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Implement optimized complete Complex division, add tests class for it

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Commander Tvis 2020-07-03 15:50:14 +07:00
parent e64a6796ea
commit 73005f715a
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2 changed files with 95 additions and 5 deletions
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51
kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt
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@ -9,11 +9,20 @@ import scientifik.memory.MemoryWriter
import kotlin.math.*
/**
* A complex conjugate.
* This complex's conjugate.
*/
val Complex.conjugate: Complex
get() = Complex(re, -im)
/**
* This complex's reciprocal.
*/
val Complex.reciprocal: Complex
get() {
val scale = re * re + im * im
return Complex(re / scale, -im / scale)
}
/**
* Absolute value of complex number.
*/
@ -46,16 +55,48 @@ object ComplexField : ExtendedField<Complex> {
override fun multiply(a: Complex, b: Complex): Complex =
Complex(a.re * b.re - a.im * b.im, a.re * b.im + a.im * b.re)
override fun divide(a: Complex, b: Complex): Complex {
val scale = b.re * b.re + b.im * b.im
return a * Complex(b.re / scale, -b.im / scale)
override fun divide(a: Complex, b: Complex): Complex = when {
b.re.isNaN() || b.im.isNaN() -> Complex(Double.NaN, Double.NaN)
(if (b.im < 0) -b.im else +b.im) < (if (b.re < 0) -b.re else +b.re) -> {
val wr = b.im / b.re
val wd = b.re + wr * b.im
if (wd.isNaN() || wd == 0.0)
Complex(Double.NaN, Double.NaN)
else
Complex((a.re + a.im * wr) / wd, (a.im - a.re * wr) / wd)
}
b.im == 0.0 -> Complex(Double.NaN, Double.NaN)
else -> {
val wr = b.re / b.im
val wd = b.im + wr * b.re
if (wd.isNaN() || wd == 0.0)
Complex(Double.NaN, Double.NaN)
else
Complex((a.re * wr + a.im) / wd, (a.im * wr - a.re) / wd)
}
}
override fun sin(arg: Complex): Complex = i * (exp(-i * arg) - exp(i * arg)) / 2
override fun cos(arg: Complex): Complex = (exp(-i * arg) + exp(i * arg)) / 2
override fun tan(arg: Complex): Complex {
val e1 = exp(-i * arg)
val e2 = exp(i * arg)
return i * (e1 - e2) / (e1 + e2)
}
override fun asin(arg: Complex): Complex = -i * ln(sqrt(one - arg pow 2) + i * arg)
override fun acos(arg: Complex): Complex = PI_DIV_2 + i * ln(sqrt(one - arg pow 2) + i * arg)
override fun atan(arg: Complex): Complex = i * (ln(one - i * arg) - ln(one + i * arg)) / 2
override fun atan(arg: Complex): Complex {
val iArg = i * arg
return i * (ln(one - iArg) - ln(one + iArg)) / 2
}
override fun sinh(arg: Complex): Complex = (exp(arg) - exp(-arg)) / 2
override fun cosh(arg: Complex): Complex = (exp(arg) + exp(-arg)) / 2

49
kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexTest.kt Normal file
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@ -0,0 +1,49 @@
package scientifik.kmath.operations
import kotlin.math.PI
import kotlin.test.Test
import kotlin.test.assertEquals
internal class ComplexFieldTest {
@Test
fun testAddition() {
assertEquals(Complex(42, 42), ComplexField { Complex(16, 16) + Complex(26, 26) })
assertEquals(Complex(42, 16), ComplexField { Complex(16, 16) + 26 })
assertEquals(Complex(42, 16), ComplexField { 26 + Complex(16, 16) })
}
@Test
fun testSubtraction() {
assertEquals(Complex(42, 42), ComplexField { Complex(86, 55) - Complex(44, 13) })
assertEquals(Complex(42, 56), ComplexField { Complex(86, 56) - 44 })
assertEquals(Complex(42, 56), ComplexField { 86 - Complex(44, -56) })
}
@Test
fun testMultiplication() {
assertEquals(Complex(42, 42), ComplexField { Complex(4.2, 0) * Complex(10, 10) })
assertEquals(Complex(42, 21), ComplexField { Complex(4.2, 2.1) * 10 })
assertEquals(Complex(42, 21), ComplexField { 10 * Complex(4.2, 2.1) })
}
@Test
fun testDivision() {
assertEquals(Complex(42, 42), ComplexField { Complex(0, 168) / Complex(2, 2) })
assertEquals(Complex(42, 56), ComplexField { Complex(86, 56) - 44 })
assertEquals(Complex(42, 56), ComplexField { 86 - Complex(44, -56) })
assertEquals(Complex(Double.NaN, Double.NaN), ComplexField { Complex(1, 1) / Complex(Double.NaN, Double.NaN) })
assertEquals(Complex(Double.NaN, Double.NaN), ComplexField { Complex(1, 1) / Complex(0, 0) })
}
@Test
fun testSine() {
assertEquals(Complex(1.2246467991473532E-16, 0), ComplexField { sin(PI.toComplex()) })
assertEquals(Complex(0, 11.548739357257748), ComplexField { sin(i * PI.toComplex()) })
assertEquals(Complex(0, 1.1752011936438014), ComplexField { sin(i) })
}
@Test
fun testArcsine() {
assertEquals(Complex(0, -0.0), ComplexField { asin(zero) })
}
}