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//! An implementation of the CSR sparse matrix format. //! //! This is the module-level documentation. See [`CsrMatrix`] for the main documentation of the //! CSC implementation. use crate::cs::{CsLane, CsLaneIter, CsLaneIterMut, CsLaneMut, CsMatrix}; use crate::csc::CscMatrix; use crate::pattern::{SparsityPattern, SparsityPatternFormatError, SparsityPatternIter}; use crate::{SparseEntry, SparseEntryMut, SparseFormatError, SparseFormatErrorKind}; use nalgebra::Scalar; use num_traits::One; use std::slice::{Iter, IterMut}; /// A CSR representation of a sparse matrix. /// /// The Compressed Sparse Row (CSR) format is well-suited as a general-purpose storage format /// for many sparse matrix applications. /// /// # Usage /// /// ```rust /// use nalgebra_sparse::csr::CsrMatrix; /// use nalgebra::{DMatrix, Matrix3x4}; /// use matrixcompare::assert_matrix_eq; /// /// // The sparsity patterns of CSR matrices are immutable. This means that you cannot dynamically /// // change the sparsity pattern of the matrix after it has been constructed. The easiest /// // way to construct a CSR matrix is to first incrementally construct a COO matrix, /// // and then convert it to CSR. /// # use nalgebra_sparse::coo::CooMatrix; /// # let coo = CooMatrix::<f64>::new(3, 3); /// let csr = CsrMatrix::from(&coo); /// /// // Alternatively, a CSR matrix can be constructed directly from raw CSR data. /// // Here, we construct a 3x4 matrix /// let row_offsets = vec![0, 3, 3, 5]; /// let col_indices = vec![0, 1, 3, 1, 2]; /// let values = vec![1.0, 2.0, 3.0, 4.0, 5.0]; /// /// // The dense representation of the CSR data, for comparison /// let dense = Matrix3x4::new(1.0, 2.0, 0.0, 3.0, /// 0.0, 0.0, 0.0, 0.0, /// 0.0, 4.0, 5.0, 0.0); /// /// // The constructor validates the raw CSR data and returns an error if it is invalid. /// let csr = CsrMatrix::try_from_csr_data(3, 4, row_offsets, col_indices, values) /// .expect("CSR data must conform to format specifications"); /// assert_matrix_eq!(csr, dense); /// /// // A third approach is to construct a CSR matrix from a pattern and values. Sometimes this is /// // useful if the sparsity pattern is constructed separately from the values of the matrix. /// let (pattern, values) = csr.into_pattern_and_values(); /// let csr = CsrMatrix::try_from_pattern_and_values(pattern, values) /// .expect("The pattern and values must be compatible"); /// /// // Once we have constructed our matrix, we can use it for arithmetic operations together with /// // other CSR matrices and dense matrices/vectors. /// let x = csr; /// # #[allow(non_snake_case)] /// let xTx = x.transpose() * &x; /// let z = DMatrix::from_fn(4, 8, |i, j| (i as f64) * (j as f64)); /// let w = 3.0 * xTx * z; /// /// // Although the sparsity pattern of a CSR matrix cannot be changed, its values can. /// // Here are two different ways to scale all values by a constant: /// let mut x = x; /// x *= 5.0; /// x.values_mut().iter_mut().for_each(|x_i| *x_i *= 5.0); /// ``` /// /// # Format /// /// An `m x n` sparse matrix with `nnz` non-zeros in CSR format is represented by the /// following three arrays: /// /// - `row_offsets`, an array of integers with length `m + 1`. /// - `col_indices`, an array of integers with length `nnz`. /// - `values`, an array of values with length `nnz`. /// /// The relationship between the arrays is described below. /// /// - Each consecutive pair of entries `row_offsets[i] .. row_offsets[i + 1]` corresponds to an /// offset range in `col_indices` that holds the column indices in row `i`. /// - For an entry represented by the index `idx`, `col_indices[idx]` stores its column index and /// `values[idx]` stores its value. /// /// The following invariants must be upheld and are enforced by the data structure: /// /// - `row_offsets[0] == 0` /// - `row_offsets[m] == nnz` /// - `row_offsets` is monotonically increasing. /// - `0 <= col_indices[idx] < n` for all `idx < nnz`. /// - The column indices associated with each row are monotonically increasing (see below). /// /// The CSR format is a standard sparse matrix format (see [Wikipedia article]). The format /// represents the matrix in a row-by-row fashion. The entries associated with row `i` are /// determined as follows: /// /// ```rust /// # let row_offsets: Vec<usize> = vec![0, 0]; /// # let col_indices: Vec<usize> = vec![]; /// # let values: Vec<i32> = vec![]; /// # let i = 0; /// let range = row_offsets[i] .. row_offsets[i + 1]; /// let row_i_cols = &col_indices[range.clone()]; /// let row_i_vals = &values[range]; /// /// // For each pair (j, v) in (row_i_cols, row_i_vals), we obtain a corresponding entry /// // (i, j, v) in the matrix. /// assert_eq!(row_i_cols.len(), row_i_vals.len()); /// ``` /// /// In the above example, for each row `i`, the column indices `row_i_cols` must appear in /// monotonically increasing order. In other words, they must be *sorted*. This criterion is not /// standard among all sparse matrix libraries, but we enforce this property as it is a crucial /// assumption for both correctness and performance for many algorithms. /// /// Note that the CSR and CSC formats are essentially identical, except that CSC stores the matrix /// column-by-column instead of row-by-row like CSR. /// /// [Wikipedia article]: https://en.wikipedia.org/wiki/Sparse_matrix#Compressed_sparse_row_(CSR,_CRS_or_Yale_format) #[derive(Debug, Clone, PartialEq, Eq)] pub struct CsrMatrix<T> { // Rows are major, cols are minor in the sparsity pattern pub(crate) cs: CsMatrix<T>, } impl<T> CsrMatrix<T> { /// Constructs a CSR representation of the (square) `n x n` identity matrix. #[inline] pub fn identity(n: usize) -> Self where T: Scalar + One, { Self { cs: CsMatrix::identity(n), } } /// Create a zero CSR matrix with no explicitly stored entries. pub fn zeros(nrows: usize, ncols: usize) -> Self { Self { cs: CsMatrix::new(nrows, ncols), } } /// Try to construct a CSR matrix from raw CSR data. /// /// It is assumed that each row contains unique and sorted column indices that are in /// bounds with respect to the number of columns in the matrix. If this is not the case, /// an error is returned to indicate the failure. /// /// An error is returned if the data given does not conform to the CSR storage format. /// See the documentation for [CsrMatrix](struct.CsrMatrix.html) for more information. pub fn try_from_csr_data( num_rows: usize, num_cols: usize, row_offsets: Vec<usize>, col_indices: Vec<usize>, values: Vec<T>, ) -> Result<Self, SparseFormatError> { let pattern = SparsityPattern::try_from_offsets_and_indices( num_rows, num_cols, row_offsets, col_indices, ) .map_err(pattern_format_error_to_csr_error)?; Self::try_from_pattern_and_values(pattern, values) } /// Try to construct a CSR matrix from a sparsity pattern and associated non-zero values. /// /// Returns an error if the number of values does not match the number of minor indices /// in the pattern. pub fn try_from_pattern_and_values( pattern: SparsityPattern, values: Vec<T>, ) -> Result<Self, SparseFormatError> { if pattern.nnz() == values.len() { Ok(Self { cs: CsMatrix::from_pattern_and_values(pattern, values), }) } else { Err(SparseFormatError::from_kind_and_msg( SparseFormatErrorKind::InvalidStructure, "Number