source: tags/3.3.2/HeuristicLab.ExtLibs/HeuristicLab.ALGLIB/2.5.0/ALGLIB-2.5.0/inverseupdate.cs @ 13398

/*************************************************************************
Copyright (c) 2005-2007, Sergey Bochkanov (ALGLIB project).

>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the 
License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses

>>> END OF LICENSE >>>
*************************************************************************/


namespace alglib {
  public class inverseupdate {
    /*************************************************************************
    Inverse matrix update by the Sherman-Morrison formula

    The algorithm updates matrix A^-1 when adding a number to an element
    of matrix A.

    Input parameters:
        InvA    -   inverse of matrix A.
                    Array whose indexes range within [0..N-1, 0..N-1].
        N       -   size of matrix A.
        UpdRow  -   row where the element to be updated is stored.
        UpdColumn - column where the element to be updated is stored.
        UpdVal  -   a number to be added to the element.


    Output parameters:
        InvA    -   inverse of modified matrix A.

      -- ALGLIB --
         Copyright 2005 by Bochkanov Sergey
    *************************************************************************/
    public static void rmatrixinvupdatesimple(ref double[,] inva,
        int n,
        int updrow,
        int updcolumn,
        double updval) {
      double[] t1 = new double[0];
      double[] t2 = new double[0];
      int i = 0;
      double lambda = 0;
      double vt = 0;
      int i_ = 0;

      System.Diagnostics.Debug.Assert(updrow >= 0 & updrow < n, "RMatrixInvUpdateSimple: incorrect UpdRow!");
      System.Diagnostics.Debug.Assert(updcolumn >= 0 & updcolumn < n, "RMatrixInvUpdateSimple: incorrect UpdColumn!");
      t1 = new double[n - 1 + 1];
      t2 = new double[n - 1 + 1];

      //
      // T1 = InvA * U
      //
      for (i_ = 0; i_ <= n - 1; i_++) {
        t1[i_] = inva[i_, updrow];
      }

      //
      // T2 = v*InvA
      //
      for (i_ = 0; i_ <= n - 1; i_++) {
        t2[i_] = inva[updcolumn, i_];
      }

      //
      // Lambda = v * InvA * U
      //
      lambda = updval * inva[updcolumn, updrow];

      //
      // InvA = InvA - correction
      //
      for (i = 0; i <= n - 1; i++) {
        vt = updval * t1[i];
        vt = vt / (1 + lambda);
        for (i_ = 0; i_ <= n - 1; i_++) {
          inva[i, i_] = inva[i, i_] - vt * t2[i_];
        }
      }
    }


    /*************************************************************************
    Inverse matrix update by the Sherman-Morrison formula

    The algorithm updates matrix A^-1 when adding a vector to a row
    of matrix A.

    Input parameters:
        InvA    -   inverse of matrix A.
                    Array whose indexes range within [0..N-1, 0..N-1].
        N       -   size of matrix A.
        UpdRow  -   the row of A whose vector V was added.
                    0 <= Row <= N-1
        V       -   the vector to be added to a row.
                    Array whose index ranges within [0..N-1].

    Output parameters:
        InvA    -   inverse of modified matrix A.

      -- ALGLIB --
         Copyright 2005 by Bochkanov Sergey
    *************************************************************************/
    public static void rmatrixinvupdaterow(ref double[,] inva,
        int n,
        int updrow,
        ref double[] v) {
      double[] t1 = new double[0];
      double[] t2 = new double[0];
      int i = 0;
      int j = 0;
      double lambda = 0;
      double vt = 0;
      int i_ = 0;

      t1 = new double[n - 1 + 1];
      t2 = new double[n - 1 + 1];

      //
      // T1 = InvA * U
      //
      for (i_ = 0; i_ <= n - 1; i_++) {
        t1[i_] = inva[i_, updrow];
      }

      //
      // T2 = v*InvA
      // Lambda = v * InvA * U
      //
      for (j = 0; j <= n - 1; j++) {
        vt = 0.0;
        for (i_ = 0; i_ <= n - 1; i_++) {
          vt += v[i_] * inva[i_, j];
        }
        t2[j] = vt;
      }
      lambda = t2[updrow];

      //
      // InvA = InvA - correction
      //
      for (i = 0; i <= n - 1; i++) {
        vt = t1[i] / (1 + lambda);
        for (i_ = 0; i_ <= n - 1; i_++) {
          inva[i, i_] = inva[i, i_] - vt * t2[i_];
        }
      }
    }


    /*************************************************************************
    Inverse matrix update by the Sherman-Morrison formula

    The algorithm updates matrix A^-1 when adding a vector to a column
    of matrix A.

