Examples of no.uib.cipr.matrix.Matrix

no.uib.cipr.matrix.Matrix
Basic matrix interface. It holds doubles in a rectangular 2D array, and it is used alongside Vector in numerical computations. Implementing classes decides on the actual storage.
Basic operations

Use numRows and numColumns to get the basic size of a matrix. get(int,int) gets an element, and there are corresponding set(int,int,double) and add(int,int,double) methods as well. Note that matrix indices are zero-based (typical for Java and C). This means that the row-indices range from 0 to numRows-1, likewise for the columns. It is legal to have numRows or numColumns equal zero.

Other basic operations are zero which zeros all the entries of the matrix, which can be cheaper than either zeroing the matrix manually, or creating a new matrix, and the operation copy which creates a deep copy of the matrix. This copy has separate storage, but starts with the same contents as the current matrix.

Iterators

The matrix interface extends Iterable, and the iterator returns a MatrixEntry which contains current index and entry value. Note that the iterator may skip non-zero entries. Using an iterator, many simple and efficient algorithms can be created. The iterator also permits changing values in the matrix, however only non-zero entries can be changed.

Basic linear algebra

A large selection of basic linear algebra operations are available. To ensure high efficiency, little or no internal memory allocation is done, and the user is required to supply the output arguments.

The operations available include:

Additions

Matrices can be added to each other, even if their underlying matrix structures are different.

Multiplications

A matrix can be multiplied with vectors and other matrices. For increased efficiency, a multiplication can be combined with addition and scaling, and transpose matrix multiplications are also available.

Rank-updates

A matrix can be efficiently updated using low-rank updates. The updates can be contained in both matrices or vectors.

Transpositions

In-place transpositions of square matrices is supported, and the transpose of a matrix can be stored in another matrix of compatible size (possibly non-rectangular)

Solvers

Many dense and structured sparse matrices have fast, direct solvers, and can be used to solve linear systems without creating a factorization. These solvers are typically backed by subroutines in LAPACK

        super.setUp();
    }


    public void testTriDiagonal() {
        int n = Utilities.getInt(1, 10);
        Matrix A = new DenseMatrix(n, n);
        Vector x = new DenseVector(n);


        for (int i = 0; i < n; ++i) {
            A.set(i, i, 2);
            x.set(i, 1);
        }
        for (int i = 0; i < n - 1; ++i) {
            A.set(i, i + 1, -1);
            A.set(i + 1, i, -1);
        }


        testFactorization(A, x);
    }

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        testFactorization(A, x);
    }


    public void testPentaDiagonal() {
        int n = Utilities.getInt(1, 10);
        Matrix A = new DenseMatrix(n, n);
        Vector x = new DenseVector(n);


        for (int i = 0; i < n; ++i) {
            A.set(i, i, 4);
            x.set(i, 1);
        }
        for (int i = 0; i < n - 1; ++i) {
            A.set(i, i + 1, -1);
            A.set(i + 1, i, -1);
        }
        for (int i = 0; i < n - 2; ++i) {
            A.set(i, i + 2, -1);
            A.set(i + 2, i, -1);
        }


        testFactorization(A, x);
    }

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    MatrixInfo mi = new MatrixInfo(false, MatrixInfo.MatrixField.Real, MatrixInfo.MatrixSymmetry.General);
    writer.printMatrixInfo(mi);
    writer.printMatrixSize(new MatrixSize(mat.numRows(), mat.numColumns(), mat.numColumns() * mat.numRows()), mi);
    writer.printArray(mat.getData());
    writer.close();
    Matrix newMat = new DenseMatrix(new MatrixVectorReader(new FileReader(matrixFile)));


    MatrixTestAbstract.assertEquals(mat, newMat);
  }

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    /**
     * We can't zero, so we do without
     */
    @Override
    public void testCopy() {
        Matrix Ac = A.copy();
        assertEquals(Ad, Ac);
    }

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        c.factor(L.copy());


    assert I != null;
        c.solve(I);


        Matrix J = I.mult(L, new DenseMatrix(n, n));
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j)
                if (i != j)
                    assertEquals(J.get(i, j), 0, 1e-10);
                else
                    assertEquals(J.get(i, j), 1, 1e-10);
    }

