334 lines
9.9 KiB
Python
334 lines
9.9 KiB
Python
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# This testfile tests SymPy <-> NumPy compatibility
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# Don't test any SymPy features here. Just pure interaction with NumPy.
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# Always write regular SymPy tests for anything, that can be tested in pure
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# Python (without numpy). Here we test everything, that a user may need when
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# using SymPy with NumPy
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from sympy.external.importtools import version_tuple
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from sympy.external import import_module
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numpy = import_module('numpy')
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if numpy:
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array, matrix, ndarray = numpy.array, numpy.matrix, numpy.ndarray
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else:
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#bin/test will not execute any tests now
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disabled = True
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from sympy.core.numbers import (Float, Integer, Rational)
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from sympy.core.symbol import (Symbol, symbols)
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from sympy.functions.elementary.trigonometric import sin
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from sympy.matrices.dense import (Matrix, list2numpy, matrix2numpy, symarray)
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from sympy.utilities.lambdify import lambdify
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import sympy
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import mpmath
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from sympy.abc import x, y, z
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from sympy.utilities.decorator import conserve_mpmath_dps
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from sympy.utilities.exceptions import ignore_warnings
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from sympy.testing.pytest import raises
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# first, systematically check, that all operations are implemented and don't
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# raise an exception
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def test_systematic_basic():
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def s(sympy_object, numpy_array):
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_ = [sympy_object + numpy_array,
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numpy_array + sympy_object,
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sympy_object - numpy_array,
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numpy_array - sympy_object,
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sympy_object * numpy_array,
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numpy_array * sympy_object,
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sympy_object / numpy_array,
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numpy_array / sympy_object,
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sympy_object ** numpy_array,
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numpy_array ** sympy_object]
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x = Symbol("x")
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y = Symbol("y")
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sympy_objs = [
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Rational(2, 3),
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Float("1.3"),
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x,
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y,
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pow(x, y)*y,
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Integer(5),
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Float(5.5),
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]
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numpy_objs = [
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array([1]),
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array([3, 8, -1]),
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array([x, x**2, Rational(5)]),
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array([x/y*sin(y), 5, Rational(5)]),
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]
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for x in sympy_objs:
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for y in numpy_objs:
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s(x, y)
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# now some random tests, that test particular problems and that also
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# check that the results of the operations are correct
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def test_basics():
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one = Rational(1)
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zero = Rational(0)
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assert array(1) == array(one)
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assert array([one]) == array([one])
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assert array([x]) == array([x])
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assert array(x) == array(Symbol("x"))
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assert array(one + x) == array(1 + x)
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X = array([one, zero, zero])
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assert (X == array([one, zero, zero])).all()
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assert (X == array([one, 0, 0])).all()
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def test_arrays():
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one = Rational(1)
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zero = Rational(0)
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X = array([one, zero, zero])
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Y = one*X
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X = array([Symbol("a") + Rational(1, 2)])
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Y = X + X
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assert Y == array([1 + 2*Symbol("a")])
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Y = Y + 1
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assert Y == array([2 + 2*Symbol("a")])
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Y = X - X
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assert Y == array([0])
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def test_conversion1():
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a = list2numpy([x**2, x])
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#looks like an array?