of values and column indices must be the same", )) } } /// The number of rows in the matrix. #[inline] pub fn nrows(&self) -> usize { self.cs.pattern().major_dim() } /// The number of columns in the matrix. #[inline] pub fn ncols(&self) -> usize { self.cs.pattern().minor_dim() } /// The number of non-zeros in the matrix. /// /// Note that this corresponds to the number of explicitly stored entries, *not* the actual /// number of algebraically zero entries in the matrix. Explicitly stored entries can still /// be zero. Corresponds to the number of entries in the sparsity pattern. #[inline] pub fn nnz(&self) -> usize { self.cs.pattern().nnz() } /// The row offsets defining part of the CSR format. #[inline] pub fn row_offsets(&self) -> &[usize] { let (offsets, _, _) = self.cs.cs_data(); offsets } /// The column indices defining part of the CSR format. #[inline] pub fn col_indices(&self) -> &[usize] { let (_, indices, _) = self.cs.cs_data(); indices } /// The non-zero values defining part of the CSR format. #[inline] pub fn values(&self) -> &[T] { self.cs.values() } /// Mutable access to the non-zero values. #[inline] pub fn values_mut(&mut self) -> &mut [T] { self.cs.values_mut() } /// An iterator over non-zero triplets (i, j, v). /// /// The iteration happens in row-major fashion, meaning that i increases monotonically, /// and j increases monotonically within each row. /// /// Examples /// -------- /// ``` /// # use nalgebra_sparse::csr::CsrMatrix; /// let row_offsets = vec![0, 2, 3, 4]; /// let col_indices = vec![0, 2, 1, 0]; /// let values = vec![1, 2, 3, 4]; /// let mut csr = CsrMatrix::try_from_csr_data(3, 4, row_offsets, col_indices, values) /// .unwrap(); /// /// let triplets: Vec<_> = csr.triplet_iter().map(|(i, j, v)| (i, j, *v)).collect(); /// assert_eq!(triplets, vec![(0, 0, 1), (0, 2, 2), (1, 1, 3), (2, 0, 4)]); /// ``` pub fn triplet_iter(&self) -> CsrTripletIter<T> { CsrTripletIter { pattern_iter: self.pattern().entries(), values_iter: self.values().iter(), } } /// A mutable iterator over non-zero triplets (i, j, v). /// /// Iteration happens in the same order as for [triplet_iter](#method.triplet_iter). /// /// Examples /// -------- /// ``` /// # use nalgebra_sparse::csr::CsrMatrix; /// # let row_offsets = vec![0, 2, 3, 4]; /// # let col_indices = vec![0, 2, 1, 0]; /// # let values = vec![1, 2, 3, 4]; /// // Using the same data as in the `triplet_iter` example /// let mut csr = CsrMatrix::try_from_csr_data(3, 4, row_offsets, col_indices, values) /// .unwrap(); /// /// // Zero out lower-triangular terms /// csr.triplet_iter_mut() /// .filter(|(i, j, _)| j < i) /// .for_each(|(_, _, v)| *v = 0); /// /// let triplets: Vec<_> = csr.triplet_iter().map(|(i, j, v)| (i, j, *v)).collect(); /// assert_eq!(triplets, vec![(0, 0, 1), (0, 2, 2), (1, 1, 3), (2, 0, 0)]); /// ``` pub fn triplet_iter_mut(&mut self) -> CsrTripletIterMut<T> { let (pattern, values) = self.cs.pattern_and_values_mut(); CsrTripletIterMut { pattern_iter: pattern.entries(), values_mut_iter: values.iter_mut(), } } /// Return the row at the given row index. /// /// Panics /// ------ /// Panics if row index is out of bounds. #[inline] pub fn row(&self, index: usize) -> CsrRow<T> { self.get_row(index).expect("Row index must be in bounds") } /// Mutable row access for the given row index. /// /// Panics /// ------ /// Panics if row index is out of bounds. #[inline] pub fn row_mut(&mut self, index: usize) -> CsrRowMut<T> { self.get_row_mut(index) .expect("Row index must be in bounds") } /// Return the row at the given row index, or `None` if out of bounds. #[inline] pub fn get_row(&self, index: