Doc update. Name refactoring in NDField
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@ -36,7 +36,7 @@ fun ComplexOperations.doSomethingWithComplex(c1: Complex, c2: Complex, c3: Compl
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ComplexOperations.doComethingWithComplex(c1,c2,c3)
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ComplexOperations.doComethingWithComplex(c1,c2,c3)
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```
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```
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In fact, whole parts of proram could run in a mathematical context or even multiple nested contexts.
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In fact, whole parts of program could run in a mathematical context or even multiple nested contexts.
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In `kmath` contexts are responsible not only for operations, but also for raw object creation and advanced features.
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In `kmath` contexts are responsible not only for operations, but also for raw object creation and advanced features.
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38
doc/operations.md
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38
doc/operations.md
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@ -0,0 +1,38 @@
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## Spaces and fields
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An obvious first choice of mathematical objects to implement in context-oriented style are algebra elements like spaces,
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rings and fields. Those are located in a `scientifik.kmath.operations.Algebra.kt` file. Alongside algebric context
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themselves, the file includes definitions for algebra elements such as `FieldElement`. A `FieldElement` object
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stores a reference to the `Field` which contains a additive and multiplicative operations for it, meaning
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it has one fixed context attached to it and does not require explicit external context. So those `MathElements` could be
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operated without context:
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```kotlin
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val c1 = Complex(1.0, 2.0)
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val c2 = ComplexField.i
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val c3 = c1 + c2
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```
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`ComplexField` also features special operations to mix complex numbers with real numbers like:
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```kotlin
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val c1 = Complex(1.0,2.0)
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val c2 = ComplexField.run{ c1 - 1.0} //returns [re:0.0, im: 2.0]
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val c3 = ComplexField.run{ c1 - i*2.0}
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```
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**Note**: In theory it is possible to add behaviors directly to the context, but currently kotlin syntax does not support
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that. Watch [KT-10468](https://youtrack.jetbrains.com/issue/KT-10468) for news.
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## Nested fields
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Algebra contexts allow to create more complex structures. For example, it is possible to create a `Matrix` from complex
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elements like this:
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```kotlin
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val element = NDElements.create(field = ComplexField, shape = intArrayOf(2,2)){index: IntArray ->
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Complex(index[0] - index[1], index[0] + index[1])
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}
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```
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The `element` in this example is a member of `Field` of 2-d structures, each element of which is a member of its own
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`ComplexField`. The important thing is that one does not need to create a special nd-structure to hold complex
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numbers and implements operations on it, one need just to provide a field for its elements.
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**Note**: Fields themselves do not solve problem of JVM boxing, but it is possible to solve with special contexts like
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`BufferSpec`. This feature is in development phase.
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@ -18,6 +18,15 @@ object ComplexField : Field<Complex> {
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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
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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
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operator fun Double.plus(c: Complex) = this.toComplex() + c
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operator fun Double.minus(c: Complex) = this.toComplex() - c
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operator fun Complex.plus(d: Double) = d + this
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operator fun Complex.minus(d: Double) = this - d.toComplex()
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operator fun Double.times(c: Complex) = Complex(c.re * this, c.im * this)
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}
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}
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/**
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/**
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@ -46,13 +55,3 @@ data class Complex(val re: Double, val im: Double) : FieldElement<Complex, Compl
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}
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}
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fun Double.toComplex() = Complex(this, 0.0)
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fun Double.toComplex() = Complex(this, 0.0)
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operator fun Double.plus(c: Complex) = this.toComplex() + c
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operator fun Double.minus(c: Complex) = this.toComplex() - c
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operator fun Complex.plus(d: Double) = d + this
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operator fun Complex.minus(d: Double) = this - d.toComplex()
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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
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//typealias NDFieldFactory<T> = (IntArray)->NDField<T>
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//typealias NDFieldFactory<T> = (IntArray)->NDField<T>
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object NDArrays {
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object NDElements {
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/**
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/**
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* Create a platform-optimized NDArray of doubles
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* Create a platform-optimized NDArray of doubles
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*/
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*/
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fun realNDArray(shape: IntArray, initializer: DoubleField.(IntArray) -> Double = { 0.0 }): NDElement<Double, DoubleField> {
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fun realNDElement(shape: IntArray, initializer: DoubleField.(IntArray) -> Double = { 0.0 }): NDElement<Double, DoubleField> {
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return ExtendedNDField(shape, DoubleField).produce(initializer)
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return ExtendedNDField(shape, DoubleField).produce(initializer)
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}
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}
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fun real1DArray(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): NDElement<Double, DoubleField> {
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fun real1DElement(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): NDElement<Double, DoubleField> {