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assert isinstance(a, ndarray)
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assert a[0] == x**2
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assert a[1] == x
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assert len(a) == 2
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#yes, it's the array
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def test_conversion2():
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a = 2*list2numpy([x**2, x])
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b = list2numpy([2*x**2, 2*x])
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assert (a == b).all()
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one = Rational(1)
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zero = Rational(0)
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X = list2numpy([one, zero, zero])
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Y = one*X
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X = list2numpy([Symbol("a") + Rational(1, 2)])
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Y = X + X
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assert Y == array([1 + 2*Symbol("a")])
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Y = Y + 1
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assert Y == array([2 + 2*Symbol("a")])
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Y = X - X
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assert Y == array([0])
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def test_list2numpy():
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assert (array([x**2, x]) == list2numpy([x**2, x])).all()
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def test_Matrix1():
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m = Matrix([[x, x**2], [5, 2/x]])
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assert (array(m.subs(x, 2)) == array([[2, 4], [5, 1]])).all()
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m = Matrix([[sin(x), x**2], [5, 2/x]])
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assert (array(m.subs(x, 2)) == array([[sin(2), 4], [5, 1]])).all()
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def test_Matrix2():
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m = Matrix([[x, x**2], [5, 2/x]])
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with ignore_warnings(PendingDeprecationWarning):
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assert (matrix(m.subs(x, 2)) == matrix([[2, 4], [5, 1]])).all()
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m = Matrix([[sin(x), x**2], [5, 2/x]])
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with ignore_warnings(PendingDeprecationWarning):
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assert (matrix(m.subs(x, 2)) == matrix([[sin(2), 4], [5, 1]])).all()
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def test_Matrix3():
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a = array([[2, 4], [5, 1]])
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assert Matrix(a) == Matrix([[2, 4], [5, 1]])
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assert Matrix(a) != Matrix([[2, 4], [5, 2]])
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a = array([[sin(2), 4], [5, 1]])
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assert Matrix(a) == Matrix([[sin(2), 4], [5, 1]])
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assert Matrix(a) != Matrix([[sin(0), 4], [5, 1]])
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def test_Matrix4():
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with ignore_warnings(PendingDeprecationWarning):
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a = matrix([[2, 4], [5, 1]])
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assert Matrix(a) == Matrix([[2, 4], [5, 1]])
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assert Matrix(a) != Matrix([[2, 4], [5, 2]])
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with ignore_warnings(PendingDeprecationWarning):
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a = matrix([[sin(2), 4], [5, 1]])
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assert Matrix(a) == Matrix([[sin(2), 4], [5, 1]])
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assert Matrix(a) != Matrix([[sin(0), 4], [5, 1]])
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def test_Matrix_sum():
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M = Matrix([[1, 2, 3], [x, y, x], [2*y, -50, z*x]])
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with ignore_warnings(PendingDeprecationWarning):
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m = matrix([[2, 3, 4], [x, 5, 6], [x, y, z**2]])
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assert M + m == Matrix([[3, 5, 7], [2*x, y + 5, x + 6], [2*y + x, y - 50, z*x + z**2]])
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assert m + M == Matrix([[3, 5, 7], [2*x, y + 5, x + 6], [2*y + x, y - 50, z*x + z**2]])
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assert M + m == M.add(m)
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def test_Matrix_mul():
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M = Matrix([[1, 2, 3], [x, y, x]])
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with ignore_warnings(PendingDeprecationWarning):
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m = matrix([[2, 4], [x, 6], [x, z**2]])
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assert M*m == Matrix([
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[ 2 + 5*x, 16 + 3*z**2],
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[2*x + x*y + x**2, 4*x + 6*y + x*z**2],
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])
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assert m*M == Matrix([
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[ 2 + 4*x, 4 + 4*y, 6 + 4*x],
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[ 7*x, 2*x + 6*y, 9*x],
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[x + x*z**2, 2*x + y*z**2, 3*x + x*z**2],
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])
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a = array([2])
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assert a[0] * M == 2 * M
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assert M * a[0] == 2 * M
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def test_Matrix_array():
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class matarray:
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def __array__(self):
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from numpy import array
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return array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
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matarr = matarray()
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assert Matrix(matarr) == Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
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def test_matrix2numpy():
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a = matrix2numpy(Matrix([[1, x**2], [3*sin(x), 0]]))
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assert isinstance(a, ndarray)
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assert a.shape == (2, 2)
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assert a[0, 0] == 1
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assert a[0, 1] == x**2
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assert a[1, 0] == 3*sin(x)
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assert a[1, 1] == 0
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def test_matrix2numpy_conversion():
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a = Matrix([[1, 2, sin(x)], [x**2, x, Rational(1, 2)]])