usize) -> Option<CsrRow<T>> { self.cs.get_lane(index).map(|lane| CsrRow { lane }) } /// Mutable row access for the given row index, or `None` if out of bounds. #[inline] pub fn get_row_mut(&mut self, index: usize) -> Option<CsrRowMut<T>> { self.cs.get_lane_mut(index).map(|lane| CsrRowMut { lane }) } /// An iterator over rows in the matrix. pub fn row_iter(&self) -> CsrRowIter<T> { CsrRowIter { lane_iter: CsLaneIter::new(self.pattern(), self.values()), } } /// A mutable iterator over rows in the matrix. pub fn row_iter_mut(&mut self) -> CsrRowIterMut<T> { let (pattern, values) = self.cs.pattern_and_values_mut(); CsrRowIterMut { lane_iter: CsLaneIterMut::new(pattern, values), } } /// Disassembles the CSR matrix into its underlying offset, index and value arrays. /// /// If the matrix contains the sole reference to the sparsity pattern, /// then the data is returned as-is. Otherwise, the sparsity pattern is cloned. /// /// Examples /// -------- /// /// ``` /// # use nalgebra_sparse::csr::CsrMatrix; /// let row_offsets = vec![0, 2, 3, 4]; /// let col_indices = vec![0, 2, 1, 0]; /// let values = vec![1, 2, 3, 4]; /// let mut csr = CsrMatrix::try_from_csr_data( /// 3, /// 4, /// row_offsets.clone(), /// col_indices.clone(), /// values.clone()) /// .unwrap(); /// let (row_offsets2, col_indices2, values2) = csr.disassemble(); /// assert_eq!(row_offsets2, row_offsets); /// assert_eq!(col_indices2, col_indices); /// assert_eq!(values2, values); /// ``` pub fn disassemble(self) -> (Vec<usize>, Vec<usize>, Vec<T>) { self.cs.disassemble() } /// Returns the sparsity pattern and values associated with this matrix. pub fn into_pattern_and_values(self) -> (SparsityPattern, Vec<T>) { self.cs.into_pattern_and_values() } /// Returns a reference to the sparsity pattern and a mutable reference to the values. #[inline] pub fn pattern_and_values_mut(&mut self) -> (&SparsityPattern, &mut [T]) { self.cs.pattern_and_values_mut() } /// Returns a reference to the underlying sparsity pattern. pub fn pattern(&self) -> &SparsityPattern { self.cs.pattern() } /// Reinterprets the CSR matrix as its transpose represented by a CSC matrix. /// /// This operation does not touch the CSR data, and is effectively a no-op. pub fn transpose_as_csc(self) -> CscMatrix<T> { let (pattern, values) = self.cs.take_pattern_and_values(); CscMatrix::try_from_pattern_and_values(pattern, values).unwrap() } /// Returns an entry for the given row/col indices, or `None` if the indices are out of bounds. /// /// Each call to this function incurs the cost of a binary search among the explicitly /// stored column entries for the given row. pub fn get_entry(&self, row_index: usize, col_index: usize) -> Option<SparseEntry<T>> { self.cs.get_entry(row_index, col_index) } /// Returns a mutable entry for the given row/col indices, or `None` if the indices are out /// of bounds. /// /// Each call to this function incurs the cost of a binary search among the explicitly /// stored column entries for the given row. pub fn get_entry_mut( &mut self, row_index: usize, col_index: usize, ) -> Option<SparseEntryMut<T>> { self.cs.get_entry_mut(row_index, col_index) } /// Returns an entry for the given row/col indices. /// /// Same as `get_entry`, except that it directly panics upon encountering row/col indices /// out of bounds. /// /// Panics /// ------ /// Panics if `row_index` or `col_index` is out of bounds. pub fn index_entry(&self, row_index: usize, col_index: usize) -> SparseEntry<T> { self.get_entry(row_index, col_index) .expect("Out of bounds matrix indices encountered") } /// Returns a mutable entry for the given row/col indices. /// /// Same as `get_entry_mut`, except that it directly panics upon encountering row/col indices /// out of bounds. /// /// Panics /// ------ /// Panics if `row_index` or `col_index` is out of bounds. pub fn index_entry_mut(&mut self, row_index: usize, col_index: usize) -> SparseEntryMut<T> { self.get_entry_mut(row_index, col_index) .expect("Out of bounds matrix indices encountered") } /// Returns a triplet of slices `(row_offsets, col_indices, values)` that make up the CSR data. pub fn csr_data(&self) -> (&[usize], &[usize], &[T]) { self.cs.cs_data() } /// Returns a triplet of slices `(row_offsets, col_indices, values)` that make up the CSR data, /// where the `values` array is mutable. pub fn csr_data_mut(&mut self) -> (&[usize], &[usize], &mut [T]) { self.cs.cs_data_mut() } /// Creates a sparse matrix that contains only the explicit entries decided by the /// given predicate. pub fn filter<P>(&self, predicate: P) -> Self where T: Clone, P: Fn(usize, usize, &T) -> bool, { Self { cs: self .cs .filter(|row_idx, col_idx, v| predicate(row_idx, col_idx, v)), } } /// Returns a new matrix representing the upper triangular part of this matrix. /// /// The result includes the diagonal of the matrix. pub fn upper_triangle(&self) -> Self where T: Clone, { self.filter(|i, j, _| i <= j) } /// Returns a new matrix representing the lower triangular part of this matrix. /// /// The result includes the diagonal of the matrix. pub fn lower_triangle(&self) -> Self where T: Clone, { self.filter(|i, j, _| i >= j) } /// Returns the diagonal of the matrix as a sparse matrix. pub fn diagonal_as_csr(&self) -> Self where T: Clone, { Self { cs: self.cs.diagonal_as_matrix(), } } /// Compute the transpose of the matrix. pub fn transpose(&self) -> CsrMatrix<T> where T: Scalar, { CscMatrix::from(self).transpose_as_csr() } } /// Convert pattern format errors into more meaningful CSR-specific errors. /// /// This ensures that the terminology is consistent: we are talking about rows and columns, /// not lanes, major and minor dimensions. fn pattern_format_error_to_csr_error(err: SparsityPatternFormatError) -> SparseFormatError { use SparseFormatError as E; use SparseFormatErrorKind as K; use SparsityPatternFormatError::DuplicateEntry as PatternDuplicateEntry; use SparsityPatternFormatError::*; match err { InvalidOffsetArrayLength => E::from_kind_and_msg( K::InvalidStructure, "Length of row offset array is not equal to nrows + 1.", ), InvalidOffsetFirstLast => E::from_kind_and_msg( K::InvalidStructure, "First or last row offset is inconsistent with format specification.", ), NonmonotonicOffsets => E::from_kind_and_msg( K::InvalidStructure, "Row offsets are not monotonically increasing.", ), NonmonotonicMinorIndices => E::from_kind_and_msg( K::InvalidStructure, "Column indices are not monotonically increasing (sorted) within each row.", ), MinorIndexOutOfBounds => { E::from_kind_and_msg(K::IndexOutOfBounds, "Column indices are out of bounds.") } PatternDuplicateEntry => { E::from_kind_and_msg(K::DuplicateEntry, "Matrix data contains duplicate entries.") } } } /// Iterator type for iterating over triplets in a CSR matrix. #[derive(Debug)] pub struct CsrTripletIter<'a, T> { pattern_iter: SparsityPatternIter<'a>, values_iter: Iter<'a, T>, } impl<'a, T: Clone> CsrTripletIter<'a, T> { /// Adapts the triplet iterator to return owned values. /// /// The triplet iterator returns references to the values. This method adapts the iterator /// so that the values are cloned. #[inline] pub fn cloned_values(self) -> impl 'a + Iterator<Item = (usize, usize, T)> { self.map(|(i, j, v)| (i, j, v.clone())) } } impl<'a, T> Iterator for