254 lines
7.8 KiB
Python
254 lines
7.8 KiB
Python
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import pytest
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import sys
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from mpmath import *
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def test_matrix_basic():
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A1 = matrix(3)
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for i in range(3):
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A1[i,i] = 1
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assert A1 == eye(3)
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assert A1 == matrix(A1)
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A2 = matrix(3, 2)
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assert not A2._matrix__data
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A3 = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
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assert list(A3) == list(range(1, 10))
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A3[1,1] = 0
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assert not (1, 1) in A3._matrix__data
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A4 = matrix([[1, 2, 3], [4, 5, 6]])
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A5 = matrix([[6, -1], [3, 2], [0, -3]])
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assert A4 * A5 == matrix([[12, -6], [39, -12]])
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assert A1 * A3 == A3 * A1 == A3
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pytest.raises(ValueError, lambda: A2*A2)
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l = [[10, 20, 30], [40, 0, 60], [70, 80, 90]]
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A6 = matrix(l)
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assert A6.tolist() == l
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assert A6 == eval(repr(A6))
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A6 = fp.matrix(A6)
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assert A6 == eval(repr(A6))
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assert A6*1j == eval(repr(A6*1j))
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assert A3 * 10 == 10 * A3 == A6
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assert A2.rows == 3
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assert A2.cols == 2
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A3.rows = 2
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A3.cols = 2
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assert len(A3._matrix__data) == 3
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assert A4 + A4 == 2*A4
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pytest.raises(ValueError, lambda: A4 + A2)
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assert sum(A1 - A1) == 0
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A7 = matrix([[1, 2], [3, 4], [5, 6], [7, 8]])
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x = matrix([10, -10])
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assert A7*x == matrix([-10, -10, -10, -10])
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A8 = ones(5)
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assert sum((A8 + 1) - (2 - zeros(5))) == 0
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assert (1 + ones(4)) / 2 - 1 == zeros(4)
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assert eye(3)**10 == eye(3)
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pytest.raises(ValueError, lambda: A7**2)
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A9 = randmatrix(3)
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A10 = matrix(A9)
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A9[0,0] = -100
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assert A9 != A10
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assert nstr(A9)
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def test_matmul():
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"""
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Test the PEP465 "@" matrix multiplication syntax.
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To avoid syntax errors when importing this file in Python 3.5 and below, we have to use exec() - sorry for that.
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"""
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# TODO remove exec() wrapper as soon as we drop support for Python <= 3.5
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if sys.hexversion < 0x30500f0:
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# we are on Python < 3.5
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pytest.skip("'@' (__matmul__) is only supported in Python 3.5 or newer")
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A4 = matrix([[1, 2, 3], [4, 5, 6]])
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A5 = matrix([[6, -1], [3, 2], [0, -3]])
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exec("assert A4 @ A5 == A4 * A5")
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def test_matrix_slices():
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A = matrix([ [1, 2, 3],
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[4, 5 ,6],
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[7, 8 ,9]])
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V = matrix([1,2,3,4,5])
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# Get slice
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assert A[:,:] == A
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assert A[:,1] == matrix([[2],[5],[8]])
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assert A[2,:] == matrix([[7, 8 ,9]])
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assert A[1:3,1:3] == matrix([[5,6],[8,9]])
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assert V[2:4] == matrix([3,4])
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pytest.raises(IndexError, lambda: A[:,1:6])
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# Assign slice with matrix
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A1 = matrix(3)
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A1[:,:] = A
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assert A1[:,:] == matrix([[1, 2, 3],
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[4, 5 ,6],
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[7, 8 ,9]])
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A1[0,:] = matrix([[10, 11, 12]])
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assert A1 == matrix([ [10, 11, 12],
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[4, 5 ,6],
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[7, 8 ,9]])
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A1[:,2] = matrix([[13], [14], [15]])
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assert A1 == matrix([ [10, 11, 13],
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[4, 5 ,14],
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[7, 8 ,15]])
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A1[:2,:2] = matrix([[16, 17], [18 , 19]])
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assert A1 == matrix([ [16, 17, 13],
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[18, 19 ,14],
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[7, 8 ,15]])
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V[1:3] = 10
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assert V == matrix([1,10,10,4,5])
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with pytest.raises(ValueError):
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A1[2,:] = A[:,1]
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with pytest.raises(IndexError):
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A1[2,1:20] = A[:,:]
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# Assign slice with scalar
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A1[:,2] = 10
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assert A1 == matrix([ [16, 17, 10],
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[18, 19 ,10],
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[7, 8 ,10]])
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A1[:,:] = 40
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for x in A1:
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assert x == 40
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def test_matrix_power():
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A = matrix([[1, 2], [3, 4]])
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assert A**2 == A*A
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assert A**3 == A*A*A
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assert A**-1 == inverse(A)
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assert A**-2 == inverse(A*A)
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def test_matrix_transform():
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A = matrix([[1, 2], [3, 4], [5, 6]])
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assert A.T == A.transpose() == matrix([[1, 3, 5], [2, 4, 6]])
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swap_row(A, 1, 2)
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assert A == matrix([[1, 2], [5, 6], [3, 4]])
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l = [1, 2]
