implement svd function and tests for it

kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleLinearOpsTensorAlgebra.kt

@@ -3,6 +3,8 @@ package space.kscience.kmath.tensors.core
 import space.kscience.kmath.tensors.LinearOpsTensorAlgebra
 import space.kscience.kmath.nd.as1D
 import space.kscience.kmath.nd.as2D
+import kotlin.math.abs
+import kotlin.math.min
 
 public class DoubleLinearOpsTensorAlgebra :
     LinearOpsTensorAlgebra<Double, DoubleTensor, IntTensor>,
@@ -89,8 +91,81 @@ 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> {
-        TODO("ALYA")
+        val size = this.shape.size
+        val commonShape = this.shape.sliceArray(0 until size - 2)
+        val (n, m) = this.shape.sliceArray(size - 2 until size)
+        val resU = zeros(commonShape + intArrayOf(n, min(n, m)))
+        val resS = zeros(commonShape + intArrayOf(min(n, m)))
+        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())
+        }
+        return Triple(resU, resS, resV.transpose(size - 2, size - 1))
     }
 
     override fun DoubleTensor.symEig(eigenvectors: Boolean): Pair<DoubleTensor, DoubleTensor> {

kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt

@@ -122,4 +122,36 @@ class TestDoubleLinearOpsTensorAlgebra {
 
         assertTrue { p.dot(tensor).buffer.array().epsEqual(l.dot(u).buffer.array()) }
     }
+
+    @Test
+    fun svd1d() = DoubleLinearOpsTensorAlgebra {
+        val tensor2 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+
+        val res = svd1d(tensor2)
+
+        assertTrue(res.shape contentEquals intArrayOf(2))
+        assertTrue { abs(abs(res.buffer.array()[res.bufferStart]) -  0.386) < 0.01}
+        assertTrue { abs(abs(res.buffer.array()[res.bufferStart + 1]) -  0.922) < 0.01}
+    }
+
+    @Test
+    fun svd() = DoubleLinearOpsTensorAlgebra {
+        val epsilon = 1e-10
+        fun test_tensor(tensor: DoubleTensor) {
+            val svd = tensor.svd()
+
+            val tensorSVD = svd.first
+                .dot(
+                    diagonalEmbedding(svd.second, 0, 0, 1)
+                        .dot(svd.third.transpose(0, 1))
+                )
+
+            for ((x1, x2) in tensor.buffer.array() zip tensorSVD.buffer.array()) {
+                assertTrue { abs(x1 - x2) < epsilon }
+            }
+        }
+        test_tensor(fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)))
+        test_tensor(fromArray(intArrayOf(2, 2), doubleArrayOf(-1.0, 0.0, 239.0, 238.0)))
+
+    }
 }