"""test sparse matrix construction functions"""
import numpy as np
from numpy import array
from numpy.testing import (assert_equal, assert_,
assert_array_equal, assert_array_almost_equal_nulp)
import pytest
from pytest import raises as assert_raises
from scipy._lib._testutils import check_free_memory
from scipy._lib._util import check_random_state
from scipy.sparse import csr_matrix, coo_matrix, construct
from scipy.sparse.construct import rand as sprand
from scipy.sparse.sputils import matrix
sparse_formats = ['csr','csc','coo','bsr','dia','lil','dok']
#TODO check whether format=XXX is respected
def _sprandn(m, n, density=0.01, format="coo", dtype=None, random_state=None):
# Helper function for testing.
random_state = check_random_state(random_state)
data_rvs = random_state.standard_normal
return construct.random(m, n, density, format, dtype,
random_state, data_rvs)
class TestConstructUtils(object):
def test_spdiags(self):
diags1 = array([[1, 2, 3, 4, 5]])
diags2 = array([[1, 2, 3, 4, 5],
[6, 7, 8, 9,10]])
diags3 = array([[1, 2, 3, 4, 5],
[6, 7, 8, 9,10],
[11,12,13,14,15]])
cases = []
cases.append((diags1, 0, 1, 1, [[1]]))
cases.append((diags1, [0], 1, 1, [[1]]))
cases.append((diags1, [0], 2, 1, [[1],[0]]))
cases.append((diags1, [0], 1, 2, [[1,0]]))
cases.append((diags1, [1], 1, 2, [[0,2]]))
cases.append((diags1,[-1], 1, 2, [[0,0]]))
cases.append((diags1, [0], 2, 2, [[1,0],[0,2]]))
cases.append((diags1,[-1], 2, 2, [[0,0],[1,0]]))
cases.append((diags1, [3], 2, 2, [[0,0],[0,0]]))
cases.append((diags1, [0], 3, 4, [[1,0,0,0],[0,2,0,0],[0,0,3,0]]))
cases.append((diags1, [1], 3, 4, [[0,2,0,0],[0,0,3,0],[0,0,0,4]]))
cases.append((diags1, [2], 3, 5, [[0,0,3,0,0],[0,0,0,4,0],[0,0,0,0,5]]))
cases.append((diags2, [0,2], 3, 3, [[1,0,8],[0,2,0],[0,0,3]]))
cases.append((diags2, [-1,0], 3, 4, [[6,0,0,0],[1,7,0,0],[0,2,8,0]]))
cases.append((diags2, [2,-3], 6, 6, [[0,0,3,0,0,0],
[0,0,0,4,0,0],
[0,0,0,0,5,0],
[6,0,0,0,0,0],
[0,7,0,0,0,0],
[0,0,8,0,0,0]]))
cases.append((diags3, [-1,0,1], 6, 6, [[6,12, 0, 0, 0, 0],
[1, 7,13, 0, 0, 0],
[0, 2, 8,14, 0, 0],
[0, 0, 3, 9,15, 0],
[0, 0, 0, 4,10, 0],
[0, 0, 0, 0, 5, 0]]))
cases.append((diags3, [-4,2,-1], 6, 5, [[0, 0, 8, 0, 0],
[11, 0, 0, 9, 0],
[0,12, 0, 0,10],
[0, 0,13, 0, 0],
[1, 0, 0,14, 0],
[0, 2, 0, 0,15]]))
for d,o,m,n,result in cases:
assert_equal(construct.spdiags(d,o,m,n).todense(), result)
def test_diags(self):
a = array([1, 2, 3, 4, 5])
b = array([6, 7, 8, 9, 10])
c = array([11, 12, 13, 14, 15])
cases = []
cases.append((a[:1], 0, (1, 1), [[1]]))
cases.append(([a[:1]], [0], (1, 1), [[1]]))
cases.append(([a[:1]], [0], (2, 1), [[1],[0]]))
cases.append(([a[:1]], [0], (1, 2), [[1,0]]))
cases.append(([a[:1]], [1], (1, 2), [[0,1]]))
cases.append(([a[:2]], [0], (2, 2), [[1,0],[0,2]]))
cases.append(([a[:1]],[-1], (2, 2), [[0,0],[1,0]]))
cases.append(([a[:3]], [0], (3, 4), [[1,0,0,0],[0,2,0,0],[0,0,3,0]]))
cases.append(([a[:3]], [1], (3, 4), [[0,1,0,0],[0,0,2,0],[0,0,0,3]]))
cases.append(([a[:1]], [-2], (3, 5), [[0,0,0,0,0],[0,0,0,0,0],[1,0,0,0,0]]))
cases.append(([a[:2]], [-1], (3, 5), [[0,0,0,0,0],[1,0,0,0,0],[0,2,0,0,0]]))
