Doc update. Name refactoring in NDField

This commit is contained in:
Alexander Nozik 2018-12-26 14:35:51 +03:00
parent db37c19ed0
commit ad5e14e9a2
7 changed files with 66 additions and 29 deletions

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@ -36,7 +36,7 @@ fun ComplexOperations.doSomethingWithComplex(c1: Complex, c2: Complex, c3: Compl
ComplexOperations.doComethingWithComplex(c1,c2,c3) ComplexOperations.doComethingWithComplex(c1,c2,c3)
``` ```
In fact, whole parts of proram could run in a mathematical context or even multiple nested contexts. In fact, whole parts of program could run in a mathematical context or even multiple nested contexts.
In `kmath` contexts are responsible not only for operations, but also for raw object creation and advanced features. In `kmath` contexts are responsible not only for operations, but also for raw object creation and advanced features.

38
doc/operations.md Normal file
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@ -0,0 +1,38 @@
## Spaces and fields
An obvious first choice of mathematical objects to implement in context-oriented style are algebra elements like spaces,
rings and fields. Those are located in a `scientifik.kmath.operations.Algebra.kt` file. Alongside algebric context
themselves, the file includes definitions for algebra elements such as `FieldElement`. A `FieldElement` object
stores a reference to the `Field` which contains a additive and multiplicative operations for it, meaning
it has one fixed context attached to it and does not require explicit external context. So those `MathElements` could be
operated without context:
```kotlin
val c1 = Complex(1.0, 2.0)
val c2 = ComplexField.i
val c3 = c1 + c2
```
`ComplexField` also features special operations to mix complex numbers with real numbers like:
```kotlin
val c1 = Complex(1.0,2.0)
val c2 = ComplexField.run{ c1 - 1.0} //returns [re:0.0, im: 2.0]
val c3 = ComplexField.run{ c1 - i*2.0}
```
**Note**: In theory it is possible to add behaviors directly to the context, but currently kotlin syntax does not support
that. Watch [KT-10468](https://youtrack.jetbrains.com/issue/KT-10468) for news.
## Nested fields
Algebra contexts allow to create more complex structures. For example, it is possible to create a `Matrix` from complex
elements like this:
```kotlin
val element = NDElements.create(field = ComplexField, shape = intArrayOf(2,2)){index: IntArray ->
Complex(index[0] - index[1], index[0] + index[1])
}
```
The `element` in this example is a member of `Field` of 2-d structures, each element of which is a member of its own
`ComplexField`. The important thing is that one does not need to create a special nd-structure to hold complex
numbers and implements operations on it, one need just to provide a field for its elements.
**Note**: Fields themselves do not solve problem of JVM boxing, but it is possible to solve with special contexts like
`BufferSpec`. This feature is in development phase.

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@ -18,6 +18,15 @@ object ComplexField : Field<Complex> {
override fun divide(a: Complex, b: Complex): Complex = Complex(a.re * b.re + a.im * b.im, a.re * b.im - a.im * b.re) / b.square override fun divide(a: Complex, b: Complex): Complex = Complex(a.re * b.re + a.im * b.im, a.re * b.im - a.im * b.re) / b.square
operator fun Double.plus(c: Complex) = this.toComplex() + c
operator fun Double.minus(c: Complex) = this.toComplex() - c
operator fun Complex.plus(d: Double) = d + this
operator fun Complex.minus(d: Double) = this - d.toComplex()
operator fun Double.times(c: Complex) = Complex(c.re * this, c.im * this)
} }
/** /**
@ -46,13 +55,3 @@ data class Complex(val re: Double, val im: Double) : FieldElement<Complex, Compl
} }
fun Double.toComplex() = Complex(this, 0.0) fun Double.toComplex() = Complex(this, 0.0)
operator fun Double.plus(c: Complex) = this.toComplex() + c
operator fun Double.minus(c: Complex) = this.toComplex() - c
operator fun Complex.plus(d: Double) = d + this
operator fun Complex.minus(d: Double) = this - d.toComplex()
operator fun Double.times(c: Complex) = Complex(c.re * this, c.im * this)

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@ -173,27 +173,27 @@ class GenericNDField<T : Any, F : Field<T>>(shape: IntArray, field: F) : NDField
//typealias NDFieldFactory<T> = (IntArray)->NDField<T> //typealias NDFieldFactory<T> = (IntArray)->NDField<T>
object NDArrays { object NDElements {
/** /**
* Create a platform-optimized NDArray of doubles * Create a platform-optimized NDArray of doubles
