linearDependencies.js

import SingularValueDecomposition from './svd.js';
import Matrix from './matrix.js';

function xrange(n, exception) {
  let range = [];
  for (let i = 0; i < n; i++) {
    if (i !== exception) {
      range.push(i);
    }
  }
  return range;
}

function dependenciesOneRow(
  error,
  matrix,
  index,
  thresholdValue = 10e-10,
  thresholdError = 10e-10,
) {
  if (error > thresholdError) {
    return new Array(matrix.rows + 1).fill(0);
  } else {
    let returnArray = matrix.addRow(index, [0]);
    for (let i = 0; i < returnArray.rows; i++) {
      if (Math.abs(returnArray.get(i, 0)) < thresholdValue) {
        returnArray.set(i, 0, 0);
      }
    }
    return returnArray.to1DArray();
  }
}

export function linearDependencies(matrix, options = {}) {
  const { thresholdValue = 10e-10, thresholdError = 10e-10 } = options;
  matrix = Matrix.checkMatrix(matrix);

  let n = matrix.rows;
  let results = new Matrix(n, n);

  for (let i = 0; i < n; i++) {
    let b = Matrix.columnVector(matrix.getRow(i));
    let Abis = matrix.subMatrixRow(xrange(n, i)).transpose();
    let svd = new SingularValueDecomposition(Abis);
    let x = svd.solve(b);
    let error = Matrix.sub(b, Abis.mmul(x)).abs().max();
    results.setRow(
      i,
      dependenciesOneRow(error, x, i, thresholdValue, thresholdError),
    );
  }
  return results;
}