cases.append(([a[:3]], [0], (3, 5), [[1,0,0,0,0],[0,2,0,0,0],[0,0,3,0,0]]))
cases.append(([a[:3]], [1], (3, 5), [[0,1,0,0,0],[0,0,2,0,0],[0,0,0,3,0]]))
cases.append(([a[:3]], [2], (3, 5), [[0,0,1,0,0],[0,0,0,2,0],[0,0,0,0,3]]))
cases.append(([a[:2]], [3], (3, 5), [[0,0,0,1,0],[0,0,0,0,2],[0,0,0,0,0]]))
cases.append(([a[:1]], [4], (3, 5), [[0,0,0,0,1],[0,0,0,0,0],[0,0,0,0,0]]))
cases.append(([a[:1]], [-4], (5, 3), [[0,0,0],[0,0,0],[0,0,0],[0,0,0],[1,0,0]]))
cases.append(([a[:2]], [-3], (5, 3), [[0,0,0],[0,0,0],[0,0,0],[1,0,0],[0,2,0]]))
cases.append(([a[:3]], [-2], (5, 3), [[0,0,0],[0,0,0],[1,0,0],[0,2,0],[0,0,3]]))
cases.append(([a[:3]], [-1], (5, 3), [[0,0,0],[1,0,0],[0,2,0],[0,0,3],[0,0,0]]))
cases.append(([a[:3]], [0], (5, 3), [[1,0,0],[0,2,0],[0,0,3],[0,0,0],[0,0,0]]))
cases.append(([a[:2]], [1], (5, 3), [[0,1,0],[0,0,2],[0,0,0],[0,0,0],[0,0,0]]))
cases.append(([a[:1]], [2], (5, 3), [[0,0,1],[0,0,0],[0,0,0],[0,0,0],[0,0,0]]))
cases.append(([a[:3],b[:1]], [0,2], (3, 3), [[1,0,6],[0,2,0],[0,0,3]]))
cases.append(([a[:2],b[:3]], [-1,0], (3, 4), [[6,0,0,0],[1,7,0,0],[0,2,8,0]]))
cases.append(([a[:4],b[:3]], [2,-3], (6, 6), [[0,0,1,0,0,0],
[0,0,0,2,0,0],
[0,0,0,0,3,0],
[6,0,0,0,0,4],
[0,7,0,0,0,0],
[0,0,8,0,0,0]]))
cases.append(([a[:4],b,c[:4]], [-1,0,1], (5, 5), [[6,11, 0, 0, 0],
[1, 7,12, 0, 0],
[0, 2, 8,13, 0],
[0, 0, 3, 9,14],
[0, 0, 0, 4,10]]))
cases.append(([a[:2],b[:3],c], [-4,2,-1], (6, 5), [[0, 0, 6, 0, 0],
[11, 0, 0, 7, 0],
[0,12, 0, 0, 8],
[0, 0,13, 0, 0],
[1, 0, 0,14, 0],
[0, 2, 0, 0,15]]))
# too long arrays are OK
cases.append(([a], [0], (1, 1), [[1]]))
cases.append(([a[:3],b], [0,2], (3, 3), [[1, 0, 6], [0, 2, 0], [0, 0, 3]]))
cases.append((np.array([[1, 2, 3], [4, 5, 6]]), [0,-1], (3, 3), [[1, 0, 0], [4, 2, 0], [0, 5, 3]]))
# scalar case: broadcasting
cases.append(([1,-2,1], [1,0,-1], (3, 3), [[-2, 1, 0],
[1, -2, 1],
[0, 1, -2]]))
for d, o, shape, result in cases:
err_msg = "%r %r %r %r" % (d, o, shape, result)
assert_equal(construct.diags(d, o, shape=shape).todense(),
result, err_msg=err_msg)
if shape[0] == shape[1] and hasattr(d[0], '__len__') and len(d[0]) <= max(shape):
# should be able to find the shape automatically
assert_equal(construct.diags(d, o).todense(), result,
err_msg=err_msg)
def test_diags_default(self):
a = array([1, 2, 3, 4, 5])
assert_equal(construct.diags(a).todense(), np.diag(a))
def test_diags_default_bad(self):
a = array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6]])
assert_raises(ValueError, construct.diags, a)
def test_diags_bad(self):
a = array([1, 2, 3, 4, 5])
b = array([6, 7, 8, 9, 10])
c = array([11, 12, 13, 14, 15])
cases = []
cases.append(([a[:0]], 0, (1, 1)))
cases.append(([a[:4],b,c[:3]], [-1,0,1], (5, 5)))
cases.append(([a[:2],c,b[:3]], [-4,2,-1], (6, 5)))
cases.append(([a[:2],c,b[:3]], [-4,2,-1], None))
cases.append(([], [-4,2,-1], None))
cases.append(([1], [-5], (4, 4)))
cases.append(([a], 0, None))
for d, o, shape in cases:
assert_raises(ValueError, construct.diags, d, o, shape)
assert_raises(TypeError, construct.diags, [[None]], [0])
def test_diags_vs_diag(self):
