2 releases
0.2.3 | Sep 9, 2023 |
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0.2.2 | Sep 9, 2023 |
#6 in #equations
44KB
984 lines
csparse21
Solving large systems of complex-valued* linear equations using sparse matrix methods.
* this is a fork** of sparse21 for complex-valued sparse matrices.
** it would probably be better to make sparse21 work for generic type arguments but I don't have time for that.
use num_complex::Complex64;
let mut m = csparse21::Matrix::from_entries(vec![
(0, 0, Complex64{re: 1.0 , im: 1.0}),
(0, 1, Complex64{re: 1.0 , im: 1.0}),
(0, 2, Complex64{re: 1.0 , im: 1.0}),
(1, 1, Complex64{re: 2.0 , im: 1.0}),
(1, 2, Complex64{re: 5.0 , im: 1.0}),
(2, 0, Complex64{re: 2.0 , im: 1.0}),
(2, 1, Complex64{re: 5.0 , im: 1.0}),
(2, 2, Complex64{re: -1.0, im: 1.0}),
]);
let soln = m.solve(vec![
Complex64{re: 6.0, im: 5.0},
Complex64{re:-4.0, im: 27.0},
Complex64{re: 5.0, im: -5.0},
]);
Sparse methods are primarily valuable for systems in which the number of non-zero entries is substantially less than the overall size of the matrix. Such situations are common in physical systems, including electronic circuit simulation. All elements of a sparse matrix are assumed to be zero-valued unless indicated otherwise.
Usage
CSparse21 exposes two primary data structures:
Matrix
represents anComplex64
-valued sparse matrixSystem
represents a system of linear equations of the formAx=b
, including aMatrix
(A) and right-hand-sideVec
(b).
Once matrices and systems have been created, their primary public method is solve
, which returns a (dense) Vec
solution-vector.
Matrix
CSparse21 matrices can be constructed from a handful of data-sources
Matrix::new
creates an empty matrix, to which elements can be added via the add_element
and add_elements
methods.
let mut m = Matrix::new();
m.add_element(0, 0, Complex64{re:11.0, im: 12.0});
m.add_element(7, 0, Complex64{re:22.0, im: 23.0});
m.add_element(0, 7, Complex64{re:33.0, im: 0.0});
m.add_element(7, 7, Complex64{re:44.0, im: -3.0});
let mut m = Matrix::new();
m.add_elements(vec![
(0, 0, Complex64{re: 1.0 , im: 1.0}),
(0, 1, Complex64{re: 1.0 , im: 1.0}),
(0, 2, Complex64{re: 1.0 , im: 1.0}),
(2, 1, Complex64{re: 5.0 , im: 1.0}),
(2, 2, Complex64{re: -1.0, im: 1.0}),
]);
The arguments to add_element
are a row (usize
), column (usize
), and value (Complex64
).
Adding elements (plural) via add_elements
takes a vector of (usize, usize, Complex64)
tuples, representing the row, col, and val.
Unlike common mathematical notation, all locations in csparse21
matrices and vectors are zero-indexed.
Adding a non-zero at the "first" matrix element therefore implies calling add_element(0, 0, val)
.
Creating a Matrix
from data entries with Matrix::from_entries
:
let mut m = Matrix::from_entries(vec![
(0, 0, Complex64{re: 1.0 , im: 1.0}),
(0, 1, Complex64{re: 1.0 , im: 1.0}),
(0, 2, Complex64{re: 1.0 , im: 1.0}),
(1, 1, Complex64{re: 2.0 , im: 1.0}),
(1, 2, Complex64{re: 5.0 , im: 1.0}),
(2, 0, Complex64{re: 2.0 , im: 1.0}),
(2, 1, Complex64{re: 5.0 , im: 1.0}),
(2, 2, Complex64{re: -1.0, im: 1.0}),
]);
The Matrix::identity
method returns a new identity matrix of size (n x n):
let mut m = Matrix::identity(3);
Solving
CSparse21 matrices are built for solving equation-systems. The primary public method of a Matrix
is solve()
, which accepts a Vec
right-hand-side as its sole argument, and returns a solution Vec
of the same size.
Matrix Mutability
You may have noticed all examples to date declare matrices as mut
, perhaps unnecessarily. This is on purpose. The Matrix::solve
method (un-rustily) modifies the matrix in-place. For larger matrices, the in-place modification saves orders of magnitude of memory, as well as time creating and destroying elements. While in-place self-modification falls out of line with the Rust ethos, it follows a long lineage of scientific computing tools for this and similar tasks.
So: in order to be solved, matrices must be declared mut
.
Dependencies
~320KB