diff --git a/CHANGELOG.md b/CHANGELOG.md index 4bcc57810..ef675b692 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -2,7 +2,7 @@ ## [Unreleased] ### Added - +- Better trigonometric and hyperbolic functions for `AutoDiffField` (https://github.com/mipt-npm/kmath/pull/140). ### Changed ### Deprecated @@ -10,7 +10,7 @@ ### Removed ### Fixed - +- `symbol` method in `MstExtendedField` (https://github.com/mipt-npm/kmath/pull/140) ### Security ## [0.1.4] diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt index 8bc3f2936..d701dbfc8 100644 --- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt +++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt @@ -226,11 +226,11 @@ fun > AutoDiffField.tanh(x: Variable): Va } fun > AutoDiffField.asinh(x: Variable): Variable = - derive(variable { asin(x.value) }) { z -> x.d += z.d / sqrt(one + x.value * x.value) } + derive(variable { asinh(x.value) }) { z -> x.d += z.d / sqrt(one + x.value * x.value) } fun > AutoDiffField.acosh(x: Variable): Variable = - derive(variable { acos(x.value) }) { z -> x.d += z.d / (sqrt((x.value - one) * (x.value + one))) } + derive(variable { acosh(x.value) }) { z -> x.d += z.d / (sqrt((x.value - one) * (x.value + one))) } fun > AutoDiffField.atanh(x: Variable): Variable = - derive(variable { atan(x.value) }) { z -> x.d += z.d / (one - x.value * x.value) } + derive(variable { atanh(x.value) }) { z -> x.d += z.d / (one - x.value * x.value) } diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt index c08a63ccb..aba6c06ca 100644 --- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt +++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt @@ -3,19 +3,19 @@ package scientifik.kmath.misc import scientifik.kmath.operations.RealField import scientifik.kmath.structures.asBuffer import kotlin.math.PI +import kotlin.math.pow +import kotlin.math.sqrt import kotlin.test.Test import kotlin.test.assertEquals import kotlin.test.assertTrue class AutoDiffTest { - fun Variable(int: Int): Variable = Variable(int.toDouble()) - - fun deriv(body: AutoDiffField.() -> Variable): DerivationResult = + inline fun deriv(body: AutoDiffField.() -> Variable): DerivationResult = RealField.deriv(body) @Test fun testPlusX2() { - val x = Variable(3) // diff w.r.t this x at 3 + val x = Variable(3.0) // diff w.r.t this x at 3 val y = deriv { x + x } assertEquals(6.0, y.value) // y = x + x = 6 assertEquals(2.0, y.deriv(x)) // dy/dx = 2 @@ -24,8 +24,8 @@ class AutoDiffTest { @Test fun testPlus() { // two variables - val x = Variable(2) - val y = Variable(3) + val x = Variable(2.0) + val y = Variable(3.0) val z = deriv { x + y } assertEquals(5.0, z.value) // z = x + y = 5 assertEquals(1.0, z.deriv(x)) // dz/dx = 1 @@ -35,8 +35,8 @@ class AutoDiffTest { @Test fun testMinus() { // two variables - val x = Variable(7) - val y = Variable(3) + val x = Variable(7.0) + val y = Variable(3.0) val z = deriv { x - y } assertEquals(4.0, z.value) // z = x - y = 4 assertEquals(1.0, z.deriv(x)) // dz/dx = 1 @@ -45,7 +45,7 @@ class AutoDiffTest { @Test fun testMulX2() { - val x = Variable(3) // diff w.r.t this x