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################################################################################
# Copyright (C) 2013 Jaakko Luttinen
#
# This file is licensed under the MIT License.
################################################################################
"""
Unit tests for bayespy.utils.linalg module.
"""
import numpy as np
from .. import misc
from .. import linalg
class TestDot(misc.TestCase):
def test_dot(self):
"""
Test dot product multiple multi-dimensional arrays.
"""
# If no arrays, return 0
self.assertAllClose(linalg.dot(),
0)
# If only one array, return itself
self.assertAllClose(linalg.dot([[1,2,3],
[4,5,6]]),
[[1,2,3],
[4,5,6]])
# Basic test of two arrays: (2,3) * (3,2)
self.assertAllClose(linalg.dot([[1,2,3],
[4,5,6]],
[[7,8],
[9,1],
[2,3]]),
[[31,19],
[85,55]])
# Basic test of four arrays: (2,3) * (3,2) * (2,1) * (1,2)
self.assertAllClose(linalg.dot([[1,2,3],
[4,5,6]],
[[7,8],
[9,1],
[2,3]],
[[4],
[5]],
[[6,7]]),
[[1314,1533],
[3690,4305]])
# Test broadcasting: (2,2,2) * (2,2,2,2)
self.assertAllClose(linalg.dot([[[1,2],
[3,4]],
[[5,6],
[7,8]]],
[[[[1,2],
[3,4]],
[[5,6],
[7,8]]],
[[[9,1],
[2,3]],
[[4,5],
[6,7]]]]),
[[[[ 7, 10],
[ 15, 22]],
[[ 67, 78],
[ 91, 106]]],
[[[ 13, 7],
[ 35, 15]],
[[ 56, 67],
[ 76, 91]]]])
# Inconsistent shapes: (2,3) * (2,3)
self.assertRaises(ValueError,
linalg.dot,
[[1,2,3],
[4,5,6]],
[[1,2,3],
[4,5,6]])
# Other axes do not broadcast: (2,2,2) * (3,2,2)
self.assertRaises(ValueError,
linalg.dot,
[[[1,2],
[3,4]],
[[5,6],
[7,8]]],
[[[1,2],
[3,4]],
[[5,6],
[7,8]],
[[9,1],
[2,3]]])
# Do not broadcast matrix axes: (2,1) * (3,2)
self.assertRaises(ValueError,
linalg.dot,
[[1],
[2]],
[[1,2,3],
[4,5,6]])
# Do not accept less than 2-D arrays: (2) * (2,2)
self.assertRaises(ValueError,
linalg.dot,
[1,2],
[[1,2,3],
[4,5,6]])
class TestBandedSolve(misc.TestCase):
def test_block_banded_solve(self):
"""
Test the Gaussian elimination algorithm for block-banded matrices.
"""
#
# Create a block-banded matrix
#
# Number of blocks
N = 40
# Random sizes of the blocks
#D = np.random.randint(5, 10, size=N)
# Fixed sizes of the blocks
D = 5*np.ones(N, dtype=np.int64)
# Some helpful variables to create the covariances
W = [np.random.randn(D[i], 2*D[i])
for i in range(N)]
# The diagonal blocks (covariances)
A = [np.dot(W[i], W[i].T) for i in range(N)]
# The superdiagonal blocks (cross-covariances)
B = [np.dot(W[i][:,-1:], W[i+1][:,:1].T) for i in range(N-1)]
C = misc.block_banded(A, B)
# Create the system to be solved: y=C*x
x_true = np.random.randn(np.sum(D))
y = np.dot(C, x_true)
x_true = np.reshape(x_true, (N, -1))
y = np.reshape(y, (N, -1))
#
# Run tests
#
# The correct inverse
invC = np.linalg.inv(C)
# Inverse from the function that is tested
(invA, invB, x, ldet) = linalg.block_banded_solve(np.asarray(A),
np.asarray(B),
np.asarray(y))
# Check that you get the correct number of blocks
self.assertEqual(len(invA), N)
self.assertEqual(len(invB), N-1)
# Check each block
i0 = 0
for i in range(N-1):
i1 = i0 + D[i]
i2 = i1 + D[i+1]
# Check diagonal block
self.assertTrue(np.allclose(invA[i], invC[i0:i1, i0:i1]))
# Check super-diagonal block
self.assertTrue(np.allclose(invB[i], invC[i0:i1, i1:i2]))
i0 = i1
# Check last block
self.assertTrue(np.allclose(invA[-1], invC[i0:, i0:]))
# Check the solution of the system
self.assertTrue(np.allclose(x_true, x))
# Check the log determinant
self.assertAlmostEqual(ldet/np.linalg.slogdet(C)[1], 1)
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