Examples of org.ejml.data.DenseMatrix64F

org.ejml.data.DenseMatrix64F

DenseMatrix64F is a dense matrix with elements that are 64-bit floats (doubles). A matrix is the fundamental data structure in linear algebra. Unlike a sparse matrix, there is no compression in a dense matrix and every element is stored in memory. This allows for fast reads and writes to the matrix.

To keep the code manageable and the library easier to use only basic functions for accessing and editing elements are provided in this class. The numerous operations which can be performed on DenseMatrix64F are contained in various other classes, where the most common operations can be found in the {@link org.ejml.ops.CommonOps} and {@link org.ejml.ops.SpecializedOps} classes.

The matrix is stored internally in a row-major 1D array format:

data[ y*numCols + x ] = data[y][x]

For example:
data =

a₁₁ a₁₂ a₁₃ a₁₄ a₂₁ a₂₂ a₂₃ a₂₄ a₃₁ a₃₂ a₃₃ a₃₄ a₄₁ a₄₂ a₄₃ a₄₄

An alternative to working directly with DenseMatrix64 is {@link org.ejml.simple.SimpleMatrix}. SimpleMatrix is a wrapper around DenseMatrix64F that provides an easier to use object oriented way of manipulating matrices, at the cost of efficiency.
@see org.ejml.ops.CommonOps @see org.ejml.ops.SpecializedOps @see org.ejml.simple.SimpleMatrix @author Peter Abeles


        // now try it against a more standard matrix
        SimpleMatrix a = SimpleMatrix.random(3,3, 0, 1, rand);
        inv = a.pseudoInverse();


        DenseMatrix64F d_inv = new DenseMatrix64F(3,3);
        CommonOps.invert(a.mat,d_inv);


         EjmlUnitTests.assertEquals(d_inv,inv.mat,1e-8);
    }

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    public void solve() {
        SimpleMatrix a = SimpleMatrix.random(3,3, 0, 1, rand);
        SimpleMatrix b = SimpleMatrix.random(3,2, 0, 1, rand);
        SimpleMatrix c = a.solve(b);


        DenseMatrix64F c_dense = new DenseMatrix64F(3,2);
        CommonOps.solve(a.mat,b.mat,c_dense);


        EjmlUnitTests.assertEquals(c_dense,c.mat,1e-8);
    }

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    /**
     * Compute a solution for a system with more variables than equations
     */
    public void underDetermined_tall_solve() {
        // create a matrix where two rows are linearly dependent
        DenseMatrix64F A = new DenseMatrix64F(3,2,true,1,2,1,2,2,4);


        DenseMatrix64F y = new DenseMatrix64F(3,1,true,4,4,8);
        assertTrue(solver.setA(A));


        DenseMatrix64F x = new DenseMatrix64F(2,1);
        solver.solve(y,x);


        DenseMatrix64F found = new DenseMatrix64F(3,1);
        CommonOps.mult(A, x, found);


        // there are multiple 'x' which will generate the same solution, see if this is one of them
        assertTrue(MatrixFeatures.isEquals(y, found, 1e-8));
    }

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    public void solve_notsquare() {
        SimpleMatrix a = SimpleMatrix.random(6,3, 0, 1, rand);
        SimpleMatrix b = SimpleMatrix.random(6,2, 0, 1, rand);
        SimpleMatrix c = a.solve(b);


        DenseMatrix64F c_dense = new DenseMatrix64F(3,2);
        CommonOps.solve(a.mat,b.mat,c_dense);


        EjmlUnitTests.assertEquals(c_dense,c.mat,1e-8);
    }

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    /**
     * Compute a solution for a system with more variables than equations
     */
    public void singular_solve() {
        // create a matrix where two rows are linearly dependent
        DenseMatrix64F A = new DenseMatrix64F(3,3,true,1,2,3,2,3,4,2,3,4);


        DenseMatrix64F y = new DenseMatrix64F(3,1,true,4,7,7);
        assertTrue(solver.setA(A));


        DenseMatrix64F x = new DenseMatrix64F(3,1);
        solver.solve(y,x);


        DenseMatrix64F found = new DenseMatrix64F(3,1);
        CommonOps.mult(A, x, found);


        // there are multiple 'x' which will generate the same solution, see if this is one of them
        assertTrue(MatrixFeatures.isEquals(y, found, 1e-8));
    }

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    @Test
    public void set_double() {
        SimpleMatrix a = new SimpleMatrix(3,3);
        a.set(16.0);


        DenseMatrix64F d = new DenseMatrix64F(3,3);
        CommonOps.fill(d, 16.0);


        EjmlUnitTests.assertEquals(d,a.mat,1e-8);
    }

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    /**
     * Compute the pseudo inverse a system with more variables than equations
     */
    public void singular_inv() {
        // create a matrix where two rows are linearly dependent
        DenseMatrix64F A = new DenseMatrix64F(3,3,true,1,2,3,2,3,4,2,3,4);


        DenseMatrix64F y = new DenseMatrix64F(3,1,true,4,7,7);
        assertTrue(solver.setA(A));


        DenseMatrix64F x = new DenseMatrix64F(3,1);
        solver.solve(y,x);


        // now test the pseudo inverse
        DenseMatrix64F A_pinv = new DenseMatrix64F(3,3);
        DenseMatrix64F found = new DenseMatrix64F(3,1);
        solver.invert(A_pinv);


        CommonOps.mult(A_pinv,y,found);


        assertTrue(MatrixFeatures.isEquals(x, found,1e-8));

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    @Test
    public void zero() {
        SimpleMatrix a = SimpleMatrix.random(3,3, 0, 1, rand);
        a.zero();


        DenseMatrix64F d = new DenseMatrix64F(3,3);


        EjmlUnitTests.assertEquals(d,a.mat,1e-8);
    }

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    }


    @Test
    public void reshape() {
        SimpleMatrix a = SimpleMatrix.random(3,3, 0, 1, rand);
        DenseMatrix64F b = a.mat.copy();


        a.reshape(2,3);
        b.reshape(2,3, false);


        EjmlUnitTests.assertEquals(b,a.mat,1e-8);
    }

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    Random rand = new Random(0xff);




    @Test
    public void invert_inplace() {
        DenseMatrix64F L = createRandomLowerTriangular();


        DenseMatrix64F L_inv = L.copy();


        TriangularSolver.invertLower(L_inv.data,L.numRows);


        DenseMatrix64F I = new DenseMatrix64F(L.numRows,L.numCols);


        CommonOps.mult(L,L_inv,I);


        assertTrue(MatrixFeatures.isIdentity(I,1e-8));
    }

View Full Code Here

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