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Upgrade AutoDiff support of trigonometric ops, also fix some problems with MstAlgebra #140

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CommanderTvis merged 5 commits from autodiff-update into dev 2020-09-20 18:21:37 +03:00
Conversation 1 Commits 5 Files Changed 4 +171 -49
4 changed files with 171 additions and 49 deletions
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4
CHANGELOG.md
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@ -2,7 +2,7 @@
## [Unreleased] ## [Unreleased]
### Added ### Added
- Better trigonometric and hyperbolic functions for `AutoDiffField` (https://github.com/mipt-npm/kmath/pull/140).
### Changed ### Changed
### Deprecated ### Deprecated
@ -10,7 +10,7 @@
### Removed ### Removed
### Fixed ### Fixed
- `symbol` method in `MstExtendedField` (https://github.com/mipt-npm/kmath/pull/140)
### Security ### Security
## [0.1.4] ## [0.1.4]

26
kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MstAlgebra.kt
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@ -38,7 +38,9 @@ object MstSpace : Space<MST>, NumericAlgebra<MST> {
* [Ring] over [MST] nodes. * [Ring] over [MST] nodes.
*/ */
object MstRing : Ring<MST>, NumericAlgebra<MST> { object MstRing : Ring<MST>, NumericAlgebra<MST> {
override val zero: MST = number(0.0) override val zero: MST
get() = MstSpace.zero
override val one: MST = number(1.0) override val one: MST = number(1.0)
override fun number(value: Number): MST = MstSpace.number(value) override fun number(value: Number): MST = MstSpace.number(value)
@ -59,8 +61,11 @@ object MstRing : Ring<MST>, NumericAlgebra<MST> {
* [Field] over [MST] nodes. * [Field] over [MST] nodes.
*/ */
object MstField : Field<MST> { object MstField : Field<MST> {
override val zero: MST = number(0.0) override val zero: MST
override val one: MST = number(1.0) get() = MstRing.zero
override val one: MST
get() = MstRing.one
override fun symbol(value: String): MST = MstRing.symbol(value) override fun symbol(value: String): MST = MstRing.symbol(value)
override fun number(value: Number): MST = MstRing.number(value) override fun number(value: Number): MST = MstRing.number(value)
@ -79,14 +84,25 @@ object MstField : Field<MST> {
* [ExtendedField] over [MST] nodes. * [ExtendedField] over [MST] nodes.
*/ */
object MstExtendedField : ExtendedField<MST> { object MstExtendedField : ExtendedField<MST> {
override val zero: MST = number(0.0) override val zero: MST
override val one: MST = number(1.0) get() = MstField.zero
override val one: MST
get() = MstField.one
override fun symbol(value: String): MST = MstField.symbol(value)
override fun sin(arg: MST): MST = unaryOperation(TrigonometricOperations.SIN_OPERATION, arg) override fun sin(arg: MST): MST = unaryOperation(TrigonometricOperations.SIN_OPERATION, arg)
override fun cos(arg: MST): MST = unaryOperation(TrigonometricOperations.COS_OPERATION, arg) override fun cos(arg: MST): MST = unaryOperation(TrigonometricOperations.COS_OPERATION, arg)
override fun tan(arg: MST): MST = unaryOperation(TrigonometricOperations.TAN_OPERATION, arg)
override fun asin(arg: MST): MST = unaryOperation(TrigonometricOperations.ASIN_OPERATION, arg) override fun asin(arg: MST): MST = unaryOperation(TrigonometricOperations.ASIN_OPERATION, arg)
override fun acos(arg: MST): MST = unaryOperation(TrigonometricOperations.ACOS_OPERATION, arg) override fun acos(arg: MST): MST = unaryOperation(TrigonometricOperations.ACOS_OPERATION, arg)
override fun atan(arg: MST): MST = unaryOperation(TrigonometricOperations.ATAN_OPERATION, arg) override fun atan(arg: MST): MST = unaryOperation(TrigonometricOperations.ATAN_OPERATION, arg)
