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Golub-Kahan SVD algorithm for KMP tensors #499

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grinisrit wants to merge 64 commits from dev into dev
pull from: dev
merge into: kscience:dev
Conversation 1 Commits 64 Files Changed 9 +64 -6
4 changed files with 64 additions and 6 deletions
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6
benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/SVDBenchmark.kt
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@ -8,7 +8,7 @@ import kotlinx.benchmark.Benchmark
import kotlinx.benchmark.Blackhole
import kotlinx.benchmark.Scope
import kotlinx.benchmark.State
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.svd
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.svdGolubKahan
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.svdPowerMethod
@ -26,9 +26,9 @@ class SVDBenchmark {
}
@Benchmark
fun svdGolabKahan(blackhole: Blackhole) {
fun svdGolubKahan(blackhole: Blackhole) {
blackhole.consume(
tensor.svd()
tensor.svdGolubKahan()
)
}
}

6
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
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@ -834,6 +834,10 @@ public open class DoubleTensorAlgebra :
}
override fun StructureND<Double>.svd(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
return this.svdGolubKahan()
}
public fun StructureND<Double>.svdGolubKahan(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
val size = tensor.dimension
val commonShape = tensor.shape.sliceArray(0 until size - 2)
val (n, m) = tensor.shape.sliceArray(size - 2 until size)
@ -855,7 +859,7 @@ public open class DoubleTensorAlgebra :
.slice(matrix.bufferStart until matrix.bufferStart + matrixSize)
.toDoubleArray()
)
curMatrix.as2D().svdHelper(uTensors[index].as2D(), sTensorVectors[index], vTensors[index].as2D())
curMatrix.as2D().svdGolubKahanHelper(uTensors[index].as2D(), sTensorVectors[index], vTensors[index].as2D())
}
return Triple(uTensor.transpose(), sTensor, vTensor)

2
kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/linUtils.kt
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@ -372,7 +372,7 @@ private fun SIGN(a: Double, b: Double): Double {
else
return -abs(a)
}
internal fun MutableStructure2D<Double>.svdHelper(u: MutableStructure2D<Double>, w: BufferedTensor<Double>, v: MutableStructure2D<Double>) {
internal fun MutableStructure2D<Double>.svdGolubKahanHelper(u: MutableStructure2D<Double>, w: BufferedTensor<Double>, v: MutableStructure2D<Double>) {
val shape = this.shape
val m = shape.component1()
val n = shape.component2()

56
kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt
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@ -179,7 +179,7 @@ internal class TestDoubleLinearOpsTensorAlgebra {
2.000000, 3.000000, 4.000000,
3.000000, 4.000000, 5.000000,
4.000000, 5.000000, 6.000000,
5.000000, 6.000000, 7.000000
5.000000, 6.000000, 9.000000
)
testSVDFor(fromArray(intArrayOf(5, 3), buffer1))
val buffer2 = doubleArrayOf(
@ -198,10 +198,52 @@ internal class TestDoubleLinearOpsTensorAlgebra {
testSVDFor(tensor2)
}
@Test
fun testSVDGolubKahan() = DoubleTensorAlgebra{
testSVDGolubKahanFor(fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)))
testSVDGolubKahanFor(fromArray(intArrayOf(2, 2), doubleArrayOf(-1.0, 0.0, 239.0, 238.0)))
val buffer1 = doubleArrayOf(
1.000000, 2.000000, 3.000000,
2.000000, 3.000000, 4.000000,
3.000000, 4.000000, 5.000000,
4.000000, 5.000000, 6.000000,
5.000000, 6.000000, 9.000000
)
testSVDGolubKahanFor(fromArray(intArrayOf(5, 3), buffer1))
val buffer2 = doubleArrayOf(
1.0, 2.0, 3.0, 2.0, 3.0,
4.0, 3.0, 4.0, 5.0, 4.0,
5.0, 6.0, 5.0, 6.0, 7.0
)
testSVDGolubKahanFor(fromArray(intArrayOf(3, 5), buffer2))
}
@Test
fun testBatchedSVDGolubKahan() = DoubleTensorAlgebra{
val tensor1 = randomNormal(intArrayOf(2, 5, 3), 0)
testSVDGolubKahanFor(tensor1)
val tensor2 = DoubleTensorAlgebra.randomNormal(intArrayOf(30, 30, 30), 0)
testSVDGolubKahanFor(tensor2)
}
@Test
fun testSVDPowerMethod() = DoubleTensorAlgebra{
testSVDPowerMethodFor(fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)))
testSVDPowerMethodFor(fromArray(intArrayOf(2, 2), doubleArrayOf(-1.0, 0.0, 239.0, 238.0)))
val buffer1 = doubleArrayOf(
1.000000, 2.000000, 3.000000,
2.000000, 3.000000, 4.000000,
3.000000, 4.000000, 5.000000,
4.000000, 5.000000, 6.000000,
5.000000, 6.000000, 9.000000
)
testSVDPowerMethodFor(fromArray(intArrayOf(5, 3), buffer1))
val buffer2 = doubleArrayOf(
1.0, 2.0, 3.0, 2.0, 3.0,
4.0, 3.0, 4.0, 5.0, 4.0,
5.0, 6.0, 5.0, 6.0, 7.0
)
testSVDPowerMethodFor(fromArray(intArrayOf(3, 5), buffer2))
}
@Test
@ -237,6 +279,18 @@ private fun DoubleTensorAlgebra.testSVDFor(tensor: DoubleTensor) {
assertTrue(tensor.eq(tensorSVD))
}
private fun DoubleTensorAlgebra.testSVDGolubKahanFor(tensor: DoubleTensor) {
val svd = tensor.svdGolubKahan()
val tensorSVD = svd.first
.dot(
diagonalEmbedding(svd.second)
.dot(svd.third.transpose())
)
assertTrue(tensor.eq(tensorSVD))
}
private fun DoubleTensorAlgebra.testSVDPowerMethodFor(tensor: DoubleTensor, epsilon: Double = 1e-10) {
val svd = tensor.svdPowerMethod()