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swap_row(l, 0, 1)
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assert l == [2, 1]
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assert extend(eye(3), [1,2,3]) == matrix([[1,0,0,1],[0,1,0,2],[0,0,1,3]])
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def test_matrix_conjugate():
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A = matrix([[1 + j, 0], [2, j]])
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assert A.conjugate() == matrix([[mpc(1, -1), 0], [2, mpc(0, -1)]])
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assert A.transpose_conj() == A.H == matrix([[mpc(1, -1), 2],
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[0, mpc(0, -1)]])
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def test_matrix_creation():
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assert diag([1, 2, 3]) == matrix([[1, 0, 0], [0, 2, 0], [0, 0, 3]])
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A1 = ones(2, 3)
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assert A1.rows == 2 and A1.cols == 3
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for a in A1:
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assert a == 1
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A2 = zeros(3, 2)
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assert A2.rows == 3 and A2.cols == 2
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for a in A2:
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assert a == 0
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assert randmatrix(10) != randmatrix(10)
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one = mpf(1)
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assert hilbert(3) == matrix([[one, one/2, one/3],
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[one/2, one/3, one/4],
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[one/3, one/4, one/5]])
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def test_norms():
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# matrix norms
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A = matrix([[1, -2], [-3, -1], [2, 1]])
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assert mnorm(A,1) == 6
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assert mnorm(A,inf) == 4
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assert mnorm(A,'F') == sqrt(20)
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# vector norms
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assert norm(-3) == 3
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x = [1, -2, 7, -12]
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assert norm(x, 1) == 22
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assert round(norm(x, 2), 10) == 14.0712472795
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assert round(norm(x, 10), 10) == 12.0054633727
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assert norm(x, inf) == 12
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def test_vector():
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x = matrix([0, 1, 2, 3, 4])
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assert x == matrix([[0], [1], [2], [3], [4]])
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assert x[3] == 3
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assert len(x._matrix__data) == 4
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assert list(x) == list(range(5))
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x[0] = -10
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x[4] = 0
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assert x[0] == -10
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assert len(x) == len(x.T) == 5
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assert x.T*x == matrix([[114]])
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def test_matrix_copy():
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A = ones(6)
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B = A.copy()
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C = +A
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assert A == B
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assert A == C
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B[0,0] = 0
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assert A != B
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C[0,0] = 42
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assert A != C
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def test_matrix_numpy():
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try:
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import numpy
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except ImportError:
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return
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l = [[1, 2], [3, 4], [5, 6]]
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a = numpy.array(l)
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assert matrix(l) == matrix(a)
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def test_interval_matrix_scalar_mult():
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"""Multiplication of iv.matrix and any scalar type"""
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a = mpi(-1, 1)
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b = a + a * 2j
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c = mpf(42)
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d = c + c * 2j
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e = 1.234
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f = fp.convert(e)
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g = e + e * 3j
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h = fp.convert(g)
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M = iv.ones(1)
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for x in [a, b, c, d, e, f, g, h]:
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assert x * M == iv.matrix([x])
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assert M * x == iv.matrix([x])
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@pytest.mark.xfail()
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def test_interval_matrix_matrix_mult():
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"""Multiplication of iv.matrix and other matrix types"""
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A = ones(1)
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B = fp.ones(1)
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M = iv.ones(1)
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for X in [A, B, M]:
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assert X * M == iv.matrix(X)
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assert X * M == X
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assert M * X == iv.matrix(X)
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assert M * X == X
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def test_matrix_conversion_to_iv():
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# Test that matrices with foreign datatypes are properly converted
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for other_type_eye in [eye(3), fp.eye(3), iv.eye(3)]:
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A = iv.matrix(other_type_eye)
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B = iv.eye(3)
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assert type(A[0,0]) == type(B[0,0])
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assert A.tolist() == B.tolist()
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def test_interval_matrix_mult_bug():
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# regression test for interval matrix multiplication:
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# result must be nonzero-width and contain the exact result
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x = convert('1.00000000000001') # note: this is implicitly rounded to some near mpf float value
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A = matrix([[x]])
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B = iv.matrix(A)
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C = iv.matrix([[x]])
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assert B == C
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B = B * B
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C = C * C
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assert B == C
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assert B[0, 0].delta > 1e-16
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assert B[0, 0].delta < 3e-16
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assert C[0, 0].delta > 1e-16
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assert C[0, 0].delta < 3e-16
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assert mp.mpf('1.00000000000001998401444325291756783368705994138804689654') in B[0, 0]
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assert mp.mpf('1.00000000000001998401444325291756783368705994138804689654') in C[0, 0]
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# the following caused an error before the bug was fixed
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assert iv.matrix(mp.eye(2)) * (iv.ones(2) + mpi(1, 2)) == iv.matrix([[mpi(2, 3), mpi(2, 3)], [mpi(2, 3), mpi(2, 3)]])
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