Determinant and permanent: Difference between revisions
Added Kotlin
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julia> det(A), perm(A)
(-360.0,900)</lang>
=={{header|Kotlin}}==
<lang scala>// version 1.1.2
typealias Matrix = Array<DoubleArray>
fun johnsonTrotter(n: Int): Pair<List<IntArray>, List<Int>> {
val p = IntArray(n) { it } // permutation
val q = IntArray(n) { it } // inverse permutation
val d = IntArray(n) { -1 } // direction = 1 or -1
var sign = 1
val perms = mutableListOf<IntArray>()
val signs = mutableListOf<Int>()
fun permute(k: Int) {
if (k >= n) {
perms.add(p.copyOf())
signs.add(sign)
sign *= -1
return
}
permute(k + 1)
for (i in 0 until k) {
val z = p[q[k] + d[k]]
p[q[k]] = z
p[q[k] + d[k]] = k
q[z] = q[k]
q[k] += d[k]
permute(k + 1)
}
d[k] *= -1
}
permute(0)
return perms to signs
}
fun determinant(m: Matrix): Double {
val (sigmas, signs) = johnsonTrotter(m.size)
var sum = 0.0
for ((i, sigma) in sigmas.withIndex()) {
var prod = 1.0
for ((j, s) in sigma.withIndex()) prod *= m[j][s]
sum += signs[i] * prod
}
return sum
}
fun permanent(m: Matrix) : Double {
val (sigmas, _) = johnsonTrotter(m.size)
var sum = 0.0
for (sigma in sigmas) {
var prod = 1.0
for ((i, s) in sigma.withIndex()) prod *= m[i][s]
sum += prod
}
return sum
}
fun main(args: Array<String>) {
val m1 = arrayOf(
doubleArrayOf(1.0)
)
val m2 = arrayOf(
doubleArrayOf(1.0, 2.0),
doubleArrayOf(3.0, 4.0)
)
val m3 = arrayOf(
doubleArrayOf(2.0, 9.0, 4.0),
doubleArrayOf(7.0, 5.0, 3.0),
doubleArrayOf(6.0, 1.0, 8.0)
)
val m4 = arrayOf(
doubleArrayOf( 1.0, 2.0, 3.0, 4.0),
doubleArrayOf( 4.0, 5.0, 6.0, 7.0),
doubleArrayOf( 7.0, 8.0, 9.0, 10.0),
doubleArrayOf(10.0, 11.0, 12.0, 13.0)
)
val matrices = arrayOf(m1, m2, m3, m4)
for (m in matrices) {
println("m${m.size} -> ")
println(" determinant = ${determinant(m)}")
println(" permanent = ${permanent(m)}\n")
}
}</lang>
{{out}}
<pre>
m1 ->
determinant = 1.0
permanent = 1.0
m2 ->
determinant = -2.0
permanent = 10.0
m3 ->
determinant = -360.0
permanent = 900.0
m4 ->
determinant = 0.0
permanent = 29556.0
</pre>
=={{header|Lua}}==
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