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Extending from Algebra

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This commit is contained in:
Roland Grinis 2021-04-30 14:38:03 +01:00
parent bd068b2c14
commit e5e62bc544
12 changed files with 56 additions and 64 deletions
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4
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt
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@ -5,13 +5,15 @@
package space.kscience.kmath.tensors.api
import space.kscience.kmath.operations.Algebra
/**
* Algebra over a ring on [TensorStructure].
* For more information: https://proofwiki.org/wiki/Definition:Algebra_over_Ring
*
* @param T the type of items in the tensors.
*/
public interface TensorAlgebra<T> {
public interface TensorAlgebra<T>: Algebra<TensorStructure<T>> {
/**
* Returns a single tensor value of unit dimension. The tensor shape must be equal to [1].

3
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/BroadcastDoubleTensorAlgebra.kt
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@ -14,7 +14,7 @@ import space.kscience.kmath.tensors.core.broadcastTo
* Basic linear algebra operations implemented with broadcasting.
* For more information: https://pytorch.org/docs/stable/notes/broadcasting.html
*/
public class BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
override fun TensorStructure<Double>.plus(other: TensorStructure<Double>): DoubleTensor {
val broadcast = broadcastTensors(tensor, other.tensor)
@ -89,5 +89,4 @@ public class BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
newOther.buffer.array()[tensor.bufferStart + i]
}
}
}

8
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/DoubleAnalyticTensorAlgebra.kt
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@ -11,10 +11,9 @@ import space.kscience.kmath.tensors.core.DoubleTensor
import space.kscience.kmath.tensors.core.tensor
import kotlin.math.*
public class DoubleAnalyticTensorAlgebra:
public object DoubleAnalyticTensorAlgebra :
AnalyticTensorAlgebra<Double>,
DoubleTensorAlgebra()
{
DoubleTensorAlgebra() {
override fun TensorStructure<Double>.exp(): DoubleTensor = tensor.map(::exp)
override fun TensorStructure<Double>.log(): DoubleTensor = tensor.map(::ln)
@ -50,6 +49,3 @@ public class DoubleAnalyticTensorAlgebra:
override fun TensorStructure<Double>.floor(): DoubleTensor = tensor.map(::floor)
}
public inline fun <R> DoubleAnalyticTensorAlgebra(block: DoubleAnalyticTensorAlgebra.() -> R): R =
DoubleAnalyticTensorAlgebra().block()

10
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/DoubleLinearOpsTensorAlgebra.kt
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@ -21,7 +21,7 @@ import space.kscience.kmath.tensors.core.pivInit
import kotlin.math.min
public class DoubleLinearOpsTensorAlgebra :
public object DoubleLinearOpsTensorAlgebra :
LinearOpsTensorAlgebra<Double>,
DoubleTensorAlgebra() {
@ -30,8 +30,8 @@ public class DoubleLinearOpsTensorAlgebra :
override fun TensorStructure<Double>.det(): DoubleTensor = detLU(1e-9)
public fun TensorStructure<Double>.luFactor(epsilon: Double): Pair<DoubleTensor, IntTensor> =
computeLU(tensor, epsilon) ?:
throw RuntimeException("Tensor contains matrices which are singular at precision $epsilon")
computeLU(tensor, epsilon)
?: throw RuntimeException("Tensor contains matrices which are singular at precision $epsilon")
public fun TensorStructure<Double>.luFactor(): Pair<DoubleTensor, IntTensor> = luFactor(1e-9)
@ -175,8 +175,4 @@ public class DoubleLinearOpsTensorAlgebra :
override fun TensorStructure<Double>.lu(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> = lu(1e-9)
}
public inline fun <R> DoubleLinearOpsTensorAlgebra(block: DoubleLinearOpsTensorAlgebra.() -> R): R =
DoubleLinearOpsTensorAlgebra().block()

