461 lines
15 KiB
Python
461 lines
15 KiB
Python
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from __future__ import division, absolute_import, print_function
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try:
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# Accessing collections abstract classes from collections
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# has been deprecated since Python 3.3
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import collections.abc as collections_abc
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except ImportError:
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import collections as collections_abc
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import numpy as np
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from numpy import matrix, asmatrix, bmat
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from numpy.testing import (
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assert_, assert_equal, assert_almost_equal, assert_array_equal,
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assert_array_almost_equal, assert_raises
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)
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from numpy.linalg import matrix_power
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from numpy.matrixlib import mat
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class TestCtor(object):
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def test_basic(self):
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A = np.array([[1, 2], [3, 4]])
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mA = matrix(A)
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assert_(np.all(mA.A == A))
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B = bmat("A,A;A,A")
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C = bmat([[A, A], [A, A]])
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D = np.array([[1, 2, 1, 2],
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[3, 4, 3, 4],
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[1, 2, 1, 2],
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[3, 4, 3, 4]])
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assert_(np.all(B.A == D))
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assert_(np.all(C.A == D))
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E = np.array([[5, 6], [7, 8]])
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AEresult = matrix([[1, 2, 5, 6], [3, 4, 7, 8]])
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assert_(np.all(bmat([A, E]) == AEresult))
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vec = np.arange(5)
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mvec = matrix(vec)
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assert_(mvec.shape == (1, 5))
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def test_exceptions(self):
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# Check for ValueError when called with invalid string data.
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assert_raises(ValueError, matrix, "invalid")
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def test_bmat_nondefault_str(self):
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A = np.array([[1, 2], [3, 4]])
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B = np.array([[5, 6], [7, 8]])
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Aresult = np.array([[1, 2, 1, 2],
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[3, 4, 3, 4],
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[1, 2, 1, 2],
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[3, 4, 3, 4]])
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mixresult = np.array([[1, 2, 5, 6],
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[3, 4, 7, 8],
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[5, 6, 1, 2],
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[7, 8, 3, 4]])
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assert_(np.all(bmat("A,A;A,A") == Aresult))
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assert_(np.all(bmat("A,A;A,A", ldict={'A':B}) == Aresult))
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assert_raises(TypeError, bmat, "A,A;A,A", gdict={'A':B})
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assert_(
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np.all(bmat("A,A;A,A", ldict={'A':A}, gdict={'A':B}) == Aresult))
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b2 = bmat("A,B;C,D", ldict={'A':A,'B':B}, gdict={'C':B,'D':A})
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assert_(np.all(b2 == mixresult))
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class TestProperties(object):
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def test_sum(self):
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"""Test whether matrix.sum(axis=1) preserves orientation.
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Fails in NumPy <= 0.9.6.2127.
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"""
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M = matrix([[1, 2, 0, 0],
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[3, 4, 0, 0],
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[1, 2, 1, 2],
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[3, 4, 3, 4]])
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sum0 = matrix([8, 12, 4, 6])
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sum1 = matrix([3, 7, 6, 14]).T
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sumall = 30
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assert_array_equal(sum0, M.sum(axis=0))
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assert_array_equal(sum1, M.sum(axis=1))
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assert_equal(sumall, M.sum())
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assert_array_equal(sum0, np.sum(M, axis=0))
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assert_array_equal(sum1, np.sum(M, axis=1))
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assert_equal(sumall, np.sum(M))
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def test_prod(self):
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x = matrix([[1, 2, 3], [4, 5, 6]])
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assert_equal(x.prod(), 720)
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assert_equal(x.prod(0), matrix([[4, 10, 18]]))
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assert_equal(x.prod(1), matrix([[6], [120]]))
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assert_equal(np.prod(x), 720)
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assert_equal(np.prod(x, axis=0), matrix([[4, 10, 18]]))
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assert_equal(np.prod(x, axis=1), matrix([[6], [120]]))
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y = matrix([0, 1, 3])
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assert_(y.prod() == 0)
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def test_max(self):
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x = matrix([[1, 2, 3], [4, 5, 6]])
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assert_equal(x.max(), 6)
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assert_equal(x.max(0), matrix([[4, 5, 6]]))
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assert_equal(x.max(1), matrix([[3], [6]]))
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assert_equal(np.max(x), 6)
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assert_equal(np.max(x, axis=0), matrix([[4, 5, 6]]))
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assert_equal(np.max(x, axis=1), matrix([[3], [6]]))
