scipy tutorial - Baustatik-Info-Server

SciPy Reference Guide, Release 0.8.dev
3.14 Sparse matrices (scipy.sparse)
3.14.1 Sparse Matrices
Scipy 2D sparse matrix module.
Original code by Travis Oliphant. Modified and extended by Ed Schofield, Robert Cimrman, and Nathan Bell.
There are seven available sparse matrix types:
1. csc_matrix: Compressed Sparse Column format
2. csr_matrix: Compressed Sparse Row format
3. bsr_matrix: Block Sparse Row format
4. lil_matrix: List of Lists format
5. dok_matrix: Dictionary of Keys format
6. coo_matrix: COOrdinate format (aka IJV, triplet format)
7. dia_matrix: DIAgonal format
To construct a matrix efficiently, use either lil_matrix (recommended) or dok_matrix. The lil_matrix class supports
basic slicing and fancy indexing with a similar syntax to NumPy arrays. As illustrated below, the COO format may
also be used to efficiently construct matrices.
To perform manipulations such as multiplication or inversion, first convert the matrix to either CSC or CSR format.
The lil_matrix format is row-based, so conversion to CSR is efficient, whereas conversion to CSC is less so.
All conversions among the CSR, CSC, and COO formats are efficient, linear-time operations.
3.14.2 Example 1
Construct a 1000x1000 lil_matrix and add some values to it:
>>> from scipy import sparse, linsolve
>>> from numpy import linalg
>>> from numpy.random import rand
>>> A = sparse.lil_matrix((1000, 1000))
>>> A[0, :100] = rand(100)
>>> A[1, 100:200] = A[0, :100]
>>> A.setdiag(rand(1000))
Now convert it to CSR format and solve A x = b for x:
>>> A = A.tocsr()
>>> b = rand(1000)
>>> x = linsolve.spsolve(A, b)
Convert it to a dense matrix and solve, and check that the result is the same:
>>> x_ = linalg.solve(A.todense(), b)
Now we can compute norm of the error with:
348 Chapter 3. Reference