def nonzerodiag(nrow, colind, rowptr):
"""
Given the sparsity pattern of a square sparse matrix in compressed row
(csr) format, attempt to find a *row* permutation so the row-permuted
matrix has a nonzero diagonal, if this is possible. This function assumes
that the matrix indexing is 0-based. Note that in general, this function
does not preserve symmetry. The method used is a depth-first search with
lookahead described in [Duff81a]_ and [Duff81b]_.
:parameters:
:nrow: The number of rows of the input matrix.
:colind: An integer array (or list) of length nnz giving the column
indices of the nonzero elements in each row.
:rowptr: An integer array (or list) of length nrow+1 giving the
indices of the first element of each row in colind.
:returns:
:perm: An integer array of length nrow giving the variable permutation.
If irow and jcol are two integer arrays describing the pattern of
the input matrix in triple format, perm[irow] and jcol
describe the permuted matrix.
:nzdiag: The number of nonzeros on the diagonal of the permuted matrix.
"""
lenrows = rowptr[1:] - rowptr[:-1]
perm, nzdiag = _mc21.mc21ad(colind + 1, rowptr[:-1] + 1, lenrows)
return (perm - 1, nzdiag)
def test_spec_sheet(self):
"""Solve example from the spec sheet.
Ordering
http://www.hsl.rl.ac.uk/specs/mc21.pdf
"""
n = 4
icn = np.array([1, 4, 3, 4, 1, 4, 2, 4], dtype=np.int32)
ip = np.array([1, 3, 5, 7], dtype=np.int32)
lenr = np.array([2, 2, 2, 2], dtype=np.int32)
iperm, numnz = _mc21.mc21ad(icn, ip, lenr)
assert np.array_equal(iperm, np.array([1, 4, 2, 3]))
import numpy as np from hsl.ordering import _mc21 n = 4 icn = np.array([1, 4, 3, 4, 1, 4, 2, 4], dtype=np.int32) ip = np.array([1, 3, 5, 7], dtype=np.int32) lenr = np.array([2, 2, 2, 2], dtype=np.int32) iperm, numnz = _mc21.mc21ad(icn, ip, lenr) print 'iperm = ', iperm, ' (1-based)' print 'numnz = ', numnz