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def test_min(self):
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x = matrix([[1, 2, 3], [4, 5, 6]])
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assert_equal(x.min(), 1)
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assert_equal(x.min(0), matrix([[1, 2, 3]]))
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assert_equal(x.min(1), matrix([[1], [4]]))
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assert_equal(np.min(x), 1)
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assert_equal(np.min(x, axis=0), matrix([[1, 2, 3]]))
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assert_equal(np.min(x, axis=1), matrix([[1], [4]]))
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def test_ptp(self):
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x = np.arange(4).reshape((2, 2))
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assert_(x.ptp() == 3)
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assert_(np.all(x.ptp(0) == np.array([2, 2])))
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assert_(np.all(x.ptp(1) == np.array([1, 1])))
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def test_var(self):
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x = np.arange(9).reshape((3, 3))
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mx = x.view(np.matrix)
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assert_equal(x.var(ddof=0), mx.var(ddof=0))
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assert_equal(x.var(ddof=1), mx.var(ddof=1))
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def test_basic(self):
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import numpy.linalg as linalg
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A = np.array([[1., 2.],
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[3., 4.]])
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mA = matrix(A)
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assert_(np.allclose(linalg.inv(A), mA.I))
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assert_(np.all(np.array(np.transpose(A) == mA.T)))
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assert_(np.all(np.array(np.transpose(A) == mA.H)))
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assert_(np.all(A == mA.A))
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B = A + 2j*A
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mB = matrix(B)
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assert_(np.allclose(linalg.inv(B), mB.I))
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assert_(np.all(np.array(np.transpose(B) == mB.T)))
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assert_(np.all(np.array(np.transpose(B).conj() == mB.H)))
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def test_pinv(self):
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x = matrix(np.arange(6).reshape(2, 3))
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xpinv = matrix([[-0.77777778, 0.27777778],
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[-0.11111111, 0.11111111],
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[ 0.55555556, -0.05555556]])
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assert_almost_equal(x.I, xpinv)
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def test_comparisons(self):
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A = np.arange(100).reshape(10, 10)
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mA = matrix(A)
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mB = matrix(A) + 0.1
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assert_(np.all(mB == A+0.1))
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assert_(np.all(mB == matrix(A+0.1)))
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assert_(not np.any(mB == matrix(A-0.1)))
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assert_(np.all(mA < mB))
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assert_(np.all(mA <= mB))
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assert_(np.all(mA <= mA))
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assert_(not np.any(mA < mA))
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assert_(not np.any(mB < mA))
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assert_(np.all(mB >= mA))
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assert_(np.all(mB >= mB))
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assert_(not np.any(mB > mB))
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assert_(np.all(mA == mA))
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assert_(not np.any(mA == mB))
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assert_(np.all(mB != mA))
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assert_(not np.all(abs(mA) > 0))
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assert_(np.all(abs(mB > 0)))
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def test_asmatrix(self):
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A = np.arange(100).reshape(10, 10)
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mA = asmatrix(A)
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A[0, 0] = -10
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assert_(A[0, 0] == mA[0, 0])
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def test_noaxis(self):
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A = matrix([[1, 0], [0, 1]])
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assert_(A.sum() == matrix(2))
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assert_(A.mean() == matrix(0.5))
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def test_repr(self):
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A = matrix([[1, 0], [0, 1]])
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assert_(repr(A) == "matrix([[1, 0],\n [0, 1]])")
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def test_make_bool_matrix_from_str(self):
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A = matrix('True; True; False')
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B = matrix([[True], [True], [False]])
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assert_array_equal(A, B)
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class TestCasting(object):
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def test_basic(self):
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A = np.arange(100).reshape(10, 10)
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mA = matrix(A)
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mB = mA.copy()
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O = np.ones((10, 10), np.float64) * 0.1
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mB = mB + O
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assert_(mB.dtype.type == np.float64)
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assert_(np.all(mA != mB))
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assert_(np.all(mB == mA+0.1))
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mC = mA.copy()
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O = np.ones((10, 10), np.complex128)
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mC = mC * O
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assert_(mC.dtype.type == np.complex128)
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assert_(np.all(mA != mB))
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class TestAlgebra(object):
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def test_basic(self):
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import numpy.linalg as linalg
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A = np.array([[1., 2.], [3., 4.]])
