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477 lines
20 KiB
Python
477 lines
20 KiB
Python
6 years ago
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"""test sparse matrix construction functions"""
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from __future__ import division, print_function, absolute_import
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import numpy as np
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from numpy import array, matrix
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from numpy.testing import (assert_equal, assert_,
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assert_array_equal, assert_array_almost_equal_nulp)
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import pytest
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from pytest import raises as assert_raises
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from scipy._lib._testutils import check_free_memory
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from scipy.sparse import csr_matrix, coo_matrix
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from scipy.sparse import construct
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from scipy.sparse.construct import rand as sprand
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sparse_formats = ['csr','csc','coo','bsr','dia','lil','dok']
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#TODO check whether format=XXX is respected
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def _sprandn(m, n, density=0.01, format="coo", dtype=None, random_state=None):
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# Helper function for testing.
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if random_state is None:
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random_state = np.random
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elif isinstance(random_state, (int, np.integer)):
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random_state = np.random.RandomState(random_state)
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data_rvs = random_state.randn
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return construct.random(m, n, density, format, dtype,
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random_state, data_rvs)
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class TestConstructUtils(object):
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def test_spdiags(self):
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diags1 = array([[1, 2, 3, 4, 5]])
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diags2 = array([[1, 2, 3, 4, 5],
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[6, 7, 8, 9,10]])
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diags3 = array([[1, 2, 3, 4, 5],
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[6, 7, 8, 9,10],
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[11,12,13,14,15]])
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cases = []
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cases.append((diags1, 0, 1, 1, [[1]]))
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cases.append((diags1, [0], 1, 1, [[1]]))
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cases.append((diags1, [0], 2, 1, [[1],[0]]))
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cases.append((diags1, [0], 1, 2, [[1,0]]))
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cases.append((diags1, [1], 1, 2, [[0,2]]))
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cases.append((diags1,[-1], 1, 2, [[0,0]]))
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cases.append((diags1, [0], 2, 2, [[1,0],[0,2]]))
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cases.append((diags1,[-1], 2, 2, [[0,0],[1,0]]))
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cases.append((diags1, [3], 2, 2, [[0,0],[0,0]]))
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cases.append((diags1, [0], 3, 4, [[1,0,0,0],[0,2,0,0],[0,0,3,0]]))
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cases.append((diags1, [1], 3, 4, [[0,2,0,0],[0,0,3,0],[0,0,0,4]]))
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cases.append((diags1, [2], 3, 5, [[0,0,3,0,0],[0,0,0,4,0],[0,0,0,0,5]]))
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cases.append((diags2, [0,2], 3, 3, [[1,0,8],[0,2,0],[0,0,3]]))
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cases.append((diags2, [-1,0], 3, 4, [[6,0,0,0],[1,7,0,0],[0,2,8,0]]))
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cases.append((diags2, [2,-3], 6, 6, [[0,0,3,0,0,0],
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[0,0,0,4,0,0],
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[0,0,0,0,5,0],
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[6,0,0,0,0,0],
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[0,7,0,0,0,0],
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[0,0,8,0,0,0]]))
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cases.append((diags3, [-1,0,1], 6, 6, [[6,12, 0, 0, 0, 0],
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[1, 7,13, 0, 0, 0],
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[0, 2, 8,14, 0, 0],
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[0, 0, 3, 9,15, 0],
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[0, 0, 0, 4,10, 0],
