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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
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kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt
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@ -161,76 +161,6 @@ internal class TestDoubleLinearOpsTensorAlgebra {
assertTrue { abs(abs(res.mutableBuffer.array()[res.bufferStart + 1]) - 0.922) < 0.01 } assertTrue { abs(abs(res.mutableBuffer.array()[res.bufferStart + 1]) - 0.922) < 0.01 }
} }
@Test
fun testSVD() = DoubleTensorAlgebra{
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 testSVDError() = DoubleTensorAlgebra{
// val buffer = 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, 7.000000
// )
// testSVDFor(fromArray(intArrayOf(5, 3), buffer))
// }
@Test
fun testBatchedSVD() = DoubleTensorAlgebra {
val tensor = randomNormal(intArrayOf(2, 5, 3), 0)
val (tensorU, tensorS, tensorV) = tensor.svd()
val tensorSVD = tensorU dot (diagonalEmbedding(tensorS) dot tensorV.transpose())
assertTrue(tensor.eq(tensorSVD))
}
@Test
fun testSVDGolabKahan() = DoubleTensorAlgebra{
testSVDGolabKahanFor(fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)))
testSVDGolabKahanFor(fromArray(intArrayOf(2, 2), doubleArrayOf(-1.0, 0.0, 239.0, 238.0)))
val buffer = 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, 7.000000
)
testSVDGolabKahanFor(fromArray(intArrayOf(5, 3), buffer))
}
// @Test
// fun testSVDGolabKahanError() = DoubleTensorAlgebra{
// val buffer = 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
// )
// testSVDGolabKahanFor(fromArray(intArrayOf(3, 5), buffer))
// }
// @Test
// fun testSVDGolabKahanBig() = DoubleTensorAlgebra{
// val tensor = DoubleTensorAlgebra.randomNormal(intArrayOf(100, 100, 100), 0)
// testSVDGolabKahanFor(tensor)
// }
//
// @Test
// fun testSVDBig() = DoubleTensorAlgebra{
// val tensor = DoubleTensorAlgebra.randomNormal(intArrayOf(100, 100, 100), 0)
// testSVDFor(tensor)
// }
@Test
fun testBatchedSVDGolabKahan() = DoubleTensorAlgebra{
val tensor = randomNormal(intArrayOf(2, 5, 3), 0)
val (tensorU, tensorS, tensorV) = tensor.svdGolabKahan()
val tensorSVD = tensorU dot (diagonalEmbedding(tensorS) dot tensorV.transpose())
assertTrue(tensor.eq(tensorSVD))
}
@Test @Test
fun testBatchedSymEig() = DoubleTensorAlgebra { fun testBatchedSymEig() = DoubleTensorAlgebra {
val tensor = randomNormal(shape = intArrayOf(2, 3, 3), 0) val tensor = randomNormal(shape = intArrayOf(2, 3, 3), 0)
@ -240,24 +170,63 @@ internal class TestDoubleLinearOpsTensorAlgebra {
assertTrue(tensorSigma.eq(tensorSigmaCalc)) assertTrue(tensorSigma.eq(tensorSigmaCalc))
} }
@Test
} fun testSVD() = DoubleTensorAlgebra{
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)))
private fun DoubleTensorAlgebra.testSVDFor(tensor: DoubleTensor, epsilon: Double = 1e-10) { val buffer1 = doubleArrayOf(
val svd = tensor.svd() 1.000000, 2.000000, 3.000000,
2.000000, 3.000000, 4.000000,
val tensorSVD = svd.first 3.000000, 4.000000, 5.000000,
.dot( 4.000000, 5.000000, 6.000000,
diagonalEmbedding(svd.second) 5.000000, 6.000000, 7.000000
.dot(svd.third.transpose())
) )
testSVDFor(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
)
testSVDFor(fromArray(intArrayOf(3, 5), buffer2))
}
assertTrue(tensor.eq(tensorSVD, epsilon)) @Test
fun testBatchedSVD() = DoubleTensorAlgebra{
val tensor1 = randomNormal(intArrayOf(2, 5, 3), 0)
testSVDFor(tensor1)
val tensor2 = DoubleTensorAlgebra.randomNormal(intArrayOf(30, 30, 30), 0)
testSVDFor(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)))
}
@Test
fun testBatchedSVDPowerMethod() = DoubleTensorAlgebra {
val tensor1 = randomNormal(intArrayOf(2, 5, 3), 0)
testSVDPowerMethodFor(tensor1)
val tensor2 = DoubleTensorAlgebra.randomNormal(intArrayOf(30, 30, 30), 0)
testSVDPowerMethodFor(tensor2)
}
// @Test
// fun testSVDPowerMethodError() = DoubleTensorAlgebra{
// val buffer = 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, 7.000000
// )
// testSVDPowerMethodFor(fromArray(intArrayOf(5, 3), buffer))
// }
} }
private fun DoubleTensorAlgebra.testSVDGolabKahanFor(tensor: DoubleTensor) { private fun DoubleTensorAlgebra.testSVDFor(tensor: DoubleTensor) {
val svd = tensor.svdGolabKahan() val svd = tensor.svd()
val tensorSVD = svd.first val tensorSVD = svd.first
.dot( .dot(
@ -268,4 +237,14 @@ private fun DoubleTensorAlgebra.testSVDGolabKahanFor(tensor: DoubleTensor) {
assertTrue(tensor.eq(tensorSVD)) assertTrue(tensor.eq(tensorSVD))
} }
private fun DoubleTensorAlgebra.testSVDPowerMethodFor(tensor: DoubleTensor, epsilon: Double = 1e-10) {
val svd = tensor.svdPowerMethod()
val tensorSVD = svd.first
.dot(
diagonalEmbedding(svd.second)
.dot(svd.third.transpose())
)
assertTrue(tensor.eq(tensorSVD, epsilon))
}