    Input parameters:
        InvA        -   inverse of matrix A.
                        Array whose indexes range within [0..N-1, 0..N-1].
        N           -   size of matrix A.
        UpdColumn   -   the column of A whose vector U was added.
                        0 <= UpdColumn <= N-1
        U           -   the vector to be added to a column.
                        Array whose index ranges within [0..N-1].

    Output parameters:
        InvA        -   inverse of modified matrix A.

      -- ALGLIB --
         Copyright 2005 by Bochkanov Sergey
    *************************************************************************/
    public static void rmatrixinvupdatecolumn(ref double[,] inva,
        int n,
        int updcolumn,
        ref double[] u) {
      double[] t1 = new double[0];
      double[] t2 = new double[0];
      int i = 0;
      double lambda = 0;
      double vt = 0;
      int i_ = 0;

      t1 = new double[n - 1 + 1];
      t2 = new double[n - 1 + 1];

      //
      // T1 = InvA * U
      // Lambda = v * InvA * U
      //
      for (i = 0; i <= n - 1; i++) {
        vt = 0.0;
        for (i_ = 0; i_ <= n - 1; i_++) {
          vt += inva[i, i_] * u[i_];
        }
        t1[i] = vt;
      }
      lambda = t1[updcolumn];

      //
      // T2 = v*InvA
      //
      for (i_ = 0; i_ <= n - 1; i_++) {
        t2[i_] = inva[updcolumn, i_];
      }

      //
      // InvA = InvA - correction
      //
      for (i = 0; i <= n - 1; i++) {
        vt = t1[i] / (1 + lambda);
        for (i_ = 0; i_ <= n - 1; i_++) {
          inva[i, i_] = inva[i, i_] - vt * t2[i_];
        }
      }
    }


    /*************************************************************************
    Inverse matrix update by the Sherman-Morrison formula

    The algorithm computes the inverse of matrix A+u*v’ by using the given matrix
    A^-1 and the vectors u and v.

    Input parameters:
        InvA    -   inverse of matrix A.
                    Array whose indexes range within [0..N-1, 0..N-1].
        N       -   size of matrix A.
        U       -   the vector modifying the matrix.
                    Array whose index ranges within [0..N-1].
        V       -   the vector modifying the matrix.
                    Array whose index ranges within [0..N-1].

    Output parameters:
        InvA - inverse of matrix A + u*v'.

      -- ALGLIB --
         Copyright 2005 by Bochkanov Sergey
    *************************************************************************/
    public static void rmatrixinvupdateuv(ref double[,] inva,
        int n,
        ref double[] u,
        ref double[] v) {
      double[] t1 = new double[0];
      double[] t2 = new double[0];
      int i = 0;
      int j = 0;
      double lambda = 0;
      double vt = 0;
      int i_ = 0;

      t1 = new double[n - 1 + 1];
      t2 = new double[n - 1 + 1];

      //
      // T1 = InvA * U
      // Lambda = v * T1
      //
      for (i = 0; i <= n - 1; i++) {
        vt = 0.0;
        for (i_ = 0; i_ <= n - 1; i_++) {
          vt += inva[i, i_] * u[i_];
        }
        t1[i] = vt;
      }
      lambda = 0.0;
      for (i_ = 0; i_ <= n - 1; i_++) {
        lambda += v[i_] * t1[i_];
      }

      //
      // T2 = v*InvA
      //
      for (j = 0; j <= n - 1; j++) {
        vt = 0.0;
        for (i_ = 0; i_ <= n - 1; i_++) {
          vt += v[i_] * inva[i_, j];
        }
        t2[j] = vt;
      }

      //
      // InvA = InvA - correction
      //
      for (i = 0; i <= n - 1; i++) {
        vt = t1[i] / (1 + lambda);
        for (i_ = 0; i_ <= n - 1; i_++) {
          inva[i, i_] = inva[i, i_] - vt * t2[i_];
        }
      }
    }


    public static void shermanmorrisonsimpleupdate(ref double[,] inva,
        int n,
        int updrow,
        int updcolumn,
        double updval) {
      double[] t1 = new double[0];
      double[] t2 = new double[0];
      int i = 0;
      double lambda = 0;
      double vt = 0;
      int i_ = 0;

      t1 = new double[n + 1];
      t2 = new double[n + 1];

