Specialised matrices

Vectorz supports a wide range of specialised matrix classes.

The reason for this is simple: specialised matrix classes provide much more efficient operations in certain situations. For example, multiplying a large vector by a diagonal matrix can easily be 100x faster using the specialised DiagonalMatrix implementation.

When to use

Specialised matrices have both advantages and disadvantages: whether you use them or not is a judgement call. If in doubt, you should benchmark for your specific use case.

Pros:

• Use much less storage space: e.g. a diagonal n*n matrix requires only n elements of storage
• Provide fast, optimised operations

Cons:

• Elements are constrained, so specialised matrices are usually not fully mutable. Use the isFullyMutable method to check this property for a given matrix instance.
• Slower for arbitrary operations not suited to this matrix type

Classes available

Here are some of the specialised matrix classes available in Vectorz:

• AMatrix : base class for all matrix types
• Matrix : general purpose matrix, backed by a fully packed double[] array
• DiagonalMatrix : a square diagonal matrix. all values not on the main diagonal are constrained to 0.0
• StridedMatrix : a matrix backed by a double[] array but supporting strided indexing and offsets into the array. Very useful for lightweight views / submatrices of a regular Matrix.
• ZeroMatrix : an immutable matrix filled with zeros. Requires no storage for elements, and supports very fast operations.
• IdentityMatrix : an immutable identity matrix. Requires no storage for elements. Requires no storage for elements, and supports very fast operations.
• ScalarMatrix : an efficient matrix which represents scaling by a single scalar value.
• PermutationMatrix : a square matrix that permutes another matrix. Has a single 1.0 in each row and column. Can be used to efficiently permute vectors or other matrices.
• RowMatrix : an efficient lightweight matrix with a single row.
• ColumnMatrix : an efficient lightweight matrix with a single column.