override fun sinh(arg: MST): MST = unaryOperation(HyperbolicOperations.SINH_OPERATION, arg)
override fun cosh(arg: MST): MST = unaryOperation(HyperbolicOperations.COSH_OPERATION, arg)
override fun tanh(arg: MST): MST = unaryOperation(HyperbolicOperations.TANH_OPERATION, arg)
override fun asinh(arg: MST): MST = unaryOperation(HyperbolicOperations.ASINH_OPERATION, arg)
override fun acosh(arg: MST): MST = unaryOperation(HyperbolicOperations.ACOSH_OPERATION, arg)
override fun atanh(arg: MST): MST = unaryOperation(HyperbolicOperations.ATANH_OPERATION, arg)
override fun add(a: MST, b: MST): MST = MstField.add(a, b) override fun add(a: MST, b: MST): MST = MstField.add(a, b)
override fun multiply(a: MST, k: Number): MST = MstField.multiply(a, k) override fun multiply(a: MST, k: Number): MST = MstField.multiply(a, k)
override fun multiply(a: MST, b: MST): MST = MstField.multiply(a, b) override fun multiply(a: MST, b: MST): MST = MstField.multiply(a, b)

52
kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt
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@ -65,7 +65,6 @@ inline fun <T : Any, F : Field<T>> F.deriv(body: AutoDiffField<T, F>.() -> Varia
} }
} }
abstract class AutoDiffField<T : Any, F : Field<T>> : Field<Variable<T>> { abstract class AutoDiffField<T : Any, F : Field<T>> : Field<Variable<T>> {
abstract val context: F abstract val context: F
@ -152,7 +151,6 @@ internal class AutoDiffContext<T : Any, F : Field<T>>(override val context: F) :
// Basic math (+, -, *, /) // Basic math (+, -, *, /)
override fun add(a: Variable<T>, b: Variable<T>): Variable<T> = derive(variable { a.value + b.value }) { z -> override fun add(a: Variable<T>, b: Variable<T>): Variable<T> = derive(variable { a.value + b.value }) { z ->
a.d += z.d a.d += z.d
b.d += z.d b.d += z.d
@ -173,38 +171,66 @@ internal class AutoDiffContext<T : Any, F : Field<T>>(override val context: F) :
} }
} }
// Extensions for differentiation of various basic mathematical functions
// x ^ 2
fun <T : Any, F : Field<T>> AutoDiffField<T, F>.sqr(x: Variable<T>): Variable<T> = fun <T : Any, F : Field<T>> AutoDiffField<T, F>.sqr(x: Variable<T>): Variable<T> =
derive(variable { x.value * x.value }) { z -> x.d += z.d * 2 * x.value } derive(variable { x.value * x.value }) { z -> x.d += z.d * 2 * x.value }
// x ^ 1/2
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sqrt(x: Variable<T>): Variable<T> = fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sqrt(x: Variable<T>): Variable<T> =
derive(variable { sqrt(x.value) }) { z -> x.d += z.d * 0.5 / z.value } derive(variable { sqrt(x.value) }) { z -> x.d += z.d * 0.5 / z.value }
// x ^ y (const)
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Double): Variable<T> = fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Double): Variable<T> =
derive(variable { power(x.value, y) }) { z -> x.d += z.d * y * power(x.value, y - 1) } derive(variable { power(x.value, y) }) { z -> x.d += z.d * y * power(x.value, y - 1) }
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Int): Variable<T> = pow(x, y.toDouble()) fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Int): Variable<T> =
pow(x, y.toDouble())
// exp(x)
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.exp(x: Variable<T>): Variable<T> = fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.exp(x: Variable<T>): Variable<T> =
derive(variable { exp(x.value) }) { z -> x.d += z.d * z.value } derive(variable { exp(x.value) }) { z -> x.d += z.d * z.value }
// ln(x)
