Examples of org.jquantlib.math.matrixutilities.Matrix

Package org.jquantlib.math.matrixutilities

Examples of org.jquantlib.math.matrixutilities.Matrix

org.jquantlib.math.matrixutilities.Matrix
Bidimensional matrix operations
Performance of multidimensional arrays is a big concern in Java. This is because multidimensional arrays are stored as arrays of arrays, spanning this concept to as many depths as necessary. In C++, a multidimensional array is stored internally as a unidimensional array where depths are stacked together one after another. A very simple calculation is needed in order to map multiple dimensional indexes to an unidimensional index.
This class provides a C/C++ like approach of internal unidimensional array backing a conceptual bidimensional matrix. This mapping is provided by method op(int row, int col) which is responsible for returning the physical address of the desired tuple , given a certain access method.
The mentioned access method is provided by a concrete implementation of {@link Address} which is passed to constructors.Doing so, it is possible to access the same underlying unidimensional data storage in various different ways, which allows us obtain another Matrix (see method {@link Matrix#range(int,int,int,int) and alike}) from an existing Matrix without any need of copying the underlying data. Certain operations benefit a lot from such approach, like {@link Matrix#transpose()} whichpresents constant execution time.
The price we have to pay for such flexibility and benefits is that an access method is necessary, which means that a the bytecode may potentially need a dereference to a class which contain the concrete implementation of method op(int row, int col). In order to keep this cost at minimum, implementation of access method keep indexes at hand whenever possible, in order to being able to calculate the actual unidimensional index as fast as possible. This additional dereference impacts performance more or less in the same ways dereference impacts performance when a bidimensional array (double[][]) is employed. Contrary to the bidimensional implementation, our implementation can potentially benefit from bytecode inlining, which means that calculation of the unidimensional index can be performed potentially faster than calculation of address location when a bidimensional array (double[][]) is used as underlying storage.

Assignment operations
```
 opr method     this    right    result --- ---------- ------- -------- ------ =   assign     Matrix           Matrix (1) +=  addAssign  Matrix  Matrix   this -=  subAssign  Matrix  Matrix   this *=  mulAssign  Matrix  scalar   this /=  divAssign  Matrix  scalar   this 
```
Algebraic products
```
 opr method     this    right    result --- ---------- ------- -------- ------ +   add        Matrix  Matrix   Matrix -   sub        Matrix  Matrix   Matrix -   negative   Matrix           this *   mul        Matrix  scalar   Matrix /   div        Matrix  scalar   Matrix 
```
Vectorial products
```
 method         this    right    result -------------- ------- -------- ------ mul            Matrix  Array    Array mul            Matrix  Matrix   Matrix 
```
Decompositions
```
 method         this    right    result -------------- ------- -------- ------ lu             Matrix           LUDecomposition qr             Matrix           QRDecomposition cholensky      Matrix           CholeskyDecomposition svd            Matrix           SingularValueDecomposition eigenvalue     Matrix           EigenvalueDecomposition 
```
Element iterators
```
 method         this    right    result ------------   ------- -------- ------ rowIterator    Matrix           RowIterator columnIterator Matrix           ColumnIterator 
```
Miscellaneous
```
 method         this    right    result -------------- ------- -------- ------ transpose      Matrix           Matrix diagonal       Matrix           Array determinant    Matrix           double inverse        Matrix           Matrix solve          Matrix           Matrix swap           Matrix  Matrix   this range          Matrix  Matrix   Matrix 
```
(1): clone()
(2): Unary + is equivalent to: array.clone()
(3): Unary ? is equivalent to: array.clone().mulAssign(-1)
@note This class is not thread-safe @author Richard Gomes

            this.j_ = j;
            this.param_ = param;
        }


        public double op(final double t) {
            final Matrix m = param_.diffusion(t);
            return m.constRangeRow(i_).innerProduct(m.constRangeRow(j_));
        }

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     */
    @Override
    public Matrix covarianceDiscretization(
                final StochasticProcess sp,
                /* @Time */final double t0, /* @Real */ final Array x0, /* @Time */final double dt) {
        final Matrix sigma = sp.diffusion(t0, x0);
        return sigma.mul(sigma.transpose()).mulAssign(dt);
    }

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        final Array drift = process.drift(process.time(date18.clone()), new Array(1).fill(5.6));
        System.out.println("The drift of the process after time = 18th day from today with value of the stock as specified from the quote");


        //Calculating the diffusion of the process after time = 18th day from today with value of the stock as specified from the quote
        //The diffusion = volatiltiy of the stochastic process
        final Matrix diffusion = process.diffusion(process.time(date18.clone()), new Array(1).fill(5.6));
        System.out.println("The diffusion of the process after time = 18th day from today with value of the stock as specified from the quote");


