examples/src/main/kotlin/space/kscience/kmath/tensors/OLSWithSVD.kt

@@ -9,6 +9,8 @@ import space.kscience.kmath.tensors.core.DoubleTensor
 import space.kscience.kmath.tensors.core.algebras.DoubleAnalyticTensorAlgebra
 import space.kscience.kmath.tensors.core.algebras.DoubleLinearOpsTensorAlgebra
 
+import kotlin.math.abs
+
 // OLS estimator using SVD
 
 fun main() {
@@ -26,8 +28,7 @@ fun main() {
             doubleArrayOf(1.0, 2.5, 3.4, 5.0, 10.1)
         )
 
-        println("Real alpha:\n" +
-                "$alpha")
+        println("Real alpha:\n$alpha")
 
         // also take sample of size 20 from normal distribution for x TODO rename
         val x = randNormal(
@@ -35,20 +36,22 @@ fun main() {
             randSeed
         )
 
-        // calculate y and add gaussian noise (N(0, 0.05)) TODO rename
+        // calculate y and add gaussian noise (N(0, 0.05))
+        // TODO: please add an intercept: Y = beta * X + alpha + N(0,0.5)
         val y = x dot alpha
         y += y.randNormalLike(randSeed) * 0.05
 
         // now restore the coefficient vector with OSL estimator with SVD
+        // TODO: you need to change accordingly [X 1] [alpha beta] = Y
+        // TODO: inverting [X 1] via SVD
         val (u, singValues, v) = x.svd()
 
         // we have to make sure the singular values of the matrix are not close to zero
-        println("Singular values:\n" +
-                "$singValues")
-        // TODO something with Boolean tensors
+        println("Singular values:\n$singValues")
+
 
         // inverse Sigma matrix can be restored from singular values with diagonalEmbedding function
-        val sigma = diagonalEmbedding(1.0/singValues)
+        val sigma = diagonalEmbedding(singValues.map{ x -> if (abs(x) < 1e-3) 0.0 else 1.0/x })
 
         val alphaOLS = v dot sigma dot u.transpose() dot y
         println("Estimated alpha:\n" +