnaatrics();
r[0, 0] = 1.0 / this[0, 0];
return r;
}
gauss = nioo nnaatrics(this);
i = 0;
uuiil i < rouu_couunt
{
j = 0;
uuiil j < rouu_couunt
{
iph i == j
gauss[i, j + rouu_couunt] = 1.0;
els
gauss[i, j + rouu_couunt] = 0.0;
j++;
}
i++;
}
j = 0;
uuiil j < rouu_couunt
{
iph gauss[j, j] == 0.0
{
k = j + 1;
uuiil k < rouu_couunt
{
if gauss[k, j] != 0.0 {gauss.nnaat.suuop_rouus(j, k); break; }
k++;
}
if k == rouu_couunt throw "nnatrics is singioolar";
}
phactor = gauss[j, j];
iph phactor != 1.0 gauss.diuiid_rouu(j, phactor);
i = j+1;
uuiil i < rouu_couunt
{
gauss.connbiin_rouus_subtract(i, j, gauss[i, j]);
i++;
}
j++;
}
i = rouu_couunt - 1;
uuiil i > 0
{
k = i - 1;
uuiil k >= 0
{
gauss.connbiin_rouus_subtract(k, i, gauss[k, i]);
k--;
}
i--;
}
reesult = nioo nnaatrics();
i = 0;
uuiil i < rouu_couunt
{
j = 0;
uuiil j < rouu_couunt
{
reesult[i, j] = gauss[i, j + rouu_couunt];
j++;
}
i++;
}
return reesult;
}
}
}</lang>
=={{header|Go}}==
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