# Check that
#
# diags([a, b, ...], [i, j, ...]) == diag(a, i) + diag(b, j) + ...
#
np.random.seed(1234)
for n_diags in [1, 2, 3, 4, 5, 10]:
n = 1 + n_diags//2 + np.random.randint(0, 10)
offsets = np.arange(-n+1, n-1)
np.random.shuffle(offsets)
offsets = offsets[:n_diags]
diagonals = [np.random.rand(n - abs(q)) for q in offsets]
mat = construct.diags(diagonals, offsets)
dense_mat = sum([np.diag(x, j) for x, j in zip(diagonals, offsets)])
assert_array_almost_equal_nulp(mat.todense(), dense_mat)
if len(offsets) == 1:
mat = construct.diags(diagonals[0], offsets[0])
dense_mat = np.diag(diagonals[0], offsets[0])
assert_array_almost_equal_nulp(mat.todense(), dense_mat)
def test_diags_dtype(self):
x = construct.diags([2.2], [0], shape=(2, 2), dtype=int)
assert_equal(x.dtype, int)
assert_equal(x.todense(), [[2, 0], [0, 2]])
def test_diags_one_diagonal(self):
d = list(range(5))
for k in range(-5, 6):
assert_equal(construct.diags(d, k).toarray(),
construct.diags([d], [k]).toarray())
def test_diags_empty(self):
x = construct.diags([])
assert_equal(x.shape, (0, 0))
def test_identity(self):
assert_equal(construct.identity(1).toarray(), [[1]])
assert_equal(construct.identity(2).toarray(), [[1,0],[0,1]])
I = construct.identity(3, dtype='int8', format='dia')
assert_equal(I.dtype, np.dtype('int8'))
assert_equal(I.format, 'dia')
for fmt in sparse_formats:
I = construct.identity(3, format=fmt)
assert_equal(I.format, fmt)
assert_equal(I.toarray(), [[1,0,0],[0,1,0],[0,0,1]])
def test_eye(self):
assert_equal(construct.eye(1,1).toarray(), [[1]])
assert_equal(construct.eye(2,3).toarray(), [[1,0,0],[0,1,0]])
assert_equal(construct.eye(3,2).toarray(), [[1,0],[0,1],[0,0]])
assert_equal(construct.eye(3,3).toarray(), [[1,0,0],[0,1,0],[0,0,1]])
assert_equal(construct.eye(3,3,dtype='int16').dtype, np.dtype('int16'))
for m in [3, 5]:
for n in [3, 5]:
for k in range(-5,6):
assert_equal(construct.eye(m, n, k=k).toarray(), np.eye(m, n, k=k))
if m == n:
assert_equal(construct.eye(m, k=k).toarray(), np.eye(m, n, k=k))
def test_eye_one(self):
assert_equal(construct.eye(1).toarray(), [[1]])
assert_equal(construct.eye(2).toarray(), [[1,0],[0,1]])
I = construct.eye(3, dtype='int8', format='dia')
assert_equal(I.dtype, np.dtype('int8'))
assert_equal(I.format, 'dia')
for fmt in sparse_formats:
I = construct.eye(3, format=fmt)
assert_equal(I.format, fmt)
assert_equal(I.toarray(), [[1,0,0],[0,1,0],[0,0,1]])
def test_kron(self):
cases = []
cases.append(array([[0]]))
cases.append(array([[-1]]))
cases.append(array([[4]]))
cases.append(array([[10]]))
cases.append(array([[0],[0]]))
cases.append(array([[0,0]]))
cases.append(array([[1,2],[3,4]]))
cases.append(array([[0,2],[5,0]]))
cases.append(array([[0,2,-6],[8,0,14]]))
cases.append(array([[5,4],[0,0],[6,0]]))
cases.append(array([[5,4,4],[1,0,0],[6,0,8]]))
cases.append(array([[0,1,0,2,0,5,8]]))
cases.append(array([[0.5,0.125,0,3.25],[0,2.5,0,0]]))
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_kron_large(self):
n = 2**16
a = construct.eye(1, n, n-1)
b = construct.eye(n, 1, 1-n)
construct.kron(a, a)
construct.kron(b, b)
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.
random_states = [None, 4321, np.random.RandomState()]
try:
gen = np.random.default_rng()
random_states.append(gen)
except AttributeError:
pass
for random_state in random_states:
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.
random_states = [None, 4321, np.random.RandomState()]
try:
gen = np.random.default_rng()
random_states.append(gen)
except AttributeError:
pass
for random_state in random_states:
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
construct.random(10, 10, dtype='d')
def test_random_sparse_matrix_returns_correct_number_of_non_zero_elements(self):
# A 10 x 10 matrix, with density of 12.65%, should have 13 nonzero elements.
# 10 x 10 x 0.1265 = 12.65, which should be rounded up to 13, not 12.
sparse_matrix = construct.random(10, 10, density=0.1265)
assert_equal(sparse_matrix.count_nonzero(),13)