      //
      // T1 = InvA * U
      //
      for (i_ = 1; i_ <= n; i_++) {
        t1[i_] = inva[i_, updrow];
      }

      //
      // T2 = v*InvA
      //
      for (i_ = 1; i_ <= n; i_++) {
        t2[i_] = inva[updcolumn, i_];
      }

      //
      // Lambda = v * InvA * U
      //
      lambda = updval * inva[updcolumn, updrow];

      //
      // InvA = InvA - correction
      //
      for (i = 1; i <= n; i++) {
        vt = updval * t1[i];
        vt = vt / (1 + lambda);
        for (i_ = 1; i_ <= n; i_++) {
          inva[i, i_] = inva[i, i_] - vt * t2[i_];
        }
      }
    }


    public static void shermanmorrisonupdaterow(ref double[,] inva,
        int n,
        int updrow,
        ref double[] v) {
      double[] t1 = new double[0];
      double[] t2 = new double[0];
      int i = 0;
      int j = 0;
      double lambda = 0;
      double vt = 0;
      int i_ = 0;

      t1 = new double[n + 1];
      t2 = new double[n + 1];

      //
      // T1 = InvA * U
      //
      for (i_ = 1; i_ <= n; i_++) {
        t1[i_] = inva[i_, updrow];
      }

      //
      // T2 = v*InvA
      // Lambda = v * InvA * U
      //
      for (j = 1; j <= n; j++) {
        vt = 0.0;
        for (i_ = 1; i_ <= n; i_++) {
          vt += v[i_] * inva[i_, j];
        }
        t2[j] = vt;
      }
      lambda = t2[updrow];

      //
      // InvA = InvA - correction
      //
      for (i = 1; i <= n; i++) {
        vt = t1[i] / (1 + lambda);
        for (i_ = 1; i_ <= n; i_++) {
          inva[i, i_] = inva[i, i_] - vt * t2[i_];
        }
      }
    }


    public static void shermanmorrisonupdatecolumn(ref double[,] inva,
        int n,
        int updcolumn,
        ref double[] u) {
      double[] t1 = new double[0];
      double[] t2 = new double[0];
      int i = 0;
      double lambda = 0;
      double vt = 0;
      int i_ = 0;

      t1 = new double[n + 1];
      t2 = new double[n + 1];

      //
      // T1 = InvA * U
      // Lambda = v * InvA * U
      //
      for (i = 1; i <= n; i++) {
        vt = 0.0;
        for (i_ = 1; i_ <= n; i_++) {
          vt += inva[i, i_] * u[i_];
        }
        t1[i] = vt;
      }
      lambda = t1[updcolumn];

      //
      // T2 = v*InvA
      //
      for (i_ = 1; i_ <= n; i_++) {
        t2[i_] = inva[updcolumn, i_];
      }

      //
      // InvA = InvA - correction
      //
      for (i = 1; i <= n; i++) {
        vt = t1[i] / (1 + lambda);
        for (i_ = 1; i_ <= n; i_++) {
          inva[i, i_] = inva[i, i_] - vt * t2[i_];
        }
      }
    }


    public static void shermanmorrisonupdateuv(ref double[,] inva,
        int n,
        ref double[] u,
        ref double[] v) {
      double[] t1 = new double[0];
      double[] t2 = new double[0];
      int i = 0;
      int j = 0;
      double lambda = 0;
      double vt = 0;
      int i_ = 0;

      t1 = new double[n + 1];
      t2 = new double[n + 1];

      //
      // T1 = InvA * U
      // Lambda = v * T1
      //
      for (i = 1; i <= n; i++) {
        vt = 0.0;
        for (i_ = 1; i_ <= n; i_++) {
          vt += inva[i, i_] * u[i_];
        }
        t1[i] = vt;
      }
      lambda = 0.0;
      for (i_ = 1; i_ <= n; i_++) {
        lambda += v[i_] * t1[i_];
      }

      //
      // T2 = v*InvA
      //
      for (j = 1; j <= n; j++) {
        vt = 0.0;
        for (i_ = 1; i_ <= n; i_++) {
          vt += v[i_] * inva[i_, j];
        }
        t2[j] = vt;
      }

      //
      // InvA = InvA - correction
      //
      for (i = 1; i <= n; i++) {
        vt = t1[i] / (1 + lambda);
        for (i_ = 1; i_ <= n; i_++) {
          inva[i, i_] = inva[i, i_] - vt * t2[i_];
        }
      }
    }
  }
}