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mA = matrix(A)
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B = np.identity(2)
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for i in range(6):
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assert_(np.allclose((mA ** i).A, B))
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B = np.dot(B, A)
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Ainv = linalg.inv(A)
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B = np.identity(2)
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for i in range(6):
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assert_(np.allclose((mA ** -i).A, B))
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B = np.dot(B, Ainv)
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assert_(np.allclose((mA * mA).A, np.dot(A, A)))
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assert_(np.allclose((mA + mA).A, (A + A)))
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assert_(np.allclose((3*mA).A, (3*A)))
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mA2 = matrix(A)
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mA2 *= 3
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assert_(np.allclose(mA2.A, 3*A))
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def test_pow(self):
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"""Test raising a matrix to an integer power works as expected."""
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m = matrix("1. 2.; 3. 4.")
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m2 = m.copy()
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m2 **= 2
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mi = m.copy()
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mi **= -1
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m4 = m2.copy()
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m4 **= 2
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assert_array_almost_equal(m2, m**2)
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assert_array_almost_equal(m4, np.dot(m2, m2))
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assert_array_almost_equal(np.dot(mi, m), np.eye(2))
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def test_scalar_type_pow(self):
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m = matrix([[1, 2], [3, 4]])
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for scalar_t in [np.int8, np.uint8]:
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two = scalar_t(2)
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assert_array_almost_equal(m ** 2, m ** two)
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def test_notimplemented(self):
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'''Check that 'not implemented' operations produce a failure.'''
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A = matrix([[1., 2.],
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[3., 4.]])
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# __rpow__
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with assert_raises(TypeError):
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1.0**A
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# __mul__ with something not a list, ndarray, tuple, or scalar
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with assert_raises(TypeError):
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A*object()
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class TestMatrixReturn(object):
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def test_instance_methods(self):
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a = matrix([1.0], dtype='f8')
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methodargs = {
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'astype': ('intc',),
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'clip': (0.0, 1.0),
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'compress': ([1],),
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'repeat': (1,),
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'reshape': (1,),
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'swapaxes': (0, 0),
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'dot': np.array([1.0]),
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}
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excluded_methods = [
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'argmin', 'choose', 'dump', 'dumps', 'fill', 'getfield',
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'getA', 'getA1', 'item', 'nonzero', 'put', 'putmask', 'resize',
