KGPython/vue/node_modules/ml-matrix/src/dc/evd.js

import Matrix from '../matrix';
import WrapperMatrix2D from '../wrap/WrapperMatrix2D';

import { hypotenuse } from './util';

export default class EigenvalueDecomposition {
  constructor(matrix, options = {}) {
    const { assumeSymmetric = false } = options;

    matrix = WrapperMatrix2D.checkMatrix(matrix);
    if (!matrix.isSquare()) {
      throw new Error('Matrix is not a square matrix');
    }

    if (matrix.isEmpty()) {
      throw new Error('Matrix must be non-empty');
    }

    let n = matrix.columns;
    let V = new Matrix(n, n);
    let d = new Float64Array(n);
    let e = new Float64Array(n);
    let value = matrix;
    let i, j;

    let isSymmetric = false;
    if (assumeSymmetric) {
      isSymmetric = true;
    } else {
      isSymmetric = matrix.isSymmetric();
    }

    if (isSymmetric) {
      for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
          V.set(i, j, value.get(i, j));
        }
      }
      tred2(n, e, d, V);
      tql2(n, e, d, V);
    } else {
      let H = new Matrix(n, n);
      let ort = new Float64Array(n);
      for (j = 0; j < n; j++) {
        for (i = 0; i < n; i++) {
          H.set(i, j, value.get(i, j));
        }
      }
      orthes(n, H, ort, V);
      hqr2(n, e, d, V, H);
    }

    this.n = n;
    this.e = e;
    this.d = d;
    this.V = V;
  }

  get realEigenvalues() {
    return Array.from(this.d);
  }

  get imaginaryEigenvalues() {
    return Array.from(this.e);
  }

  get eigenvectorMatrix() {
    return this.V;
  }

  get diagonalMatrix() {
    let n = this.n;
    let e = this.e;
    let d = this.d;
    let X = new Matrix(n, n);
    let i, j;
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        X.set(i, j, 0);
      }
      X.set(i, i, d[i]);
      if (e[i] > 0) {
        X.set(i, i + 1, e[i]);
      } else if (e[i] < 0) {
        X.set(i, i - 1, e[i]);
      }
    }
    return X;
  }
}

function tred2(n, e, d, V) {
  let f, g, h, i, j, k, hh, scale;

  for (j = 0; j < n; j++) {
    d[j] = V.get(n - 1, j);
  }

  for (i = n - 1; i > 0; i--) {
    scale = 0;
    h = 0;
    for (k = 0; k < i; k++) {
      scale = scale + Math.abs(d[k]);
    }

    if (scale === 0) {
      e[i] = d[i - 1];
      for (j = 0; j < i; j++) {
        d[j] = V.get(i - 1, j);
        V.set(i, j, 0);
        V.set(j, i, 0);
      }
    } else {
      for (k = 0; k < i; k++) {
        d[k] /= scale;
        h += d[k] * d[k];
      }

      f = d[i - 1];
      g = Math.sqrt(h);
      if (f > 0) {
        g = -g;
      }

      e[i] = scale * g;
      h = h - f * g;
      d[i - 1] = f - g;
      for (j = 0; j < i; j++) {
        e[j] = 0;
      }

      for (j = 0; j < i; j++) {
        f = d[j];
        V.set(j, i, f);
        g = e[j] + V.get(j, j) * f;
        for (k = j + 1; k <= i - 1; k++) {
          g += V.get(k, j) * d[k];
          e[k] += V.get(k, j) * f;
        }
        e[j] = g;
      }

      f = 0;
      for (j = 0; j < i; j++) {
        e[j] /= h;
        f += e[j] * d[j];
      }

      hh = f / (h + h);
      for (j = 0; j < i; j++) {
        e[j] -= hh * d[j];
      }

      for (j = 0; j < i; j++) {
        f = d[j];
        g = e[j];
        for (k = j; k <= i - 1; k++) {
          V.set(k, j, V.get(k, j) - (f * e[k] + g * d[k]));
        }
        d[j] = V.get(i - 1, j);
        V.set(i, j, 0);
      }
    }
    d[i] = h;
  }

  for (i = 0; i < n - 1; i++) {
    V.set(n - 1, i, V.get(i, i));
    V.set(i, i, 1);
    h = d[i + 1];
    if (h !== 0) {
      for (k = 0; k <= i; k++) {
        d[k] = V.get(k, i + 1) / h;
      }

      for (j = 0; j <= i; j++) {
        g = 0;
        for (k = 0; k <= i; k++) {
          g += V.get(k, i + 1) * V.get(k, j);
        }
        for (k = 0; k <= i; k++) {
          V.set(k, j, V.get(k, j) - g * d[k]);
        }
      }
    }

    for (k = 0; k <= i; k++) {
      V.set(k, i + 1, 0);
    }
  }

  for (j = 0; j < n; j++) {
    d[j] = V.get(n - 1, j);
    V.set(n - 1, j, 0);
  }

