/*
 * Carrot2 project.
 *
 * Copyright (C) 2002-2020, Dawid Weiss, Stanisław Osiński.
 * All rights reserved.
 *
 * Refer to the full license file "carrot2.LICENSE"
 * in the root folder of the repository checkout or at:
 * https://www.carrot2.org/carrot2.LICENSE
 */
package org.carrot2.math.mahout;

public class SingularValueDecomposition {

  private final double[][] u;
  private final double[][] v;

  private final double[] s;

  private final int m;
  private final int n;

  private boolean transpositionNeeded = false;

  public SingularValueDecomposition(Matrix arg) {
    if (arg.numRows() < arg.numCols()) {
      transpositionNeeded = true;
    }

    // Derived from LINPACK code.
    // Initialize.
    double[][] a;
    if (transpositionNeeded) {
      // use the transpose Matrix
      m = arg.numCols();
      n = arg.numRows();
      a = new double[m][n];
      for (int i = 0; i < m; i++) {
        for (int j = 0; j < n; j++) {
          a[i][j] = arg.get(j, i);
        }
      }
    } else {
      m = arg.numRows();
      n = arg.numCols();
      a = new double[m][n];
      for (int i = 0; i < m; i++) {
        for (int j = 0; j < n; j++) {
          a[i][j] = arg.get(i, j);
        }
      }
    }

    int nu = Math.min(m, n);
    s = new double[Math.min(m + 1, n)];
    u = new double[m][nu];
    v = new double[n][n];
    double[] e = new double[n];
    double[] work = new double[m];
    boolean wantu = true;
    boolean wantv = true;

    // Reduce A to bidiagonal form, storing the diagonal elements
    // in s and the super-diagonal elements in e.

    int nct = Math.min(m - 1, n);
    int nrt = Math.max(0, Math.min(n - 2, m));
    for (int k = 0; k < Math.max(nct, nrt); k++) {
      if (k < nct) {

        // Compute the transformation for the k-th column and
        // place the k-th diagonal in s[k].
        // Compute 2-norm of k-th column without under/overflow.
        s[k] = 0;
        for (int i = k; i < m; i++) {
          s[k] = Algebra.hypot(s[k], a[i][k]);
        }
        if (s[k] != 0.0) {
          if (a[k][k] < 0.0) {
            s[k] = -s[k];
          }
          for (int i = k; i < m; i++) {
            a[i][k] /= s[k];
          }
          a[k][k] += 1.0;
        }
        s[k] = -s[k];
      }
      for (int j = k + 1; j < n; j++) {
        if (k < nct && s[k] != 0.0) {

          // Apply the transformation.

          double t = 0;
          for (int i = k; i < m; i++) {
            t += a[i][k] * a[i][j];
          }
          t = -t / a[k][k];
          for (int i = k; i < m; i++) {
            a[i][j] += t * a[i][k];
          }
        }

        // Place the k-th row of A into e for the
        // subsequent calculation of the row transformation.

        e[j] = a[k][j];
      }
      if (wantu && k < nct) {

        // Place the transformation in U for subsequent back
        // multiplication.

        for (int i = k; i < m; i++) {
          u[i][k] = a[i][k];
        }
      }
      if (k < nrt) {

        // Compute the k-th row transformation and place the
        // k-th super-diagonal in e[k].
        // Compute 2-norm without under/overflow.
        e[k] = 0;
        for (int i = k + 1; i < n; i++) {
          e[k] = Algebra.hypot(e[k], e[i]);
        }
        if (e[k] != 0.0) {
          if (e[k + 1] < 0.0) {
            e[k] = -e[k];
          }
          for (int i = k + 1; i < n; i++) {
            e[i] /= e[k];
          }
          e[k + 1] += 1.0;
        }
        e[k] = -e[k];
        if (k + 1 < m && e[k] != 0.0) {

          // Apply the transformation.

          for (int i = k + 1; i < m; i++) {
            work[i] = 0.0;
          }
          for (int j = k + 1; j < n; j++) {
            for (int i = k + 1; i < m; i++) {
              work[i] += e[j] * a[i][j];
            }
          }
          for (int j = k + 1; j < n; j++) {
            double t = -e[j] / e[k + 1];
            for (int i = k + 1; i < m; i++) {
              a[i][j] += t * work[i];
            }
          }
        }
        if (wantv) {

