functions renamed, svd (Golab Kahan) now works by default
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@ -833,8 +833,33 @@ public open class DoubleTensorAlgebra :
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return qTensor to rTensor
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return qTensor to rTensor
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}
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}
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override fun StructureND<Double>.svd(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> =
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override fun StructureND<Double>.svd(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
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svd(epsilon = 1e-10)
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val size = tensor.dimension
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val commonShape = tensor.shape.sliceArray(0 until size - 2)
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val (n, m) = tensor.shape.sliceArray(size - 2 until size)
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val uTensor = zeros(commonShape + intArrayOf(m, n))
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val sTensor = zeros(commonShape + intArrayOf(m))
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val vTensor = zeros(commonShape + intArrayOf(m, m))
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val matrices = tensor.matrices
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val uTensors = uTensor.matrices
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val sTensorVectors = sTensor.vectors
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val vTensors = vTensor.matrices
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for (index in matrices.indices) {
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val matrix = matrices[index]
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val matrixSize = matrix.shape.reduce { acc, i -> acc * i }
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val curMatrix = DoubleTensor(
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matrix.shape,
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matrix.mutableBuffer.array()
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.slice(matrix.bufferStart until matrix.bufferStart + matrixSize)
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.toDoubleArray()
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)
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curMatrix.as2D().svdHelper(uTensors[index].as2D(), sTensorVectors[index], vTensors[index].as2D())
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}
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return Triple(uTensor.transpose(), sTensor, vTensor)
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}
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/**
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/**
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* Singular Value Decomposition.
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* Singular Value Decomposition.
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@ -849,7 +874,7 @@ public open class DoubleTensorAlgebra :
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* i.e., the precision with which the cosine approaches 1 in an iterative algorithm.
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* i.e., the precision with which the cosine approaches 1 in an iterative algorithm.
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* @return a triple `Triple(U, S, V)`.
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* @return a triple `Triple(U, S, V)`.
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*/
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*/
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public fun StructureND<Double>.svd(epsilon: Double): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
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public fun StructureND<Double>.svdPowerMethod(epsilon: Double = 1e-10): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
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val size = tensor.dimension
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val size = tensor.dimension
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val commonShape = tensor.shape.sliceArray(0 until size - 2)
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val commonShape = tensor.shape.sliceArray(0 until size - 2)
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val (n, m) = tensor.shape.sliceArray(size - 2 until size)
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val (n, m) = tensor.shape.sliceArray(size - 2 until size)
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@ -876,40 +901,12 @@ public open class DoubleTensorAlgebra :
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.slice(matrix.bufferStart until matrix.bufferStart + matrixSize)
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.slice(matrix.bufferStart until matrix.bufferStart + matrixSize)
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.toDoubleArray()
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.toDoubleArray()
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)
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)
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svdHelper(curMatrix, usv, m, n, epsilon)
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svdPowerMethodHelper(curMatrix, usv, m, n, epsilon)
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}
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}
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return Triple(uTensor.transpose(), sTensor, vTensor.transpose())
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return Triple(uTensor.transpose(), sTensor, vTensor.transpose())
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}
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}
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public fun StructureND<Double>.svdGolabKahan(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
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val size = tensor.dimension
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val commonShape = tensor.shape.sliceArray(0 until size - 2)
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val (n, m) = tensor.shape.sliceArray(size - 2 until size)
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val uTensor = zeros(commonShape + intArrayOf(m, n))
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val sTensor = zeros(commonShape + intArrayOf(m))
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val vTensor = zeros(commonShape + intArrayOf(m, m))
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val matrices = tensor.matrices
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val uTensors = uTensor.matrices
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val sTensorVectors = sTensor.vectors
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val vTensors = vTensor.matrices
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for (index in matrices.indices) {
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val matrix = matrices[index]
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val matrixSize = matrix.shape.reduce { acc, i -> acc * i }
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val curMatrix = DoubleTensor(
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matrix.shape,
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matrix.mutableBuffer.array()
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.slice(matrix.bufferStart until matrix.bufferStart + matrixSize)
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.toDoubleArray()
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)
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curMatrix.as2D().svdGolabKahanHelper(uTensors[index].as2D(), sTensorVectors[index], vTensors[index].as2D())
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}
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return Triple(uTensor.transpose(), sTensor, vTensor)
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}
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override fun StructureND<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> = symEigJacobi(maxIteration = 50, epsilon = 1e-15)
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override fun StructureND<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> = symEigJacobi(maxIteration = 50, epsilon = 1e-15)
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/**
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/**
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@ -935,7 +932,7 @@ public open class DoubleTensorAlgebra :
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}
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}
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}
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}
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val (u, s, v) = tensor.svd(epsilon)
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val (u, s, v) = tensor.svd()
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val shp = s.shape + intArrayOf(1)
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val shp = s.shape + intArrayOf(1)
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val utv = u.transpose() dot v
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val utv = u.transpose() dot v
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val n = s.shape.last()
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val n = s.shape.last()
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@ -300,7 +300,7 @@ internal fun DoubleTensorAlgebra.svd1d(a: DoubleTensor, epsilon: Double = 1e-10)
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}
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}
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}
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}
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internal fun DoubleTensorAlgebra.svdHelper(
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internal fun DoubleTensorAlgebra.svdPowerMethodHelper(
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matrix: DoubleTensor,
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matrix: DoubleTensor,
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USV: Triple<BufferedTensor<Double>, BufferedTensor<Double>, BufferedTensor<Double>>,
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USV: Triple<BufferedTensor<Double>, BufferedTensor<Double>, BufferedTensor<Double>>,
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m: Int, n: Int, epsilon: Double,
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m: Int, n: Int, epsilon: Double,
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@ -372,7 +372,7 @@ private fun SIGN(a: Double, b: Double): Double {
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else
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else
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return -abs(a)
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return -abs(a)
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}
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}
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internal fun MutableStructure2D<Double>.svdGolabKahanHelper(u: MutableStructure2D<Double>, w: BufferedTensor<Double>, v: MutableStructure2D<Double>) {
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internal fun MutableStructure2D<Double>.svdHelper(u: MutableStructure2D<Double>, w: BufferedTensor<Double>, v: MutableStructure2D<Double>) {
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val shape = this.shape
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val shape = this.shape
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val m = shape.component1()
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val m = shape.component1()
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val n = shape.component2()
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val n = shape.component2()
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