  V.set(n - 1, n - 1, 1);
  e[0] = 0;
}

function tql2(n, e, d, V) {
  let g, h, i, j, k, l, m, p, r, dl1, c, c2, c3, el1, s, s2, iter;

  for (i = 1; i < n; i++) {
    e[i - 1] = e[i];
  }

  e[n - 1] = 0;

  let f = 0;
  let tst1 = 0;
  let eps = Number.EPSILON;

  for (l = 0; l < n; l++) {
    tst1 = Math.max(tst1, Math.abs(d[l]) + Math.abs(e[l]));
    m = l;
    while (m < n) {
      if (Math.abs(e[m]) <= eps * tst1) {
        break;
      }
      m++;
    }

    if (m > l) {
      iter = 0;
      do {
        iter = iter + 1;

        g = d[l];
        p = (d[l + 1] - g) / (2 * e[l]);
        r = hypotenuse(p, 1);
        if (p < 0) {
          r = -r;
        }

        d[l] = e[l] / (p + r);
        d[l + 1] = e[l] * (p + r);
        dl1 = d[l + 1];
        h = g - d[l];
        for (i = l + 2; i < n; i++) {
          d[i] -= h;
        }

        f = f + h;

        p = d[m];
        c = 1;
        c2 = c;
        c3 = c;
        el1 = e[l + 1];
        s = 0;
        s2 = 0;
        for (i = m - 1; i >= l; i--) {
          c3 = c2;
          c2 = c;
          s2 = s;
          g = c * e[i];
          h = c * p;
          r = hypotenuse(p, e[i]);
          e[i + 1] = s * r;
          s = e[i] / r;
          c = p / r;
          p = c * d[i] - s * g;
          d[i + 1] = h + s * (c * g + s * d[i]);

          for (k = 0; k < n; k++) {
            h = V.get(k, i + 1);
            V.set(k, i + 1, s * V.get(k, i) + c * h);
            V.set(k, i, c * V.get(k, i) - s * h);
          }
        }

        p = (-s * s2 * c3 * el1 * e[l]) / dl1;
        e[l] = s * p;
        d[l] = c * p;
      } while (Math.abs(e[l]) > eps * tst1);
    }
    d[l] = d[l] + f;
    e[l] = 0;
  }

  for (i = 0; i < n - 1; i++) {
    k = i;
    p = d[i];
    for (j = i + 1; j < n; j++) {
      if (d[j] < p) {
        k = j;
        p = d[j];
      }
    }

    if (k !== i) {
      d[k] = d[i];
      d[i] = p;
      for (j = 0; j < n; j++) {
        p = V.get(j, i);
        V.set(j, i, V.get(j, k));
        V.set(j, k, p);
      }
    }
  }
}

function orthes(n, H, ort, V) {
  let low = 0;
  let high = n - 1;
  let f, g, h, i, j, m;
  let scale;

  for (m = low + 1; m <= high - 1; m++) {
    scale = 0;
    for (i = m; i <= high; i++) {
      scale = scale + Math.abs(H.get(i, m - 1));
    }

    if (scale !== 0) {
      h = 0;
      for (i = high; i >= m; i--) {
        ort[i] = H.get(i, m - 1) / scale;
        h += ort[i] * ort[i];
      }

      g = Math.sqrt(h);
      if (ort[m] > 0) {
        g = -g;
      }

      h = h - ort[m] * g;
      ort[m] = ort[m] - g;

      for (j = m; j < n; j++) {
        f = 0;
        for (i = high; i >= m; i--) {
          f += ort[i] * H.get(i, j);
        }

        f = f / h;
        for (i = m; i <= high; i++) {
          H.set(i, j, H.get(i, j) - f * ort[i]);
        }
      }

      for (i = 0; i <= high; i++) {
        f = 0;
        for (j = high; j >= m; j--) {
          f += ort[j] * H.get(i, j);
        }