          // Place the transformation in V for subsequent
          // back multiplication.

          for (int i = k + 1; i < n; i++) {
            v[i][k] = e[i];
          }
        }
      }
    }

    // Set up the final bidiagonal matrix or order p.

    int p = Math.min(n, m + 1);
    if (nct < n) {
      s[nct] = a[nct][nct];
    }
    if (m < p) {
      s[p - 1] = 0.0;
    }
    if (nrt + 1 < p) {
      e[nrt] = a[nrt][p - 1];
    }
    e[p - 1] = 0.0;

    // If required, generate U.

    if (wantu) {
      for (int j = nct; j < nu; j++) {
        for (int i = 0; i < m; i++) {
          u[i][j] = 0.0;
        }
        u[j][j] = 1.0;
      }
      for (int k = nct - 1; k >= 0; k--) {
        if (s[k] != 0.0) {
          for (int j = k + 1; j < nu; j++) {
            double t = 0;
            for (int i = k; i < m; i++) {
              t += u[i][k] * u[i][j];
            }
            t = -t / u[k][k];
            for (int i = k; i < m; i++) {
              u[i][j] += t * u[i][k];
            }
          }
          for (int i = k; i < m; i++) {
            u[i][k] = -u[i][k];
          }
          u[k][k] = 1.0 + u[k][k];
          for (int i = 0; i < k - 1; i++) {
            u[i][k] = 0.0;
          }
        } else {
          for (int i = 0; i < m; i++) {
            u[i][k] = 0.0;
          }
          u[k][k] = 1.0;
        }
      }
    }

    // If required, generate V.

    if (wantv) {
      for (int k = n - 1; k >= 0; k--) {
        if (k < nrt && e[k] != 0.0) {
          for (int j = k + 1; j < nu; j++) {
            double t = 0;
            for (int i = k + 1; i < n; i++) {
              t += v[i][k] * v[i][j];
            }
            t = -t / v[k + 1][k];
            for (int i = k + 1; i < n; i++) {
              v[i][j] += t * v[i][k];
            }
          }
        }
        for (int i = 0; i < n; i++) {
          v[i][k] = 0.0;
        }
        v[k][k] = 1.0;
      }
    }

    // Main iteration loop for the singular values.

    int pp = p - 1;
    // int iter = 0;
    double eps = Math.pow(2.0, -52.0);
    while (p > 0) {
      int k;

      // Here is where a test for too many iterations would go.

      // This section of the program inspects for
      // negligible elements in the s and e arrays.  On
      // completion the variables kase and k are set as follows.

      // kase = 1     if s(p) and e[k-1] are negligible and k<p
      // kase = 2     if s(k) is negligible and k<p
      // kase = 3     if e[k-1] is negligible, k<p, and
      //              s(k), ..., s(p) are not negligible (qr step).
      // kase = 4     if e(p-1) is negligible (convergence).

      for (k = p - 2; k >= -1; k--) {
        if (k == -1) {
          break;
        }
        if (Math.abs(e[k]) <= eps * (Math.abs(s[k]) + Math.abs(s[k + 1]))) {
          e[k] = 0.0;
          break;
        }
      }
      int kase;
      if (k == p - 2) {
        kase = 4;
      } else {
        int ks;
        for (ks = p - 1; ks >= k; ks--) {
          if (ks == k) {
            break;
          }
          double t = (ks == p ? 0.0 : Math.abs(e[ks])) + (ks == k + 1 ? 0.0 : Math.abs(e[ks - 1]));
          if (Math.abs(s[ks]) <= eps * t) {
            s[ks] = 0.0;
            break;
          }
        }
        if (ks == k) {
          kase = 3;
        } else if (ks == p - 1) {
          kase = 1;
        } else {
          kase = 2;
          k = ks;
        }
      }
      k++;

      // Perform the task indicated by kase.

      switch (kase) {

          // Deflate negligible s(p).

