From b77bfeb372cef83e7c4a62e4f2e79e7282b58df1 Mon Sep 17 00:00:00 2001 From: Iaroslav Postovalov Date: Tue, 11 Aug 2020 14:58:28 +0700 Subject: [PATCH] Provide basic tests for complex numbers, also fix complex division --- .../scientifik/kmath/operations/Complex.kt | 107 +++++++++++++----- .../kmath/operations/ComplexFieldTest.kt | 46 ++++++++ .../kmath/operations/ComplexTest.kt | 38 +++++++ 3 files changed, 161 insertions(+), 30 deletions(-) create mode 100644 kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexFieldTest.kt create mode 100644 kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexTest.kt diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt index 0ce144a33..ef4c9bcf1 100644 --- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt +++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt @@ -8,15 +8,41 @@ import scientifik.memory.MemorySpec import scientifik.memory.MemoryWriter import kotlin.math.* +/** + * 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. + */ +val Complex.r: Double + get() = sqrt(re * re + im * im) + +/** + * An angle between vector represented by complex number and X axis. + */ +val Complex.theta: Double + get() = atan(im / re) + private val PI_DIV_2 = Complex(PI / 2, 0) /** * A field of [Complex]. */ -object ComplexField : ExtendedField { - override val zero: Complex = Complex(0.0, 0.0) - - override val one: Complex = Complex(1.0, 0.0) +object ComplexField : ExtendedField, Norm { + override val zero: Complex = 0.0.toComplex() + override val one: Complex = 1.0.toComplex() /** * The imaginary unit. @@ -30,19 +56,53 @@ object ComplexField : ExtendedField { 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 norm = b.re * b.re + b.im * b.im - return Complex((a.re * b.re + a.im * b.im) / norm, (a.re * b.im - a.im * b.re) / norm) + 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 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 power(arg: Complex, pow: Number): Complex = - arg.r.pow(pow.toDouble()) * (cos(pow.toDouble() * arg.theta) + i * sin(pow.toDouble() * arg.theta)) + 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(1 - (arg * arg)) + i * arg) + override fun acos(arg: Complex): Complex = PI_DIV_2 + i * ln(sqrt(1 - (arg * arg)) + i * arg) + + override fun atan(arg: Complex): Complex { + val iArg = i * arg + return i * (ln(1 - iArg) - ln(1 + iArg)) / 2 + } + + override fun power(arg: Complex, pow: Number): Complex = if (arg.im == 0.0) + arg.re.pow(pow.toDouble()).toComplex() + else + exp(pow * ln(arg)) override fun exp(arg: Complex): Complex = exp(arg.re) * (cos(arg.im) + i * sin(arg.im)) @@ -93,6 +153,8 @@ object ComplexField : ExtendedField { */ operator fun Double.times(c: Complex): Complex = Complex(c.re * this, c.im * this) + override fun norm(arg: Complex): Complex = arg.conjugate * arg + override fun symbol(value: String): Complex = if (value == "i") i else super.symbol(value) } @@ -105,12 +167,12 @@ object ComplexField : ExtendedField { data class Complex(val re: Double, val im: Double) : FieldElement, Comparable { constructor(re: Number, im: Number) : this(re.toDouble(), im.toDouble()) + override val context: ComplexField get() = ComplexField + override fun unwrap(): Complex = this override fun Complex.wrap(): Complex = this - override val context: ComplexField get() = ComplexField - override fun compareTo(other: Complex): Int = r.compareTo(other.r) companion object : MemorySpec { @@ -126,28 +188,13 @@ data class Complex(val re: Double, val im: Double) : FieldElement Complex): Buffer { return MemoryBuffer.create(Complex, size, init) diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexFieldTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexFieldTest.kt new file mode 100644 index 000000000..4722929cf --- /dev/null +++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexFieldTest.kt @@ -0,0 +1,46 @@ +package scientifik.kmath.operations + +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 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() }) + } +} diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexTest.kt new file mode 100644 index 000000000..e2132b75f --- /dev/null +++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexTest.kt @@ -0,0 +1,38 @@ +package scientifik.kmath.operations + +import kotlin.test.Test +import kotlin.test.assertEquals + +internal class ComplexTest { + @Test + fun conjugate() { + assertEquals( + Complex(0, -42), (ComplexField.i * 42).conjugate + ) + } + + @Test + fun reciprocal() { + assertEquals(Complex(0.5, -0.0), 2.toComplex().reciprocal) + } + + @Test + fun r() { + assertEquals(kotlin.math.sqrt(2.0), (ComplexField.i + 1.0.toComplex()).r) + } + + @Test + fun theta() { + assertEquals(0.0, 1.toComplex().theta) + } + + @Test + fun toComplex() { + assertEquals(Complex(42, 0), 42.toComplex()) + assertEquals(Complex(42.0, 0), 42.0.toComplex()) + assertEquals(Complex(42f, 0), 42f.toComplex()) + assertEquals(Complex(42.0, 0), 42.0.toComplex()) + assertEquals(Complex(42.toByte(), 0), 42.toByte().toComplex()) + assertEquals(Complex(42.toShort(), 0), 42.toShort().toComplex()) + } +} \ No newline at end of file