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[0, 0, 0, 0, 5, 0]]))
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cases.append((diags3, [-4,2,-1], 6, 5, [[0, 0, 8, 0, 0],
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[11, 0, 0, 9, 0],
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[0,12, 0, 0,10],
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[0, 0,13, 0, 0],
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[1, 0, 0,14, 0],
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[0, 2, 0, 0,15]]))
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for d,o,m,n,result in cases:
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assert_equal(construct.spdiags(d,o,m,n).todense(), result)
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def test_diags(self):
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a = array([1, 2, 3, 4, 5])
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b = array([6, 7, 8, 9, 10])
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c = array([11, 12, 13, 14, 15])
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cases = []
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cases.append((a[:1], 0, (1, 1), [[1]]))
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cases.append(([a[:1]], [0], (1, 1), [[1]]))
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cases.append(([a[:1]], [0], (2, 1), [[1],[0]]))
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cases.append(([a[:1]], [0], (1, 2), [[1,0]]))
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cases.append(([a[:1]], [1], (1, 2), [[0,1]]))
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cases.append(([a[:2]], [0], (2, 2), [[1,0],[0,2]]))
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cases.append(([a[:1]],[-1], (2, 2), [[0,0],[1,0]]))
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cases.append(([a[:3]], [0], (3, 4), [[1,0,0,0],[0,2,0,0],[0,0,3,0]]))
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cases.append(([a[:3]], [1], (3, 4), [[0,1,0,0],[0,0,2,0],[0,0,0,3]]))
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cases.append(([a[:1]], [-2], (3, 5), [[0,0,0,0,0],[0,0,0,0,0],[1,0,0,0,0]]))
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cases.append(([a[:2]], [-1], (3, 5), [[0,0,0,0,0],[1,0,0,0,0],[0,2,0,0,0]]))
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cases.append(([a[:3]], [0], (3, 5), [[1,0,0,0,0],[0,2,0,0,0],[0,0,3,0,0]]))
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cases.append(([a[:3]], [1], (3, 5), [[0,1,0,0,0],[0,0,2,0,0],[0,0,0,3,0]]))
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cases.append(([a[:3]], [2], (3, 5), [[0,0,1,0,0],[0,0,0,2,0],[0,0,0,0,3]]))
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cases.append(([a[:2]], [3], (3, 5), [[0,0,0,1,0],[0,0,0,0,2],[0,0,0,0,0]]))
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cases.append(([a[:1]], [4], (3, 5), [[0,0,0,0,1],[0,0,0,0,0],[0,0,0,0,0]]))
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cases.append(([a[:1]], [-4], (5, 3), [[0,0,0],[0,0,0],[0,0,0],[0,0,0],[1,0,0]]))
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cases.append(([a[:2]], [-3], (5, 3), [[0,0,0],[0,0,0],[0,0,0],[1,0,0],[0,2,0]]))
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cases.append(([a[:3]], [-2], (5, 3), [[0,0,0],[0,0,0],[1,0,0],[0,2,0],[0,0,3]]))
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cases.append(([a[:3]], [-1], (5, 3), [[0,0,0],[1,0,0],[0,2,0],[0,0,3],[0,0,0]]))
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cases.append(([a[:3]], [0], (5, 3), [[1,0,0],[0,2,0],[0,0,3],[0,0,0],[0,0,0]]))
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cases.append(([a[:2]], [1], (5, 3), [[0,1,0],[0,0,2],[0,0,0],[0,0,0],[0,0,0]]))
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cases.append(([a[:1]], [2], (5, 3), [[0,0,1],[0,0,0],[0,0,0],[0,0,0],[0,0,0]]))
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cases.append(([a[:3],b[:1]], [0,2], (3, 3), [[1,0,6],[0,2,0],[0,0,3]]))
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cases.append(([a[:2],b[:3]], [-1,0], (3, 4), [[6,0,0,0],[1,7,0,0],[0,2,8,0]]))
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cases.append(([a[:4],b[:3]], [2,-3], (6, 6), [[0,0,1,0,0,0],
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[0,0,0,2,0,0],
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[0,0,0,0,3,0],
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[6,0,0,0,0,4],
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[0,7,0,0,0,0],
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[0,0,8,0,0,0]]))
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cases.append(([a[:4],b,c[:4]], [-1,0,1], (5, 5), [[6,11, 0, 0, 0],
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[1, 7,12, 0, 0],
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[0, 2, 8,13, 0],
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[0, 0, 3, 9,14],
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[0, 0, 0, 4,10]]))
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cases.append(([a[:2],b[:3],c], [-4,2,-1], (6, 5), [[0, 0, 6, 0, 0],
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[11, 0, 0, 7, 0],
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[0,12, 0, 0, 8],
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[0, 0,13, 0, 0],
