// Singular Value Decomposition implementation
function SVD() {
};

/* Below singular value decomposition (svd) code including hypot function is adopted from https://github.com/dragonfly-ai/JamaJS
   Some changes are applied to make the code compatible with the fcose code and to make it independent from Jama.
   Input matrix is changed to a 2D array instead of Jama matrix. Matrix dimensions are taken according to 2D array instead of using Jama functions.
   An object that includes singular value components is created for return. 
   The types of input parameters of the hypot function are removed. 
   let is used instead of var for the variable initialization.
*/
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SVD.svd = function (A) {
  this.U = null;
  this.V = null;
  this.s = null;
  this.m = 0;
  this.n = 0;
  this.m = A.length;
  this.n = A[0].length;
  let nu = Math.min(this.m, this.n);
  this.s = (function (s) {
    let a = [];
    while (s-- > 0)
      a.push(0);
    return a;
  })(Math.min(this.m + 1, this.n));
  this.U = (function (dims) {
    let allocate = function (dims) {
      if (dims.length == 0) {
        return 0;
      } else {
        let array = [];
        for (let i = 0; i < dims[0]; i++) {
          array.push(allocate(dims.slice(1)));
        }
        return array;
      }
    };
    return allocate(dims);
  })([this.m, nu]);
  this.V = (function (dims) {
    let allocate = function (dims) {
      if (dims.length == 0) {
        return 0;
      } else {
        let array = [];
        for (let i = 0; i < dims[0]; i++) {
          array.push(allocate(dims.slice(1)));
        }
        return array;
      }
    };
    return allocate(dims);
  })([this.n, this.n]);
  let e = (function (s) {
    let a = [];
    while (s-- > 0)
      a.push(0);
    return a;
  })(this.n);
  let work = (function (s) {
    let a = [];
    while (s-- > 0)
      a.push(0);
    return a;
  })(this.m);
  let wantu = true;
  let wantv = true;
  let nct = Math.min(this.m - 1, this.n);
  let nrt = Math.max(0, Math.min(this.n - 2, this.m));
  for (let k = 0; k < Math.max(nct, nrt); k++) {
    if (k < nct) {
      this.s[k] = 0;
      for (let i = k; i < this.m; i++) {
        this.s[k] = SVD.hypot(this.s[k], A[i][k]);
      }
      ;
      if (this.s[k] !== 0.0) {
        if (A[k][k] < 0.0) {
          this.s[k] = -this.s[k];
        }
        for (let i = k; i < this.m; i++) {
          A[i][k] /= this.s[k];
        }
        ;
        A[k][k] += 1.0;
      }
      this.s[k] = -this.s[k];
    }
    for (let j = k + 1; j < this.n; j++) {
      if ((function (lhs, rhs) {
        return lhs && rhs;
      })((k < nct), (this.s[k] !== 0.0))) {
        let t = 0;
        for (let i = k; i < this.m; i++) {
          t += A[i][k] * A[i][j];
        }
        ;
        t = -t / A[k][k];
        for (let i = k; i < this.m; i++) {
          A[i][j] += t * A[i][k];
        }
        ;
      }
      e[j] = A[k][j];
    }
    ;
    if ((function (lhs, rhs) {
      return lhs && rhs;
    })(wantu, (k < nct))) {
      for (let i = k; i < this.m; i++) {
        this.U[i][k] = A[i][k];
      }
      ;
    }
    if (k < nrt) {
      e[k] = 0;
      for (let i = k + 1; i < this.n; i++) {
        e[k] = SVD.hypot(e[k], e[i]);
      }
      ;
      if (e[k] !== 0.0) {
        if (e[k + 1] < 0.0) {
          e[k] = -e[k];
        }
        for (let i = k + 1; i < this.n; i++) {
          e[i] /= e[k];
        }
        ;
        e[k + 1] += 1.0;
      }
      e[k] = -e[k];
      if ((function (lhs, rhs) {
        return lhs && rhs;
      })((k + 1 < this.m), (e[k] !== 0.0))) {
        for (let i = k + 1; i < this.m; i++) {
          work[i] = 0.0;
        }
        ;
        for (let j = k + 1; j < this.n; j++) {
          for (let i = k + 1; i < this.m; i++) {
            work[i] += e[j] * A[i][j];
          }
          ;
        }
        ;
        for (let j = k + 1; j < this.n; j++) {
          let t = -e[j] / e[k + 1];
