Lattices

This library offers an object-oriented abstraction for modelling multidimensional rectangular lattices. It is designed to be scalable in terms of performance and memory usage. Its architecture was inspired by the Colt library, but the current design and its implementation has been brought into the modern Java world.

The library contains of two modules. The io.jenetics.lattices.structure module defines the mapping values of multi-dimensional coordinates onto one-dimensional arrays. This module also contains view- and projection functions. The main module, io.jenetics.lattices contains the multi-dimensional data structures and matrix classes for doing linear algebra.

Note: The main design principle of the library is, that everything is a view. No data is actually copied for every transformation applied. A copy is only performed, if explicitly requested. Mutability is embraced.

Build the library

Lattices requires at least Java 17 to compile and run.

Check out the master branch from GitHub.

$ git clone https://github.com/jenetics/lattices.git <builddir>

Lattices uses Gradle as build system.

io.jenetics.lattices.structure

This module is used for defining the mappings from n-d space to the 1-d space. It doesn't contain any concrete data structures containing n-dimensional points.

// Interface for calculating the array offset for a given 2-d coordinate.
public interface Mapper2d {
    // Return the (array) offset (index) of the given [row, col] point.
    int offset(int row, int col);
    // Return the index point for the given (array) offset.
    Index2d index(int offset);
}

The main entry point for creating mapper functions is the Structure<N>d class, which can be created the following way.

// Defining the extent of the 2-d structure.
final var extent = new Extent2d(100, 400);

// Creating the 2-d structure.
final var structure = new Structure2d(extent);

// The structure layout.
final var layout = structure.layout();

// Creating the array, which holds the values to be stored.
final var values = new double[extent.cells()];

// Set the value 'Math.PI' at the point [20, 30];
values[layout.offset(20, 30)] = Math.PI;

Beside this basic functionality, the View and Projection functions are able to do some basic transformations of the n-d data, without copying actual data.

// Create the range of the view to be created.
final var range = new Range2d(
    // Start index of the range.
    new Index2d(5, 5),
    // Extent of the range.
    new Extend2d(50, 50)
);

// Create the view function with the given range.
final var view = View2d.of(range)

// Create a new structure (view) from the previous one.
final var structure2 = view.apply(structure);

// The value Math.PI is now located at position [15, 25], 
// since we we created a view from the original structure, 
// which started at point [5, 5].    
assert values[structure2.layout().offset(15, 25)] == Math.PI;

The view functions don't change the dimensionality of the structure, in contrast to the projection functions, which reduces the dimensionality by one.

// Create a projection for row 20.
final var projection = Projection2d.row(20);

// Create a one-dimensional structure.
final Structure1d structure3 = projection.apply(structure);

// At index 25, we can access our stored value.
assert values[structure3.layout().offset(30)] == Math.PI;

It is off course possible to create a projection from a structure view.

// Create a projection for row 20.
final var projection = Projection2d.row(15);

// Create a one-dimensional structure.
final Structure1d structure4 = projection.apply(structure2);

// At index 25, we can access our stored value.
assert values[structure4.layout().offset(25)] == Math.PI;

Or you can compose projection and view functions.

// Create a projection for row 20.
final var projection = Projection2d.row(15)
    .compose(View2d.of(range));

// Create a one-dimensional structure.
final Structure1d structure5 = projection.apply(structure);

// At index 25, we can access our stored value.
assert values[structure5.offset(25)] == Math.PI;

io.jenetics.lattices.grid

This module defines multi-dimensional data structures and matrix classes for doing linear algebra.

Grid

Grids are multidimensional views onto one-dimensional arrays. This approach makes the implementation of the matrices in this library very flexible and configurable. It is possible to configure the structure (extent and iteration order) independently of the layout of the underlying array (dense or sparse). How this can be done is shown in the following example.

// Double array, which is created somewhere else.
final var data = new double[10*15];
// Wrap the data into an array. This is just a view, no
// actual data are copied.
final var array = new DenseDoubleArray(data);

// Define the structure (extent) of your 2-d grid.
final var structure = new Structure2d(new Extent2d(10, 15));
// Create the grid with your defined structure and data.
// The grid is a 2-d view onto your one-dimensional double array.
final var grid = new DoubleGrid2d(structure, array);

// Assign each grid element the value 42.
grid.forEach((i, j) -> grid.set(i, j, 42.0));

// The value is written to the underlying double[] array
for (var value : data) {
    assertThat(value).isEqualTo(42.0);
}

Matrix

Matrices are extending grids and share the same design principles. They are also highly configurable and are just multidimensional views onto the underlying one-dimensional arrays. Additionally, they support the usual linear algebra functionality.

// Creating matrix via factory.
final var A = DoubleMatrix2d.DENSE.create(3, 3);
A.assign(new double[][] {
    {1, 2, 3},
    {4, 5, 6},
    {7, 8, 9}
});

// "Direct" creation from element array. Faster and
// doesn't create additional objects.
final var B = DoubleMatrix2d.of(
    new Extent2d(3, 3),
    10, 11, 12
    13, 14, 15,
    16, 17, 18
);
    
// Create a new matrix with the same extent than B.
var C = B.like();

// Do the matrix multiplication C = A*B.
A.mult(B, C);

// Multiply A*B and let C create.
C = A.mult(B, null);
    
// The result of the multiplication.    
// [[84.0, 90.0, 96.0]
//  [201.0, 216.0, 231.0]
//  [318.0, 342.0, 366.0]]

The Algebra and the Blas class contains additional operations.