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[1, 0, 0,14, 0],
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[0, 2, 0, 0,15]]))
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# too long arrays are OK
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cases.append(([a], [0], (1, 1), [[1]]))
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cases.append(([a[:3],b], [0,2], (3, 3), [[1, 0, 6], [0, 2, 0], [0, 0, 3]]))
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cases.append((np.array([[1, 2, 3], [4, 5, 6]]), [0,-1], (3, 3), [[1, 0, 0], [4, 2, 0], [0, 5, 3]]))
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# scalar case: broadcasting
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cases.append(([1,-2,1], [1,0,-1], (3, 3), [[-2, 1, 0],
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[1, -2, 1],
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[0, 1, -2]]))
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for d, o, shape, result in cases:
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err_msg = "%r %r %r %r" % (d, o, shape, result)
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assert_equal(construct.diags(d, o, shape=shape).todense(),
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result, err_msg=err_msg)
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if shape[0] == shape[1] and hasattr(d[0], '__len__') and len(d[0]) <= max(shape):
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# should be able to find the shape automatically
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assert_equal(construct.diags(d, o).todense(), result,
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err_msg=err_msg)
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def test_diags_default(self):
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a = array([1, 2, 3, 4, 5])
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assert_equal(construct.diags(a).todense(), np.diag(a))
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def test_diags_default_bad(self):
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a = array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6]])
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assert_raises(ValueError, construct.diags, a)
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def test_diags_bad(self):
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a = array([1, 2, 3, 4, 5])
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b = array([6, 7, 8, 9, 10])
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c = array([11, 12, 13, 14, 15])
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cases = []
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cases.append(([a[:0]], 0, (1, 1)))
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cases.append(([a[:4],b,c[:3]], [-1,0,1], (5, 5)))
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cases.append(([a[:2],c,b[:3]], [-4,2,-1], (6, 5)))
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cases.append(([a[:2],c,b[:3]], [-4,2,-1], None))
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cases.append(([], [-4,2,-1], None))
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cases.append(([1], [-5], (4, 4)))
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cases.append(([a], 0, None))
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for d, o, shape in cases:
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assert_raises(ValueError, construct.diags, d, o, shape)
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assert_raises(TypeError, construct.diags, [[None]], [0])
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def test_diags_vs_diag(self):
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# Check that
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#
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# diags([a, b, ...], [i, j, ...]) == diag(a, i) + diag(b, j) + ...
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#
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np.random.seed(1234)
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for n_diags in [1, 2, 3, 4, 5, 10]:
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n = 1 + n_diags//2 + np.random.randint(0, 10)
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offsets = np.arange(-n+1, n-1)
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np.random.shuffle(offsets)
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offsets = offsets[:n_diags]
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diagonals = [np.random.rand(n - abs(q)) for q in offsets]
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mat = construct.diags(diagonals, offsets)
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dense_mat = sum([np.diag(x, j) for x, j in zip(diagonals, offsets)])
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assert_array_almost_equal_nulp(mat.todense(), dense_mat)
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if len(offsets) == 1:
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mat = construct.diags(diagonals[0], offsets[0])
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dense_mat = np.diag(diagonals[0], offsets[0])
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assert_array_almost_equal_nulp(mat.todense(), dense_mat)
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def test_diags_dtype(self):