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'searchsorted', 'setflags', 'setfield', 'sort',
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'partition', 'argpartition',
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'take', 'tofile', 'tolist', 'tostring', 'tobytes', 'all', 'any',
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'sum', 'argmax', 'argmin', 'min', 'max', 'mean', 'var', 'ptp',
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'prod', 'std', 'ctypes', 'itemset',
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]
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for attrib in dir(a):
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if attrib.startswith('_') or attrib in excluded_methods:
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continue
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f = getattr(a, attrib)
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if isinstance(f, collections_abc.Callable):
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# reset contents of a
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a.astype('f8')
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a.fill(1.0)
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if attrib in methodargs:
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args = methodargs[attrib]
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else:
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args = ()
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b = f(*args)
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assert_(type(b) is matrix, "%s" % attrib)
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assert_(type(a.real) is matrix)
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assert_(type(a.imag) is matrix)
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c, d = matrix([0.0]).nonzero()
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assert_(type(c) is np.ndarray)
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assert_(type(d) is np.ndarray)
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class TestIndexing(object):
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def test_basic(self):
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x = asmatrix(np.zeros((3, 2), float))
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y = np.zeros((3, 1), float)
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y[:, 0] = [0.8, 0.2, 0.3]
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x[:, 1] = y > 0.5
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assert_equal(x, [[0, 1], [0, 0], [0, 0]])
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class TestNewScalarIndexing(object):
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a = matrix([[1, 2], [3, 4]])
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def test_dimesions(self):
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a = self.a
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x = a[0]
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assert_equal(x.ndim, 2)
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def test_array_from_matrix_list(self):
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a = self.a
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x = np.array([a, a])
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assert_equal(x.shape, [2, 2, 2])
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def test_array_to_list(self):
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|
a = self.a
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assert_equal(a.tolist(), [[1, 2], [3, 4]])
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|
|
|
||
|
|
def test_fancy_indexing(self):
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|
a = self.a
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|
|
x = a[1, [0, 1, 0]]
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||
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|
assert_(isinstance(x, matrix))
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||
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|
assert_equal(x, matrix([[3, 4, 3]]))
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||
|
|
x = a[[1, 0]]
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||
|
|
assert_(isinstance(x, matrix))
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||
|
|
assert_equal(x, matrix([[3, 4], [1, 2]]))
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||
|
|
x = a[[[1], [0]], [[1, 0], [0, 1]]]
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||
