Examples of Jama.Matrix

Jama.Matrix
Jama = Java Matrix class.
The Java Matrix Class provides the fundamental operations of numerical linear algebra. Various constructors create Matrices from two dimensional arrays of double precision floating point numbers. Various "gets" and "sets" provide access to submatrices and matrix elements. Several methods implement basic matrix arithmetic, including matrix addition and multiplication, matrix norms, and element-by-element array operations. Methods for reading and printing matrices are also included. All the operations in this version of the Matrix Class involve real matrices. Complex matrices may be handled in a future version.
Five fundamental matrix decompositions, which consist of pairs or triples of matrices, permutation vectors, and the like, produce results in five decomposition classes. These decompositions are accessed by the Matrix class to compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions. The five decompositions are:
- Cholesky Decomposition of symmetric, positive definite matrices.
- LU Decomposition of rectangular matrices.
- QR Decomposition of rectangular matrices.
- Singular Value Decomposition of rectangular matrices.
- Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.
Example of use:
Solve a linear system A x = b and compute the residual norm, ||b - A x||.
```
 double[][] vals = {{1.,2.,3},{4.,5.,6.},{7.,8.,10.}}; Matrix A = new Matrix(vals); Matrix b = Matrix.random(3,1); Matrix x = A.solve(b); Matrix r = A.times(x).minus(b); double rnorm = r.normInf(); 
```
@author The MathWorks, Inc. and the National Institute of Standards and Technology. @version 5 August 1998

        { 0, 0, v2z, 0, 0, -v1z }, { 0, 0, 0, 0, 1, 0 } };


    double[][] arrayb = { { 1 }, { 1 }, { 0 }, { 0 }, { 0 }, { 0 } };
    //t double[][] arrayb ={{1,1,1,0,0,0,0,0,0}};


    Matrix A = new Matrix(arraya);
    Matrix b = new Matrix(arrayb);
    Matrix x = A.solve(b);


    BetaVertex vf1 = new BetaVertex(x.get(0, 0), x.get(1, 0), x.get(2, 0));
    BetaVertex vf2 = new BetaVertex(x.get(3, 0), x.get(4, 0), x.get(5, 0));


    //BetaVertex v3 = new BetaVertex();
    //BetaVertex v4 = new BetaVertex();


    Sector3D out = new Sector3D(vf1, vf2, v1, v2, 2, st1, st2);

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      q1 = templatePoints.get(r1);
      q2 = templatePoints.get(r2);
      q3 = templatePoints.get(r3);


      double[][] array1 = { { p1.x, p1.y, 1 }, { p2.x, p2.y, 1 }, { p3.x, p3.y, 1 } };
      Matrix matrix = new Matrix(array1);


      try {
        double[][] vector1_ = { { q1.x }, { q2.x }, { q3.x } };
        Matrix vector1 = new Matrix(vector1_);


        Matrix result1 = matrix.solve(vector1);
        double[][] zeile1 = result1.getArray();


        double[][] vector2_ = { { q1.y }, { q2.y }, { q3.y } };
        Matrix vector2 = new Matrix(vector2_);


        Matrix result2 = matrix.solve(vector2);
        double[][] zeile2 = result2.getArray();


        double a11 = zeile1[0][0];
        double a12 = zeile1[1][0];
        double a13 = zeile1[2][0];

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          alfa[k][j] += poli[k] * poli[j];
        }
      }
    }


    Matrix mAlfa = new Matrix(alfa);
    Matrix mBeta = new Matrix(beta);
    Matrix mA = new Matrix(order + 1, 1);
    mA = mAlfa.solve(mBeta);
    beta = mA.getArrayCopy();
    for (int i = 0; i <= order; i++) {
      a[i] = beta[i][0];
    }
    return a;
  }

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   */
  public static double[] fitSVD(int ndata, double[] x, double[] y, double[] sd, int order) {
    if ((y.length < ndata) || (x.length < ndata) || ((sd != null) && (sd.length < ndata))) {
      throw new IllegalArgumentException("data paramenters incorrect too short vector");
    }
    Matrix A = new Matrix(ndata, order + 1);
    double[] b = new double[ndata];
    SingularValueDecomposition SVD;
    double[] a = new double[order + 1];
    double xVal;
    double yVal;
    double small = 0.0000000001 * ndata;
    double[] coeff = new double[order + 1];
    double[][] U;
    double[][] V;
    double[] w;


    if (sd == null) {
      sd = new double[ndata];
      for (int i = 0; i < ndata; i++) {
        sd[i] = 1;
      }
    }


    for (int i = 0; i < ndata; i++) {
      A.set(i, 0, 1 / sd[i]);
    }
    for (int i = 0; i < ndata; i++) {
      xVal = 1;
      yVal = 1;
      for (int j = 1; j <= order; j++) {
        xVal *= x[i];
        yVal += xVal;
        A.set(i, j, xVal / sd[i]);
      }
      b[i] = yVal / sd[i];
    }
    SVD = A.svd();
    U = (SVD.getU()).getArray();
    V = (SVD.getV()).getArray();
    w = SVD.getSingularValues();


    for (int j = 0; j <= order; j++) {

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  /**
   * computes the variance of the extimator of the variance
   */
  protected double calcExtimatorVar(int K, int polyOrder) {
    Matrix X = new Matrix(K, polyOrder + 1);
    Matrix Xt = new Matrix(polyOrder + 1, K);
    Matrix square = new Matrix(K, K);
    for (int i = 0; i < K; i++) {
      for (int j = 0; j <= polyOrder; j++) {
        X.set(i, j, (Math.pow((4 * ((double) i + 1) - 1) / (2 * (double) K), j)));
      }
    }
    Xt = X.transpose();
    square = Xt.times(X);
    square = square.inverse();
    //System.out.println("calcConst "+square.get(0,0));
    return (.645 * square.get(0, 0));
  }