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x = construct.diags([2.2], [0], shape=(2, 2), dtype=int)
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assert_equal(x.dtype, int)
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assert_equal(x.todense(), [[2, 0], [0, 2]])
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def test_diags_one_diagonal(self):
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d = list(range(5))
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for k in range(-5, 6):
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assert_equal(construct.diags(d, k).toarray(),
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construct.diags([d], [k]).toarray())
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def test_diags_empty(self):
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x = construct.diags([])
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assert_equal(x.shape, (0, 0))
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def test_identity(self):
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assert_equal(construct.identity(1).toarray(), [[1]])
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assert_equal(construct.identity(2).toarray(), [[1,0],[0,1]])
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I = construct.identity(3, dtype='int8', format='dia')
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assert_equal(I.dtype, np.dtype('int8'))
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assert_equal(I.format, 'dia')
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for fmt in sparse_formats:
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I = construct.identity(3, format=fmt)
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assert_equal(I.format, fmt)
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assert_equal(I.toarray(), [[1,0,0],[0,1,0],[0,0,1]])
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def test_eye(self):
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assert_equal(construct.eye(1,1).toarray(), [[1]])
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assert_equal(construct.eye(2,3).toarray(), [[1,0,0],[0,1,0]])
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assert_equal(construct.eye(3,2).toarray(), [[1,0],[0,1],[0,0]])
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assert_equal(construct.eye(3,3).toarray(), [[1,0,0],[0,1,0],[0,0,1]])
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assert_equal(construct.eye(3,3,dtype='int16').dtype, np.dtype('int16'))
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for m in [3, 5]:
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for n in [3, 5]:
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for k in range(-5,6):
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assert_equal(construct.eye(m, n, k=k).toarray(), np.eye(m, n, k=k))
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if m == n:
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assert_equal(construct.eye(m, k=k).toarray(), np.eye(m, n, k=k))
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def test_eye_one(self):
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assert_equal(construct.eye(1).toarray(), [[1]])
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assert_equal(construct.eye(2).toarray(), [[1,0],[0,1]])
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I = construct.eye(3, dtype='int8', format='dia')
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assert_equal(I.dtype, np.dtype('int8'))
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assert_equal(I.format, 'dia')
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for fmt in sparse_formats:
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I = construct.eye(3, format=fmt)
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assert_equal(I.format, fmt)
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assert_equal(I.toarray(), [[1,0,0],[0,1,0],[0,0,1]])
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def test_kron(self):
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cases = []
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cases.append(array([[0]]))
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cases.append(array([[-1]]))
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cases.append(array([[4]]))
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cases.append(array([[10]]))
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cases.append(array([[0],[0]]))
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cases.append(array([[0,0]]))
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cases.append(array([[1,2],[3,4]]))
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cases.append(array([[0,2],[5,0]]))
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cases.append(array([[0,2,-6],[8,0,14]]))
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cases.append(array([[5,4],[0,0],[6,0]]))
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cases.append(array([[5,4,4],[1,0,0],[6,0,8]]))
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cases.append(array([[0,1,0,2,0,5,8]]))
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cases.append(array([[0.5,0.125,0,3.25],[0,2.5,0,0]]))
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|
