8.4 KiB
8.4 KiB
id | title | challengeType | forumTopicId |
---|---|---|---|
5e6decd8ec8d7db960950d1c | LU decomposition | 5 | 385280 |
Description
Instructions
[L, U, P]
.
Tests
tests:
- text: <code>luDecomposition</code> should be a function.
testString: assert(typeof luDecomposition == 'function');
- text: <code>luDecomposition([[1, 3, 5], [2, 4, 7], [1, 1, 0]])</code> should return a array.
testString: assert(Array.isArray(luDecomposition([[1, 3, 5], [2, 4, 7], [1, 1, 0]])));
- text: <code>luDecomposition([[1, 3, 5], [2, 4, 7], [1, 1, 0]])</code> should return <code>[[[1, 0, 0], [0.5, 1, 0], [0.5, -1, 1]], [[2, 4, 7], [0, 1, 1.5], [0, 0, -2]], [[0, 1, 0], [1, 0, 0], [0, 0, 1]]]</code>.
testString: assert.deepEqual(luDecomposition([[1, 3, 5], [2, 4, 7], [1, 1, 0]]), [[[1, 0, 0], [0.5, 1, 0], [0.5, -1, 1]], [[2, 4, 7], [0, 1, 1.5], [0, 0, -2]], [[0, 1, 0], [1, 0, 0], [0, 0, 1]]]);
- text: <code>luDecomposition([[11, 9, 24, 2], [1, 5, 2, 6], [3, 17, 18, 1], [2, 5, 7, 1]])</code> should return <code>[[[1, 0, 0, 0], [0.2727272727272727, 1, 0, 0], [0.09090909090909091, 0.2875, 1, 0], [0.18181818181818182, 0.23124999999999996, 0.0035971223021580693, 1]], [[11, 9, 24, 2], [0, 14.545454545454547, 11.454545454545455, 0.4545454545454546], [0, 0, -3.4749999999999996, 5.6875], [0, 0, 0, 0.510791366906476]], [[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]]]</code>.
testString: assert.deepEqual(luDecomposition([[11, 9, 24, 2], [1, 5, 2, 6], [3, 17, 18, 1], [2, 5, 7, 1]]), [[[1, 0, 0, 0], [0.2727272727272727, 1, 0, 0], [0.09090909090909091, 0.2875, 1, 0], [0.18181818181818182, 0.23124999999999996, 0.0035971223021580693, 1]], [[11, 9, 24, 2], [0, 14.545454545454547, 11.454545454545455, 0.4545454545454546], [0, 0, -3.4749999999999996, 5.6875], [0, 0, 0, 0.510791366906476]], [[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]]]);
- text: <code>luDecomposition([[1, 1, 1], [4, 3, -1], [3, 5, 3]])</code> should return <code>[[[1, 0, 0], [0.75, 1, 0], [0.25, 0.09090909090909091, 1]], [[4, 3, -1], [0, 2.75, 3.75], [0, 0, 0.9090909090909091]], [[0, 1, 0], [0, 0, 1], [1, 0, 0]]]</code>.
testString: assert.deepEqual(luDecomposition([[1, 1, 1], [4, 3, -1], [3, 5, 3]]), [[[1, 0, 0], [0.75, 1, 0], [0.25, 0.09090909090909091, 1]], [[4, 3, -1], [0, 2.75, 3.75], [0, 0, 0.9090909090909091]], [[0, 1, 0], [0, 0, 1], [1, 0, 0]]]);
- text: <code>luDecomposition([[1, -2, 3], [2, -5, 12], [0, 2, -10]])</code> should return <code>[[[1, 0, 0], [0, 1, 0], [0.5, 0.25, 1]], [[2, -5, 12], [0, 2, -10], [0, 0, -0.5]], [[0, 1, 0], [0, 0, 1], [1, 0, 0]]]</code>.
testString: assert.deepEqual(luDecomposition([[1, -2, 3], [2, -5, 12], [0, 2, -10]]), [[[1, 0, 0], [0, 1, 0], [0.5, 0.25, 1]], [[2, -5, 12], [0, 2, -10], [0, 0, -0.5]], [[0, 1, 0], [0, 0, 1], [1, 0, 0]]]);
Challenge Seed
function luDecomposition(A) {
}
Solution
function luDecomposition(A) {
function dotProduct(a, b) {
var sum = 0;
for (var i = 0; i < a.length; i++)
sum += a[i] * b[i]
return sum;
}
function matrixMul(A, B) {
var result = new Array(A.length);
for (var i = 0; i < A.length; i++)
result[i] = new Array(B[0].length)
var aux = new Array(B.length);
for (var j = 0; j < B[0].length; j++) {
for (var k = 0; k < B.length; k++)
aux[k] = B[k][j];
for (var i = 0; i < A.length; i++)
result[i][j] = dotProduct(A[i], aux);
}
return result;
}
function pivotize(m) {
var n = m.length;
var id = new Array(n);
for (var i = 0; i < n; i++) {
id[i] = new Array(n);
id[i].fill(0)
id[i][i] = 1;
}
for (var i = 0; i < n; i++) {
var maxm = m[i][i];
var row = i;
for (var j = i; j < n; j++)
if (m[j][i] > maxm) {
maxm = m[j][i];
row = j;
}
if (i != row) {
var tmp = id[i];
id[i] = id[row];
id[row] = tmp;
}
}
return id;
}
var n = A.length;
var L = new Array(n);
for (var i = 0; i < n; i++) { L[i] = new Array(n); L[i].fill(0) }
var U = new Array(n);
for (var i = 0; i < n; i++) { U[i] = new Array(n); U[i].fill(0) }
var P = pivotize(A);
var A2 = matrixMul(P, A);
for (var j = 0; j < n; j++) {
L[j][j] = 1;
for (var i = 0; i < j + 1; i++) {
var s1 = 0;
for (var k = 0; k < i; k++)
s1 += U[k][j] * L[i][k];
U[i][j] = A2[i][j] - s1;
}
for (var i = j; i < n; i++) {
var s2 = 0;
for (var k = 0; k < j; k++)
s2 += U[k][j] * L[i][k];
L[i][j] = (A2[i][j] - s2) / U[j][j];
}
}
return [L, U, P];
}