        f = f / h;
        for (j = m; j <= high; j++) {
          H.set(i, j, H.get(i, j) - f * ort[j]);
        }
      }

      ort[m] = scale * ort[m];
      H.set(m, m - 1, scale * g);
    }
  }

  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      V.set(i, j, i === j ? 1 : 0);
    }
  }

  for (m = high - 1; m >= low + 1; m--) {
    if (H.get(m, m - 1) !== 0) {
      for (i = m + 1; i <= high; i++) {
        ort[i] = H.get(i, m - 1);
      }

      for (j = m; j <= high; j++) {
        g = 0;
        for (i = m; i <= high; i++) {
          g += ort[i] * V.get(i, j);
        }

        g = g / ort[m] / H.get(m, m - 1);
        for (i = m; i <= high; i++) {
          V.set(i, j, V.get(i, j) + g * ort[i]);
        }
      }
    }
  }
}

function hqr2(nn, e, d, V, H) {
  let n = nn - 1;
  let low = 0;
  let high = nn - 1;
  let eps = Number.EPSILON;
  let exshift = 0;
  let norm = 0;
  let p = 0;
  let q = 0;
  let r = 0;
  let s = 0;
  let z = 0;
  let iter = 0;
  let i, j, k, l, m, t, w, x, y;
  let ra, sa, vr, vi;
  let notlast, cdivres;

  for (i = 0; i < nn; i++) {
    if (i < low || i > high) {
      d[i] = H.get(i, i);
      e[i] = 0;
    }

    for (j = Math.max(i - 1, 0); j < nn; j++) {
      norm = norm + Math.abs(H.get(i, j));
    }
  }

  while (n >= low) {
    l = n;
    while (l > low) {
      s = Math.abs(H.get(l - 1, l - 1)) + Math.abs(H.get(l, l));
      if (s === 0) {
        s = norm;
      }
      if (Math.abs(H.get(l, l - 1)) < eps * s) {
        break;
      }
      l--;
    }

    if (l === n) {
      H.set(n, n, H.get(n, n) + exshift);
      d[n] = H.get(n, n);
      e[n] = 0;
      n--;
      iter = 0;
    } else if (l === n - 1) {
      w = H.get(n, n - 1) * H.get(n - 1, n);
      p = (H.get(n - 1, n - 1) - H.get(n, n)) / 2;
      q = p * p + w;
      z = Math.sqrt(Math.abs(q));
      H.set(n, n, H.get(n, n) + exshift);
      H.set(n - 1, n - 1, H.get(n - 1, n - 1) + exshift);
      x = H.get(n, n);

      if (q >= 0) {
        z = p >= 0 ? p + z : p - z;
        d[n - 1] = x + z;
        d[n] = d[n - 1];
        if (z !== 0) {
          d[n] = x - w / z;
        }
        e[n - 1] = 0;
        e[n] = 0;
        x = H.get(n, n - 1);
        s = Math.abs(x) + Math.abs(z);
        p = x / s;
        q = z / s;
        r = Math.sqrt(p * p + q * q);
        p = p / r;
        q = q / r;

        for (j = n - 1; j < nn; j++) {
          z = H.get(n - 1, j);
          H.set(n - 1, j, q * z + p * H.get(n, j));
          H.set(n, j, q * H.get(n, j) - p * z);
        }

        for (i = 0; i <= n; i++) {
          z = H.get(i, n - 1);
          H.set(i, n - 1, q * z + p * H.get(i, n));
          H.set(i, n, q * H.get(i, n) - p * z);
        }

        for (i = low; i <= high; i++) {
          z = V.get(i, n - 1);
          V.set(i, n - 1, q * z + p * V.get(i, n));
          V.set(i, n, q * V.get(i, n) - p * z);
        }
      } else {
        d[n - 1] = x + p;
        d[n] = x + p;
        e[n - 1] = z;
        e[n] = -z;
      }

      n = n - 2;
      iter = 0;
    } else {
      x = H.get(n, n);
      y = 0;
      w = 0;
      if (l < n) {
        y = H.get(n - 1, n - 1);
        w = H.get(n, n - 1) * H.get(n - 1, n);
      }

      if (iter === 10) {
        exshift += x;
        for (i = low; i <= n; i++) {
          H.set(i, i, H.get(i, i) - x);
        }
        s = Math.abs(H.get(n, n - 1)) + Math.abs(H.get(n - 1, n - 2));
        // eslint-disable-next-line no-multi-assign
        x = y = 0.75 * s;
        w = -0.4375 * s * s;
      }

