Numerical integration: Difference between revisions
Added Kotlin
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Line 2,612:
simpson(x -> x, 0, 6000, 6000000)
(0.25000000000000006,4.605170384957135,1.25e7,1.8e7)
</pre>
=={{header|Kotlin}}==
<lang scala>// version 1.1.1
typealias Func = (Double) -> Double
fun integrate(a: Double, b: Double, n: Int, f: Func) {
val h = (b - a) / n
val sum = DoubleArray(5)
for (i in 0 until n) {
val x = a + i * h
sum[0] += f(x)
sum[1] += f(x + h / 2.0)
sum[2] += f(x + h)
sum[3] += (f(x) + f(x + h)) / 2.0
sum[4] += (f(x) + 4.0 * f(x + h / 2.0) + f(x + h)) / 6.0
}
val methods = listOf("LeftRect ", "MidRect ", "RightRect", "Trapezium", "Simpson ")
for (i in 0..4) println("${methods[i]} = ${"%f".format(sum[i] * h)}")
println()
}
fun main(args: Array<String>) {
integrate(0.0, 1.0, 100) { it * it * it }
integrate(1.0, 100.0, 1_000) { 1.0 / it }
integrate(0.0, 5000.0, 5_000_000) { it }
integrate(0.0, 6000.0, 6_000_000) { it }
}</lang>
{{out}}
<pre>
LeftRect = 0.245025
MidRect = 0.249988
RightRect = 0.255025
Trapezium = 0.250025
Simpson = 0.250000
LeftRect = 4.654991
MidRect = 4.604763
RightRect = 4.556981
Trapezium = 4.605986
Simpson = 4.605170
LeftRect = 12499997.500000
MidRect = 12500000.000000
RightRect = 12500002.500000
Trapezium = 12500000.000000
Simpson = 12500000.000000
LeftRect = 17999997.000000
MidRect = 18000000.000000
RightRect = 18000003.000000
Trapezium = 18000000.000000
Simpson = 18000000.000000
</pre>
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