||
|
|
for a in cases:
|
||
|
|
for b in cases:
|
||
|
|
result = construct.kron(csr_matrix(a),csr_matrix(b)).todense()
|
||
|
|
expected = np.kron(a,b)
|
||
|
|
assert_array_equal(result,expected)
|
||
|
|
|
||
|
|
def test_kronsum(self):
|
||
|
|
cases = []
|
||
|
|
|
||
|
|
cases.append(array([[0]]))
|
||
|
|
cases.append(array([[-1]]))
|
||
|
|
cases.append(array([[4]]))
|
||
|
|
cases.append(array([[10]]))
|
||
|
|
cases.append(array([[1,2],[3,4]]))
|
||
|
|
cases.append(array([[0,2],[5,0]]))
|
||
|
|
cases.append(array([[0,2,-6],[8,0,14],[0,3,0]]))
|
||
|
|
cases.append(array([[1,0,0],[0,5,-1],[4,-2,8]]))
|
||
|
|
|
||
|
|
for a in cases:
|
||
|
|
for b in cases:
|
||
|
|
result = construct.kronsum(csr_matrix(a),csr_matrix(b)).todense()
|
||
|
|
expected = np.kron(np.eye(len(b)), a) + \
|
||
|
|
np.kron(b, np.eye(len(a)))
|
||
|
|
assert_array_equal(result,expected)
|
||
|
|
|
||
|
|
def test_vstack(self):
|
||
|
|
|
||
|
|
A = coo_matrix([[1,2],[3,4]])
|
||
|
|
B = coo_matrix([[5,6]])
|
||
|
|
|
||
|
|
expected = matrix([[1, 2],
|
||
|
|
[3, 4],
|
||
|
|
[5, 6]])
|
||
|
|
assert_equal(construct.vstack([A,B]).todense(), expected)
|
||
|
|
assert_equal(construct.vstack([A,B], dtype=np.float32).dtype, np.float32)
|
||
|
|
assert_equal(construct.vstack([A.tocsr(),B.tocsr()]).todense(),
|
||
|
|
expected)
|
||
|
|
assert_equal(construct.vstack([A.tocsr(),B.tocsr()], dtype=np.float32).dtype,
|
||
|
|
np.float32)
|
||
|
|
assert_equal(construct.vstack([A.tocsr(),B.tocsr()],
|
||
|
|
dtype=np.float32).indices.dtype, np.int32)
|
||
|
|
assert_equal(construct.vstack([A.tocsr(),B.tocsr()],
|
||
|
|
dtype=np.float32).indptr.dtype, np.int32)
|
||
|
|
|
||
|
|
def test_hstack(self):
|
||
|
|
|
||
|
|
A = coo_matrix([[1,2],[3,4]])
|
||
|
|
B = coo_matrix([[5],[6]])
|
||
|
|
|
||
|
|
expected = matrix([[1, 2, 5],
|
||
|
|
[3, 4, 6]])
|
||
|
|
assert_equal(construct.hstack([A,B]).todense(), expected)
|
||
|
|
assert_equal(construct.hstack([A,B], dtype=np.float32).dtype, np.float32)
|
||
|
|
assert_equal(construct.hstack([A.tocsc(),B.tocsc()]).todense(),
|
||
|
|
expected)
|
||
|
|
assert_equal(construct.hstack([A.tocsc(),B.tocsc()], dtype=np.float32).dtype,
|
||
|
|
np.float32)
|
||
|
|
|
||
|
|
def test_bmat(self):
|
||
|
|
|
||
|
|
A = coo_matrix([[1,2],[3,4]])
|
||
|
|
B = coo_matrix([[5],[6]])
|
||
|
|
C = coo_matrix([[7]])
|
||
|
|
D = coo_matrix((0,0))
|
||
|
|
|
||
|
|
expected = matrix([[1, 2, 5],
|
||
|
|
[3, 4, 6],
|
||
|
|
[0, 0, 7]])
|
||
|
|
assert_equal(construct.bmat([[A,B],[None,C]]).todense(), expected)
|
||
|
|
|
||
|
|
expected = matrix([[1, 2, 0],
|
||
|
|
[3, 4, 0],
|
||
|
|
[0, 0, 7]])
|
||
|
|
assert_equal(construct.bmat([[A,None],[None,C]]).todense(), expected)
|
||
|
|
|
||
|
|
expected = matrix([[0, 5],
|
||
|
|
[0, 6],
|
||
|
|
[7, 0]])
|
||
|
|
assert_equal(construct.bmat([[None,B],[C,None]]).todense(), expected)
|
||
|
|
|
||
|
|
expected = matrix(np.empty((0,0)))
|
||
|
|
assert_equal(construct.bmat([[None,None]]).todense(), expected)
|
||
|
|
assert_equal(construct.bmat([[None,D],[D,None]]).todense(), expected)
|
||
|
|
|
||
|
|
# test bug reported in gh-5976
|
||
|
|
expected = matrix([[7]])
|
||
|
|
assert_equal(construct.bmat([[None,D],[C,None]]).todense(), expected)
|
||
|
|
|
||
|
|
# test failure cases
|
||
|
|
with assert_raises(ValueError) as excinfo:
|
||
|
|
construct.bmat([[A], [B]])
|
||
|
|
excinfo.match(r'Got blocks\[1,0\]\.shape\[1\] == 1, expected 2')
|
||
|
|
|
||
|
|
with assert_raises(ValueError) as excinfo:
|
||
|
|
construct.bmat([[A, C]])
|
||
|
|
excinfo.match(r'Got blocks\[0,1\]\.shape\[0\] == 1, expected 2')
|
||
|
|
|
||
|
|
@pytest.mark.slow
|
||
|
|
def test_concatenate_int32_overflow(self):
|
||
|
|
""" test for indptr overflow when concatenating matrices """
|
||
|
|
check_free_memory(30000)
|
||
|
|
|
||
|
|
n = 33000
|
||
|
|
A = csr_matrix(np.ones((n, n), dtype=bool))
|
||
|
|
B = A.copy()
|
||
|
|
C = construct._compressed_sparse_stack((A,B), 0)
|
||
|
|
|
||
|
|
assert_(np.all(np.equal(np.diff(C.indptr), n)))
|
||
|
|
assert_equal(C.indices.dtype, np.int64)
|
||
|
|
assert_equal(C.indptr.dtype, np.int64)
|
||
|
|
|
||
|
|
def test_block_diag_basic(self):
|
||
|
|
""" basic test for block_diag """
|
||
|
|
A = coo_matrix([[1,2],[3,4]])
|
||
|
|
B = coo_matrix([[5],[6]])
|
||
|
|
C = coo_matrix([[7]])
|
||
|
|
|
||
|
|
expected = matrix([[1, 2, 0, 0],
|
||
|
|
[3, 4, 0, 0],
|
||
|
|
[0, 0, 5, 0],
|
||
|
|
[0, 0, 6, 0],
|
||
|
|
[0, 0, 0, 7]])
|
||
|
|
|
||
|
|
assert_equal(construct.block_diag((A, B, C)).todense(), expected)
|
||
|
|
|
||
|
|
def test_block_diag_scalar_1d_args(self):
|
||
|
|
""" block_diag with scalar and 1d arguments """
|
||
|
|
# one 1d matrix and a scalar
|
||
|
|
assert_array_equal(construct.block_diag([[2,3], 4]).toarray(),
|
||
|
|
[[2, 3, 0], [0, 0, 4]])
|
||
|
|
|
||
|
|
def test_block_diag_1(self):
|
||
|
|
""" block_diag with one matrix """
|
||
|
|
assert_equal(construct.block_diag([[1, 0]]).todense(),
|
||
|
|
matrix([[1, 0]]))
|
||
|
|
assert_equal(construct.block_diag([[[1, 0]]]).todense(),
|
||
|
|
matrix([[1, 0]]))
|
||
|
|
assert_equal(construct.block_diag([[[1], [0]]]).todense(),
|
||
|
|
matrix([[1], [0]]))
|
||
|
|
# just on scalar
|
||
|
|
assert_equal(construct.block_diag([1]).todense(),
|
||
|
|
matrix([[1]]))
|
||
|
|
|
||
|
|
def test_random_sampling(self):