at 3 + val x = Variable(3.0) // diff w.r.t this x at 3 val y = deriv { x * x } assertEquals(9.0, y.value) // y = x * x = 9 assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7 @@ -53,7 +53,7 @@ class AutoDiffTest { @Test fun testSqr() { - val x = Variable(3) + val x = Variable(3.0) val y = deriv { sqr(x) } assertEquals(9.0, y.value) // y = x ^ 2 = 9 assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7 @@ -61,7 +61,7 @@ class AutoDiffTest { @Test fun testSqrSqr() { - val x = Variable(2) + val x = Variable(2.0) val y = deriv { sqr(sqr(x)) } assertEquals(16.0, y.value) // y = x ^ 4 = 16 assertEquals(32.0, y.deriv(x)) // dy/dx = 4 * x^3 = 32 @@ -69,7 +69,7 @@ class AutoDiffTest { @Test fun testX3() { - val x = Variable(2) // diff w.r.t this x at 2 + val x = Variable(2.0) // diff w.r.t this x at 2 val y = deriv { x * x * x } assertEquals(8.0, y.value) // y = x * x * x = 8 assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x * x = 12 @@ -77,8 +77,8 @@ class AutoDiffTest { @Test fun testDiv() { - val x = Variable(5) - val y = Variable(2) + val x = Variable(5.0) + val y = Variable(2.0) val z = deriv { x / y } assertEquals(2.5, z.value) // z = x / y = 2.5 assertEquals(0.5, z.deriv(x)) // dz/dx = 1 / y = 0.5 @@ -87,7 +87,7 @@ class AutoDiffTest { @Test fun testPow3() { - val x = Variable(2) // diff w.r.t this x at 2 + val x = Variable(2.0) // diff w.r.t this x at 2 val y = deriv { pow(x, 3) } assertEquals(8.0, y.value) // y = x ^ 3 = 8 assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x ^ 2 = 12 @@ -95,8 +95,8 @@ class AutoDiffTest { @Test fun testPowFull() { - val x = Variable(2) - val y = Variable(3) + val x = Variable(2.0) + val y = Variable(3.0) val z = deriv { pow(x, y) } assertApprox(8.0, z.value) // z = x ^ y = 8 assertApprox(12.0, z.deriv(x)) // dz/dx = y * x ^ (y - 1) = 12 @@ -105,7 +105,7 @@ class AutoDiffTest { @Test fun testFromPaper() { - val x = Variable(3) + val x = Variable(3.0) val y = deriv { 2 * x + x * x * x } assertEquals(33.0, y.value) // y = 2 * x + x * x * x = 33 assertEquals(29.0, y.deriv(x)) // dy/dx = 2 + 3 * x * x = 29 @@ -113,9 +113,9 @@ class AutoDiffTest { @Test fun testInnerVariable() { - val x = Variable(1) + val x = Variable(1.0) val y = deriv { - Variable(1) * x + Variable(1.0) * x } assertEquals(1.0, y.value) // y = x ^ n = 1 assertEquals(1.0, y.deriv(x)) // dy/dx = n * x ^ (n - 1) = n - 1 @@ -124,9 +124,9 @@ class AutoDiffTest { @Test fun testLongChain() { val n = 10_000 - val x = Variable(1) + val x = Variable(1.0) val y = deriv { - var res = Variable(1) + var res = Variable(1.0) for (i in 1..n) res *= x res } @@ -136,7 +136,7 @@ class AutoDiffTest { @Test fun testExample() { - val x = Variable(2) + val x = Variable(2.0) val y = deriv { sqr(x) + 5 * x + 3 } assertEquals(17.0, y.value) // the value of result (y) assertEquals(9.0, y.deriv(x)) // dy/dx @@ -144,7 +144,7 @@ class AutoDiffTest { @Test fun testSqrt() { - val x = Variable(16) + val x = Variable(16.0) val y = deriv { sqrt(x) } assertEquals(4.0, y.value) // y = x ^ 1/2 = 4 assertEquals(1.0 / 8, y.deriv(x)) // dy/dx = 1/2 / x ^ 1/4 = 1/8 @@ -152,18 +152,98 @@ class AutoDiffTest { @Test fun testSin() { - val x = Variable(PI / 6) + val x = Variable(PI / 6.0) val y = deriv { sin(x) } - assertApprox(0.5, y.value) // y = sin(PI/6) = 0.5 - assertApprox(kotlin.math.sqrt(3.0) / 2, y.deriv(x)) // dy/dx = cos(PI/6) = sqrt(3)/2 + assertApprox(0.5, y.value) // y = sin(PI/6) = 0.5 + assertApprox(sqrt(3.0) / 2, y.deriv(x)) // dy/dx = cos(pi/6) = sqrt(3)/2 } @Test fun testCos() { val x = Variable(PI / 6) val y = deriv { cos(x) } - assertApprox(kotlin.math.sqrt(3.0) / 2, y.value) // y = cos(PI/6) = sqrt(3)/2 - assertApprox(-0.5, y.deriv(x)) // dy/dx = -sin(PI/6) = -0.5 + assertApprox(sqrt(3.0) / 2, y.value) //y = cos(pi/6) = sqrt(3)/2 + assertApprox(-0.5, y.deriv(x)) // dy/dx = -sin(pi/6) = -0.5 + } + + @Test + fun testTan() { + val x = Variable(PI / 6) + val y = deriv { tan(x) } + assertApprox(1.0 / sqrt(3.0), y.value) // y = tan(pi/6) = 1/sqrt(3) + assertApprox(4.0 / 3.0, y.deriv(x)) // dy/dx = sec(pi/6)^2 = 4/3 + } + + @Test + fun testAsin() { + val x = Variable(PI / 6) + val y = deriv { asin(x) } + assertApprox(kotlin.math.asin(PI / 6.0), y.value) // y = asin(pi/6) + assertApprox(6.0 / sqrt(36 - PI * PI), y.deriv(x)) // dy/dx = 6/sqrt(36-pi^2) + } + + @Test + fun testAcos() { + val x = Variable(PI / 6) + val y = deriv { acos(x) } + assertApprox(kotlin.math.acos(PI / 6.0), y.value) // y = acos(pi/6) + assertApprox(-6.0 / sqrt(36.0 - PI * PI), y.deriv(x)) // dy/dx = -6/sqrt(36-pi^2) + } + + @Test + fun testAtan() { + val x = Variable(PI / 6) + val y = deriv { atan(x) } + assertApprox(kotlin.math.atan(PI / 6.0), y.value) // y = atan(pi/6) + assertApprox(36.0 / (36.0 + PI * PI), y.deriv(x)) // dy/dx = 36/(36+pi^2) + } + + @Test + fun testSinh() { + val x = Variable(0.0) + val y = deriv { sinh(x) } + assertApprox(kotlin.math.sinh(0.0), y.value) // y = sinh(pi/6) + assertApprox(kotlin.math.cosh(0.0), y.deriv(x)) // dy/dx = cosh(pi/6) + } + + @Test + fun testCosh() { + val x = Variable(0.0) + val y = deriv { cosh(x) } + assertApprox(1.0, y.value) //y = cosh(pi/6) + assertApprox(0.0, y.deriv(x)) // dy/dx = sinh(pi/6) + } + + @Test + fun testTanh() { + val x = Variable(PI / 6) + val y = deriv { tanh(x) } + assertApprox(1.0 / sqrt(3.0), y.value) // y = tan(pi/6) = 1/sqrt(3) + assertApprox(1.0 / kotlin.math.cosh(PI / 6.0).pow(2), y.deriv(x)) // dy/dx = sec(PI/6)^2 + } + + @Test + fun testAsinh() { + val x = Variable(PI / 6) + val y = deriv { asinh(x) } + assertApprox(kotlin.math.asinh(PI / 6.0), y.value) // y = asinh(pi/6) + assertApprox(6.0 / sqrt(36 + PI * PI), y.deriv(x)) // dy/dx = 6/sqrt(pi^2+36) + } + + @Test + fun testAcosh() { + val x = Variable(PI / 6) + val y = deriv { acosh(x) } + assertApprox(kotlin.math.acosh(PI / 6.0), y.value) // y = acosh(pi/6) + assertApprox(-6.0 / sqrt(36.0 - PI * PI), y.deriv(x)) // dy/dx = -6/sqrt(36-pi^2) + } + + @Test + fun testAtanh() { + val x = Variable(PI / 6.0) + val y = deriv { atanh(x) } + assertApprox(kotlin.math.atanh(PI / 6.0), y.value) // y = atanh(pi/6) + assertApprox(-36.0 / (PI * PI - 36.0), y.deriv(x)) // dy/dx = -36/(pi^2-36) } @Test