const E = 0.1;

function Vec2(x1, x2) {
  this.x1 = x1;
  this.x2 = x2;
}

const calcMatrix = (m, s) => {
  return [[m[0][0](s), m[0][1](s)], [m[1][0](s), m[1][1](s)]];
};

const calcInversed = (m) => {
  const k = 1.0 / (m[0][0] * m[1][1] - m[0][1] * m[1][0]);

  return [[k * m[1][1], -k * m[0][1]], [-k * m[1][0], k * m[0][0]]];
};

const f = (p) =>
  2.0 * Math.pow(p.x1, 4) +
  Math.pow(p.x2, 4) +
  Math.pow(p.x1, 2) * p.x2 -
  5.0 * p.x1 * p.x2 +
  3 * Math.pow(p.x1, 2) +
  Math.pow(p.x2, 2) +
  8 * p.x2;

const grad = (p) =>
  new Vec2(
    8.0 * Math.pow(p.x1, 3) + 2.0 * p.x1 * (p.x2 + 3) - 5.0 * p.x2,
    Math.pow(p.x1, 2) - 5 * p.x1 + 4.0 * Math.pow(p.x2, 3) + 2.0 * p.x2 + 8
  );

const GESSE = [
  [(p) => 24.0 * Math.pow(p.x1, 2) + 2.0 * p.x2 + 3.0, (p) => 2.0 * p.x1 - 5.0],
  [(p) => 2.0 * p.x1 - 5.0, (p) => 12.0 * Math.pow(p.x2, 2) + 2.0]
];

let S = new Vec2(2.0, 1.0);

let h = 0.1;

let current = f(S);

let last,
  g,
  i = 0;

while (true) {
  last = f(S);
  const lS = S;

  g = grad(S);

  if (Math.sqrt(g.x1 * g.x1 + g.x2 * g.x2) <= E) {
    break;
  }

  const D1 = GESSE[0][0](S);
  const D2 = GESSE[0][0](S) * GESSE[1][1](S) - GESSE[0][1](S) * GESSE[1][0](S);

  const H = calcMatrix(GESSE, S);
  const INVH = calcInversed(H);

  const p = new Vec2(
    INVH[0][0] * g.x1 + INVH[0][1] * g.x2,
    INVH[1][0] * g.x1 + INVH[1][0] * g.x2
  );

  S = new Vec2(S.x1 - p.x1, S.x2 - p.x2);

  console.log(`Итерация ${i}<br>`);
  console.log(
    `<i>x<sup>(${i})</sup> =`,
    `(${lS.x1.toFixed(3)}, ${lS.x2.toFixed(3)})<sup>T</sup></i>`,
    '&nbsp;&nbsp;&nbsp;&nbsp;'
  );
  console.log(
    `<i>f(x<sup>(${i})</sup>) = ${last.toFixed(3)}</i>`,
    '&nbsp;&nbsp;&nbsp;&nbsp;'
  );
  console.log(
    `<i>∇f(x<sup>(${i})</sup>) =`,
    `(${lS.x1.toFixed(3)}, ${lS.x2.toFixed(3)})<sup>T</sup></i><br>`
  );
  console.log(
    `Матрица Гессе в точке <i>x<sup>(${i})</sup>: H(x<sup>(${i})</sup>) =`,
    `<table style="border-left: 1px solid black; border-right: 1px solid black"><tr>`,
    `<td>${H[0][0].toFixed(3)}</td>`,
    `<td>${H[0][1].toFixed(3)}</td></tr><tr>`,
    `<td>${H[1][0].toFixed(3)}</td>`,
    `<td>${H[1][1].toFixed(3)}</td></tr></table></i>`
  );

  console.log(
    `<i>p<sup>(${i})</sup> =`,
    `(${-p.x1.toFixed(3)}, ${-p.x2.toFixed(3)})<i>`,
    '&nbsp;&nbsp;&nbsp;&nbsp;'
  );
  console.log(
    `<i>x<sup>(${i})</sup> =`,
    `(${S.x1.toFixed(3)}, ${S.x2.toFixed(3)})`,
    `<br><br>`
  );

  i++;
}

console.log(
  `Результат: <i>f(x<sup>(k)</sup>)<sub>min</sub> =`,
  `${f(S).toFixed(3)}</i>, при <i>x<sup>(k)</sup> =`,
  `(${S.x1.toFixed(3)}, ${S.x2.toFixed(3)})</i>`
);