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   * Demands associati.
   */
  public Sector2D BetaCalc2D(newPoint p1, newPoint p2) {
    double[][] arraya = { { 1, 1, 0, 0 }, { 0, 0, 1, 1 }, { -p2.getX(), 0, p1.getX(), 0 }, { 0, p2.getY(), 0, -p1.getY() } };
    double[][] arrayb = { { 1 }, { 1 }, { 0 }, { 0 } };
    Matrix A = new Matrix(arraya);
    Matrix b = new Matrix(arrayb);
    Matrix x = A.solve(b);
    // Creo un nuovo settore con le soluzioni e i punti associati
    Sector2D out = new Sector2D(x.get(0, 0), x.get(1, 0), x.get(2, 0), x.get(3, 0), p1, p2);
    return out;
  }

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      }
    
      logger.info("cijMatrix after normalization = " +  this.printMatrix(cijMatrix));
      
      //transpose and multiplication
      trustScores = new Matrix(cijMatrix);
      Matrix trans = trustScores.transpose();
      
      Matrix orig = new Matrix(trans.getArray());


      //trust everyone equally in the beginning
      double tempScore = 1.0/(double)numVertices;
      double[][] tk = new double[numVertices][numVertices];
      for(int i=0;i<numVertices;i++)
      {
        for(int j=0;j<numVertices;j++) tk[i][j] = tempScore;
      }
      Matrix tkMatrix = new Matrix(tk);
      
      double[][] p = new double[numVertices][numVertices];
      for(int i=0;i<numVertices;i++)
      {
        for(int j=0;j<numVertices;j++) p[i][j] = tempScore; 
      }
      Matrix pMatrix = new Matrix(p); //preTrusted matrix
      
      double a=0.2; //TODO make this configurable
      Matrix tkplus1Matrix = null;
      
      
      for(int i=0;i<this.iterations;i++)
      {
        tkplus1Matrix = trans.times(tkMatrix);
        tkplus1Matrix = tkplus1Matrix.times(1-a);
        tkplus1Matrix = tkplus1Matrix.plus(pMatrix.times(a));
        tkMatrix = new Matrix(tkplus1Matrix.getArrayCopy());
        //System.out.println(printMatrix(tkplus1Matrix.getArray()));
        //System.out.println("row=" + tkplus1Matrix.getRowDimension() + " column="+tkplus1Matrix.getColumnDimension());
      }
      
      this.trustScores = tkMatrix;

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    this.degreeToCCarrierMatrix = createMatrix(allCarriers);
    
    System.out.println("this.degreeToCCarrierMatrix");
    this.degreeToCCarrierMatrix.print(15, 5);


    Matrix usedToCCDirectMatrix = polyofdm.cc.full.FullCC.createCancellationMatrix(allCarriers, cancellationCarriers);
    this.usedToDegreeMatrix = this.degreeToCCarrierMatrix.transpose().times(usedToCCDirectMatrix);
            
  }

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  }


  private Matrix createMatrix(int allCarriers) {
    double[] ccWeightings = createWeightings(cCarriers);


    Matrix cCarriersToCancelledDegrees = new Matrix(cCarriers.length, cCarriers.length);
    for (int degree = 0; degree < cCarriers.length; degree++) {
      for (int cCarrierIndex = 0; cCarrierIndex < cCarriers.length; cCarrierIndex++) {
        cCarriersToCancelledDegrees.set(degree, cCarrierIndex, power(cCarriers[cCarrierIndex] - ((usedCarriers.length+cCarriers.length-1)/2d), degree) * ccWeightings[cCarrierIndex]);
      }      
    }
    Utils.makeOrthoGramSchmidt(cCarriersToCancelledDegrees);
    System.out.println("cCarriersToCancelledDegrees0");
    cCarriersToCancelledDegrees.print(15, 15);
    cCarriersToCancelledDegrees = resort(cCarriersToCancelledDegrees);
    System.out.println("cCarriersToCancelledDegrees resorted");
    cCarriersToCancelledDegrees.print(15, 15);
    
    
    System.out.println("cCarriersToCancelledDegrees gram schmidt");
    cCarriersToCancelledDegrees.print(15, 15);
    
    return cCarriersToCancelledDegrees.transpose();
  }

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    }
    return product;
  }
  
  private Matrix resort(Matrix matrix) {
    Matrix m = new Matrix(matrix.getRowDimension(), matrix.getColumnDimension());
    for (int i = 0; i < matrix.getRowDimension(); i++) {
      for (int j = 0; j < matrix.getColumnDimension(); j++) {
        m.set(matrix.getRowDimension()-1-i, j, matrix.get(i, j));
      }
    }
    return m;
  }

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