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nalgebra-sparse/src/lib.rs
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//! Sparse matrices and algorithms for nalgebra.
//! Sparse matrices and algorithms for [nalgebra](https://www.nalgebra.org).
//!
//! TODO: Docs
//! This crate extends `nalgebra` with sparse matrix formats and operations on sparse matrices.
//!
//! ## Goals
//! The long-term goals for this crate are listed below.
//!
//! ### Planned functionality
//! - Provide proven sparse matrix formats in an easy-to-use and idiomatic Rust API that
//! naturally integrates with `nalgebra`.
//! - Provide additional expert-level APIs for fine-grained control over operations.
//! - Integrate well with external sparse matrix libraries.
//! - Provide native Rust high-performance routines, including parallel matrix operations.
//!
//! Below we list desired functionality. This further needs to be refined into what is needed
//! for an initial contribution, and what can be added in future contributions.
//! ## Highlighted current features
//!
//! - Sparsity pattern type. Functionality:
//! - [x] Access to offsets, indices as slices.
//! - [x] Return number of nnz
//! - [x] Access a given lane as a slice of minor indices
//! - [x] Construct from valid offset + index data
//! - [ ] Construct from unsorted (but otherwise valid) offset + index data
//! - [x] Iterate over entries (i, j) in the pattern
//! - [x] "Disassemble" the sparsity pattern into the raw index data arrays.
//! - CSR matrix type. Functionality:
//! - [x] Access to CSR data as slices.
//! - [x] Return number of nnz
//! - [x] Access a given row, which gives convenient access to the data associated
//! with a particular row
//! - [x] Construct from valid CSR data
//! - [ ] Construct from unsorted CSR data
//! - [x] Iterate over entries (i, j, v) in the matrix (+mutable).
//! - [x] Iterate over rows in the matrix (+ mutable).
//! - [x] "Disassemble" the CSR matrix into the raw CSR data arrays.
//! - [CSR](csr::CsrMatrix), [CSC](csc::CscMatrix) and [COO](coo::CooMatrix) formats, and
//! [conversions](`convert`) between them.
//! - Common arithmetic operations are implemented. See the [`ops`] module.
//! - Sparsity patterns in CSR and CSC matrices are explicitly represented by the
//! [SparsityPattern](pattern::SparsityPattern) type, which encodes the invariants of the
//! associated index data structures.
//! - [proptest strategies](`proptest`) for sparse matrices when the feature
//! `proptest-support` is enabled.
//! - [matrixcompare support](https://crates.io/crates/matrixcompare) for effortless
//! (approximate) comparison of matrices in test code (requires the `compare` feature).
//!
//! - CSC matrix type. Functionality:
//! - [x] Access to CSC data as slices.
//! - [x] Return number of nnz
//! - [x] Access a given column, which gives convenient access to the data associated
//! with a particular column
//! - [x] Construct from valid CSC data
//! - [ ] Construct from unsorted CSC data
//! - [x] Iterate over entries (i, j, v) in the matrix (+mutable).
//! - [x] Iterate over rows in the matrix (+ mutable).
//! - [x] "Disassemble" the CSC matrix into the raw CSC data arrays.
//! - COO matrix type. Functionality:
//! - [x] Construct new "empty" COO matrix
//! - [x] Construct from triplet arrays.
//! - [x] Push new triplets to the matrix.
//! - [x] Iterate over triplets.
//! - [x] "Disassemble" the COO matrix into its underlying triplet arrays.
//! - Format conversion:
//! - [x] COO -> Dense
//! - [x] CSR -> Dense
//! - [x] CSC -> Dense
//! - [x] COO -> CSR
//! - [x] COO -> CSC
//! - [x] CSR -> CSC
//! - [x] CSC -> CSR
//! - [x] CSR -> COO
//! - [x] CSC -> COO
//! - [x] Dense -> COO
//! - [x] Dense -> CSR
//! - [x] Dense -> CSC
//! - Arithmetic. In general arithmetic is only implemented between instances of the same format,
//! or between dense and instances of a given format. For example, we do not implement
//! CSR * CSC, only CSR * CSR and CSC * CSC.
//! - CSR:
//! - [ ] Dense = CSR * Dense (the other way around is not particularly useful)
//! - [ ] CSR = CSR * CSR
//! - [ ] CSR = CSR +- CSR
//! - [ ] CSR +=/-= CSR
//! - COO:
//! - [ ] Dense = COO * Dense (sometimes useful for very sparse matrices)
//! - CSC:
//! - Same as CSR
//! - Cholesky factorization (port existing factorization from nalgebra's sparse module)
//! ## Current state
//!
//! The library is in an early, but usable state. The API has been designed to be extensible,
//! but breaking changes will be necessary to implement several planned features. While it is
//! backed by an extensive test suite, it has yet to be thoroughly battle-tested in real
//! applications. Moreover, the focus so far has been on correctness and API design, with little
//! focus on performance. Future improvements will include incremental performance enhancements.
