Open epsilon to client to control numerical precision for power methods
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@ -1,7 +1,7 @@
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package space.kscience.kmath.tensors
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public interface LinearOpsTensorAlgebra<T, TensorType : TensorStructure<T>, IndexTensorType: TensorStructure<Int>> :
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public interface LinearOpsTensorAlgebra<T, TensorType : TensorStructure<T>, IndexTensorType : TensorStructure<Int>> :
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TensorPartialDivisionAlgebra<T, TensorType> {
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//https://pytorch.org/docs/stable/linalg.html#torch.linalg.det
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@ -26,6 +26,6 @@ public interface LinearOpsTensorAlgebra<T, TensorType : TensorStructure<T>, Inde
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public fun TensorType.svd(): Triple<TensorType, TensorType, TensorType>
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//https://pytorch.org/docs/stable/generated/torch.symeig.html
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public fun TensorType.symEig(eigenvectors: Boolean = true): Pair<TensorType, TensorType>
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public fun TensorType.symEig(): Pair<TensorType, TensorType>
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}
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@ -94,8 +94,10 @@ public class DoubleLinearOpsTensorAlgebra :
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return qTensor to rTensor
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}
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override fun DoubleTensor.svd(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> =
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svd(epsilon = 1e-10)
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override fun DoubleTensor.svd(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
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public fun DoubleTensor.svd(epsilon: Double): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
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val size = this.linearStructure.dim
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val commonShape = this.shape.sliceArray(0 until size - 2)
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val (n, m) = this.shape.sliceArray(size - 2 until size)
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@ -110,17 +112,20 @@ public class DoubleLinearOpsTensorAlgebra :
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matrix.shape,
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matrix.buffer.array().slice(matrix.bufferStart until matrix.bufferStart + size).toDoubleArray()
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)
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svdHelper(curMatrix, USV, m, n)
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svdHelper(curMatrix, USV, m, n, epsilon)
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}
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return Triple(resU.transpose(), resS, resV.transpose())
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}
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override fun DoubleTensor.symEig(): Pair<DoubleTensor, DoubleTensor> =
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symEig(epsilon = 1e-15)
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//http://hua-zhou.github.io/teaching/biostatm280-2017spring/slides/16-eigsvd/eigsvd.html
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override fun DoubleTensor.symEig(eigenvectors: Boolean): Pair<DoubleTensor, DoubleTensor> {
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checkSymmetric(this)
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val (u, s, v) = this.svd()
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public fun DoubleTensor.symEig(epsilon: Double): Pair<DoubleTensor, DoubleTensor> {
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checkSymmetric(this, epsilon)
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val (u, s, v) = this.svd(epsilon)
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val shp = s.shape + intArrayOf(1)
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val utv = (u.transpose() dot v).map { if (abs(it) < 0.99) 0.0 else sign(it) }
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val utv = (u.transpose() dot v).map { if (abs(it) < 0.9) 0.0 else sign(it) }
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val eig = (utv dot s.view(shp)).view(s.shape)
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return Pair(eig, v)
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}
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@ -58,7 +58,7 @@ internal inline fun <T, TensorType : TensorStructure<T>,
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}
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}
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internal inline fun DoubleTensorAlgebra.checkSymmetric(tensor: DoubleTensor): Unit =
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check(tensor.eq(tensor.transpose())){
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"Tensor is not symmetric about the last 2 dimensions"
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internal inline fun DoubleTensorAlgebra.checkSymmetric(tensor: DoubleTensor, epsilon: Double = 1e-6): Unit =
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check(tensor.eq(tensor.transpose(), epsilon)) {
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"Tensor is not symmetric about the last 2 dimensions at precision $epsilon"
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}
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@ -246,7 +246,7 @@ internal inline fun DoubleLinearOpsTensorAlgebra.svd1d(a: DoubleTensor, epsilon:
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internal inline fun DoubleLinearOpsTensorAlgebra.svdHelper(
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matrix: DoubleTensor,
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USV: Pair<BufferedTensor<Double>, Pair<BufferedTensor<Double>, BufferedTensor<Double>>>,
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m: Int, n: Int
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m: Int, n: Int, epsilon: Double
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): Unit {
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val res = ArrayList<Triple<Double, DoubleTensor, DoubleTensor>>(0)
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val (matrixU, SV) = USV
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@ -267,12 +267,12 @@ internal inline fun DoubleLinearOpsTensorAlgebra.svdHelper(
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var u: DoubleTensor
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var norm: Double
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if (n > m) {
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v = svd1d(a)
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v = svd1d(a, epsilon)
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u = matrix.dot(v)
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norm = DoubleAnalyticTensorAlgebra { (u dot u).sqrt().value() }
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u = u.times(1.0 / norm)
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} else {
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u = svd1d(a)
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u = svd1d(a, epsilon)
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v = matrix.transpose(0, 1).dot(u)
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norm = DoubleAnalyticTensorAlgebra { (v dot v).sqrt().value() }
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v = v.times(1.0 / norm)
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@ -143,7 +143,7 @@ class TestDoubleLinearOpsTensorAlgebra {
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val tensorSigma = tensor + tensor.transpose()
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val (tensorS, tensorV) = tensorSigma.symEig()
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val tensorSigmaCalc = tensorV dot (diagonalEmbedding(tensorS) dot tensorV.transpose())
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assertTrue(tensorSigma.eq(tensorSigmaCalc, 0.01))
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assertTrue(tensorSigma.eq(tensorSigmaCalc))
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}
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