5
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/DoubleTensorAlgebra.kt
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@ -23,6 +23,7 @@ import kotlin.math.abs
public open class DoubleTensorAlgebra : TensorPartialDivisionAlgebra<Double> {
public companion object : DoubleTensorAlgebra()
override fun TensorStructure<Double>.value(): Double {
check(tensor.shape contentEquals intArrayOf(1)) {
@ -395,7 +396,3 @@ public open class DoubleTensorAlgebra : TensorPartialDivisionAlgebra<Double> {
DoubleTensor(tensor.shape, getRandomNormals(tensor.shape.reduce(Int::times), seed))
}
public inline fun <R> DoubleTensorAlgebra(block: DoubleTensorAlgebra.() -> R): R =
DoubleTensorAlgebra().block()

4
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/broadcastUtils.kt
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@ -1,11 +1,7 @@
package space.kscience.kmath.tensors.core
import space.kscience.kmath.tensors.core.algebras.BroadcastDoubleTensorAlgebra
import kotlin.math.max
public inline fun <R> BroadcastDoubleTensorAlgebra(block: BroadcastDoubleTensorAlgebra.() -> R): R =
BroadcastDoubleTensorAlgebra().block()
internal inline fun multiIndexBroadCasting(tensor: DoubleTensor, resTensor: DoubleTensor, linearSize: Int) {
for (linearIndex in 0 until linearSize) {
val totalMultiIndex = resTensor.linearStructure.index(linearIndex)

3
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/linUtils.kt
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@ -4,6 +4,7 @@ import space.kscience.kmath.nd.MutableStructure1D
import space.kscience.kmath.nd.MutableStructure2D
import space.kscience.kmath.nd.as1D
import space.kscience.kmath.nd.as2D
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.tensors.core.algebras.DoubleAnalyticTensorAlgebra
import space.kscience.kmath.tensors.core.algebras.DoubleLinearOpsTensorAlgebra
import kotlin.math.abs
@ -251,7 +252,7 @@ internal inline fun DoubleLinearOpsTensorAlgebra.qrHelper(
}
}
}
r[j, j] = DoubleAnalyticTensorAlgebra { (v dot v).sqrt().value() }
r[j, j] = DoubleAnalyticTensorAlgebra.invoke { (v dot v).sqrt().value() }
for (i in 0 until n) {
qM[i, j] = vv[i] / r[j, j]
}

16
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestBroadcasting.kt
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@ -1,13 +1,15 @@
package space.kscience.kmath.tensors.core
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.tensors.core.algebras.BroadcastDoubleTensorAlgebra
import space.kscience.kmath.tensors.core.algebras.DoubleTensorAlgebra
import kotlin.test.Test
import kotlin.test.assertTrue
class TestBroadcasting {
internal class TestBroadcasting {
@Test
fun broadcastShapes() = DoubleTensorAlgebra {
fun broadcastShapes() = DoubleTensorAlgebra.invoke {
assertTrue(
broadcastShapes(
intArrayOf(2, 3), intArrayOf(1, 3), intArrayOf(1, 1, 1)
@ -22,7 +24,7 @@ class TestBroadcasting {
}
@Test
fun broadcastTo() = DoubleTensorAlgebra {
fun broadcastTo() = DoubleTensorAlgebra.invoke {
val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val tensor2 = fromArray(intArrayOf(1, 3), doubleArrayOf(10.0, 20.0, 30.0))
@ -32,7 +34,7 @@ class TestBroadcasting {
}
@Test
fun broadcastTensors() = DoubleTensorAlgebra {
fun broadcastTensors() = DoubleTensorAlgebra.invoke {
val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val tensor2 = fromArray(intArrayOf(1, 3), doubleArrayOf(10.0, 20.0, 30.0))
val tensor3 = fromArray(intArrayOf(1, 1, 1), doubleArrayOf(500.0))
@ -49,7 +51,7 @@ class TestBroadcasting {
}
@Test
fun broadcastOuterTensors() = DoubleTensorAlgebra {
fun broadcastOuterTensors() = DoubleTensorAlgebra.invoke {
val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val tensor2 = fromArray(intArrayOf(1, 3), doubleArrayOf(10.0, 20.0, 30.0))
val tensor3 = fromArray(intArrayOf(1, 1, 1), doubleArrayOf(500.0))
@ -66,7 +68,7 @@ class TestBroadcasting {
}
@Test
fun broadcastOuterTensorsShapes() = DoubleTensorAlgebra {
fun broadcastOuterTensorsShapes() = DoubleTensorAlgebra.invoke {
val tensor1 = fromArray(intArrayOf(2, 1, 3, 2, 3), DoubleArray(2 * 1 * 3 * 2 * 3) {0.0})
val tensor2 = fromArray(intArrayOf(4, 2, 5, 1, 3, 3), DoubleArray(4 * 2 * 5 * 1 * 3 * 3) {0.0})
val tensor3 = fromArray(intArrayOf(1, 1), doubleArrayOf(500.0))
@ -79,7 +81,7 @@ class TestBroadcasting {
}
@Test
fun minusTensor() = BroadcastDoubleTensorAlgebra {
fun minusTensor() = BroadcastDoubleTensorAlgebra.invoke {
val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val tensor2 = fromArray(intArrayOf(1, 3), doubleArrayOf(10.0, 20.0, 30.0))
val tensor3 = fromArray(intArrayOf(1, 1, 1), doubleArrayOf(500.0))