//!
//! Current limitations:
//!
//! - Limited or no availability of sparse system solvers.
//! - Limited support for complex numbers. Currently only arithmetic operations that do not
//! rely on particular properties of complex numbers, such as e.g. conjugation, are
//! supported.
//! - No integration with external libraries.
//!
//! # Usage
//!
//! Add the following to your `Cargo.toml` file:
//!
//! ```toml
//! [dependencies]
//! nalgebra_sparse = "0.1"
//! ```
//!
//! # Supported matrix formats
//!
//! | Format | Notes |
//! | ------------------------|--------------------------------------------- |
//! | [COO](`coo::CooMatrix`) | Well-suited for matrix construction. <br /> Ill-suited for algebraic operations. |
//! | [CSR](`csr::CsrMatrix`) | Immutable sparsity pattern, suitable for algebraic operations. <br /> Fast row access. |
//! | [CSC](`csr::CscMatrix`) | Immutable sparsity pattern, suitable for algebraic operations. <br /> Fast column access. |
//!
//! What format is best to use depends on the application. The most common use case for sparse
//! matrices in science is the solution of sparse linear systems. Here we can differentiate between
//! two common cases:
//!
//! - Direct solvers. Typically, direct solvers take their input in CSR or CSC format.
//! - Iterative solvers. Many iterative solvers require only matrix-vector products,
//! for which the CSR or CSC formats are suitable.
//!
//! The [COO](coo::CooMatrix) format is primarily intended for matrix construction.
//! A common pattern is to use COO for construction, before converting to CSR or CSC for use
//! in a direct solver or for computing matrix-vector products in an iterative solver.
//! Some high-performance applications might also directly manipulate the CSR and/or CSC
//! formats.
//!
//! # Example: COO -> CSR -> matrix-vector product
//!
//! ```rust
//! use nalgebra_sparse::{coo::CooMatrix, csr::CsrMatrix};
//! use nalgebra::{DMatrix, DVector};
//! use matrixcompare::assert_matrix_eq;
//!
//! // The dense representation of the matrix
//! let dense = DMatrix::from_row_slice(3, 3,
//! &[1.0, 0.0, 3.0,
//! 2.0, 0.0, 1.3,
//! 0.0, 0.0, 4.1]);
//!
//! // Build the equivalent COO representation. We only add the non-zero values
//! let mut coo = CooMatrix::new(3, 3);
//! // We can add elements in any order. For clarity, we do so in row-major order here.
//! coo.push(0, 0, 1.0);
//! coo.push(0, 2, 3.0);
//! coo.push(1, 0, 2.0);
//! coo.push(1, 2, 1.3);
//! coo.push(2, 2, 4.1);
//!
//! // The simplest way to construct a CSR matrix is to first construct a COO matrix, and
//! // then convert it to CSR. The `From` trait is implemented for conversions between different
//! // sparse matrix types.
//! // Alternatively, we can construct a matrix directly from the CSR data.
//! // See the docs for CsrMatrix for how to do that.
//! let csr = CsrMatrix::from(&coo);
//!
//! // Let's check that the CSR matrix and the dense matrix represent the same matrix.
//! // We can use macros from the `matrixcompare` crate to easily do this, despite the fact that
//! // we're comparing across two different matrix formats. Note that these macros are only really
//! // appropriate for writing tests, however.
//! assert_matrix_eq!(csr, dense);
//!
//! let x = DVector::from_column_slice(&[1.3, -4.0, 3.5]);
//!
//! // Compute the matrix-vector product y = A * x. We don't need to specify the type here,
//! // but let's just do it to make sure we get what we expect
//! let y: DVector<_> = &csr * &x;
//!
//! // Verify the result with a small element-wise absolute tolerance
//! let y_expected = DVector::from_column_slice(&[11.8, 7.15, 14.35]);
//! assert_matrix_eq!(y, y_expected, comp = abs, tol = 1e-9);
//!
//! // The above expression is simple, and gives easy to read code, but if we're doing this in a
//! // loop, we'll have to keep allocating new vectors. If we determine that this is a bottleneck,
//! // then we can resort to the lower level APIs for more control over the operations
//! {
//! use nalgebra_sparse::ops::{Op, serial::spmm_csr_dense};
//! let mut y = y;
//! // Compute y <- 0.0 * y + 1.0 * csr * dense. We store the result directly in `y`, without
//! // any immediate allocations
//! spmm_csr_dense(0.0, &mut y, 1.0, Op::NoOp(&csr), Op::NoOp(&x));
//! assert_matrix_eq!(y, y_expected, comp = abs, tol = 1e-9);
//! }
//! ```
//!
//! TODO: Write docs on the following:
//!