1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476
use crate::array_backend::Array2; use crate::errors::StructureError; use crate::indexing::SpIndex; use crate::IndPtrBase; use std::ops::Deref; #[cfg(feature = "serde")] mod serde_traits; #[cfg(feature = "serde")] use serde_traits::{CsMatBaseShadow, CsVecBaseShadow, Deserialize, Serialize}; 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(Eq, PartialEq, Debug, Copy, Clone, Hash)] #[cfg_attr(feature = "serde", derive(Deserialize))] #[cfg_attr( feature = "serde", serde( try_from = "CsMatBaseShadow<N, I, IptrStorage, IndStorage, DataStorage, Iptr>" ) )] pub struct CsMatBase<N, I, IptrStorage, IndStorage, DataStorage, Iptr = I> where I: SpIndex, Iptr: SpIndex, IptrStorage: Deref<Target = [Iptr]>, IndStorage: Deref<Target = [I]>, DataStorage: Deref<Target = [N]>, { storage: CompressedStorage, nrows: usize, ncols: usize, #[cfg_attr(feature = "serde", serde(flatten))] indptr: IndPtrBase<Iptr, IptrStorage>, indices: IndStorage, data: DataStorage, } pub type CsMatI<N, I, Iptr = I> = CsMatBase<N, I, Vec<Iptr>, Vec<I>, Vec<N>, Iptr>; pub type CsMatViewI<'a, N, I, Iptr = I> = CsMatBase<N, I, &'a [Iptr], &'a [I], &'a [N], Iptr>; pub type CsMatViewMutI<'a, N, I, Iptr = I> = CsMatBase<N, I, &'a [Iptr], &'a [I], &'a mut [N], Iptr>; pub type CsMatVecView_<'a, N, I, Iptr = I> = CsMatBase<N, I, Array2<Iptr>, &'a [I], &'a [N], Iptr>; 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>; pub type CsStructureViewI<'a, I, Iptr = I> = CsMatViewI<'a, (), I, Iptr>; pub type CsStructureView<'a> = CsStructureViewI<'a, usize>; pub type CsStructureI<I, Iptr = I> = CsMatI<(), I, Iptr>; pub type CsStructure = CsStructureI<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(Eq, PartialEq, Debug, Copy, Clone, Hash)] #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))] #[cfg_attr( feature = "serde", serde(try_from = "CsVecBaseShadow<IStorage, DStorage, N, I>") )] pub struct CsVecBase<IStorage, DStorage, N, I: SpIndex = usize> where IStorage: Deref<Target = [I]>, DStorage: Deref<Target = [N]>, { dim: usize, indices: IStorage, data: DStorage, } pub type CsVecI<N, I = usize> = CsVecBase<Vec<I>, Vec<N>, N, I>; pub type CsVecViewI<'a, N, I = usize> = CsVecBase<&'a [I], &'a [N], N, I>; pub type CsVecViewMutI<'a, N, I = usize> = CsVecBase<&'a [I], &'a mut [N], N, I>; pub type CsVecView<'a, N> = CsVecViewI<'a, N>; pub type CsVecViewMut<'a, N> = CsVecViewMutI<'a, N>; pub type CsVec<N> = CsVecI<N>; /// 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, Hash)] 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::{ CsMat, CsMatBase, CsMatI, CsMatVecView, CsMatVecView_, CsMatView, CsMatViewI, CsMatViewMut, CsMatViewMutI, CsStructure, CsStructureI, CsStructureView, CsStructureViewI, CsVec, CsVecBase, CsVecI, CsVecView, CsVecViewI, CsVecViewMut, CsVecViewMutI, SparseMat, TriMat, TriMatBase, TriMatI, TriMatIter, TriMatView, TriMatViewI, TriMatViewMut, TriMatViewMutI, }; } /// 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; } pub(crate) mod utils { use super::*; use ndarray::Axis; use std::convert::TryInto; /// Check the structure of `CsMat` components /// This will ensure that: /// * indptr is of length `outer_dim() + 1` /// * indices and data have the same length, `nnz == indptr[outer_dims()]` /// * indptr is sorted /// * indptr values do not exceed [`usize::MAX`](usize::MAX)`/ 2`, as that would mean /// indices and indptr would take more space than the addressable memory /// * indices is sorted for each outer slice /// * indices are lower than `inner_dims()` pub(crate) fn check_compressed_structure<I: SpIndex, Iptr: SpIndex>( inner: usize, outer: usize, indptr: &[Iptr], indices: &[I], ) -> Result<(), StructureError> { let indptr = crate::IndPtrView::new_checked(indptr).map_err(|(_, e)| e)?; if