      if (iter === 30) {
        s = (y - x) / 2;
        s = s * s + w;
        if (s > 0) {
          s = Math.sqrt(s);
          if (y < x) {
            s = -s;
          }
          s = x - w / ((y - x) / 2 + s);
          for (i = low; i <= n; i++) {
            H.set(i, i, H.get(i, i) - s);
          }
          exshift += s;
          // eslint-disable-next-line no-multi-assign
          x = y = w = 0.964;
        }
      }

      iter = iter + 1;

      m = n - 2;
      while (m >= l) {
        z = H.get(m, m);
        r = x - z;
        s = y - z;
        p = (r * s - w) / H.get(m + 1, m) + H.get(m, m + 1);
        q = H.get(m + 1, m + 1) - z - r - s;
        r = H.get(m + 2, m + 1);
        s = Math.abs(p) + Math.abs(q) + Math.abs(r);
        p = p / s;
        q = q / s;
        r = r / s;
        if (m === l) {
          break;
        }
        if (
          Math.abs(H.get(m, m - 1)) * (Math.abs(q) + Math.abs(r)) <
          eps *
            (Math.abs(p) *
              (Math.abs(H.get(m - 1, m - 1)) +
                Math.abs(z) +
                Math.abs(H.get(m + 1, m + 1))))
        ) {
          break;
        }
        m--;
      }

      for (i = m + 2; i <= n; i++) {
        H.set(i, i - 2, 0);
        if (i > m + 2) {
          H.set(i, i - 3, 0);
        }
      }

      for (k = m; k <= n - 1; k++) {
        notlast = k !== n - 1;
        if (k !== m) {
          p = H.get(k, k - 1);
          q = H.get(k + 1, k - 1);
          r = notlast ? H.get(k + 2, k - 1) : 0;
          x = Math.abs(p) + Math.abs(q) + Math.abs(r);
          if (x !== 0) {
            p = p / x;
            q = q / x;
            r = r / x;
          }
        }

        if (x === 0) {
          break;
        }

        s = Math.sqrt(p * p + q * q + r * r);
        if (p < 0) {
          s = -s;
        }

        if (s !== 0) {
          if (k !== m) {
            H.set(k, k - 1, -s * x);
          } else if (l !== m) {
            H.set(k, k - 1, -H.get(k, k - 1));
          }

          p = p + s;
          x = p / s;
          y = q / s;
          z = r / s;
          q = q / p;
          r = r / p;

          for (j = k; j < nn; j++) {
            p = H.get(k, j) + q * H.get(k + 1, j);
            if (notlast) {
              p = p + r * H.get(k + 2, j);
              H.set(k + 2, j, H.get(k + 2, j) - p * z);
            }

            H.set(k, j, H.get(k, j) - p * x);
            H.set(k + 1, j, H.get(k + 1, j) - p * y);
          }

          for (i = 0; i <= Math.min(n, k + 3); i++) {
            p = x * H.get(i, k) + y * H.get(i, k + 1);
            if (notlast) {
              p = p + z * H.get(i, k + 2);
              H.set(i, k + 2, H.get(i, k + 2) - p * r);
            }

            H.set(i, k, H.get(i, k) - p);
            H.set(i, k + 1, H.get(i, k + 1) - p * q);
          }

          for (i = low; i <= high; i++) {
            p = x * V.get(i, k) + y * V.get(i, k + 1);
            if (notlast) {
              p = p + z * V.get(i, k + 2);
              V.set(i, k + 2, V.get(i, k + 2) - p * r);
            }

            V.set(i, k, V.get(i, k) - p);
            V.set(i, k + 1, V.get(i, k + 1) - p * q);
          }
        }
      }
    }
  }

  if (norm === 0) {
    return;
  }

  for (n = nn - 1; n >= 0; n--) {
    p = d[n];
    q = e[n];

    if (q === 0) {
      l = n;
      H.set(n, n, 1);
      for (i = n - 1; i >= 0; i--) {
        w = H.get(i, i) - p;
        r = 0;
        for (j = l; j <= n; j++) {
          r = r + H.get(i, j) * H.get(j, n);
        }