        case 1:
          {
            double f = e[p - 2];
            e[p - 2] = 0.0;
            for (int j = p - 2; j >= k; j--) {
              double t = Algebra.hypot(s[j], f);
              double cs = s[j] / t;
              double sn = f / t;
              s[j] = t;
              if (j != k) {
                f = -sn * e[j - 1];
                e[j - 1] = cs * e[j - 1];
              }
              if (wantv) {
                for (int i = 0; i < n; i++) {
                  t = cs * v[i][j] + sn * v[i][p - 1];
                  v[i][p - 1] = -sn * v[i][j] + cs * v[i][p - 1];
                  v[i][j] = t;
                }
              }
            }
          }
          break;

          // Split at negligible s(k).

        case 2:
          {
            double f = e[k - 1];
            e[k - 1] = 0.0;
            for (int j = k; j < p; j++) {
              double t = Algebra.hypot(s[j], f);
              double cs = s[j] / t;
              double sn = f / t;
              s[j] = t;
              f = -sn * e[j];
              e[j] = cs * e[j];
              if (wantu) {
                for (int i = 0; i < m; i++) {
                  t = cs * u[i][j] + sn * u[i][k - 1];
                  u[i][k - 1] = -sn * u[i][j] + cs * u[i][k - 1];
                  u[i][j] = t;
                }
              }
            }
          }
          break;

          // Perform one qr step.

        case 3:
          {

            // Calculate the shift.

            double scale =
                Math.max(
                    Math.max(
                        Math.max(
                            Math.max(Math.abs(s[p - 1]), Math.abs(s[p - 2])), Math.abs(e[p - 2])),
                        Math.abs(s[k])),
                    Math.abs(e[k]));
            double sp = s[p - 1] / scale;
            double spm1 = s[p - 2] / scale;
            double epm1 = e[p - 2] / scale;
            double sk = s[k] / scale;
            double ek = e[k] / scale;
            double b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2.0;
            double c = sp * epm1 * sp * epm1;
            double shift = 0.0;
            if (b != 0.0 || c != 0.0) {
              shift = Math.sqrt(b * b + c);
              if (b < 0.0) {
                shift = -shift;
              }
              shift = c / (b + shift);
            }
            double f = (sk + sp) * (sk - sp) + shift;
            double g = sk * ek;

            // Chase zeros.

            for (int j = k; j < p - 1; j++) {
              double t = Algebra.hypot(f, g);
              double cs = f / t;
              double sn = g / t;
              if (j != k) {
                e[j - 1] = t;
              }
              f = cs * s[j] + sn * e[j];
              e[j] = cs * e[j] - sn * s[j];
              g = sn * s[j + 1];
              s[j + 1] = cs * s[j + 1];
              if (wantv) {
                for (int i = 0; i < n; i++) {
                  t = cs * v[i][j] + sn * v[i][j + 1];
                  v[i][j + 1] = -sn * v[i][j] + cs * v[i][j + 1];
                  v[i][j] = t;
                }
              }
              t = Algebra.hypot(f, g);
              cs = f / t;
              sn = g / t;
              s[j] = t;
              f = cs * e[j] + sn * s[j + 1];
              s[j + 1] = -sn * e[j] + cs * s[j + 1];
              g = sn * e[j + 1];
              e[j + 1] = cs * e[j + 1];
              if (wantu && j < m - 1) {
                for (int i = 0; i < m; i++) {
                  t = cs * u[i][j] + sn * u[i][j + 1];
                  u[i][j + 1] = -sn * u[i][j] + cs * u[i][j + 1];
                  u[i][j] = t;
                }
              }
            }
            e[p - 2] = f;
            // iter += 1;
          }
          break;

          // Convergence.

        case 4:
          {

            // Make the singular values positive.

            if (s[k] <= 0.0) {
              s[k] = s[k] < 0.0 ? -s[k] : 0.0;
              if (wantv) {
                for (int i = 0; i <= pp; i++) {
                  v[i][k] = -v[i][k];
                }
              }
            }

            // Order the singular values.