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return realNDArray(intArrayOf(dim)) { initializer(it[0]) }
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return realNDElement(intArrayOf(dim)) { initializer(it[0]) }
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}
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}
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fun real2DArray(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): NDElement<Double, DoubleField> {
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fun real2DElement(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): NDElement<Double, DoubleField> {
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return realNDArray(intArrayOf(dim1, dim2)) { initializer(it[0], it[1]) }
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return realNDElement(intArrayOf(dim1, dim2)) { initializer(it[0], it[1]) }
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}
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}
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fun real3DArray(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }): NDElement<Double, DoubleField> {
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fun real3DElement(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }): NDElement<Double, DoubleField> {
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return realNDArray(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
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return realNDElement(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
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}
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}
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inline fun produceReal(shape: IntArray, block: ExtendedNDField<Double, DoubleField>.() -> NDStructure<Double>): NDElement<Double, DoubleField> {
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inline fun real(shape: IntArray, block: ExtendedNDField<Double, DoubleField>.() -> NDStructure<Double>): NDElement<Double, DoubleField> {
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val field = ExtendedNDField(shape, DoubleField)
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val field = ExtendedNDField(shape, DoubleField)
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return NDStructureElement(field, field.run(block))
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return NDStructureElement(field, field.run(block))
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}
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}
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@ -1,7 +1,7 @@
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package scientifik.kmath.structures
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package scientifik.kmath.structures
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import scientifik.kmath.operations.DoubleField
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import scientifik.kmath.operations.DoubleField
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import scientifik.kmath.structures.NDArrays.create
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import scientifik.kmath.structures.NDElements.create
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import kotlin.test.Test
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import kotlin.test.Test
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import kotlin.test.assertEquals
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import kotlin.test.assertEquals
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@ -1,16 +1,16 @@
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package scientifik.kmath.structures
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package scientifik.kmath.structures
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import scientifik.kmath.operations.Norm
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import scientifik.kmath.operations.Norm
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import scientifik.kmath.structures.NDArrays.produceReal
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import scientifik.kmath.structures.NDElements.real
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import scientifik.kmath.structures.NDArrays.real2DArray
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import scientifik.kmath.structures.NDElements.real2DElement
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import kotlin.math.abs
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import kotlin.math.abs
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import kotlin.math.pow
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import kotlin.math.pow
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import kotlin.test.Test
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import kotlin.test.Test
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import kotlin.test.assertEquals
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import kotlin.test.assertEquals
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class NumberNDFieldTest {
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class NumberNDFieldTest {
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val array1 = real2DArray(3, 3) { i, j -> (i + j).toDouble() }
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val array1 = real2DElement(3, 3) { i, j -> (i + j).toDouble() }
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val array2 = real2DArray(3, 3) { i, j -> (i - j).toDouble() }
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val array2 = real2DElement(3, 3) { i, j -> (i - j).toDouble() }
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@Test
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@Test
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fun testSum() {
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fun testSum() {
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@ -27,7 +27,7 @@ class NumberNDFieldTest {
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@Test
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@Test
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fun testGeneration() {
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fun testGeneration() {
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val array = real2DArray(3, 3) { i, j -> (i * 10 + j).toDouble() }
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val array = real2DElement(3, 3) { i, j -> (i * 10 + j).toDouble() }
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for (i in 0..2) {
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for (i in 0..2) {
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for (j in 0..2) {
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for (j in 0..2) {
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@ -64,7 +64,7 @@ class NumberNDFieldTest {
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@Test
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@Test
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fun testInternalContext() {
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fun testInternalContext() {
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produceReal(array1.shape) {
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real(array1.shape) {
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with(L2Norm) {
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with(L2Norm) {
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1 + norm(array1) + exp(array2)
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1 + norm(array1) + exp(array2)
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}
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}
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@ -9,7 +9,7 @@ class LazyNDFieldTest {
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@Test
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@Test
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fun testLazyStructure() {
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fun testLazyStructure() {
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var counter = 0
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var counter = 0
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val regularStructure = NDArrays.create(IntField, intArrayOf(2, 2, 2)) { it[0] + it[1] - it[2] }
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val regularStructure = NDElements.create(IntField, intArrayOf(2, 2, 2)) { it[0] + it[1] - it[2] }
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val result = (regularStructure.lazy() + 2).transform {
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val result = (regularStructure.lazy() + 2).transform {
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counter++
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counter++
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it * it
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it * it
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