Data update

Task/Gaussian-elimination/EasyLang/gaussian-elimination.easy

@@ -0,0 +1,37 @@
+proc gauss_elim . a[][] b[] x[] .
+   n = len a[][]
+   for i to n
+      maxr = i
+      maxv = abs a[i][i]
+      for j = i + 1 to n
+         if abs a[j][i] > maxv
+            maxr = j
+            maxv = abs a[j][i]
+         .
+      .
+      if maxr <> i
+         swap a[maxr][] a[i][]
+         swap b[maxr] b[i]
+      .
+      for j = i + 1 to n
+         f = a[j][i] / a[i][i]
+         for k = i to n
+            a[j][k] -= f * a[i][k]
+         .
+         b[j] -= f * b[i]
+      .
+   .
+   x[] = [ ]
+   len x[] n
+   for i = n downto 1
+      rhs = b[i]
+      for j = i + 1 to n
+         rhs -= a[i][j] * x[j]
+      .
+      x[i] = rhs / a[i][i]
+   .
+.
+a[][] = [ [ 1.00 0.00 0.00 0.00 0.00 0.00 ] [ 1.00 0.63 0.39 0.25 0.16 0.10 ] [ 1.00 1.26 1.58 1.98 2.49 3.13 ] [ 1.00 1.88 3.55 6.70 12.62 23.80 ] [ 1.00 2.51 6.32 15.88 39.90 100.28 ] [ 1.00 3.14 9.87 31.01 97.41 306.02 ] ]
+b[] = [ -0.01 0.61 0.91 0.99 0.60 0.02 ]
+gauss_elim a[][] b[] x[]
+print x[]

Task/Gaussian-elimination/Scala/gaussian-elimination.scala

@@ -0,0 +1,99 @@
+object GaussianElimination {
+  def solve(a: Array[Array[Double]], b: Array[Array[Double]]): Double = {
+    if (a == null || b == null || a.length == 0 || b.length == 0) {
+      throw new IllegalArgumentException("Invalid dimensions")
+    }
+
+    val n = b.length
+    val p = b(0).length
+
+    if (a.length != n || a(0).length != n) {
+      throw new IllegalArgumentException("Invalid dimensions")
+    }
+
+    var det = 1.0
+
+    for (i <- 0 until n - 1) {
+      var k = i
+
+      for (j <- i + 1 until n) {
+        if (Math.abs(a(j)(i)) > Math.abs(a(k)(i))) {
+          k = j
+        }
+      }
+
+      if (k != i) {
+        det = -det
+
+        for (j <- i until n) {
+          val s = a(i)(j)
+          a(i)(j) = a(k)(j)
+          a(k)(j) = s
+        }
+
+        for (j <- 0 until p) {
+          val s = b(i)(j)
+          b(i)(j) = b(k)(j)
+          b(k)(j) = s
+        }
+      }
+
+      for (j <- i + 1 until n) {
+        val s = a(j)(i) / a(i)(i)
+
+        for (k <- i + 1 until n) {
+          a(j)(k) -= s * a(i)(k)
+        }
+
+        for (k <- 0 until p) {
+          b(j)(k) -= s * b(i)(k)
+        }
+      }
+    }
+
+    for (i <- n - 1 to 0 by -1) {
+      for (j <- i + 1 until n) {
+        val s = a(i)(j)
+
+        for (k <- 0 until p) {
+          b(i)(k) -= s * b(j)(k)
+        }
+      }
+
+      val s = a(i)(i)
+      det *= s
+
+      for (k <- 0 until p) {
+        b(i)(k) /= s
+      }
+    }
+
+    det
+  }
+
+  def main(args: Array[String]): Unit = {
+    val a = Array(
+      Array(4.0, 1.0, 0.0, 0.0, 0.0),
+      Array(1.0, 4.0, 1.0, 0.0, 0.0),
+      Array(0.0, 1.0, 4.0, 1.0, 0.0),
+      Array(0.0, 0.0, 1.0, 4.0, 1.0),
+      Array(0.0, 0.0, 0.0, 1.0, 4.0)
+    )
+
+    val b = Array(
+      Array(1.0 / 2.0),
+      Array(2.0 / 3.0),
+      Array(3.0 / 4.0),
+      Array(4.0 / 5.0),
+      Array(5.0 / 6.0)
+    )
+
+    val x = Array(39.0 / 400.0, 11.0 / 100.0, 31.0 / 240.0, 37.0 / 300.0, 71.0 / 400.0)
+
+    println("det: " + solve(a, b))
+
+    for (i <- 0 until 5) {
+      printf("%12.8f %12.4e\n", b(i)(0), b(i)(0) - x(i))
+    }
+  }
+}