Cholesky decomp tests and checks - det to be fixed

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

@@ -67,9 +67,10 @@ public class DoubleLinearOpsTensorAlgebra :
     }
 
     override fun DoubleTensor.cholesky(): DoubleTensor {
-        //positive definite check
         checkSymmetric(this)
         checkSquareMatrix(shape)
+        //TODO("Andrei the det routine has bugs")
+        //checkPositiveDefinite(this)
 
         val n = shape.last()
         val lTensor = zeroesLike()

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

@@ -61,4 +61,11 @@ internal inline fun <T, TensorType : TensorStructure<T>,
 internal inline fun DoubleTensorAlgebra.checkSymmetric(tensor: DoubleTensor, epsilon: Double = 1e-6): Unit =
     check(tensor.eq(tensor.transpose(), epsilon)) {
         "Tensor is not symmetric about the last 2 dimensions at precision $epsilon"
-    }
+    }
+
+internal inline fun DoubleLinearOpsTensorAlgebra.checkPositiveDefinite(tensor: DoubleTensor): Unit {
+    for( mat in tensor.matrixSequence())
+        check(mat.asTensor().detLU().value() > 0.0){
+            "Tensor contains matrices which are not positive definite ${mat.asTensor().detLU().value()}"
+        }
+}

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

@@ -112,6 +112,19 @@ class TestDoubleLinearOpsTensorAlgebra {
         assertTrue((p dot tensor).eq(l dot u))
     }
 
+    @Test
+    fun testCholesky() = DoubleLinearOpsTensorAlgebra {
+        val tensor = randNormal(intArrayOf(2, 5, 5), 0)
+        val sigma = (tensor dot tensor.transpose()) + diagonalEmbedding(
+            fromArray(intArrayOf(2, 5), DoubleArray(10) { 0.1 })
+        )
+        //checkPositiveDefinite(sigma) sigma must be positive definite
+        val low = sigma.cholesky()
+        val sigmChol = low dot low.transpose()
+        assertTrue(sigma.eq(sigmChol))
+
+    }
+
     @Test
     fun testSVD1D() = DoubleLinearOpsTensorAlgebra {
         val tensor2 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))