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use std::ops::Deref; use indexing::SpIndex; use array_backend::Array2; pub use self::csmat::{CompressedStorage}; /// Compressed matrix in the CSR or CSC format, with sorted indices. /// /// This sparse matrix format is the preferred format for performing arithmetic /// operations. Constructing a sparse matrix directly in this format requires /// a deep knowledge of its internals. For easier matrix construction, the /// [triplet format](struct.TripletMatBase) is preferred. /// /// The `CsMatBase` type is parameterized by the scalar type `N`, the indexing /// type `I`, the indexing storage backend types `IptrStorage` and `IndStorage`, /// and the value storage backend type `DataStorage`. Convenient aliases are /// available to specify frequent variants: [`CsMat`] refers to a sparse matrix /// that owns its data, similar to `Vec<T>`; [`CsMatView`] refers to a sparse matrix /// that borrows its data, similar to `& [T]`; and [`CsMatViewMut`] refers to a sparse /// matrix borrowing its data, with a mutable borrow for its values. No mutable /// borrow is allowed for the structure of the matrix, allowing the invariants /// to be preserved. /// /// Additionaly, the type aliases [`CsMatI`], [`CsMatViewI`] and /// [`CsMatViewMutI`] can be used to choose an index type different from the /// default `usize`. /// /// [`CsMat`]: type.CsMat.html /// [`CsMatView`]: type.CsMatView.html /// [`CsMatViewMut`]: type.CsMatViewMut.html /// [`CsMatI`]: type.CsMatI.html /// [`CsMatViewI`]: type.CsMatViewI.html /// [`CsMatViewMutI`]: type.CsMatViewMutI.html /// /// ## Storage format /// /// In the compressed storage format, the non-zero values of a sparse matrix /// are stored as the row and column location of the non-zero values, with /// a compression along the rows (CSR) or columns (CSC) indices. The dimension /// along which the storage is compressed is referred to as the *outer dimension*, /// the other dimension is called the *inner dimension*. For clarity, the /// remaining explanation will assume a CSR matrix, but the information stands /// for CSC matrices as well. /// /// ### Indptr /// /// An index pointer array `indptr` of size corresponding to the number of rows /// stores the cumulative sum of non-zero elements for each row. For instance, /// the number of non-zero elements of the i-th row can be obtained by computing /// `indptr[i + 1] - indptr[i]`. The total number of non-zero elements is thus /// `nnz = indptr[nb_rows + 1]`. This index pointer array can then be used to /// efficiently index the `indices` and `data` array, which respectively contain /// the column indices and the values of the non-zero elements. /// /// ### Indices and data /// /// The non-zero locations and values are stored in arrays of size `nnz`, `indices` /// and `data`. For row `i`, the non-zeros are located in the slices /// `indices[indptr[i]..indptr[i+1]]` and `data[indptr[i]..indptr[i+1]]`. We /// require and enforce sorted indices for each row. /// /// ## Construction /// /// A sparse matrix can be directly constructed by providing its index pointer, /// indices and data arrays. The coherence of the provided structure is then /// verified. /// /// For situations where the compressed structure is hard to figure out up front, /// the [triplet format](struct.TriMatBase.html) can be used. A matrix in the /// triplet format can then be efficiently converted to a `CsMat`. /// /// Alternately, a sparse matrix can be constructed from other sparse matrices /// using [`vstack`], [`hstack`] or [`bmat`]. /// /// [`vstack`]: fn.vstack.html /// [`hstack`]: fn.hstack.html /// [`bmat`]: fn.bmat.html #[derive(PartialEq, Debug)] pub struct CsMatBase<N, I, IptrStorage, IndStorage, DataStorage> where I: SpIndex, IptrStorage: Deref<Target=[I]>, IndStorage: Deref<Target=[I]>, DataStorage: Deref<Target=[N]> { storage: CompressedStorage, nrows : usize, ncols : usize, indptr : IptrStorage, indices : IndStorage, data : DataStorage } pub type CsMatI<N, I> = CsMatBase<N, I, Vec<I>, Vec<I>, Vec<N>>; pub type CsMatViewI<'a, N, I> = CsMatBase<N, I, &'a [I], &'a [I], &'a [N]>; pub type CsMatViewMutI<'a, N, I> = CsMatBase<N, I, &'a [I], &'a [I], &'a mut [N]>; pub type CsMatVecView_<'a, N, I> = CsMatBase<N, I, Array2<I>, &'a [I], &'a [N]>; pub type CsMat<N> = CsMatI<N, usize>; pub type CsMatView<'a, N> = CsMatViewI<'a, N, usize>; pub type CsMatViewMut<'a, N> = CsMatViewMutI<'a, N, usize>; // FIXME: a fixed size array would be better, but no Deref impl pub type CsMatVecView<'a, N> = CsMatVecView_<'a, N, usize>; /// A sparse vector, storing the indices of its non-zero data. /// /// A `CsVec` represents a sparse vector by storing a sorted `indices()` array /// containing the locations of the non-zero values and a `data()` array /// containing the corresponding values. The format is compatible with `CsMat`, /// ie a `CsVec` can represent the row of a CSR matrix without any copying. /// /// Similar to [`CsMat`] and [`TriMat`], the `CsVecBase` type is parameterized /// over the indexing storage backend `IStorage` and the data storage backend /// `DStorage`. Type aliases are provided for common cases: [`CsVec`] represents /// a sparse vector owning its data, with `Vec`s as storage backends; /// [`CsVecView`] represents a sparse vector borrowing its data, using slices /// as storage backends; and [`CsVecViewMut`] represents a sparse vector that /// mutably borrows its data (but immutably borrows its indices). /// /// Additionaly, the type aliases [`CsVecI`], [`CsVecViewI`], and /// [`CsVecViewMutI`] can be used to choose an index type different from the /// default `usize`. /// /// [`CsMat`]: struct.CsMatBase.html /// [`TriMat`]: struct.TriMatBase.html /// [`CsVec`]: type.CsVec.html /// [`CsVecView`]: type.CsVecView.html /// [`CsVecViewMut`]: type.CsVecViewMut.html /// [`CsVecI`]: type.CsVecI.html /// [`CsVecViewI`]: type.CsVecViewI.html /// [`CsVecViewMutI`]: type.CsVecViewMutI.html #[derive(PartialEq, Debug, Clone)] pub struct CsVecBase<IStorage, DStorage> { dim: usize, indices : IStorage, data : DStorage } pub type CsVecI<N, I> = CsVecBase<Vec<I>, Vec<N>>; pub type CsVecViewI<'a, N, I> = CsVecBase<&'a [I], &'a [N]>; pub type CsVecViewMutI<'a, N, I> = CsVecBase<&'a [I], &'a mut [N]>; pub type CsVecView<'a, N> = CsVecViewI<'a, N, usize>; pub type CsVecViewMut<'a, N> = CsVecViewMutI<'a, N, usize>; pub type CsVec<N> = CsVecI<N, usize>; impl<'a, N, I> Copy for CsVecViewI<'a, N, I> {} /// Sparse matrix in the triplet format. /// /// Sparse matrices in the triplet format use three arrays of equal sizes (accessible through the /// methods [`row_inds`], [`col_inds`], [`data`]), the first one /// storing the row indices of non-zero values, the second storing the /// corresponding column indices and the last array storing the corresponding /// scalar value. If a non-zero location is repeated in the arrays, the /// non-zero value is taken as the sum of the corresponding scalar entries. /// /// [`row_inds`]: struct.TriMatBase.html#method.row_inds /// [`col_inds`]: struct.TriMatBase.html#method.col_inds /// [`data`]: struct.TriMatBase.html#method.data /// /// This format is useful for iteratively building a sparse matrix, since the /// various non-zero entries can be specified in any order, or even partially /// as is common in physics