5
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleAnalyticTensorAlgebra.kt
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@ -1,12 +1,13 @@
package space.kscience.kmath.tensors.core
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.tensors.core.algebras.DoubleAnalyticTensorAlgebra
import kotlin.math.abs
import kotlin.math.exp
import kotlin.test.Test
import kotlin.test.assertTrue
class TestDoubleAnalyticTensorAlgebra {
internal class TestDoubleAnalyticTensorAlgebra {
val shape = intArrayOf(2, 1, 3, 2)
val buffer = doubleArrayOf(27.1, 20.0, 19.84, 23.123, 0.0, 1.0, 3.23, 133.7, 25.3, 100.3, 11.0, 12.012)
@ -26,7 +27,7 @@ class TestDoubleAnalyticTensorAlgebra {
}
@Test
fun testExp() = DoubleAnalyticTensorAlgebra {
fun testExp() = DoubleAnalyticTensorAlgebra.invoke {
tensor.exp().let {
assertTrue { shape contentEquals it.shape }
assertTrue { buffer.fmap(::exp).epsEqual(it.buffer.array())}

28
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt
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@ -1,15 +1,16 @@
package space.kscience.kmath.tensors.core
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.tensors.core.algebras.DoubleLinearOpsTensorAlgebra
import kotlin.math.abs
import kotlin.test.Test
import kotlin.test.assertEquals
import kotlin.test.assertTrue
class TestDoubleLinearOpsTensorAlgebra {
internal class TestDoubleLinearOpsTensorAlgebra {
@Test
fun testDetLU() = DoubleLinearOpsTensorAlgebra {
fun testDetLU() = DoubleLinearOpsTensorAlgebra.invoke {
val tensor = fromArray(
intArrayOf(2, 2, 2),
doubleArrayOf(
@ -34,7 +35,7 @@ class TestDoubleLinearOpsTensorAlgebra {
}
@Test
fun testDet() = DoubleLinearOpsTensorAlgebra {
fun testDet() = DoubleLinearOpsTensorAlgebra.invoke {
val expectedValue = 0.019827417
val m = fromArray(
intArrayOf(3, 3), doubleArrayOf(
@ -48,7 +49,7 @@ class TestDoubleLinearOpsTensorAlgebra {
}
@Test
fun testDetSingle() = DoubleLinearOpsTensorAlgebra {
fun testDetSingle() = DoubleLinearOpsTensorAlgebra.invoke {
val expectedValue = 48.151623
val m = fromArray(
intArrayOf(1, 1), doubleArrayOf(
@ -60,7 +61,7 @@ class TestDoubleLinearOpsTensorAlgebra {
}
@Test
fun testInvLU() = DoubleLinearOpsTensorAlgebra {
fun testInvLU() = DoubleLinearOpsTensorAlgebra.invoke {
val tensor = fromArray(
intArrayOf(2, 2, 2),
doubleArrayOf(
@ -85,14 +86,14 @@ class TestDoubleLinearOpsTensorAlgebra {
}
@Test
fun testScalarProduct() = DoubleLinearOpsTensorAlgebra {
fun testScalarProduct() = DoubleLinearOpsTensorAlgebra.invoke {
val a = fromArray(intArrayOf(3), doubleArrayOf(1.8, 2.5, 6.8))
val b = fromArray(intArrayOf(3), doubleArrayOf(5.5, 2.6, 6.4))
assertEquals(a.dot(b).value(), 59.92)
}
@Test
fun testQR() = DoubleLinearOpsTensorAlgebra {
fun testQR() = DoubleLinearOpsTensorAlgebra.invoke {
val shape = intArrayOf(2, 2, 2)
val buffer = doubleArrayOf(
1.0, 3.0,
@ -110,11 +111,10 @@ class TestDoubleLinearOpsTensorAlgebra {
assertTrue((q dot r).eq(tensor))
//todo check orthogonality/upper triang.
}
@Test
fun testLU() = DoubleLinearOpsTensorAlgebra {
