Merge remote-tracking branch 'kmath/dev' into mrfendel
This commit is contained in:
commit
dababe3075
@ -0,0 +1,91 @@
|
||||
/*
|
||||
* Copyright 2018-2023 KMath contributors.
|
||||
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
|
||||
*/
|
||||
|
||||
package space.kscience.kmath.expressions
|
||||
|
||||
import space.kscience.kmath.UnstableKMathAPI
|
||||
// Only kmath-core is needed.
|
||||
|
||||
// Let's declare some variables
|
||||
val x by symbol
|
||||
val y by symbol
|
||||
val z by symbol
|
||||
|
||||
@OptIn(UnstableKMathAPI::class)
|
||||
fun main() {
|
||||
// Let's define some random expression.
|
||||
val someExpression = Double.autodiff.differentiate {
|
||||
// We bind variables `x` and `y` to the builder scope,
|
||||
val x = bindSymbol(x)
|
||||
val y = bindSymbol(y)
|
||||
|
||||
// Then we use the bindings to define expression `xy + x + y - 1`
|
||||
x * y + x + y - 1
|
||||
}
|
||||
|
||||
// Then we can evaluate it at any point ((-1, -1) in the case):
|
||||
println(someExpression(mapOf(x to -1.0, y to -1.0)))
|
||||
// >>> -2.0
|
||||
|
||||
// We can also construct its partial derivatives:
|
||||
val dxExpression = someExpression.derivative(x) // ∂/∂x. Must be `y+1`
|
||||
val dyExpression = someExpression.derivative(y) // ∂/∂y. Must be `x+1`
|
||||
val dxdxExpression = someExpression.derivative(x, x) // ∂^2/∂x^2. Must be `0`
|
||||
|
||||
// We can evaluate them as well
|
||||
println(dxExpression(mapOf(x to 57.0, y to 6.0)))
|
||||
// >>> 7.0
|
||||
println(dyExpression(mapOf(x to -1.0, y to 179.0)))
|
||||
// >>> 0.0
|
||||
println(dxdxExpression(mapOf(x to 239.0, y to 30.0)))
|
||||
// >>> 0.0
|
||||
|
||||
// You can also provide extra arguments that obviously won't affect the result:
|
||||
println(dxExpression(mapOf(x to 57.0, y to 6.0, z to 42.0)))
|
||||
// >>> 7.0
|
||||
println(dyExpression(mapOf(x to -1.0, y to 179.0, z to 0.0)))
|
||||
// >>> 0.0
|
||||
println(dxdxExpression(mapOf(x to 239.0, y to 30.0, z to 100_000.0)))
|
||||
// >>> 0.0
|
||||
|
||||
// But in case you forgot to specify bound symbol's value, exception is thrown:
|
||||
println( runCatching { someExpression(mapOf(z to 4.0)) } )
|
||||
// >>> Failure(java.lang.IllegalStateException: Symbol 'x' is not supported in ...)
|
||||
|
||||
// The reason is that the expression is evaluated lazily,
|
||||
// and each `bindSymbol` operation actually substitutes the provided symbol with the corresponding value.
|
||||
|
||||
// For example, let there be an expression
|
||||
val simpleExpression = Double.autodiff.differentiate {
|
||||
val x = bindSymbol(x)
|
||||
x pow 2
|
||||
}
|
||||
// When you evaluate it via
|
||||
simpleExpression(mapOf(x to 1.0, y to 57.0, z to 179.0))
|
||||
// lambda above has the context of map `{x: 1.0, y: 57.0, z: 179.0}`.
|
||||
// When x is bound, you can think of it as substitution `x -> 1.0`.
|
||||
// Other values are unused which does not make any problem to us.
|
||||
// But in the case the corresponding value is not provided,
|
||||
// we cannot bind the variable. Thus, exception is thrown.
|
||||
|
||||
// There is also a function `bindSymbolOrNull` that fixes the problem:
|
||||
val fixedExpression = Double.autodiff.differentiate {
|
||||
val x = bindSymbolOrNull(x) ?: const(8.0)
|
||||
x pow -2
|
||||
}
|
||||
println(fixedExpression())
|
||||
// >>> 0.015625
|
||||
// It works!
|
||||
|
||||
// The expression provides a bunch of operations:
|
||||
// 1. Constant bindings (via `const` and `number`).
|
||||
// 2. Variable bindings (via `bindVariable`, `bindVariableOrNull`).
|
||||
// 3. Arithmetic operations (via `+`, `-`, `*`, and `-`).
|
||||
// 4. Exponentiation (via `pow` or `power`).
|
||||
// 5. `exp` and `ln`.
|
||||
// 6. Trigonometrical functions (`sin`, `cos`, `tan`, `cot`).
|
||||
// 7. Inverse trigonometrical functions (`asin`, `acos`, `atan`, `acot`).
|
||||
// 8. Hyperbolic functions and inverse hyperbolic functions.
|
||||
}
|
Loading…
Reference in New Issue
Block a user