          for (let i = k + 1; i < this.m; i++) {
            A[i][j] += t * work[i];
          }
          ;
        }
        ;
      }
      if (wantv) {
        for (let i = k + 1; i < this.n; i++) {
          this.V[i][k] = e[i];
        };
      }
    }
  };
  let p = Math.min(this.n, this.m + 1);
  if (nct < this.n) {
    this.s[nct] = A[nct][nct];
  }
  if (this.m < p) {
    this.s[p - 1] = 0.0;
  }
  if (nrt + 1 < p) {
    e[nrt] = A[nrt][p - 1];
  }
  e[p - 1] = 0.0;
  if (wantu) {
    for (let j = nct; j < nu; j++) {
      for (let i = 0; i < this.m; i++) {
        this.U[i][j] = 0.0;
      }
      ;
      this.U[j][j] = 1.0;
    };
    for (let k = nct - 1; k >= 0; k--) {
      if (this.s[k] !== 0.0) {
        for (let j = k + 1; j < nu; j++) {
          let t = 0;
          for (let i = k; i < this.m; i++) {
            t += this.U[i][k] * this.U[i][j];
          };
          t = -t / this.U[k][k];
          for (let i = k; i < this.m; i++) {
            this.U[i][j] += t * this.U[i][k];
          };
        };
        for (let i = k; i < this.m; i++) {
          this.U[i][k] = -this.U[i][k];
        };
        this.U[k][k] = 1.0 + this.U[k][k];
        for (let i = 0; i < k - 1; i++) {
          this.U[i][k] = 0.0;
        };
      } else {
        for (let i = 0; i < this.m; i++) {
          this.U[i][k] = 0.0;
        };
        this.U[k][k] = 1.0;
      }
    };
  }
  if (wantv) {
    for (let k = this.n - 1; k >= 0; k--) {
      if ((function (lhs, rhs) {
        return lhs && rhs;
      })((k < nrt), (e[k] !== 0.0))) {
        for (let j = k + 1; j < nu; j++) {
          let t = 0;
          for (let i = k + 1; i < this.n; i++) {
            t += this.V[i][k] * this.V[i][j];
          };
          t = -t / this.V[k + 1][k];
          for (let i = k + 1; i < this.n; i++) {
            this.V[i][j] += t * this.V[i][k];
          };
        };
      }
      for (let i = 0; i < this.n; i++) {
        this.V[i][k] = 0.0;
      };
      this.V[k][k] = 1.0;
    };
  }
  let pp = p - 1;
  let iter = 0;
  let eps = Math.pow(2.0, -52.0);
  let tiny = Math.pow(2.0, -966.0);
  while ((p > 0)) {
    let k = void 0;
    let kase = void 0;
    for (k = p - 2; k >= -1; k--) {
      if (k === -1) {
        break;
      }
      if (Math.abs(e[k]) <= tiny + eps * (Math.abs(this.s[k]) + Math.abs(this.s[k + 1]))) {
        e[k] = 0.0;
        break;
      }
    };
    if (k === p - 2) {
      kase = 4;
    } else {
      let ks = void 0;
      for (ks = p - 1; ks >= k; ks--) {
        if (ks === k) {
          break;
        }
        let t = (ks !== p ? Math.abs(e[ks]) : 0.0) + (ks !== k + 1 ? Math.abs(e[ks - 1]) : 0.0);
        if (Math.abs(this.s[ks]) <= tiny + eps * t) {
          this.s[ks] = 0.0;
          break;
        }
      };
      if (ks === k) {
        kase = 3;
      } else if (ks === p - 1) {
        kase = 1;
      } else {
        kase = 2;
        k = ks;
      }
    }
    k++;
    switch ((kase)) {
      case 1:
        {
          let f = e[p - 2];
          e[p - 2] = 0.0;
          for (let j = p - 2; j >= k; j--) {
            let t = SVD.hypot(this.s[j], f);
            let cs = this.s[j] / t;
            let sn = f / t;
            this.s[j] = t;
            if (j !== k) {
              f = -sn * e[j - 1];
              e[j - 1] = cs * e[j - 1];
            }
            if (wantv) {
              for (let i = 0; i < this.n; i++) {
                t = cs * this.V[i][j] + sn * this.V[i][p - 1];
                this.V[i][p - 1] = -sn * this.V[i][j] + cs * this.V[i][p - 1];
                this.V[i][j] = t;
              };
            }
          };
        };
        break;
      case 2:
        {
          let f = e[k - 1];
          e[k - 1] = 0.0;
          for (let j = k; j < p; j++) {
            let t = SVD.hypot(this.s[j], f);
            let cs = this.s[j] / t;
            let sn = f / t;
            this.s[j] = t;
            f = -sn * e[j];
            e[j] = cs * e[j];
            if (wantu) {
