Approaching SymEig through SVD

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

@@ -67,7 +67,7 @@ public class DoubleLinearOpsTensorAlgebra :
     }
 
     override fun DoubleTensor.cholesky(): DoubleTensor {
-        // todo checks
+        checkSymmetric(this)
         checkSquareMatrix(shape)
 
         val n = shape.last()
@@ -113,7 +113,9 @@ public class DoubleLinearOpsTensorAlgebra :
     }
 
     override fun DoubleTensor.symEig(eigenvectors: Boolean): Pair<DoubleTensor, DoubleTensor> {
-        TODO()
+        checkSymmetric(this)
+        val svd = this.svd()
+        TODO("U might have some columns negative to V")
     }
 
     public fun DoubleTensor.detLU(): DoubleTensor {

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

@@ -58,3 +58,7 @@ internal inline fun <T, TensorType : TensorStructure<T>,
     }
 }
 
+internal inline fun DoubleTensorAlgebra.checkSymmetric(tensor: DoubleTensor): Unit =
+    check(tensor.eq(tensor.transpose())){
+        "Tensor is not symmetric about the last 2 dimensions"
+    }

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

@@ -140,9 +140,9 @@ class TestDoubleLinearOpsTensorAlgebra {
     @Ignore
     fun testBatchedSymEig() = DoubleLinearOpsTensorAlgebra {
         val tensor = randNormal(shape = intArrayOf(5, 2, 2), 0)
-        val tensorSigma = tensor + tensor.transpose(1, 2)
+        val tensorSigma = tensor + tensor.transpose()
         val (tensorS, tensorV) = tensorSigma.symEig()
-        val tensorSigmaCalc = tensorV dot (diagonalEmbedding(tensorS) dot tensorV.transpose(1, 2))
+        val tensorSigmaCalc = tensorV dot (diagonalEmbedding(tensorS) dot tensorV.transpose())
         assertTrue(tensorSigma.eq(tensorSigmaCalc))
     }