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Matrix multiplication: Difference between revisions
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By contrast, A×B is for element-by-element multiplication of arrays of the same shape, and if they are simple elements, this is ordinary multiplication.
=={{header|Generic}}==
{{trans|Generic}}
<lang cpp>--------------------- Full MATRIX Class --------------------
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|AppleScript}}==
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