CAT

cat.ts

const A = [41600];

const t = [0];  

const B = [
  4256.6,
  4272.37,
  4288.8,
  4305.9,
  4323.71,
  4342.26,
  4361.57,
  4381.69,
  4402.64,
  4424.45,
  4447.17,
  4470.82
];

const s = [...Array(12).keys()].map((e, i) => (i + 1) / 12);

const calculateCAT = (
  A: number[],
  t: number[],
  B: number[],
  s: number[],
  maxCAT = 1000,
): number => {
  const resolution = 1000;

  const tryCAT = (cat: number) => {
    const firstTerm = A.reduce(
      (acc, Aj, j) => acc + Aj / Math.pow(1 + cat, t[j]),
      0
    );

    const secondTerm = B.reduce(
      (acc, Bk, k) => acc + Bk / Math.pow(1 + cat, s[k]),
      0
    );

    return Math.abs(firstTerm - secondTerm);
  };

  const calculateCATInternal = (low: number, up: number): number => {
    const pivot = Math.ceil((low + up) / 2);

    const pivotValue = tryCAT(pivot / resolution);
    const left = tryCAT((pivot - 1) / resolution);
    const right = tryCAT((pivot + 1) / resolution);

    if (left > pivotValue && right > pivotValue) {
      return pivot / resolution;
    } else if (left < pivotValue) {
      return calculateCATInternal(low, pivot);
    } else {
      return calculateCATInternal(pivot, up);
    }
  };

  return calculateCATInternal(0, maxCAT * resolution);
};

console.log(calculateCAT(A, t, B, s));