with partial derivatives equations. /// /// This format cannot be used for arithmetic operations. Arithmetic operations /// are more efficient in the [compressed format](struct.CsMatBase.html). /// A matrix in the triplet format can be converted to the compressed format /// using the methods [`to_csc`] and [`to_csr`]. /// /// [`to_csc`]: struct.TriMatBase.html#method.to_csc /// [`to_csr`]: struct.TriMatBase.html#method.to_csr /// /// The `TriMatBase` type is parameterized by the storage type for the row and /// column indices, `IStorage`, and by the storage type for the non-zero values /// `DStorage`. Convenient aliases are availaible to specify frequent variant: /// [`TriMat`] refers to a triplet matrix owning the storage of its indices and /// and values, [`TriMatView`] refers to a triplet matrix with slices to store /// its indices and values, while [`TriMatViewMut`] refers to a a triplet matrix /// using mutable slices. /// /// Additionaly, the type aliases [`TriMatI`], [`TriMatViewI`] and /// [`TriMatViewMutI`] can be used to choose an index type different from the /// default `usize`. /// /// [`TriMat`]: type.TriMat.html /// [`TriMatView`]: type.TriMatView.html /// [`TriMatViewMut`]: type.TriMatViewMut.html /// [`TriMatI`]: type.TriMatI.html /// [`TriMatViewI`]: type.TriMatViewI.html /// [`TriMatViewMutI`]: type.TriMatViewMutI.html #[derive(PartialEq, Debug)] pub struct TriMatBase<IStorage, DStorage> { rows: usize, cols: usize, row_inds: IStorage, col_inds: IStorage, data: DStorage, } pub type TriMatI<N, I> = TriMatBase<Vec<I>, Vec<N>>; pub type TriMatViewI<'a, N, I> = TriMatBase<&'a [I], &'a [N]>; pub type TriMatViewMutI<'a, N, I> = TriMatBase<&'a mut [I], &'a mut [N]>; pub type TriMat<N> = TriMatI<N, usize>; pub type TriMatView<'a, N> = TriMatViewI<'a, N, usize>; pub type TriMatViewMut<'a, N> = TriMatViewMutI<'a, N, usize>; /// An iterator over elements of a sparse matrix, in the triplet format /// /// The dataypes RI, CI, and DI are iterators yielding the row, column and /// values of non-zero entries. /// /// As in `TriMat`, no order guarantee is provided and the same location can /// appear multiple times. The non-zero value is then considered as the sum /// of all the entries sharing its location. #[derive(PartialEq, Debug, Clone)] pub struct TriMatIter<RI, CI, DI> { rows: usize, cols: usize, nnz: usize, row_inds: RI, col_inds: CI, data: DI, } mod prelude { pub use super::{ CsMatBase, CsMatViewI, CsMatView, CsMatViewMutI, CsMatViewMut, CsMatI, CsMat, CsMatVecView_, CsMatVecView, CsVecBase, CsVecViewI, CsVecView, CsVecViewMutI, CsVecViewMut, CsVecI, CsVec, TriMatBase, TriMat, TriMatI, TriMatView, TriMatViewI, TriMatViewMut, TriMatViewMutI, TriMatIter, SparseMat, }; } /// A trait for common members of sparse matrices pub trait SparseMat { /// The number of rows of this matrix fn rows(&self) -> usize; /// The number of columns of this matrix fn cols(&self) -> usize; /// The number of nonzeros of this matrix fn nnz(&self) -> usize; } mod utils { use indexing::SpIndex; pub fn sort_indices_data_slices<N: Copy, I:SpIndex>(indices: &mut [I], data: &mut [N], buf: &mut Vec<(I, N)>) { let len = indices.len(); assert_eq!(len, data.len()); let indices = &mut indices[..len]; let data = &mut data[..len]; buf.clear(); buf.reserve_exact(len); for i in 0..len { buf.push((indices[i], data[i])); } buf.sort_by_key(|x| x.0); for (i, &(ind, x)) in buf.iter().enumerate() { indices[i] = ind; data[i] = x; } } } pub mod csmat; pub mod triplet; pub mod vec; pub mod permutation; pub mod prod; pub mod binop; pub mod construct; pub mod linalg; pub mod symmetric; pub mod compressed; pub mod to_dense; pub mod triplet_iter;