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.ln(x: Variable<T>): Variable<T> = fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.ln(x: Variable<T>): Variable<T> =
derive(variable { ln(x.value) }) { z -> x.d += z.d / x.value } derive(variable { ln(x.value) }) { z -> x.d += z.d / x.value }
// x ^ y (any)
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Variable<T>): Variable<T> = fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Variable<T>): Variable<T> =
exp(y * ln(x)) exp(y * ln(x))
// sin(x)
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sin(x: Variable<T>): Variable<T> = fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sin(x: Variable<T>): Variable<T> =
derive(variable { sin(x.value) }) { z -> x.d += z.d * cos(x.value) } derive(variable { sin(x.value) }) { z -> x.d += z.d * cos(x.value) }
// cos(x)
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cos(x: Variable<T>): Variable<T> = fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cos(x: Variable<T>): Variable<T> =
derive(variable { cos(x.value) }) { z -> x.d -= z.d * sin(x.value) } derive(variable { cos(x.value) }) { z -> x.d -= z.d * sin(x.value) }
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.tan(x: Variable<T>): Variable<T> =
derive(variable { tan(x.value) }) { z ->
val c = cos(x.value)
x.d += z.d / (c * c)
}
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.asin(x: Variable<T>): Variable<T> =
derive(variable { asin(x.value) }) { z -> x.d += z.d / sqrt(one - x.value * x.value) }
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.acos(x: Variable<T>): Variable<T> =
derive(variable { acos(x.value) }) { z -> x.d -= z.d / sqrt(one - x.value * x.value) }
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.atan(x: Variable<T>): Variable<T> =
derive(variable { atan(x.value) }) { z -> x.d += z.d / (one + x.value * x.value) }
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sinh(x: Variable<T>): Variable<T> =
derive(variable { sin(x.value) }) { z -> x.d += z.d * cosh(x.value) }
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cosh(x: Variable<T>): Variable<T> =
derive(variable { cos(x.value) }) { z -> x.d += z.d * sinh(x.value) }
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.tanh(x: Variable<T>): Variable<T> =
derive(variable { tan(x.value) }) { z ->
val c = cosh(x.value)
x.d += z.d / (c * c)
}
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.asinh(x: Variable<T>): Variable<T> =
derive(variable { asinh(x.value) }) { z -> x.d += z.d / sqrt(one + x.value * x.value) }
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.acosh(x: Variable<T>): Variable<T> =
derive(variable { acosh(x.value) }) { z -> x.d += z.d / (sqrt((x.value - one) * (x.value + one))) }
fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.atanh(x: Variable<T>): Variable<T> =
derive(variable { atanh(x.value) }) { z -> x.d += z.d / (one - x.value * x.value) }

136
kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt
View File

@ -3,19 +3,19 @@ package scientifik.kmath.misc
import scientifik.kmath.operations.RealField import scientifik.kmath.operations.RealField
import scientifik.kmath.structures.asBuffer import scientifik.kmath.structures.asBuffer
import kotlin.math.PI import kotlin.math.PI
import kotlin.math.pow
import kotlin.math.sqrt
import kotlin.test.Test import kotlin.test.Test
import kotlin.test.assertEquals import kotlin.test.assertEquals
import kotlin.test.assertTrue import kotlin.test.assertTrue
class AutoDiffTest { class AutoDiffTest {