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b = array([[1, 2, sin(x)], [x**2, x, Rational(1, 2)]])
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assert (matrix2numpy(a) == b).all()
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assert matrix2numpy(a).dtype == numpy.dtype('object')
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c = matrix2numpy(Matrix([[1, 2], [10, 20]]), dtype='int8')
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d = matrix2numpy(Matrix([[1, 2], [10, 20]]), dtype='float64')
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assert c.dtype == numpy.dtype('int8')
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assert d.dtype == numpy.dtype('float64')
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def test_issue_3728():
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assert (Rational(1, 2)*array([2*x, 0]) == array([x, 0])).all()
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assert (Rational(1, 2) + array(
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[2*x, 0]) == array([2*x + Rational(1, 2), Rational(1, 2)])).all()
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assert (Float("0.5")*array([2*x, 0]) == array([Float("1.0")*x, 0])).all()
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assert (Float("0.5") + array(
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[2*x, 0]) == array([2*x + Float("0.5"), Float("0.5")])).all()
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@conserve_mpmath_dps
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def test_lambdify():
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mpmath.mp.dps = 16
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sin02 = mpmath.mpf("0.198669330795061215459412627")
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f = lambdify(x, sin(x), "numpy")
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prec = 1e-15
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assert -prec < f(0.2) - sin02 < prec
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# if this succeeds, it can't be a numpy function
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if version_tuple(numpy.__version__) >= version_tuple('1.17'):
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with raises(TypeError):
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f(x)
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else:
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with raises(AttributeError):
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f(x)
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def test_lambdify_matrix():
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f = lambdify(x, Matrix([[x, 2*x], [1, 2]]), [{'ImmutableMatrix': numpy.array}, "numpy"])
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assert (f(1) == array([[1, 2], [1, 2]])).all()
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def test_lambdify_matrix_multi_input():
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M = sympy.Matrix([[x**2, x*y, x*z],
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[y*x, y**2, y*z],
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[z*x, z*y, z**2]])
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f = lambdify((x, y, z), M, [{'ImmutableMatrix': numpy.array}, "numpy"])
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xh, yh, zh = 1.0, 2.0, 3.0
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expected = array([[xh**2, xh*yh, xh*zh],
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[yh*xh, yh**2, yh*zh],
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[zh*xh, zh*yh, zh**2]])
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actual = f(xh, yh, zh)
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assert numpy.allclose(actual, expected)
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def test_lambdify_matrix_vec_input():
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X = sympy.DeferredVector('X')
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M = Matrix([
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[X[0]**2, X[0]*X[1], X[0]*X[2]],
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[X[1]*X[0], X[1]**2, X[1]*X[2]],
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[X[2]*X[0], X[2]*X[1], X[2]**2]])
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f = lambdify(X, M, [{'ImmutableMatrix': numpy.array}, "numpy"])
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Xh = array([1.0, 2.0, 3.0])
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expected = array([[Xh[0]**2, Xh[0]*Xh[1], Xh[0]*Xh[2]],
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[Xh[1]*Xh[0], Xh[1]**2, Xh[1]*Xh[2]],
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[Xh[2]*Xh[0], Xh[2]*Xh[1], Xh[2]**2]])
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actual = f(Xh)
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assert numpy.allclose(actual, expected)
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def test_lambdify_transl():
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from sympy.utilities.lambdify import NUMPY_TRANSLATIONS
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for sym, mat in NUMPY_TRANSLATIONS.items():
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assert sym in sympy.__dict__
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assert mat in numpy.__dict__
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def test_symarray():
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"""Test creation of numpy arrays of SymPy symbols."""
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import numpy as np
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import numpy.testing as npt
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syms = symbols('_0,_1,_2')
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s1 = symarray("", 3)
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s2 = symarray("", 3)
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npt.assert_array_equal(s1, np.array(syms, dtype=object))
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assert s1[0] == s2[0]
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a = symarray('a', 3)
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b = symarray('b', 3)
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assert not(a[0] == b[0])
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asyms = symbols('a_0,a_1,a_2')
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npt.assert_array_equal(a, np.array(asyms, dtype=object))
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# Multidimensional checks
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a2d = symarray('a', (2, 3))
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assert a2d.shape == (2, 3)
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a00, a12 = symbols('a_0_0,a_1_2')
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assert a2d[0, 0] == a00
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assert a2d[1, 2] == a12
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a3d = symarray('a', (2, 3, 2))
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assert a3d.shape == (2, 3, 2)
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a000, a120, a121 = symbols('a_0_0_0,a_1_2_0,a_1_2_1')
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assert a3d[0, 0, 0] == a000
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assert a3d[1, 2, 0] == a120
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assert a3d[1, 2, 1] == a121
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def test_vectorize():
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assert (numpy.vectorize(
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sin)([1, 2, 3]) == numpy.array([sin(1), sin(2), sin(3)])).all()
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