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