        if (e[i] < 0) {
          z = w;
          s = r;
        } else {
          l = i;
          if (e[i] === 0) {
            H.set(i, n, w !== 0 ? -r / w : -r / (eps * norm));
          } else {
            x = H.get(i, i + 1);
            y = H.get(i + 1, i);
            q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
            t = (x * s - z * r) / q;
            H.set(i, n, t);
            H.set(
              i + 1,
              n,
              Math.abs(x) > Math.abs(z) ? (-r - w * t) / x : (-s - y * t) / z,
            );
          }

          t = Math.abs(H.get(i, n));
          if (eps * t * t > 1) {
            for (j = i; j <= n; j++) {
              H.set(j, n, H.get(j, n) / t);
            }
          }
        }
      }
    } else if (q < 0) {
      l = n - 1;

      if (Math.abs(H.get(n, n - 1)) > Math.abs(H.get(n - 1, n))) {
        H.set(n - 1, n - 1, q / H.get(n, n - 1));
        H.set(n - 1, n, -(H.get(n, n) - p) / H.get(n, n - 1));
      } else {
        cdivres = cdiv(0, -H.get(n - 1, n), H.get(n - 1, n - 1) - p, q);
        H.set(n - 1, n - 1, cdivres[0]);
        H.set(n - 1, n, cdivres[1]);
      }

      H.set(n, n - 1, 0);
      H.set(n, n, 1);
      for (i = n - 2; i >= 0; i--) {
        ra = 0;
        sa = 0;
        for (j = l; j <= n; j++) {
          ra = ra + H.get(i, j) * H.get(j, n - 1);
          sa = sa + H.get(i, j) * H.get(j, n);
        }

        w = H.get(i, i) - p;

        if (e[i] < 0) {
          z = w;
          r = ra;
          s = sa;
        } else {
          l = i;
          if (e[i] === 0) {
            cdivres = cdiv(-ra, -sa, w, q);
            H.set(i, n - 1, cdivres[0]);
            H.set(i, n, cdivres[1]);
          } else {
            x = H.get(i, i + 1);
            y = H.get(i + 1, i);
            vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
            vi = (d[i] - p) * 2 * q;
            if (vr === 0 && vi === 0) {
              vr =
                eps *
                norm *
                (Math.abs(w) +
                  Math.abs(q) +
                  Math.abs(x) +
                  Math.abs(y) +
                  Math.abs(z));
            }
            cdivres = cdiv(
              x * r - z * ra + q * sa,
              x * s - z * sa - q * ra,
              vr,
              vi,
            );
            H.set(i, n - 1, cdivres[0]);
            H.set(i, n, cdivres[1]);
            if (Math.abs(x) > Math.abs(z) + Math.abs(q)) {
              H.set(
                i + 1,
                n - 1,
                (-ra - w * H.get(i, n - 1) + q * H.get(i, n)) / x,
              );
              H.set(
                i + 1,
                n,
                (-sa - w * H.get(i, n) - q * H.get(i, n - 1)) / x,
              );
            } else {
              cdivres = cdiv(
                -r - y * H.get(i, n - 1),
                -s - y * H.get(i, n),
                z,
                q,
              );
              H.set(i + 1, n - 1, cdivres[0]);
              H.set(i + 1, n, cdivres[1]);
            }
          }

          t = Math.max(Math.abs(H.get(i, n - 1)), Math.abs(H.get(i, n)));
          if (eps * t * t > 1) {
            for (j = i; j <= n; j++) {
              H.set(j, n - 1, H.get(j, n - 1) / t);
              H.set(j, n, H.get(j, n) / t);
            }
          }
        }
      }
    }
  }

  for (i = 0; i < nn; i++) {
    if (i < low || i > high) {
      for (j = i; j < nn; j++) {
        V.set(i, j, H.get(i, j));
      }
    }
  }

  for (j = nn - 1; j >= low; j--) {
    for (i = low; i <= high; i++) {
      z = 0;
      for (k = low; k <= Math.min(j, high); k++) {
        z = z + V.get(i, k) * H.get(k, j);
      }
      V.set(i, j, z);
    }
  }
}

function cdiv(xr, xi, yr, yi) {
  let r, d;
  if (Math.abs(yr) > Math.abs(yi)) {
    r = yi / yr;
    d = yr + r * yi;
    return [(xr + r * xi) / d, (xi - r * xr) / d];
  } else {
    r = yr / yi;
    d = yi + r * yr;
    return [(r * xr + xi) / d, (r * xi - xr) / d];
  }
}