*/ */
fun realNDArray(shape: IntArray, initializer: DoubleField.(IntArray) -> Double = { 0.0 }): NDElement<Double, DoubleField> { fun realNDElement(shape: IntArray, initializer: DoubleField.(IntArray) -> Double = { 0.0 }): NDElement<Double, DoubleField> {
return ExtendedNDField(shape, DoubleField).produce(initializer) return ExtendedNDField(shape, DoubleField).produce(initializer)
} }
fun real1DArray(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): NDElement<Double, DoubleField> { fun real1DElement(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): NDElement<Double, DoubleField> {
return realNDArray(intArrayOf(dim)) { initializer(it[0]) } return realNDElement(intArrayOf(dim)) { initializer(it[0]) }
} }
fun real2DArray(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): NDElement<Double, DoubleField> { fun real2DElement(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): NDElement<Double, DoubleField> {
return realNDArray(intArrayOf(dim1, dim2)) { initializer(it[0], it[1]) } return realNDElement(intArrayOf(dim1, dim2)) { initializer(it[0], it[1]) }
} }
fun real3DArray(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }): NDElement<Double, DoubleField> { fun real3DElement(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }): NDElement<Double, DoubleField> {
return realNDArray(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) } return realNDElement(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
} }
inline fun produceReal(shape: IntArray, block: ExtendedNDField<Double, DoubleField>.() -> NDStructure<Double>): NDElement<Double, DoubleField> { inline fun real(shape: IntArray, block: ExtendedNDField<Double, DoubleField>.() -> NDStructure<Double>): NDElement<Double, DoubleField> {
val field = ExtendedNDField(shape, DoubleField) val field = ExtendedNDField(shape, DoubleField)
return NDStructureElement(field, field.run(block)) return NDStructureElement(field, field.run(block))
} }

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@ -1,7 +1,7 @@
package scientifik.kmath.structures package scientifik.kmath.structures
import scientifik.kmath.operations.DoubleField import scientifik.kmath.operations.DoubleField
import scientifik.kmath.structures.NDArrays.create import scientifik.kmath.structures.NDElements.create
import kotlin.test.Test import kotlin.test.Test
import kotlin.test.assertEquals import kotlin.test.assertEquals

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@ -1,16 +1,16 @@
package scientifik.kmath.structures package scientifik.kmath.structures
import scientifik.kmath.operations.Norm import scientifik.kmath.operations.Norm
import scientifik.kmath.structures.NDArrays.produceReal import scientifik.kmath.structures.NDElements.real
import scientifik.kmath.structures.NDArrays.real2DArray import scientifik.kmath.structures.NDElements.real2DElement
import kotlin.math.abs import kotlin.math.abs
import kotlin.math.pow import kotlin.math.pow
import kotlin.test.Test import kotlin.test.Test
import kotlin.test.assertEquals import kotlin.test.assertEquals
class NumberNDFieldTest { class NumberNDFieldTest {
val array1 = real2DArray(3, 3) { i, j -> (i + j).toDouble() } val array1 = real2DElement(3, 3) { i, j -> (i + j).toDouble() }
val array2 = real2DArray(3, 3) { i, j -> (i - j).toDouble() } val array2 = real2DElement(3, 3) { i, j -> (i - j).toDouble() }
@Test @Test
fun testSum() { fun testSum() {
@ -27,7 +27,7 @@ class NumberNDFieldTest {
@Test @Test
fun testGeneration() { fun testGeneration() {
val array = real2DArray(3, 3) { i, j -> (i * 10 + j).toDouble() } val array = real2DElement(3, 3) { i, j -> (i * 10 + j).toDouble() }
for (i in 0..2) { for (i in 0..2) {
for (j in 0..2) { for (j in 0..2) {
@ -64,7 +64,7 @@ class NumberNDFieldTest {
@Test @Test
fun testInternalContext() { fun testInternalContext() {
produceReal(array1.shape) { real(array1.shape) {
with(L2Norm) { with(L2Norm) {
1 + norm(array1) + exp(array2) 1 + norm(array1) + exp(array2)
} }

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@ -9,7 +9,7 @@ class LazyNDFieldTest {
@Test @Test
fun testLazyStructure() { fun testLazyStructure() {
var counter = 0 var counter = 0
val regularStructure = NDArrays.create(IntField, intArrayOf(2, 2, 2)) { it[0] + it[1] - it[2] } val regularStructure = NDElements.create(IntField, intArrayOf(2, 2, 2)) { it[0] + it[1] - it[2] }
val result = (regularStructure.lazy() + 2).transform { val result = (regularStructure.lazy() + 2).transform {
counter++ counter++
it * it it * it