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Conjugate transpose: Difference between revisions
Added Scala section
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end</lang>
Note: Ruby 1.9 had a bug in the Matrix#hermitian? method. It's fixed in 2.0.
=={{header|Scala}}==
<lang Scala>object ConjugateTranspose {
case class Complex(re: Double, im: Double) {
def conjugate(): Complex = Complex(re, -im)
def +(other: Complex) = Complex(re + other.re, im + other.im)
def *(other: Complex) = Complex(re * other.re - im * other.im, re * other.im + im * other.re)
override def toString(): String = {
if (im < 0) {
s"${re}${im}i"
} else {
s"${re}+${im}i"
}
}
}
case class Matrix(val entries: Vector[Vector[Complex]]) {
def *(other: Matrix): Matrix = {
new Matrix(
Vector.tabulate(entries.size, other.entries(0).size)((r, c) => {
val rightRow = entries(r)
val leftCol = other.entries.map(_(c))
rightRow.zip(leftCol)
.map{ case (x, y) => x * y } // multiply pair-wise
.foldLeft(new Complex(0,0)){ case (x, y) => x + y } // sum over all
})
)
}
def conjugateTranspose(): Matrix = {
new Matrix(
Vector.tabulate(entries(0).size, entries.size)((r, c) => entries(c)(r).conjugate)
)
}
def isHermitian(): Boolean = {
this == conjugateTranspose()
}
def isNormal(): Boolean = {
val ct = conjugateTranspose()
this * ct == ct * this
}
def isIdentity(): Boolean = {
val entriesWithIndexes = for (r <- 0 until entries.size; c <- 0 until entries(r).size) yield (r, c, entries(r)(c))
entriesWithIndexes.forall { case (r, c, x) =>
if (r == c) {
x == Complex(1.0, 0.0)
} else {
x == Complex(0.0, 0.0)
}
}
}
def isUnitary(): Boolean = {
(this * conjugateTranspose()).isIdentity()
}
override def toString(): String = {
entries.map(" " + _.mkString("[", ",", "]")).mkString("[\n", "\n", "\n]")
}
}
def main(args: Array[String]): Unit = {
val m = new Matrix(
Vector.fill(3, 3)(new Complex(Math.random() * 2 - 1.0, Math.random() * 2 - 1.0))
)
println("Matrix: " + m)
println("Conjugate Transpose: " + m.conjugateTranspose())
println("Hermitian: " + m.isHermitian())
println("Normal: " + m.isNormal())
println("Unitary: " + m.isUnitary())
}
}</lang>
{{out}}
<pre>
Matrix: [
[-0.7679977131543951-0.439979346567841i,-0.6011221529373452+0.510336881376179i,-0.22458301626795674-0.2036390034398219i]
[-0.29309032295973036+0.3034337168992096i,-0.06392399629070344-0.8178102917845342i,0.06006452944412022-0.6141208421036348i]
[0.34841978725201117+0.3778314407778909i,0.6768867572228499+0.7323625144544055i,-0.8246879334889017-0.009443253424316733i]
]
Conjugate Transpose: [
[-0.7679977131543951+0.439979346567841i,-0.29309032295973036-0.3034337168992096i,0.34841978725201117-0.3778314407778909i]
[-0.6011221529373452-0.510336881376179i,-0.06392399629070344+0.8178102917845342i,0.6768867572228499-0.7323625144544055i]
[-0.22458301626795674+0.2036390034398219i,0.06006452944412022+0.6141208421036348i,-0.8246879334889017+0.009443253424316733i]
]
Hermitian: false
Normal: false
Unitary: false
</pre>
=={{header|Sparkling}}==
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