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