Initial data commit

Task/LU-decomposition/JavaScript/lu-decomposition.js

@@ -0,0 +1,78 @@
+const mult=(a, b)=>{
+  let res = new Array(a.length);
+  for (let r = 0; r < a.length; ++r) {
+    res[r] = new Array(b[0].length);
+    for (let c = 0; c < b[0].length; ++c) {
+      res[r][c] = 0;
+      for (let i = 0; i < a[0].length; ++i)
+        res[r][c] += a[r][i] * b[i][c];
+    }
+  }
+  return res;
+}
+
+const lu = (mat) => {
+    let lower = [],upper = [],n=mat.length;;
+    for(let i=0;i<n;i++){
+        lower.push([]);
+        upper.push([]);
+        for(let j=0;j<n;j++){
+            lower[i].push(0);
+            upper[i].push(0);
+        }
+    }
+    for (let i = 0; i < n; i++) {
+        for (let k = i; k < n; k++){
+            let sum = 0;
+            for (let j = 0; j < i; j++)
+                sum += (lower[i][j] * upper[j][k]);
+            upper[i][k] = mat[i][k] - sum;
+        }
+        for (let k = i; k < n; k++) {
+            if (i == k)
+                lower[i][i] = 1;
+            else{
+                let sum = 0;
+                for (let j = 0; j < i; j++)
+                    sum += (lower[k][j] * upper[j][i]);
+                lower[k][i] = (mat[k][i] - sum) / upper[i][i];
+            }
+        }
+    }
+    return [lower,upper];
+}
+
+const pivot = (m) =>{
+    let n = m.length;
+    let id = [];
+    for(let i=0;i<n;i++){
+        id.push([]);
+        for(let j=0;j<n;j++){
+            if(i===j)
+                id[i].push(1);
+            else
+                id[i].push(0);
+        }
+    }
+    for (let i = 0; i < n; i++) {
+        let maxm = m[i][i];
+        let row = i;
+        for (let j = i; j < n; j++)
+            if (m[j][i] > maxm) {
+                maxm = m[j][i];
+                row = j;
+            }
+        if (i != row) {
+            let tmp = id[i];
+            id[i] = id[row];
+            id[row] = tmp;
+        }
+    }
+    return id;
+}
+
+const luDecomposition=(A)=>{
+    const P = pivot(A);
+    A = mult(P,A);
+    return [...lu(A),P];
+}