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Update implementation of Complex Division and Exponentiation

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Commander Tvis 2020-07-03 17:14:50 +07:00
parent 73005f715a
commit badb7b1365
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GPG Key ID: 70D5F4DCB0972F1B
2 changed files with 30 additions and 14 deletions
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17
kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt
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@ -41,8 +41,8 @@ private val PI_DIV_2 = Complex(PI / 2, 0)
* A field for complex numbers.
*/
object ComplexField : ExtendedField<Complex> {
override val zero: Complex = Complex(0, 0)
override val one: Complex = Complex(1, 0)
override val zero: Complex = 0.0.toComplex()
override val one: Complex = 1.0.toComplex()
/**
* The imaginary unit constant.
@ -90,24 +90,21 @@ object ComplexField : ExtendedField<Complex> {
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 asin(arg: Complex): Complex = -i * ln(sqrt(1 - (arg pow 2)) + i * arg)
override fun acos(arg: Complex): Complex = PI_DIV_2 + i * ln(sqrt(1 - (arg pow 2)) + i * arg)
override fun atan(arg: Complex): Complex {
val iArg = i * arg
return i * (ln(one - iArg) - ln(one + iArg)) / 2
return i * (ln(1 - iArg) - ln(1 + iArg)) / 2
}
override fun sinh(arg: Complex): Complex = (exp(arg) - exp(-arg)) / 2
override fun cosh(arg: Complex): Complex = (exp(arg) + exp(-arg)) / 2
override fun tanh(arg: Complex): Complex = (exp(arg) - exp(-arg)) / (exp(-arg) + exp(arg))
override fun asinh(arg: Complex): Complex = ln(sqrt(arg pow 2) + arg)
override fun asinh(arg: Complex): Complex = ln(sqrt((arg pow 2) + 1) + arg)
override fun acosh(arg: Complex): Complex = ln(arg + sqrt((arg - 1) * (arg + 1)))
override fun atanh(arg: Complex): Complex = (ln(arg + 1) - ln(1 - arg)) / 2
override fun power(arg: Complex, pow: Number): Complex =
arg.r.pow(pow.toDouble()) * (cos(pow.toDouble() * arg.theta) + i * sin(pow.toDouble() * arg.theta))
override fun power(arg: Complex, pow: Number): Complex = exp(ln(arg) * pow)
override fun exp(arg: Complex): Complex = exp(arg.re) * (cos(arg.im) + i * sin(arg.im))
override fun ln(arg: Complex): Complex = ln(arg.r) + i * atan2(arg.im, arg.re)

27
kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexTest.kt → kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexFieldTest.kt
View File

@ -37,13 +37,32 @@ internal class ComplexFieldTest {
@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) })
assertEquals(ComplexField { i * sinh(one) }, ComplexField { sin(i) })
assertEquals(ComplexField { i * sinh(PI.toComplex()) }, ComplexField { sin(i * PI.toComplex()) })
}
@Test
fun testArcsine() {
fun testInverseSine() {
assertEquals(Complex(0, -0.0), ComplexField { asin(zero) })
assertEquals(ComplexField { i * asinh(one) }.let { it.im.toInt() to it.re.toInt() },
ComplexField { asin(i) }.let { it.im.toInt() to it.re.toInt() })
}
@Test
fun testInverseHyperbolicSine() {
assertEquals(
ComplexField { i * PI.toComplex() / 2 }.let { it.im.toInt() to it.re.toInt() },
ComplexField { asinh(i) }.let { it.im.toInt() to it.re.toInt() })
}
@Test
fun testPower() {
assertEquals(ComplexField.zero, ComplexField { zero pow 2 })
assertEquals(ComplexField.zero, ComplexField { zero pow 2 })
assertEquals(
ComplexField { i * 8 }.let { it.im.toInt() to it.re.toInt() },
ComplexField { Complex(2, 2) pow 2 }.let { it.im.toInt() to it.re.toInt() })
}
}