LU and det refactored

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

@@ -10,43 +10,15 @@ public class DoubleLinearOpsTensorAlgebra :
     LinearOpsTensorAlgebra<Double, DoubleTensor, IntTensor>,
     DoubleTensorAlgebra() {
 
-    override fun DoubleTensor.inv(): DoubleTensor = invLU()
+    override fun DoubleTensor.inv(): DoubleTensor = invLU(1e-9)
 
-    override fun DoubleTensor.det(): DoubleTensor = detLU()
+    override fun DoubleTensor.det(): DoubleTensor = detLU(1e-9)
 
-    internal fun DoubleTensor.luForDet(forDet: Boolean = false): Pair<DoubleTensor, IntTensor> {
+    public fun DoubleTensor.lu(epsilon: Double): Pair<DoubleTensor, IntTensor> =
-        checkSquareMatrix(shape)
+        computeLU(this, epsilon) ?:
+        throw RuntimeException("Tensor contains matrices which are singular at precision $epsilon")
 
-        val luTensor = copy()
+    override fun DoubleTensor.lu(): Pair<DoubleTensor, IntTensor> = lu(1e-9)
-
-        val n = shape.size
-        val m = shape.last()
-        val pivotsShape = IntArray(n - 1) { i -> shape[i] }
-        pivotsShape[n - 2] = m + 1
-
-        val pivotsTensor = IntTensor(
-            pivotsShape,
-            IntArray(pivotsShape.reduce(Int::times)) { 0 }
-        )
-
-        for ((lu, pivots) in luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()))
-            try {
-                luHelper(lu.as2D(), pivots.as1D(), m)
-            } catch (e: RuntimeException) {
-                if (forDet) {
-                    lu.as2D()[intArrayOf(0, 0)] = 0.0
-                } else {
-                    throw IllegalStateException("LUP decomposition can't be performed")
-                }
-            }
-
-
-        return Pair(luTensor, pivotsTensor)
-    }
-
-    override fun DoubleTensor.lu(): Pair<DoubleTensor, IntTensor> {
-        return luForDet(false)
-    }
 
     override fun luPivot(
         luTensor: DoubleTensor,
@@ -79,9 +51,7 @@ public class DoubleLinearOpsTensorAlgebra :
 
     public fun DoubleTensor.cholesky(epsilon: Double): DoubleTensor {
         checkSquareMatrix(shape)
-        checkPositiveDefinite(this)
+        checkPositiveDefinite(this, epsilon)
-        //checkPositiveDefinite(this, epsilon)
-
 
         val n = shape.last()
         val lTensor = zeroesLike()
@@ -146,8 +116,12 @@ public class DoubleLinearOpsTensorAlgebra :
         return Pair(eig, v)
     }
 
-    public fun DoubleTensor.detLU(): DoubleTensor {
+    public fun DoubleTensor.detLU(epsilon: Double = 1e-9): DoubleTensor {
-        val (luTensor, pivotsTensor) = luForDet(forDet = true)
+
+        checkSquareMatrix(this.shape)
+        val luTensor = this.copy()
+        val pivotsTensor = this.setUpPivots()
+
         val n = shape.size
 
         val detTensorShape = IntArray(n - 1) { i -> shape[i] }
@@ -160,15 +134,15 @@ public class DoubleLinearOpsTensorAlgebra :
         )
 
         luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).forEachIndexed { index, (lu, pivots) ->
-            resBuffer[index] = luMatrixDet(lu.as2D(), pivots.as1D())
+            resBuffer[index] = if (luHelper(lu.as2D(), pivots.as1D(), epsilon))
+                0.0 else luMatrixDet(lu.as2D(), pivots.as1D())
         }
 
         return detTensor
     }
 
-    public fun DoubleTensor.invLU(): DoubleTensor {
+    public fun DoubleTensor.invLU(epsilon: Double = 1e-9): DoubleTensor {
-        //TODO("Andrei the det is non-zero")
+        val (luTensor, pivotsTensor) = lu(epsilon)
-        val (luTensor, pivotsTensor) = lu()
         val invTensor = luTensor.zeroesLike()
 
         val seq = luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).zip(invTensor.matrixSequence())

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

@@ -61,7 +61,13 @@ internal inline fun dotHelper(
     }
 }
 
-internal inline fun luHelper(lu: MutableStructure2D<Double>, pivots: MutableStructure1D<Int>, m: Int) {
+internal inline fun luHelper(
+    lu: MutableStructure2D<Double>,
+    pivots: MutableStructure1D<Int>,
+    epsilon: Double): Boolean {
+
+    val m = lu.rowNum
+
     for (row in 0..m) pivots[row] = row
 
     for (i in 0 until m) {
@@ -69,16 +75,15 @@ internal inline fun luHelper(lu: MutableStructure2D<Double>, pivots: MutableStru
         var maxInd = i
 
         for (k in i until m) {
-            val absA = kotlin.math.abs(lu[k, i])
+            val absA = abs(lu[k, i])
             if (absA > maxVal) {
                 maxVal = absA
                 maxInd = k
             }
         }
 
-        if (abs(maxVal) < 1e-9) {
+        if (abs(maxVal) < epsilon)
-            throw RuntimeException()
+            return true // matrix is singular
-        }
 
         if (maxInd != i) {
 
@@ -103,6 +108,34 @@ internal inline fun luHelper(lu: MutableStructure2D<Double>, pivots: MutableStru
             }
         }
     }
+    return false
+}
+
+internal inline fun <T> BufferedTensor<T>.setUpPivots(): IntTensor {
+    val n = this.shape.size
+    val m = this.shape.last()
+    val pivotsShape = IntArray(n - 1) { i -> this.shape[i] }
+    pivotsShape[n - 2] = m + 1
+
+    return IntTensor(
+        pivotsShape,
+        IntArray(pivotsShape.reduce(Int::times)) { 0 }
+    )
+}
+
+internal inline fun DoubleLinearOpsTensorAlgebra.computeLU(
+    tensor: DoubleTensor,
+    epsilon: Double): Pair<DoubleTensor, IntTensor>? {
+
+    checkSquareMatrix(tensor.shape)
+    val luTensor = tensor.copy()
+    val pivotsTensor = tensor.setUpPivots()
+
+    for ((lu, pivots) in luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()))
+        if(luHelper(lu.as2D(), pivots.as1D(), epsilon))
+            return null
+
+    return Pair(luTensor, pivotsTensor)
 }
 
 internal inline fun pivInit(

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

@@ -1,8 +1,6 @@
 package space.kscience.kmath.tensors.core
 
-import space.kscience.kmath.structures.toList
 import kotlin.math.abs
-import kotlin.test.Ignore
 import kotlin.test.Test
 import kotlin.test.assertEquals
 import kotlin.test.assertTrue
@@ -144,11 +142,9 @@ class TestDoubleLinearOpsTensorAlgebra {
         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