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        DenseCholesky c = new DenseCholesky(n, true);
        c.factor(U.copy());


        c.solve(I);


        Matrix J = I.mult(U, new DenseMatrix(n, n));
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j)
                if (i != j)
                    assertEquals(J.get(i, j), 0, 1e-10);
                else
                    assertEquals(J.get(i, j), 1, 1e-10);
    }

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        PackCholesky c = new PackCholesky(n, false);
        c.factor(L.copy());


        c.solve(I);


        Matrix J = I.mult(L, new DenseMatrix(n, n));
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j)
                if (i != j)
                    assertEquals(J.get(i, j), 0, 1e-10);
                else
                    assertEquals(J.get(i, j), 1, 1e-10);
    }

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        PackCholesky c = new PackCholesky(n, true);
        c.factor(U.copy());


        c.solve(I);


        Matrix J = I.mult(U, new DenseMatrix(n, n));
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j)
                if (i != j)
                    assertEquals(J.get(i, j), 0, 1e-10);
                else
                    assertEquals(J.get(i, j), 1, 1e-10);
    }

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    Stopwatch watch = Stopwatch.createUnstarted();
    DenseMatrix dense = new DenseMatrix(1000, 1000);
    int[][] nz = Utilities.getRowPattern(dense.numRows(), dense.numColumns(), 100);
    Utilities.rowPopulate(dense, nz);
    log.info("created matrices");
    Matrix sparse = new LinkedSparseMatrix(dense.numRows(), dense.numColumns());
    sparse.set(dense);


    for (Matrix m : Lists.newArrayList(dense, sparse)) {
      log.info("starting " + m.getClass());
      Matrix t = new DenseMatrix(m);
      t.transpose();
      Matrix o = new DenseMatrix(dense.numRows(), dense.numColumns());
      log.info("warming up " + m.getClass() + " " + o.getClass());
      for (int i = 0; i < 10; i++)
        m.mult(t, o);
      log.info("starting " + m.getClass() + " " + o.getClass());
      watch.start();
      for (int i = 0; i < 100; i++)
        m.mult(t, o);
      watch.stop();
      log.info(m.getClass() + " " + o.getClass() + " " + watch);
    }
  }

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    Stopwatch watch = Stopwatch.createUnstarted();
    DenseMatrix dense = new DenseMatrix(1000, 1000);
    int[][] nz = Utilities.getRowPattern(dense.numRows(), dense.numColumns(), 100);
    Utilities.rowPopulate(dense, nz);
    log.info("created matrices");
    Matrix sparse = new LinkedSparseMatrix(dense.numRows(), dense.numColumns());
    sparse.set(dense);


    for (Matrix m : Lists.newArrayList(dense, sparse)) {
      log.info("starting " + m.getClass());
      Matrix t = new DenseMatrix(m);
      Matrix o = new DenseMatrix(dense.numRows(), dense.numColumns());
      log.info("warming up " + m.getClass() + " " + o.getClass());
      for (int i = 0; i < 10; i++)
        m.transAmult(t, o);
      log.info("starting " + m.getClass() + " " + o.getClass());
      watch.start();
      for (int i = 0; i < 100; i++)
        m.transAmult(t, o);
      watch.stop();
      log.info(m.getClass() + " " + o.getClass() + " " + watch);
    }
  }

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no.uib.cipr.matrix.BandCholeskyTest

no.uib.cipr.matrix.BandLUTest

no.uib.cipr.matrix.DenseCholeskyTest

no.uib.cipr.matrix.DenseLUTest

no.uib.cipr.matrix.distributed.DistIterativeSolverTest$ColumnDistIterativeSolver

no.uib.cipr.matrix.distributed.DistIterativeSolverTest$DistIterativeSolver

no.uib.cipr.matrix.distributed.DistIterativeSolverTest$RowDistIterativeSolver

no.uib.cipr.matrix.distributed.TwoLevelPreconditioner

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Examples of no.uib.cipr.matrix.Matrix

Basic operations

Iterators

Basic linear algebra

Related Classes of no.uib.cipr.matrix.Matrix