|
|
assert_(isinstance(x, matrix))
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||
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|
assert_equal(x, matrix([[4, 3], [1, 2]]))
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|
|
|
||
|
|
def test_matrix_element(self):
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|
x = matrix([[1, 2, 3], [4, 5, 6]])
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|
assert_equal(x[0][0], matrix([[1, 2, 3]]))
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||
|
|
assert_equal(x[0][0].shape, (1, 3))
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||
|
|
assert_equal(x[0].shape, (1, 3))
|
||
|
|
assert_equal(x[:, 0].shape, (2, 1))
|
||
|
|
|
||
|
|
x = matrix(0)
|
||
|
|
assert_equal(x[0, 0], 0)
|
||
|
|
assert_equal(x[0], 0)
|
||
|
|
assert_equal(x[:, 0].shape, x.shape)
|
||
|
|
|
||
|
|
def test_scalar_indexing(self):
|
||
|
|
x = asmatrix(np.zeros((3, 2), float))
|
||
|
|
assert_equal(x[0, 0], x[0][0])
|
||
|
|
|
||
|
|
def test_row_column_indexing(self):
|
||
|
|
x = asmatrix(np.eye(2))
|
||
|
|
assert_array_equal(x[0,:], [[1, 0]])
|
||
|
|
assert_array_equal(x[1,:], [[0, 1]])
|
||
|
|
assert_array_equal(x[:, 0], [[1], [0]])
|
||
|
|
assert_array_equal(x[:, 1], [[0], [1]])
|
||
|
|
|
||
|
|
def test_boolean_indexing(self):
|
||
|
|
A = np.arange(6)
|
||
|
|
A.shape = (3, 2)
|
||
|
|
x = asmatrix(A)
|
||
|
|
assert_array_equal(x[:, np.array([True, False])], x[:, 0])
|
||
|
|
assert_array_equal(x[np.array([True, False, False]),:], x[0,:])
|
||
|
|
|
||
|
|
def test_list_indexing(self):
|
||
|
|
A = np.arange(6)
|
||
|
|
A.shape = (3, 2)
|
||
|
|
x = asmatrix(A)
|
||
|
|
assert_array_equal(x[:, [1, 0]], x[:, ::-1])
|
||
|
|
assert_array_equal(x[[2, 1, 0],:], x[::-1,:])
|
||
|
|
|
||
|
|
|
||
|
|
class TestPower(object):
|
||
|
|
def test_returntype(self):
|
||
|
|
a = np.array([[0, 1], [0, 0]])
|
||
|
|
assert_(type(matrix_power(a, 2)) is np.ndarray)
|
||
|
|
a = mat(a)
|
||
|
|
assert_(type(matrix_power(a, 2)) is matrix)
|
||
|
|
|
||
|
|
def test_list(self):
|
||
|
|
assert_array_equal(matrix_power([[0, 1], [0, 0]], 2), [[0, 0], [0, 0]])
|
||
|
|
|
||
|
|
|
||
|
|
class TestShape(object):
|
||
|
|
|
||
|
|
a = np.array([[1], [2]])
|
||
|
|
m = matrix([[1], [2]])
|
||
|
|
|
||
|
|
def test_shape(self):
|
||
|
|
assert_equal(self.a.shape, (2, 1))
|
||
|
|
assert_equal(self.m.shape, (2, 1))
|
||
|
|
|
||
|
|
def test_numpy_ravel(self):
|
||
|
|
assert_equal(np.ravel(self.a).shape, (2,))
|
||
|
|
assert_equal(np.ravel(self.m).shape, (2,))
|
||
|
|
|
||
|
|
def test_member_ravel(self):
|
||
|
|
assert_equal(self.a.ravel().shape, (2,))
|
||
|
|
assert_equal(self.m.ravel().shape, (1, 2))
|
||
|
|
|
||
|
|
def test_member_flatten(self):
|
||
|
|
assert_equal(self.a.flatten().shape, (2,))
|
||
|
|
assert_equal(self.m.flatten().shape, (1, 2))
|
||
|
|
|
||
|
|
def test_numpy_ravel_order(self):
|
||
|
|
x = np.array([[1, 2, 3], [4, 5, 6]])
|
||
|
|
assert_equal(np.ravel(x), [1, 2, 3, 4, 5, 6])
|
||
|
|
assert_equal(np.ravel(x, order='F'), [1, 4, 2, 5, 3, 6])
|
||
|
|
assert_equal(np.ravel(x.T), [1, 4, 2, 5, 3, 6])
|
||
|
|
assert_equal(np.ravel(x.T, order='A'), [1, 2, 3, 4, 5, 6])
|
||
|
|
x = matrix([[1, 2, 3], [4, 5, 6]])
|
||
|
|
assert_equal(np.ravel(x), [1, 2, 3, 4, 5, 6])
|
||
|
|
assert_equal(np.ravel(x, order='F'), [1, 4, 2, 5, 3, 6])
|
||
|
|
assert_equal(np.ravel(x.T), [1, 4, 2, 5, 3, 6])
|
||
|
|
assert_equal(np.ravel(x.T, order='A'), [1, 2, 3, 4, 5, 6])
|
||
|
|
|
||
|
|
def test_matrix_ravel_order(self):
|
||
|
|
x = matrix([[1, 2, 3], [4, 5, 6]])
|
||
|
|
assert_equal(x.ravel(), [[1, 2, 3, 4, 5, 6]])
|
||
|
|
assert_equal(x.ravel(order='F'), [[1, 4, 2, 5, 3, 6]])
|
||
|
|
assert_equal(x.T.ravel(), [[1, 4, 2, 5, 3, 6]])
|
||
|
|
assert_equal(x.T.ravel(order='A'), [[1, 2, 3, 4, 5, 6]])
|
||
|
|
|
||
|
|
def test_array_memory_sharing(self):
|
||
|
|
assert_(np.may_share_memory(self.a, self.a.ravel()))
|
||
|
|
assert_(not np.may_share_memory(self.a, self.a.flatten()))
|
||
|
|
|
||
|
|
def test_matrix_memory_sharing(self):
|
||
|
|
assert_(np.may_share_memory(self.m, self.m.ravel()))
|
||
|
|
assert_(not np.may_share_memory(self.m, self.m.flatten()))
|
||
|
|
|
||
|
|
def test_expand_dims_matrix(self):
|
||
|
|
# matrices are always 2d - so expand_dims only makes sense when the
|
||
|
|
# type is changed away from matrix.
|
||
|
|
a = np.arange(10).reshape((2, 5)).view(np.matrix)
|
||
|
|
expanded = np.expand_dims(a, axis=1)
|
||
|
|
assert_equal(expanded.ndim, 3)
|
||
|
|
assert_(not isinstance(expanded, np.matrix))
|