        //Calulating the standard deviation of the process after time = 18th day from today with value of the stock as specified from the quote
        //The standard deviation = volatility*sqrt(dt)
        final Matrix stdDeviation = process.stdDeviation(process.time(date18.clone()), new Array(1).fill(5.6), 0.01);
        System.out.println("The stdDeviation of the process after time = 18th day from today with value of the stock as specified from the quote");


        //Calulating the expected value of the stock quote after time = 18th day from today with the current value of the stock as specified from the quote
        //The expectedValue = intialValue*exp(drift*dt)-----can be obtained by integrating----->dx/x= drift*dt
        final Array expectation = process.expectation(process.time(date18.clone()), new Array(1).fill(5.6), 0.01);
        System.out.println("Expected value = "+expectation.first());


        //Calulating the exact value of the stock quote after time = 18th day from today with the current value of the stock as specified from the quote
        //The exact value = intialValue*exp(drift*dt)*exp(volatility*sqrt(dt))-----can be obtained by integrating----->dx/x= drift*dt+volatility*sqrt(dt)
        final Array evolve = process.evolve(process.time(date18.clone()), new Array(1).fill(6.7), .001, new Array(1).fill(new NormalDistribution().op(Math.random()) ));
        System.out.println("Exact value = "+evolve.first());


        //Calculating covariance of the process
        final Matrix covariance = process.covariance(process.time(date18.clone()),  new Array(1).fill(5.6), 0.01);
        System.out.println("Covariance = "+covariance.get(0, 0));


        clock.stopClock();
        clock.log();
    }

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    }


    @Override
    // TODO: review iterators
    public Matrix diffusion(/*@Time*/ final double t, final Array x){
        final Matrix pca = corrModel_.pseudoSqrt(t, x);
        // TODO: code review :: use of clone()
        final Array  vol = volaModel_.volatility(t, x);
        for (int i=0; i<size_; ++i) {
            pca.rangeRow(i).mulAssign(vol.get(i));
        }
        return pca;
    }

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    @Override
    public Matrix covariance(/* @Time */final double t, final Array x) {
        // TODO: code review :: use of clone()
        final Array volatility = volaModel_.volatility(t, x);
        final Matrix correlation = corrModel_.correlation(t, x);


        final Matrix tmp = new Matrix(size_, size_);
        for (int i = 0; i < size_; ++i) {
            for (int j = 0; j < size_; ++j) {
                tmp.set(i, j, volatility.get(i) * correlation.get(i, j) * volatility.get(j));
            }
        }


        return tmp;
    }

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        if (System.getProperty("EXPERIMENTAL") == null) {
            throw new UnsupportedOperationException("Work in progress");
        }


        corrMatrix_ = new Matrix(size, size);
        factors = factors != 0 ? 0 : size;
        arguments_.set(0, new ConstantParameter(rho, new BoundaryConstraint(-1.0, 1.0)));
        arguments_.set(1, new ConstantParameter(beta, new PositiveConstraint()));
        generateArguments();
    }

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                : (discretization_ == Discretization.Reflection)
                ? -Math.sqrt(-x1)
                        : 0.0;
                final double sigma2 = sigmav_ * vol;


                final Matrix result = new Matrix(2, 2);
                result.set(0, 0, vol);
                result.set(0, 1, 0.0);
                result.set(1, 0, rhov_ * sigma2);
                result.set(1, 1, sqrhov_ * sigma2);
                return result;
    }

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        final Date[] datesAxis = {date10.clone(), date15.clone(), date20.clone(), date25.clone(), date30.clone(), date40.clone() };


        final Array strikeAxis = new Array(new double[] {10,20,35,40,56,60});


        //Following is the volatility surface on which interpolations will be done
        final Matrix volatilityMatrix = new Matrix(new double[][] {
                {0.01,0.02,0.03,0.04,0.05,0.06},
                {0.02,0.03,0.04,0.05,0.06,0.07},
                {0.03,0.04,0.05,0.06,0.07,0.08},
                {0.3,0.5,0.6,0.7,0.8,0.9},
                {0.1,0.4,0.6,0.7,0.8,0.9},

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    @Override
    public final /*@Diffusion*/ Matrix diffusion(final /*@Time*/ double t, /*@Real*/ final Array x) {
        QL.require(x.size()==1 , ARRAY_1D_REQUIRED); // TODO: message
        final double v = diffusion(t, x.first());
        return new Matrix(1, 1).fill(v);
    }

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    @Override
    public final /*@StdDev*/ Matrix stdDeviation(final /*@Time*/ double t0, final /*@Real*/ Array x0, final /*@Time*/ double dt) {
        QL.require(x0.size()==1 , ARRAY_1D_REQUIRED); // TODO: message
        final double v = stdDeviation(t0, x0.first(), dt);
        return new Matrix(1, 1).fill(v);
    }

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