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

        /*
         * The JAMA constructor uses column-major array (FORTRAN convention) while SIS uses row-major
         * array. In other words, the JAMA matrix is already transposed from the SIS point of view.
         */
        matrix.transpose();
        assertEqualsJAMA(new Matrix(elements, numCol), matrix, STRICT);
    }

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            prepareNewMatrixSize(random);
            final int numRow = getNumRow();
            final int numCol = getNumCol();
            double[] elements = createRandomPositiveValues(numRow * numCol);
            final MatrixSIS matrix = Matrices.create(numRow, numCol, elements);
            final Matrix reference = new Matrix(elements, numCol).transpose();
            /*
             * Computes new random value for the argument. We mix positive and negative values,
             * but with more positive values than negative ones in order to reduce the chances
             * to have a product of zero for an element.
             */
            final int nx = random.nextInt(8) + 1;
            elements = new double[numCol * nx];
            for (int k=0; k<elements.length; k++) {
                elements[k] = 8 - random.nextDouble() * 10;
            }
            final Matrix referenceArg = new Matrix(elements, nx).transpose();
            final MatrixSIS matrixArg = Matrices.create(numCol, nx, elements);
            /*
             * Performs the multiplication and compare.
             */
            final Matrix referenceResult = reference.times(referenceArg);
            final MatrixSIS matrixResult = matrix.multiply(matrixArg);
            assertEqualsJAMA(referenceResult, matrixResult, TOLERANCE);
        }
    }

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        for (int n=0; n<NUMBER_OF_REPETITIONS; n++) {
            prepareNewMatrixSize(random);
            final int numRow = getNumRow();
            final int numCol = getNumCol();
            double[] elements = createRandomPositiveValues(numRow * numCol);
            final Matrix reference = new Matrix(elements, numCol).transpose();
            if (!(reference.det() >= DETERMINANT_THRESHOLD)) {
                continue; // To close to a singular matrix - search an other one.
            }
            final MatrixSIS matrix = Matrices.create(numRow, numCol, elements);
            /*
             * Computes new random value for the argument. We mix positive and negative values,
             * but with more positive values than negative ones in order to reduce the chances
             * to have a product of zero for an element.
             */
            final int nx = random.nextInt(8) + 1;
            elements = new double[numCol * nx];
            for (int k=0; k<elements.length; k++) {
                elements[k] = 8 - random.nextDouble() * 10;
            }
            final Matrix referenceArg = new Matrix(elements, nx).transpose();
            final MatrixSIS matrixArg = Matrices.create(numCol, nx, elements);
            /*
             * Performs the operation and compare.
             */
            final Matrix referenceResult = reference.solve(referenceArg);
            final MatrixSIS matrixResult = matrix.solve(matrixArg);
            assertEqualsJAMA(referenceResult, matrixResult, SolverTest.TOLERANCE);
        }
    }

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        for (int n=0; n<NUMBER_OF_REPETITIONS; n++) {
            prepareNewMatrixSize(random);
            final int numRow = getNumRow();
            final int numCol = getNumCol();
            final double[] elements = createRandomPositiveValues(numRow * numCol);
            final Matrix reference = new Matrix(elements, numCol).transpose();
            if (!(reference.det() >= DETERMINANT_THRESHOLD)) {
                continue; // To close to a singular matrix - search an other one.
            }
            final MatrixSIS matrix = Matrices.create(numRow, numCol, elements);
            assertEqualsJAMA(reference.inverse(), matrix.inverse(), TOLERANCE);
        }
    }

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    private Matrix cachedSigmaInverse;
    final private ExpandingArrayList<Double> pVarInGaussian;


    public MultivariateGaussian( final int numAnnotations ) {
        mu = new double[numAnnotations];
        sigma = new Matrix(numAnnotations, numAnnotations);
        pVarInGaussian = new ExpandingArrayList<>();
    }

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    public void zeroOutSigma() {
        final double[][] zeroSigma = new double[mu.length][mu.length];
        for( final double[] row : zeroSigma ) {
            Arrays.fill(row, 0);
        }
        final Matrix tmp = new Matrix(zeroSigma);
        sigma.setMatrix(0, mu.length - 1, 0, mu.length - 1, tmp);
    }

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                    randSigma[jjj][iii] *= -1.0;
                }
                if( iii != jjj ) { randSigma[iii][jjj] = 0.0; } // Sigma is a symmetric, positive-definite matrix created by taking a lower diagonal matrix and multiplying it by its transpose
            }
        }
        Matrix tmp = new Matrix( randSigma );
        tmp = tmp.times(tmp.transpose());
        sigma.setMatrix(0, mu.length - 1, 0, mu.length - 1, tmp);
    }

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    }


    public void maximizeGaussian( final List<VariantDatum> data, final double[] empiricalMu, final Matrix empiricalSigma,
                                  final double SHRINKAGE, final double DIRICHLET_PARAMETER, final double DEGREES_OF_FREEDOM ) {
        sumProb = 1E-10;
        final Matrix wishart = new Matrix(mu.length, mu.length);
        zeroOutMu();
        zeroOutSigma();
        
        int datumIndex = 0;
        for( final VariantDatum datum : data ) {
            final double prob = pVarInGaussian.get(datumIndex++);
            sumProb += prob;
            incrementMu( datum, prob );
        }
        divideEqualsMu( sumProb );


        final double shrinkageFactor = (SHRINKAGE * sumProb) / (SHRINKAGE + sumProb);
        for( int iii = 0; iii < mu.length; iii++ ) {
            for( int jjj = 0; jjj < mu.length; jjj++ ) {
                wishart.set(iii, jjj, shrinkageFactor * (mu[iii] - empiricalMu[iii]) * (mu[jjj] - empiricalMu[jjj]));
            }
        }


        datumIndex = 0;
        final Matrix pVarSigma = new Matrix(mu.length, mu.length);
        for( final VariantDatum datum : data ) {
            final double prob = pVarInGaussian.get(datumIndex++);
            for( int iii = 0; iii < mu.length; iii++ ) {
                for( int jjj = 0; jjj < mu.length; jjj++ ) {
                    pVarSigma.set(iii, jjj, prob * (datum.annotations[iii]-mu[iii]) * (datum.annotations[jjj]-mu[jjj]));
                }
            }
            sigma.plusEquals( pVarSigma );
        }

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            incrementMu( datum, prob );
        }
        divideEqualsMu( sumProb );


        datumIndex = 0;
        final Matrix pVarSigma = new Matrix(mu.length, mu.length);
        for( final VariantDatum datum : data ) {
            final double prob = pVarInGaussian.get(datumIndex++);
            for( int iii = 0; iii < mu.length; iii++ ) {
                for( int jjj = 0; jjj < mu.length; jjj++ ) {
                    pVarSigma.set(iii, jjj, prob * (datum.annotations[iii]-mu[iii]) * (datum.annotations[jjj]-mu[jjj]));
                }
            }
            sigma.plusEquals( pVarSigma );
        }
        sigma.timesEquals( 1.0 / sumProb );

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        }
        this.shrinkage = shrinkage;
        this.dirichletParameter = dirichletParameter;
        this.priorCounts = priorCounts;
        empiricalMu = new double[numAnnotations];
        empiricalSigma = new Matrix(numAnnotations, numAnnotations);
        isModelReadyForEvaluation = false;
        Arrays.fill(empiricalMu, 0.0);
        empiricalSigma.setMatrix(0, empiricalMu.length - 1, 0, empiricalMu.length - 1, Matrix.identity(empiricalMu.length, empiricalMu.length).times(200.0).inverse());
    }

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