              for (let i = 0; i < this.m; i++) {
                t = cs * this.U[i][j] + sn * this.U[i][k - 1];
                this.U[i][k - 1] = -sn * this.U[i][j] + cs * this.U[i][k - 1];
                this.U[i][j] = t;
              };
            }
          };
        };
        break;
      case 3:
        {
          let scale = Math.max(Math.max(Math.max(Math.max(Math.abs(this.s[p - 1]), Math.abs(this.s[p - 2])), Math.abs(e[p - 2])), Math.abs(this.s[k])), Math.abs(e[k]));
          let sp = this.s[p - 1] / scale;
          let spm1 = this.s[p - 2] / scale;
          let epm1 = e[p - 2] / scale;
          let sk = this.s[k] / scale;
          let ek = e[k] / scale;
          let b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2.0;
          let c = (sp * epm1) * (sp * epm1);
          let shift = 0.0;
          if ((function (lhs, rhs) {
            return lhs || rhs;
          })((b !== 0.0), (c !== 0.0))) {
            shift = Math.sqrt(b * b + c);
            if (b < 0.0) {
              shift = -shift;
            }
            shift = c / (b + shift);
          }
          let f = (sk + sp) * (sk - sp) + shift;
          let g = sk * ek;
          for (let j = k; j < p - 1; j++) {
            let t = SVD.hypot(f, g);
            let cs = f / t;
            let sn = g / t;
            if (j !== k) {
              e[j - 1] = t;
            }
            f = cs * this.s[j] + sn * e[j];
            e[j] = cs * e[j] - sn * this.s[j];
            g = sn * this.s[j + 1];
            this.s[j + 1] = cs * this.s[j + 1];
            if (wantv) {
              for (let i = 0; i < this.n; i++) {
                t = cs * this.V[i][j] + sn * this.V[i][j + 1];
                this.V[i][j + 1] = -sn * this.V[i][j] + cs * this.V[i][j + 1];
                this.V[i][j] = t;
              };
            }
            t = SVD.hypot(f, g);
            cs = f / t;
            sn = g / t;
            this.s[j] = t;
            f = cs * e[j] + sn * this.s[j + 1];
            this.s[j + 1] = -sn * e[j] + cs * this.s[j + 1];
            g = sn * e[j + 1];
            e[j + 1] = cs * e[j + 1];
            if (wantu && (j < this.m - 1)) {
              for (let i = 0; i < this.m; i++) {
                t = cs * this.U[i][j] + sn * this.U[i][j + 1];
                this.U[i][j + 1] = -sn * this.U[i][j] + cs * this.U[i][j + 1];
                this.U[i][j] = t;
              };
            }
          };
          e[p - 2] = f;
          iter = iter + 1;
        };
        break;
      case 4:
        {
          if (this.s[k] <= 0.0) {
            this.s[k] = (this.s[k] < 0.0 ? -this.s[k] : 0.0);
            if (wantv) {
              for (let i = 0; i <= pp; i++) {
                this.V[i][k] = -this.V[i][k];
              };
            }
          }
          while ((k < pp)) {
            if (this.s[k] >= this.s[k + 1]) {
              break;
            }
            let t = this.s[k];
            this.s[k] = this.s[k + 1];
            this.s[k + 1] = t;
            if (wantv && (k < this.n - 1)) {
              for (let i = 0; i < this.n; i++) {
                t = this.V[i][k + 1];
                this.V[i][k + 1] = this.V[i][k];
                this.V[i][k] = t;
              };
            }
            if (wantu && (k < this.m - 1)) {
              for (let i = 0; i < this.m; i++) {
                t = this.U[i][k + 1];
                this.U[i][k + 1] = this.U[i][k];
                this.U[i][k] = t;
              };
            }
            k++;
          };
          iter = 0;
          p--;
        };
        break;
    }
  };
  let result = {U: this.U, V: this.V, S: this.s};
  return result;
};
        
// sqrt(a^2 + b^2) without under/overflow.
SVD.hypot = function(a, b) {
   let r;
   if (Math.abs(a) > Math.abs(b)) {
      r = b/a;
      r = Math.abs(a)*Math.sqrt(1+r*r);
   } else if (b != 0) {
      r = a/b;
      r = Math.abs(b)*Math.sqrt(1+r*r);
   } else {
      r = 0.0;
   }
   return r;
};

module.exports = SVD;

