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KMP library for tensors #300

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grinisrit merged 215 commits from feature/tensor-algebra into dev 2021-05-08 09:48:04 +03:00
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3 changed files with 78 additions and 68 deletions
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66
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleLinearOpsTensorAlgebra.kt
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@ -91,29 +91,6 @@ public class DoubleLinearOpsTensorAlgebra :
return qTensor to rTensor
}
internal fun svd1d(a: DoubleTensor, epsilon: Double = 1e-10): DoubleTensor {
val (n, m) = a.shape
var v: DoubleTensor
val b: DoubleTensor
if (n > m) {
b = a.transpose(0, 1).dot(a)
v = DoubleTensor(intArrayOf(m), getRandomNormals(m, 0))
} else {
b = a.dot(a.transpose(0, 1))
v = DoubleTensor(intArrayOf(n), getRandomNormals(n, 0))
}
var lastV: DoubleTensor
while (true) {
lastV = v
v = b.dot(lastV)
val norm = DoubleAnalyticTensorAlgebra { (v dot v).sqrt().value() }
v = v.times(1.0 / norm)
if (abs(v.dot(lastV).value()) > 1 - epsilon) {
return v
}
}
}
override fun DoubleTensor.svd(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
val size = this.shape.size
@ -124,47 +101,8 @@ public class DoubleLinearOpsTensorAlgebra :
val resV = zeros(commonShape + intArrayOf(min(n, m), m))
for ((matrix, USV) in this.matrixSequence()
.zip(resU.matrixSequence().zip(resS.vectorSequence().zip(resV.matrixSequence())))) {
val res = ArrayList<Triple<Double, DoubleTensor, DoubleTensor>>(0)
val (matrixU, SV) = USV
val (matrixS, matrixV) = SV
for (k in 0 until min(n, m)) {
var a = matrix.asTensor().copy()
for ((singularValue, u, v) in res.slice(0 until k)) {
val outerProduct = DoubleArray(u.shape[0] * v.shape[0])
for (i in 0 until u.shape[0]) {
for (j in 0 until v.shape[0]) {
outerProduct[i * v.shape[0] + j] = u[i].value() * v[j].value()
}
}
a = a - singularValue.times(DoubleTensor(intArrayOf(u.shape[0], v.shape[0]), outerProduct))
}
var v: DoubleTensor
var u: DoubleTensor
var norm: Double
if (n > m) {
v = svd1d(a)
u = matrix.asTensor().dot(v)
norm = DoubleAnalyticTensorAlgebra { (u dot u).sqrt().value() }
u = u.times(1.0 / norm)
} else {
u = svd1d(a)
v = matrix.asTensor().transpose(0, 1).dot(u)
norm = DoubleAnalyticTensorAlgebra { (v dot v).sqrt().value() }
v = v.times(1.0 / norm)
}
res.add(Triple(norm, u, v))
}
val s = res.map { it.first }.toDoubleArray()
val uBuffer = res.map { it.second }.flatMap { it.buffer.array().toList() }.toDoubleArray()
val vBuffer = res.map { it.third }.flatMap { it.buffer.array().toList() }.toDoubleArray()
uBuffer.copyInto(matrixU.buffer.array())
s.copyInto(matrixS.buffer.array())
vBuffer.copyInto(matrixV.buffer.array())
}
.zip(resU.matrixSequence().zip(resS.vectorSequence().zip(resV.matrixSequence()))))
svdHelper(matrix.asTensor(), USV, m, n)
return Triple(resU, resS, resV.transpose(size - 2, size - 1))
}

