[orx-math] Add matrix and sparse matrix implementations with Cholesky and QR decompositions

2025-08-16 17:21:33 +02:00
parent e6997a968f
commit 1d81754a23
7 changed files with 1670 additions and 0 deletions
--- a/orx-math/src/jvmDemo/kotlin/matrix/DemoLeastSquares01.kt
+++ b/orx-math/src/jvmDemo/kotlin/matrix/DemoLeastSquares01.kt
@@ -0,0 +1,65 @@
+package matrix
+
+import org.openrndr.application
+import org.openrndr.color.ColorRGBa
+import org.openrndr.extra.math.matrix.Matrix
+import org.openrndr.extra.math.matrix.invertMatrixCholesky
+import org.openrndr.extra.noise.uniform
+import org.openrndr.extra.noise.uniformRing
+import org.openrndr.math.Vector2
+import kotlin.math.cos
+import kotlin.random.Random
+
+/**
+ * Demonstrate least squares method to find a regression line through noisy points
+ * Line drawn in red is the estimated line, in green is the ground-truth line
+ *
+ * Ax = b => x = A⁻¹b
+ * because A is likely inconsistent, we look for an approximate x based on AᵀA, which is consistent.
+ * x̂ = (AᵀA)⁻¹ Aᵀb
+ */
+fun main() {
+    application {
+        configure {
+            width = 720
+            height = 720
+        }
+        program {
+            extend {
+                val ls = drawer.bounds.horizontal(0.5).rotateBy(cos(seconds)*45.0)
+
+                val r = Random((seconds*10).toInt())
+
+                val pointCount = 100
+                val A = Matrix(pointCount, 2)
+                val b = Matrix(pointCount, 1)
+                for (i in 0 until pointCount) {
+
+                    val p = ls.position(Double.uniform(0.0, 1.0, r))
+                    val pr = p + Vector2.uniformRing(0.0, 130.0, r)
+
+                    A[i, 0] = 1.0
+                    A[i, 1] = pr.x
+                    b[i, 0] = pr.y
+
+                    drawer.circle(pr, 5.0)
+                }
+                val At = A.transposed()
+                val AtA = At * A
+                val Atb = At * b
+
+                val AtAI = invertMatrixCholesky(AtA)
+                val x = AtAI * Atb
+
+                val p0 = Vector2(0.0, x[0, 0])
+                val p1 = Vector2(720.0, x[0, 0] + x[1, 0] * 720.0)
+
+                drawer.stroke = ColorRGBa.RED
+                drawer.lineSegment(p0, p1)
+
+                drawer.stroke = ColorRGBa.GREEN
+                drawer.lineSegment(ls)
+            }
+        }
+    }
+}