Sparse¶
Usage
use LinearAlgebra.Sparse;
or
import LinearAlgebra.Sparse;
Support for Linear Algebra routines involving sparse data.
A high-level interface to linear algebra operations and procedures for sparse matrices (2D arrays).
Sparse matrices are represented as 2D arrays domain-mapped to a sparse layout.
All sparse operations support the CSR layout (LayoutCS.CS(compressRows=true)
)
and some operations support COO layout (default sparse array layout).
See the Sparse Primer for more information about working with sparse domains and arrays in Chapel.
Sparse Linear Algebra Interface¶
LinearAlgebra.Sparse
follows the same conventions and interface choices
as the parent module, LinearAlgebra
, with few exceptions. These
exceptions are detailed below.
Sparse Domains
In Chapel, changes to the index set of a sparse array must be made directly on the sparse domain. When working with sparse arrays that will require index modification, it is necessary to maintain access to their sparse domains as well. As a result of this, the sparse linear algebra interface provides helper functions for creating both sparse domains and sparse arrays.
A common usage of this interface might look like this:
// Create an empty 3x3 CSR domain
var D = CSRDomain(3,3);
// Create a CSR matrix over this domain
var A = CSRMatrix(D, int);
// The above is equivalent to:
// var A: [D] int;
// Add indices to the sparse domain along the diagonal
D += (0,0);
D += (1,1);
D += (2,2);
// Set all nonzero indices to the value of 1
A = 1;
// A is now a 3x3 sparse identity matrix
writeln(A);
Note
This is an early prototype package submodule. As a result, interfaces may change over the next release.
- proc CSRDomain(rows)¶
Return an empty CSR domain over parent domain:
{0..<rows, 0..<rows}
- proc CSRDomain(rows, cols)
Return an empty CSR domain over parent domain:
{0..<rows, 0..<cols}
- proc CSRDomain(space: range)
Return an empty CSR domain over parent domain:
{space, space}
- proc CSRDomain(rowSpace: range, colSpace: range)
Return an empty CSR domain over parent domain:
{rowSpace, colSpace}
- proc CSRDomain(Dom: domain)
Return a CSR domain based on domain:
Dom
If
Dom
is dense, it will be interpreted as the parent domain, and the domain returned will be empty.If
Dom
is sparse (CSR), the domain returned will contain the same nonzeros asDom
- proc CSRMatrix(Dom: domain, type eltType = real)¶
Return a CSR matrix over domain:
Dom
If
Dom
is dense, it will be interpreted as the parent domain, and the matrix returned will be empty.If
Dom
is sparse (CSR), the matrix returned will contain the same nonzeros asDom
- proc CSRMatrix(A: [?Dom] ?Atype, type eltType = Atype)
Return a CSR matrix with domain and values of
A
If
A
is dense, only the indices holding nonzero elements are added to the sparse matrix returned.If
A
is sparse (CSR), the returned sparse matrix will be a copy ofA
casted toeltType
- proc CSRMatrix(parentDom: domain(2), data: [?nnzDom] ?eltType, indices: [nnzDom], indptr: [?indDom])
Return a CSR matrix constructed from internal representation:
parentDom
: parent domain for sparse matrix, bounding box for nonzeros indicesdata
: non-zero element valuesindices
: non-zero row pointersindptr
: index pointers
- proc CSRDomain(parentDom: domain(2), indices: [?nnzDom], indptr: [?indDom])
Return a CSR domain constructed from internal representation
- proc CSRMatrix(shape: 2*(int), data: [?nnzDom] ?eltType, indices: [nnzDom], indptr: [?indDom])
Return a CSR matrix constructed from internal representation: -
shape
: (M,N) bounding box will be {0..#M,0..#N} -data
: non-zero element values -indices
: non-zero row pointers -indptr
: index pointers
- proc CSRDomain(shape: 2*(int), indices: [?nnzDom], indptr: [?indDom])
Return a CSR domain constructed from internal representation
- proc dot(A: [?Adom] ?eltType, B: [?Bdom] eltType)¶
Generic matrix multiplication,
A
andB
can be a scalar, dense vector, or sparse matrix.Note
When
A
is a vector andB
is a matrix, this function implicitly computesdot(transpose(A), B)
, which may not be as efficient as passingA
andB
in the reverse order.
- proc _array.dot(A: [])¶
Compute the dot-product
- proc _array.dot(a)
Compute the dot-product
- proc transpose(D: domain)¶
Transpose CSR domain
- proc transpose(A: [?Adom] ?eltType)
Transpose CSR matrix
- proc _array.T¶
Transpose CSR matrix
- proc _array.plus(A: [?Adom] ?eltType)¶
Element-wise addition, supports CSR and COO.
- proc _array.minus(A: [?Adom] ?eltType)¶
Element-wise subtraction, supports CSR and COO.
- proc _array.times(A)¶
Element-wise multiplication, supports CSR and COO.
- proc _array.elementDiv(A)¶
Element-wise division, supports CSR and COO.
- proc eye(Dom: domain, type eltType = real)¶
Return an identity matrix over sparse domain
Dom
- proc isDiag(A: [?D] ?eltType)¶
Return
true
if sparse matrix is diagonal. Supports CSR and COO arrays.
- proc isHermitian(A: [?D])¶
Return
true
if matrix is Hermitian. Supports CSR and COO arrays.
- proc isSymmetric(A: [?D])¶
Return
true
if sparse matrix is symmetric. Supports CSR and COO arrays.