|
||
|
|
# Simple sanity checks for sparse random sampling.
|
||
|
|
for f in sprand, _sprandn:
|
||
|
|
for t in [np.float32, np.float64, np.longdouble,
|
||
|
|
np.int32, np.int64, np.complex64, np.complex128]:
|
||
|
|
x = f(5, 10, density=0.1, dtype=t)
|
||
|
|
assert_equal(x.dtype, t)
|
||
|
|
assert_equal(x.shape, (5, 10))
|
||
|
|
assert_equal(x.nnz, 5)
|
||
|
|
|
||
|
|
x1 = f(5, 10, density=0.1, random_state=4321)
|
||
|
|
assert_equal(x1.dtype, np.double)
|
||
|
|
|
||
|
|
x2 = f(5, 10, density=0.1,
|
||
|
|
random_state=np.random.RandomState(4321))
|
||
|
|
|
||
|
|
assert_array_equal(x1.data, x2.data)
|
||
|
|
assert_array_equal(x1.row, x2.row)
|
||
|
|
assert_array_equal(x1.col, x2.col)
|
||
|
|
|
||
|
|
for density in [0.0, 0.1, 0.5, 1.0]:
|
||
|
|
x = f(5, 10, density=density)
|
||
|
|
assert_equal(x.nnz, int(density * np.prod(x.shape)))
|
||
|
|
|
||
|
|
for fmt in ['coo', 'csc', 'csr', 'lil']:
|
||
|
|
x = f(5, 10, format=fmt)
|
||
|
|
assert_equal(x.format, fmt)
|
||
|
|
|
||
|
|
assert_raises(ValueError, lambda: f(5, 10, 1.1))
|
||
|
|
assert_raises(ValueError, lambda: f(5, 10, -0.1))
|
||
|
|
|
||
|
|
def test_rand(self):
|
||
|
|
# Simple distributional checks for sparse.rand.
|
||
|
|
for random_state in None, 4321, np.random.RandomState():
|
||
|
|
x = sprand(10, 20, density=0.5, dtype=np.float64,
|
||
|
|
random_state=random_state)
|
||
|
|
assert_(np.all(np.less_equal(0, x.data)))
|
||
|
|
assert_(np.all(np.less_equal(x.data, 1)))
|
||
|
|
|
||
|
|
def test_randn(self):
|
||
|
|
# Simple distributional checks for sparse.randn.
|
||
|
|
# Statistically, some of these should be negative
|
||
|
|
# and some should be greater than 1.
|
||
|
|
for random_state in None, 4321, np.random.RandomState():
|
||
|
|
x = _sprandn(10, 20, density=0.5, dtype=np.float64,
|
||
|
|
random_state=random_state)
|
||
|
|
assert_(np.any(np.less(x.data, 0)))
|
||
|
|
assert_(np.any(np.less(1, x.data)))
|
||
|
|
|
||
|
|
def test_random_accept_str_dtype(self):
|
||
|
|
# anything that np.dtype can convert to a dtype should be accepted
|
||
|
|
# for the dtype
|
||
|
|
a = construct.random(10, 10, dtype='d')
|
||
|
|
|