76
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/linutils.kt
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@ -4,6 +4,8 @@ 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 kotlin.math.abs
import kotlin.math.min
import kotlin.math.sqrt
@ -195,8 +197,8 @@ internal inline fun DoubleLinearOpsTensorAlgebra.qrHelper(
checkSquareMatrix(matrix.shape)
val n = matrix.shape[0]
val qM = q.as2D()
val matrixT = matrix.transpose(0,1)
val qT = q.transpose(0,1)
val matrixT = matrix.transpose(0, 1)
val qT = q.transpose(0, 1)
for (j in 0 until n) {
val v = matrixT[j]
@ -216,3 +218,73 @@ internal inline fun DoubleLinearOpsTensorAlgebra.qrHelper(
}
}
}
internal inline fun DoubleLinearOpsTensorAlgebra.svd1d(a: DoubleTensor, epsilon: Double = 1e-10): DoubleTensor {
val (n, m) = a.shape
var v: DoubleTensor
val b: DoubleTensor
if (n > m) {
b = a.transpose(0, 1).dot(a)
v = DoubleTensor(intArrayOf(m), getRandomNormals(m, 0))
} else {
b = a.dot(a.transpose(0, 1))
v = DoubleTensor(intArrayOf(n), getRandomNormals(n, 0))
}
var lastV: DoubleTensor
while (true) {
lastV = v
v = b.dot(lastV)
val norm = DoubleAnalyticTensorAlgebra { (v dot v).sqrt().value() }
v = v.times(1.0 / norm)
if (abs(v.dot(lastV).value()) > 1 - epsilon) {
return v
}
}
}
internal inline fun DoubleLinearOpsTensorAlgebra.svdHelper(
matrix: DoubleTensor,
USV: Pair<BufferedTensor<Double>, Pair<BufferedTensor<Double>, BufferedTensor<Double>>>,
m: Int, n: Int
): Unit {
val res = ArrayList<Triple<Double, DoubleTensor, DoubleTensor>>(0)
val (matrixU, SV) = USV
val (matrixS, matrixV) = SV
for (k in 0 until min(n, m)) {
var a = matrix.copy()
for ((singularValue, u, v) in res.slice(0 until k)) {
val outerProduct = DoubleArray(u.shape[0] * v.shape[0])
for (i in 0 until u.shape[0]) {
for (j in 0 until v.shape[0]) {
outerProduct[i * v.shape[0] + j] = u[i].value() * v[j].value()
}
}
a = a - singularValue.times(DoubleTensor(intArrayOf(u.shape[0], v.shape[0]), outerProduct))
}
var v: DoubleTensor
var u: DoubleTensor
var norm: Double
if (n > m) {
v = svd1d(a)
u = matrix.dot(v)
norm = DoubleAnalyticTensorAlgebra { (u dot u).sqrt().value() }
u = u.times(1.0 / norm)
} else {
u = svd1d(a)
v = matrix.transpose(0, 1).dot(u)
norm = DoubleAnalyticTensorAlgebra { (v dot v).sqrt().value() }
v = v.times(1.0 / norm)
}
res.add(Triple(norm, u, v))
}
val s = res.map { it.first }.toDoubleArray()
val uBuffer = res.map { it.second }.flatMap { it.buffer.array().toList() }.toDoubleArray()
val vBuffer = res.map { it.third }.flatMap { it.buffer.array().toList() }.toDoubleArray()
uBuffer.copyInto(matrixU.buffer.array())
s.copyInto(matrixS.buffer.array())
vBuffer.copyInto(matrixV.buffer.array())
}

4
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt
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@ -124,7 +124,7 @@ class TestDoubleLinearOpsTensorAlgebra {
}
@Test
fun svd1d() = DoubleLinearOpsTensorAlgebra {
fun testSVD1D() = DoubleLinearOpsTensorAlgebra {
val tensor2 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
val res = svd1d(tensor2)
@ -135,7 +135,7 @@ class TestDoubleLinearOpsTensorAlgebra {
}
@Test
fun svd() = DoubleLinearOpsTensorAlgebra {
fun testSVD() = DoubleLinearOpsTensorAlgebra {
val epsilon = 1e-10
fun test_tensor(tensor: DoubleTensor) {
val svd = tensor.svd()