lu factorization in javascript

To perform LU factorization in JavaScript, we can implement the Doolittle algorithm. Here's a sample code snippet:

index.tsx
function luFactorization(matrix) {
  const n = matrix.length;
  const L = Array(n).fill(0).map(() => Array(n).fill(0));
  const U = Array(n).fill(0).map(() => Array(n).fill(0));

  for(let i = 0; i < n; i++) {
    L[i][i] = 1;
    for(let j = 0; j < n; j++) {
      if(j < i) {
        let sum = 0;
        for(let k = 0; k < j; k++) {
          sum += L[j][k] * U[k][i];
        }
        L[j][i] = (matrix[j][i] - sum) / U[j][j];
      } else {
        let sum = 0;
        for(let k = 0; k < i; k++) {
          sum += L[j][k] * U[k][i];
        }
        U[j][i] = matrix[j][i] - sum;
      }
    }
  }

  return { L, U };
}
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This function takes in a square matrix as input and returns two matrices: L and U. The L matrix contains the lower triangular part of the decomposition, while the U matrix contains the upper triangular part.

We first initialize the L matrix with ones on the diagonal and all other entries set to zero. The U matrix is initialized with all entries set to zero.

We then iterate through the rows and columns of the input matrix, computing the entries of the L and U matrices accordingly. The algorithm calculates the entries of each row of U and column of L sequentially, using previously computed values from the previous rows and columns respectively.

Finally, we return the L and U matrices as an object.