indptr.len() != outer + 1 { return Err(StructureError::SizeMismatch( "Indptr length does not match dimension", )); } // Make sure Iptr and I can represent all types for this size if I::from(inner).is_none() { return Err(StructureError::OutOfRange( "Index type not large enough for this matrix", )); } if Iptr::from(outer + 1).is_none() { return Err(StructureError::OutOfRange( "Iptr type not large enough for this matrix", )); } // Make sure indices can be converted to usize // this could happen if index is negative for sized types for i in indices.iter() { if i.try_index().is_none() { return Err(StructureError::OutOfRange( "Indices value out of range of usize", )); } } let nnz = indices.len(); if nnz != indptr.nnz() { return Err(StructureError::SizeMismatch( "Indices length and inpdtr's nnz do not match", )); } // check that the indices are sorted for each row for range in indptr.iter_outer_sz() { let indices = &indices[range]; // Indices must be monotonically increasing if !sorted_indices(indices) { return Err(StructureError::Unsorted("Indices are not sorted")); } // Last index (which is the largest) must be in bounds if let Some(i) = indices.last() { if i.to_usize().unwrap() >= inner { return Err(StructureError::OutOfRange( "Indice is larger than inner dimension", )); } } } Ok(()) } pub fn sorted_indices<I: SpIndex>(indices: &[I]) -> bool { for w in indices.windows(2) { // w will always be a size 2 let &[i1, i2]: &[I; 2] = w.try_into().unwrap(); if i2 <= i1 { return false; } } true } pub fn sort_indices_data_slices<N: Clone, 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, v) in indices.iter().zip(data.iter()) { buf.push((*i, v.clone())); } buf.sort_unstable_by_key(|x| x.0); for ((i, x), (ind, v)) in buf .iter() .cloned() .zip(indices.iter_mut().zip(data.iter_mut())) { *ind = i; *v = x; } } /// Return the axis which varies the fastest. For a /// `C`-style matrix this will be `Axis(1)`, for an /// 'F`-style matrix this will be `Axis(0)` pub(crate) fn fastest_axis<T>(mat: ndarray::ArrayView2<T>) -> Axis { if mat.strides()[1] > mat.strides()[0] { Axis(0) } else { Axis(1) } } pub(crate) fn slowest_axis<T>(mat: ndarray::ArrayView2<T>) -> Axis { match fastest_axis(mat) { Axis(1) => Axis(0), Axis(0) => Axis(1), _ => unreachable!(), } } } pub mod binop; pub mod compressed; pub mod construct; pub mod csmat; pub mod indptr; pub mod kronecker; pub mod linalg; pub mod permutation; pub mod prod; pub mod slicing; pub mod smmp; pub mod special_mats; pub mod symmetric; pub mod to_dense; pub mod triplet; pub mod triplet_iter; pub mod vec; pub mod visu; #[cfg(test)] mod test { use super::utils; #[test] fn test_sort_indices() { let mut idx: Vec<usize> = vec![4, 1, 6, 2]; let mut dat: Vec<i32> = vec![4, -1, 2, -3]; let mut buf: Vec<(usize, i32)> = Vec::new(); utils::sort_indices_data_slices(&mut idx[..], &mut dat[..], &mut buf); assert_eq!(idx, vec![1, 2, 4, 6]); assert_eq!(dat, vec![-1, -3, 4, 2]); } #[test] fn test_sorted_indices() { use utils::sorted_indices; assert!(sorted_indices(&[1, 2, 3])); assert!(sorted_indices(&[1, 2, 8])); assert!(!sorted_indices(&[1, 1, 3])); assert!(!sorted_indices(&[2, 1, 3])); assert!(sorted_indices(&[1, 2])); assert!(sorted_indices(&[1])); } #[test] fn test_fastest_axis() { use ndarray::{arr2, s, Array2, Axis, ShapeBuilder}; use utils::fastest_axis; let arr = arr2(&[[1, 2], [3, 4]]); assert_eq!(fastest_axis(arr.view()), Axis(1)); let arr = Array2::<i32>::zeros((10, 9)); assert_eq!(fastest_axis(arr.view()), Axis(1)); let arrslice = arr.slice(s![..;2, ..;3]); assert_eq!(fastest_axis(arrslice.view()), Axis(1)); let arr = Array2::<i32>::zeros((10, 9).f()); assert_eq!(fastest_axis(arr.view()), Axis(0)); let arrslice = arr.slice(s![..;2, ..;3]); assert_eq!(fastest_axis(arrslice.view()), Axis(0)); } }