fun testLU() = DoubleLinearOpsTensorAlgebra.invoke {
val shape = intArrayOf(2, 2, 2)
val buffer = doubleArrayOf(
1.0, 3.0,
@ -134,7 +134,7 @@ class TestDoubleLinearOpsTensorAlgebra {
}
@Test
fun testCholesky() = DoubleLinearOpsTensorAlgebra {
fun testCholesky() = DoubleLinearOpsTensorAlgebra.invoke {
val tensor = randNormal(intArrayOf(2, 5, 5), 0)
val sigma = (tensor dot tensor.transpose()) + diagonalEmbedding(
fromArray(intArrayOf(2, 5), DoubleArray(10) { 0.1 })
@ -145,7 +145,7 @@ class TestDoubleLinearOpsTensorAlgebra {
}
@Test
fun testSVD1D() = DoubleLinearOpsTensorAlgebra {
fun testSVD1D() = DoubleLinearOpsTensorAlgebra.invoke {
val tensor2 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val res = svd1d(tensor2)
@ -156,13 +156,13 @@ class TestDoubleLinearOpsTensorAlgebra {
}
@Test
fun testSVD() = DoubleLinearOpsTensorAlgebra {
fun testSVD() = DoubleLinearOpsTensorAlgebra.invoke{
testSVDFor(fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)))
testSVDFor(fromArray(intArrayOf(2, 2), doubleArrayOf(-1.0, 0.0, 239.0, 238.0)))
}
@Test
fun testBatchedSVD() = DoubleLinearOpsTensorAlgebra {
fun testBatchedSVD() = DoubleLinearOpsTensorAlgebra.invoke {
val tensor = randNormal(intArrayOf(2, 5, 3), 0)
val (tensorU, tensorS, tensorV) = tensor.svd()
val tensorSVD = tensorU dot (diagonalEmbedding(tensorS) dot tensorV.transpose())
@ -170,7 +170,7 @@ class TestDoubleLinearOpsTensorAlgebra {
}
@Test
fun testBatchedSymEig() = DoubleLinearOpsTensorAlgebra {
fun testBatchedSymEig() = DoubleLinearOpsTensorAlgebra.invoke {
val tensor = randNormal(shape = intArrayOf(2, 3, 3), 0)
val tensorSigma = tensor + tensor.transpose()
val (tensorS, tensorV) = tensorSigma.symEig()

9
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensor.kt
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@ -4,6 +4,7 @@ import space.kscience.kmath.nd.DefaultStrides
import space.kscience.kmath.nd.MutableBufferND
import space.kscience.kmath.nd.as1D
import space.kscience.kmath.nd.as2D
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.structures.DoubleBuffer
import space.kscience.kmath.structures.asMutableBuffer
import space.kscience.kmath.structures.toDoubleArray
@ -12,17 +13,17 @@ import kotlin.test.Test
import kotlin.test.assertEquals
import kotlin.test.assertTrue
class TestDoubleTensor {
internal class TestDoubleTensor {
@Test
fun valueTest() = DoubleTensorAlgebra {
fun valueTest() = DoubleTensorAlgebra.invoke {
val value = 12.5
val tensor = fromArray(intArrayOf(1), doubleArrayOf(value))
assertEquals(tensor.value(), value)
}
@Test
fun stridesTest() = DoubleTensorAlgebra {
fun stridesTest() = DoubleTensorAlgebra.invoke {
val tensor = fromArray(intArrayOf(2, 2), doubleArrayOf(3.5, 5.8, 58.4, 2.4))
assertEquals(tensor[intArrayOf(0, 1)], 5.8)
assertTrue(
@ -31,7 +32,7 @@ class TestDoubleTensor {
}
@Test
fun getTest() = DoubleTensorAlgebra {
fun getTest() = DoubleTensorAlgebra.invoke {
val tensor = fromArray(intArrayOf(1, 2, 2), doubleArrayOf(3.5, 5.8, 58.4, 2.4))
val matrix = tensor[0].as2D()
assertEquals(matrix[0, 1], 5.8)