fun Variable(int: Int): Variable<Double> = Variable(int.toDouble()) inline fun deriv(body: AutoDiffField<Double, RealField>.() -> Variable<Double>): DerivationResult<Double> =
fun deriv(body: AutoDiffField<Double, RealField>.() -> Variable<Double>): DerivationResult<Double> =
RealField.deriv(body) RealField.deriv(body)
@Test @Test
fun testPlusX2() { 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 } val y = deriv { x + x }
assertEquals(6.0, y.value) // y = x + x = 6 assertEquals(6.0, y.value) // y = x + x = 6
assertEquals(2.0, y.deriv(x)) // dy/dx = 2 assertEquals(2.0, y.deriv(x)) // dy/dx = 2
@ -24,8 +24,8 @@ class AutoDiffTest {
@Test @Test
fun testPlus() { fun testPlus() {
// two variables // two variables
val x = Variable(2) val x = Variable(2.0)
val y = Variable(3) val y = Variable(3.0)
val z = deriv { x + y } val z = deriv { x + y }
assertEquals(5.0, z.value) // z = x + y = 5 assertEquals(5.0, z.value) // z = x + y = 5
assertEquals(1.0, z.deriv(x)) // dz/dx = 1 assertEquals(1.0, z.deriv(x)) // dz/dx = 1
@ -35,8 +35,8 @@ class AutoDiffTest {
@Test @Test
fun testMinus() { fun testMinus() {
// two variables // two variables
val x = Variable(7) val x = Variable(7.0)
val y = Variable(3) val y = Variable(3.0)
val z = deriv { x - y } val z = deriv { x - y }
assertEquals(4.0, z.value) // z = x - y = 4 assertEquals(4.0, z.value) // z = x - y = 4
assertEquals(1.0, z.deriv(x)) // dz/dx = 1 assertEquals(1.0, z.deriv(x)) // dz/dx = 1
@ -45,7 +45,7 @@ class AutoDiffTest {
@Test @Test
fun testMulX2() { 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 } val y = deriv { x * x }
assertEquals(9.0, y.value) // y = x * x = 9 assertEquals(9.0, y.value) // y = x * x = 9
assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7 assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7
@ -53,7 +53,7 @@ class AutoDiffTest {
@Test @Test
fun testSqr() { fun testSqr() {
val x = Variable(3) val x = Variable(3.0)
val y = deriv { sqr(x) } val y = deriv { sqr(x) }
assertEquals(9.0, y.value) // y = x ^ 2 = 9 assertEquals(9.0, y.value) // y = x ^ 2 = 9
assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7 assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7
@ -61,7 +61,7 @@ class AutoDiffTest {
@Test @Test
fun testSqrSqr() { fun testSqrSqr() {
val x = Variable(2) val x = Variable(2.0)
val y = deriv { sqr(sqr(x)) } val y = deriv { sqr(sqr(x)) }
assertEquals(16.0, y.value) // y = x ^ 4 = 16 assertEquals(16.0, y.value) // y = x ^ 4 = 16
assertEquals(32.0, y.deriv(x)) // dy/dx = 4 * x^3 = 32 assertEquals(32.0, y.deriv(x)) // dy/dx = 4 * x^3 = 32
@ -69,7 +69,7 @@ class AutoDiffTest {
@Test @Test
fun testX3() { 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 } val y = deriv { x * x * x }
assertEquals(8.0, y.value) // y = x * x * x = 8 assertEquals(8.0, y.value) // y = x * x * x = 8
assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x * x = 12 assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x * x = 12
@ -77,8 +77,8 @@ class AutoDiffTest {
@Test @Test
fun testDiv() { fun testDiv() {
val x = Variable(5) val x = Variable(5.0)
val y = Variable(2) val y = Variable(2.0)
val z = deriv { x / y } val z = deriv { x / y }
assertEquals(2.5, z.value) // z = x / y = 2.5 assertEquals(2.5, z.value) // z = x / y = 2.5
assertEquals(0.5, z.deriv(x)) // dz/dx = 1 / y = 0.5 assertEquals(0.5, z.deriv(x)) // dz/dx = 1 / y = 0.5
@ -87,7 +87,7 @@ class AutoDiffTest {
@Test @Test
fun testPow3() { 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) } val y = deriv { pow(x, 3) }
assertEquals(8.0, y.value) // y = x ^ 3 = 8 assertEquals(8.0, y.value) // y = x ^ 3 = 8
assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x ^ 2 = 12 assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x ^ 2 = 12
@ -95,8 +95,8 @@ class AutoDiffTest {
@Test @Test
fun testPowFull() { fun testPowFull() {
val x = Variable(2) val x = Variable(2.0)
val y = Variable(3) val y = Variable(3.0)
val z = deriv { pow(x, y) } val z = deriv { pow(x, y) }
assertApprox(8.0, z.value) // z = x ^ y = 8 assertApprox(8.0, z.value) // z = x ^ y = 8
assertApprox(12.0, z.deriv(x)) // dz/dx = y * x ^ (y - 1) = 12 assertApprox(12.0, z.deriv(x)) // dz/dx = y * x ^ (y - 1) = 12
@ -105,7 +105,7 @@ class AutoDiffTest {
@Test @Test
fun testFromPaper() { fun testFromPaper() {
val x = Variable(3) val x = Variable(3.0)
val y = deriv { 2 * x + x * x * x } val y = deriv { 2 * x + x * x * x }
assertEquals(33.0, y.value) // y = 2 * x + x * x * x = 33 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 assertEquals(29.0, y.deriv(x)) // dy/dx = 2 + 3 * x * x = 29
@ -113,9 +113,9 @@ class AutoDiffTest {
@Test @Test
fun testInnerVariable() { fun testInnerVariable() {
val x = Variable(1) val x = Variable(1.0)
val y = deriv { val y = deriv {
Variable(1) * x Variable(1.0) * x
} }
assertEquals(1.0, y.value) // y = x ^ n = 1 assertEquals(1.0, y.value) // y = x ^ n = 1
assertEquals(1.0, y.deriv(x)) // dy/dx = n * x ^ (n - 1) = n - 1 assertEquals(1.0, y.deriv(x)) // dy/dx = n * x ^ (n - 1) = n - 1
@ -124,9 +124,9 @@ class AutoDiffTest {
@Test @Test
fun testLongChain() { fun testLongChain() {
val n = 10_000 val n = 10_000
val x = Variable(1) val x = Variable(1.0)
val y = deriv { val y = deriv {
var res = Variable(1) var res = Variable(1.0)
for (i in 1..n) res *= x for (i in 1..n) res *= x
res res
} }
@ -136,7 +136,7 @@ class AutoDiffTest {
@Test @Test
fun testExample() { fun testExample() {
val x = Variable(2) val x = Variable(2.0)
val y = deriv { sqr(x) + 5 * x + 3 } val y = deriv { sqr(x) + 5 * x + 3 }
assertEquals(17.0, y.value) // the value of result (y) assertEquals(17.0, y.value) // the value of result (y)
assertEquals(9.0, y.deriv(x)) // dy/dx assertEquals(9.0, y.deriv(x)) // dy/dx
@ -144,7 +144,7 @@ class AutoDiffTest {
@Test @Test
fun testSqrt() { fun testSqrt() {
val x = Variable(16) val x = Variable(16.0)
val y = deriv { sqrt(x) } val y = deriv { sqrt(x) }
assertEquals(4.0, y.value) // y = x ^ 1/2 = 4 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 assertEquals(1.0 / 8, y.deriv(x)) // dy/dx = 1/2 / x ^ 1/4 = 1/8
@ -152,18 +152,98 @@ class AutoDiffTest {
@Test @Test
fun testSin() { fun testSin() {
val x = Variable(PI / 6) val x = Variable(PI / 6.0)
val y = deriv { sin(x) } val y = deriv { sin(x) }
assertApprox(0.5, y.value) // y = sin(PI/6) = 0.5 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(sqrt(3.0) / 2, y.deriv(x)) // dy/dx = cos(pi/6) = sqrt(3)/2
} }
@Test @Test
fun testCos() { fun testCos() {
val x = Variable(PI / 6) val x = Variable(PI / 6)
val y = deriv { cos(x) } val y = deriv { cos(x) }
assertApprox(kotlin.math.sqrt(3.0) / 2, y.value) // y = cos(PI/6) = sqrt(3)/2 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 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(0)
assertApprox(kotlin.math.cosh(0.0), y.deriv(x)) // dy/dx = cosh(0)
}
@Test
fun testCosh() {
val x = Variable(0.0)
val y = deriv { cosh(x) }
assertApprox(1.0, y.value) //y = cosh(0)
assertApprox(0.0, y.deriv(x)) // dy/dx = sinh(0)
}
@Test
fun testTanh() {
val x = Variable(PI / 6)
val y = deriv { tanh(x) }
assertApprox(1.0 / sqrt(3.0), y.value) // y = tanh(pi/6)
assertApprox(1.0 / kotlin.math.cosh(PI / 6.0).pow(2), y.deriv(x)) // dy/dx = sech(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 @Test