CsrTripletIter<'a, T> { type Item = (usize, usize, &'a T); fn next(&mut self) -> Option<Self::Item> { let next_entry = self.pattern_iter.next(); let next_value = self.values_iter.next(); match (next_entry, next_value) { (Some((i, j)), Some(v)) => Some((i, j, v)), _ => None, } } } /// Iterator type for mutably iterating over triplets in a CSR matrix. #[derive(Debug)] pub struct CsrTripletIterMut<'a, T> { pattern_iter: SparsityPatternIter<'a>, values_mut_iter: IterMut<'a, T>, } impl<'a, T> Iterator for CsrTripletIterMut<'a, T> { type Item = (usize, usize, &'a mut T); #[inline] fn next(&mut self) -> Option<Self::Item> { let next_entry = self.pattern_iter.next(); let next_value = self.values_mut_iter.next(); match (next_entry, next_value) { (Some((i, j)), Some(v)) => Some((i, j, v)), _ => None, } } } /// An immutable representation of a row in a CSR matrix. #[derive(Debug, Clone, PartialEq, Eq)] pub struct CsrRow<'a, T> { lane: CsLane<'a, T>, } /// A mutable representation of a row in a CSR matrix. /// /// Note that only explicitly stored entries can be mutated. The sparsity pattern belonging /// to the row cannot be modified. #[derive(Debug, PartialEq, Eq)] pub struct CsrRowMut<'a, T> { lane: CsLaneMut<'a, T>, } /// Implement the methods common to both CsrRow and CsrRowMut macro_rules! impl_csr_row_common_methods { ($name:ty) => { impl<'a, T> $name { /// The number of global columns in the row. #[inline] pub fn ncols(&self) -> usize { self.lane.minor_dim() } /// The number of non-zeros in this row. #[inline] pub fn nnz(&self) -> usize { self.lane.nnz() } /// The column indices corresponding to explicitly stored entries in this row. #[inline] pub fn col_indices(&self) -> &[usize] { self.lane.minor_indices() } /// The values corresponding to explicitly stored entries in this row. #[inline] pub fn values(&self) -> &[T] { self.lane.values() } /// Returns an entry for the given global column index. /// /// Each call to this function incurs the cost of a binary search among the explicitly /// stored column entries. #[inline] pub fn get_entry(&self, global_col_index: usize) -> Option<SparseEntry<T>> { self.lane.get_entry(global_col_index) } } }; } impl_csr_row_common_methods!(CsrRow<'a, T>); impl_csr_row_common_methods!(CsrRowMut<'a, T>); impl<'a, T> CsrRowMut<'a, T> { /// Mutable access to the values corresponding to explicitly stored entries in this row. #[inline] pub fn values_mut(&mut self) -> &mut [T] { self.lane.values_mut() } /// Provides simultaneous access to column indices and mutable values corresponding to the /// explicitly stored entries in this row. /// /// This method primarily facilitates low-level access for methods that process data stored /// in CSR format directly. #[inline] pub fn cols_and_values_mut(&mut self) -> (&[usize], &mut [T]) { self.lane.indices_and_values_mut() } /// Returns a mutable entry for the given global column index. #[inline] pub fn get_entry_mut(&mut self, global_col_index: usize) -> Option<SparseEntryMut<T>> { self.lane.get_entry_mut(global_col_index) } } /// Row iterator for [CsrMatrix](struct.CsrMatrix.html). pub struct CsrRowIter<'a, T> { lane_iter: CsLaneIter<'a, T>, } impl<'a, T> Iterator for CsrRowIter<'a, T> { type Item = CsrRow<'a, T>; fn next(&mut self) -> Option<Self::Item> { self.lane_iter.next().map(|lane| CsrRow { lane }) } } /// Mutable row iterator for [CsrMatrix](struct.CsrMatrix.html). pub struct CsrRowIterMut<'a, T> { lane_iter: CsLaneIterMut<'a, T>, } impl<'a, T> Iterator for CsrRowIterMut<'a, T> where T: 'a, { type Item = CsrRowMut<'a, T>; fn next(&mut self) -> Option<Self::Item> { self.lane_iter.next().map(|lane| CsrRowMut { lane }) } }