21
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt
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@ -1,29 +1,30 @@
package space.kscience.kmath.tensors.core
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.tensors.core.algebras.DoubleTensorAlgebra
import kotlin.test.Test
import kotlin.test.assertFalse
import kotlin.test.assertTrue
class TestDoubleTensorAlgebra {
internal class TestDoubleTensorAlgebra {
@Test
fun doublePlus() = DoubleTensorAlgebra {
fun doublePlus() = DoubleTensorAlgebra.invoke {
val tensor = fromArray(intArrayOf(2), doubleArrayOf(1.0, 2.0))
val res = 10.0 + tensor
assertTrue(res.buffer.array() contentEquals doubleArrayOf(11.0, 12.0))
}
@Test
fun doubleDiv() = DoubleTensorAlgebra {
fun doubleDiv() = DoubleTensorAlgebra.invoke {
val tensor = fromArray(intArrayOf(2), doubleArrayOf(2.0, 4.0))
val res = 2.0/tensor
assertTrue(res.buffer.array() contentEquals doubleArrayOf(1.0, 0.5))
}
@Test
fun divDouble() = DoubleTensorAlgebra {
fun divDouble() = DoubleTensorAlgebra.invoke {
val tensor = fromArray(intArrayOf(2), doubleArrayOf(10.0, 5.0))
val res = tensor / 2.5
assertTrue(res.buffer.array() contentEquals doubleArrayOf(4.0, 2.0))
@ -39,7 +40,7 @@ class TestDoubleTensorAlgebra {
}
@Test
fun transpose3x2() = DoubleTensorAlgebra {
fun transpose3x2() = DoubleTensorAlgebra.invoke {
val tensor = fromArray(intArrayOf(3, 2), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val res = tensor.transpose(1, 0)
@ -48,7 +49,7 @@ class TestDoubleTensorAlgebra {
}
@Test
fun transpose1x2x3() = DoubleTensorAlgebra {
fun transpose1x2x3() = DoubleTensorAlgebra.invoke {
val tensor = fromArray(intArrayOf(1, 2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val res01 = tensor.transpose(0, 1)
val res02 = tensor.transpose(-3, 2)
@ -64,7 +65,7 @@ class TestDoubleTensorAlgebra {
}
@Test
fun linearStructure() = DoubleTensorAlgebra {
fun linearStructure() = DoubleTensorAlgebra.invoke {
val shape = intArrayOf(3)
val tensorA = full(value = -4.5, shape = shape)
val tensorB = full(value = 10.9, shape = shape)
@ -96,7 +97,7 @@ class TestDoubleTensorAlgebra {
}
@Test
fun dot() = DoubleTensorAlgebra {
fun dot() = DoubleTensorAlgebra.invoke {
val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val tensor11 = fromArray(intArrayOf(3, 2), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val tensor2 = fromArray(intArrayOf(3), doubleArrayOf(10.0, 20.0, 30.0))
@ -132,7 +133,7 @@ class TestDoubleTensorAlgebra {
}
@Test
fun diagonalEmbedding() = DoubleTensorAlgebra {
fun diagonalEmbedding() = DoubleTensorAlgebra.invoke {
val tensor1 = fromArray(intArrayOf(3), doubleArrayOf(10.0, 20.0, 30.0))
val tensor2 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val tensor3 = zeros(intArrayOf(2, 3, 4, 5))
@ -165,7 +166,7 @@ class TestDoubleTensorAlgebra {
}
@Test
fun testEq() = DoubleTensorAlgebra {
fun testEq() = DoubleTensorAlgebra.invoke {
val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val tensor2 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val tensor3 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 5.0))