            while (k < pp) {
              if (s[k] >= s[k + 1]) {
                break;
              }
              double t = s[k];
              s[k] = s[k + 1];
              s[k + 1] = t;
              if (wantv && k < n - 1) {
                for (int i = 0; i < n; i++) {
                  t = v[i][k + 1];
                  v[i][k + 1] = v[i][k];
                  v[i][k] = t;
                }
              }
              if (wantu && k < m - 1) {
                for (int i = 0; i < m; i++) {
                  t = u[i][k + 1];
                  u[i][k + 1] = u[i][k];
                  u[i][k] = t;
                }
              }
              k++;
            }
            // iter = 0;
            p--;
          }
          break;
        default:
          throw new IllegalStateException();
      }
    }
  }

  public double cond() {
    return s[0] / s[Math.min(m, n) - 1];
  }

  public Matrix getS() {
    double[][] s = new double[n][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        s[i][j] = 0.0;
      }
      s[i][i] = this.s[i];
    }

    return new DenseMatrix(s);
  }

  public double[] getSingularValues() {
    return s;
  }

  public Matrix getU() {
    if (transpositionNeeded) { // case numRows() < numCols()
      return new DenseMatrix(v);
    } else {
      int numCols = Math.min(m + 1, n);
      Matrix r = new DenseMatrix(m, numCols);
      for (int i = 0; i < m; i++) {
        for (int j = 0; j < numCols; j++) {
          r.set(i, j, u[i][j]);
        }
      }

      return r;
    }
  }

  public Matrix getV() {
    if (transpositionNeeded) { // case numRows() < numCols()
      int numCols = Math.min(m + 1, n);
      Matrix r = new DenseMatrix(m, numCols);
      for (int i = 0; i < m; i++) {
        for (int j = 0; j < numCols; j++) {
          r.set(i, j, u[i][j]);
        }
      }

      return r;
    } else {
      return new DenseMatrix(v);
    }
  }

  public double norm2() {
    return s[0];
  }

  public int rank() {
    double eps = Math.pow(2.0, -52.0);
    double tol = Math.max(m, n) * s[0] * eps;
    int r = 0;
    for (double value : s) {
      if (value > tol) {
        r++;
      }
    }
    return r;
  }

  Matrix getCovariance(double minSingularValue) {
    Matrix j = new DenseMatrix(s.length, s.length);
    Matrix vMat = new DenseMatrix(this.v);
    for (int i = 0; i < s.length; i++) {
      j.set(i, i, s[i] >= minSingularValue ? 1 / (s[i] * s[i]) : 0.0);
    }
    return vMat.times(j).times(vMat.transpose());
  }

  @Override
  public String toString() {
    StringBuilder buf = new StringBuilder();
    buf.append("---------------------------------------------------------------------\n");
    buf.append("SingularValueDecomposition(A) --> cond(A), rank(A), norm2(A), U, S, V\n");
    buf.append("---------------------------------------------------------------------\n");

    buf.append("cond = ");
    String unknown = "Illegal operation or error: ";
    try {
      buf.append(String.valueOf(this.cond()));
    } catch (IllegalArgumentException exc) {
      buf.append(unknown).append(exc.getMessage());
    }

    buf.append("\nrank = ");
    try {
      buf.append(String.valueOf(this.rank()));
    } catch (IllegalArgumentException exc) {
      buf.append(unknown).append(exc.getMessage());
    }

    buf.append("\nnorm2 = ");
    try {
      buf.append(String.valueOf(this.norm2()));
    } catch (IllegalArgumentException exc) {
      buf.append(unknown).append(exc.getMessage());
    }

    buf.append("\n\nU = ");
    try {
      buf.append(String.valueOf(this.getU()));
    } catch (IllegalArgumentException exc) {
      buf.append(unknown).append(exc.getMessage());
    }

    buf.append("\n\nS = ");
    try {
      buf.append(String.valueOf(this.getS()));
    } catch (IllegalArgumentException exc) {
      buf.append(unknown).append(exc.getMessage());
    }

    buf.append("\n\nV = ");
    try {
      buf.append(String.valueOf(this.getV()));
    } catch (IllegalArgumentException exc) {
      buf.append(unknown).append(exc.getMessage());
    }

    return buf.toString();
  }
}
