352 lines
10 KiB
Python
352 lines
10 KiB
Python
from sympy.concrete.summations import Sum
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from sympy.core.mod import Mod
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from sympy.core.relational import (Equality, Unequality)
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from sympy.core.symbol import Symbol
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.functions.elementary.piecewise import Piecewise
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from sympy.functions.special.gamma_functions import polygamma
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from sympy.functions.special.error_functions import (Si, Ci)
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from sympy.matrices.expressions.blockmatrix import BlockMatrix
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from sympy.matrices.expressions.matexpr import MatrixSymbol
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from sympy.matrices.expressions.special import Identity
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from sympy.utilities.lambdify import lambdify
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from sympy.abc import x, i, j, a, b, c, d
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from sympy.core import Pow
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from sympy.codegen.matrix_nodes import MatrixSolve
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from sympy.codegen.numpy_nodes import logaddexp, logaddexp2
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from sympy.codegen.cfunctions import log1p, expm1, hypot, log10, exp2, log2, Sqrt
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from sympy.tensor.array import Array
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from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct, ArrayAdd, \
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PermuteDims, ArrayDiagonal
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from sympy.printing.numpy import NumPyPrinter, SciPyPrinter, _numpy_known_constants, \
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_numpy_known_functions, _scipy_known_constants, _scipy_known_functions
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from sympy.tensor.array.expressions.from_matrix_to_array import convert_matrix_to_array
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from sympy.testing.pytest import skip, raises
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from sympy.external import import_module
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np = import_module('numpy')
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if np:
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deafult_float_info = np.finfo(np.array([]).dtype)
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NUMPY_DEFAULT_EPSILON = deafult_float_info.eps
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def test_numpy_piecewise_regression():
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"""
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NumPyPrinter needs to print Piecewise()'s choicelist as a list to avoid
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breaking compatibility with numpy 1.8. This is not necessary in numpy 1.9+.
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See gh-9747 and gh-9749 for details.
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"""
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printer = NumPyPrinter()
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p = Piecewise((1, x < 0), (0, True))
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assert printer.doprint(p) == \
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'numpy.select([numpy.less(x, 0),True], [1,0], default=numpy.nan)'
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assert printer.module_imports == {'numpy': {'select', 'less', 'nan'}}
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def test_numpy_logaddexp():
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lae = logaddexp(a, b)
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assert NumPyPrinter().doprint(lae) == 'numpy.logaddexp(a, b)'
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lae2 = logaddexp2(a, b)
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assert NumPyPrinter().doprint(lae2) == 'numpy.logaddexp2(a, b)'
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def test_sum():
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if not np:
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skip("NumPy not installed")
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s = Sum(x ** i, (i, a, b))
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f = lambdify((a, b, x), s, 'numpy')
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a_, b_ = 0, 10
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x_ = np.linspace(-1, +1, 10)
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assert np.allclose(f(a_, b_, x_), sum(x_ ** i_ for i_ in range(a_, b_ + 1)))
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s = Sum(i * x, (i, a, b))
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f = lambdify((a, b, x), s, 'numpy')
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a_, b_ = 0, 10
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x_ = np.linspace(-1, +1, 10)
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assert np.allclose(f(a_, b_, x_), sum(i_ * x_ for i_ in range(a_, b_ + 1)))
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def test_multiple_sums():
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if not np:
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skip("NumPy not installed")
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s = Sum((x + j) * i, (i, a, b), (j, c, d))
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f = lambdify((a, b, c, d, x), s, 'numpy')
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a_, b_ = 0, 10
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c_, d_ = 11, 21
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x_ = np.linspace(-1, +1, 10)
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assert np.allclose(f(a_, b_, c_, d_, x_),
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sum((x_ + j_) * i_ for i_ in range(a_, b_ + 1) for j_ in range(c_, d_ + 1)))
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def test_codegen_einsum():
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if not np:
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skip("NumPy not installed")
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M = MatrixSymbol("M", 2, 2)
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N = MatrixSymbol("N", 2, 2)
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cg = convert_matrix_to_array(M * N)
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f = lambdify((M, N), cg, 'numpy')
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ma = np.array([[1, 2], [3, 4]])
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mb = np.array([[1,-2], [-1, 3]])
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assert (f(ma, mb) == np.matmul(ma, mb)).all()
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def test_codegen_extra():
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if not np:
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skip("NumPy not installed")
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M = MatrixSymbol("M", 2, 2)
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N = MatrixSymbol("N", 2, 2)
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P = MatrixSymbol("P", 2, 2)
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Q = MatrixSymbol("Q", 2, 2)
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ma = np.array([[1, 2], [3, 4]])
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mb = np.array([[1,-2], [-1, 3]])
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mc = np.array([[2, 0], [1, 2]])
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md = np.array([[1,-1], [4, 7]])
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cg = ArrayTensorProduct(M, N)
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f = lambdify((M, N), cg, 'numpy')
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assert (f(ma, mb) == np.einsum(ma, [0, 1], mb, [2, 3])).all()
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cg = ArrayAdd(M, N)
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f = lambdify((M, N), cg, 'numpy')
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assert (f(ma, mb) == ma+mb).all()
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cg = ArrayAdd(M, N, P)
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f = lambdify((M, N, P), cg, 'numpy')
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assert (f(ma, mb, mc) == ma+mb+mc).all()
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cg = ArrayAdd(M, N, P, Q)
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f = lambdify((M, N, P, Q), cg, 'numpy')
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assert (f(ma, mb, mc, md) == ma+mb+mc+md).all()
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cg = PermuteDims(M, [1, 0])
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f = lambdify((M,), cg, 'numpy')
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assert (f(ma) == ma.T).all()
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cg = PermuteDims(ArrayTensorProduct(M, N), [1, 2, 3, 0])
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f = lambdify((M, N), cg, 'numpy')
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assert (f(ma, mb) == np.transpose(np.einsum(ma, [0, 1], mb, [2, 3]), (1, 2, 3, 0))).all()
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cg = ArrayDiagonal(ArrayTensorProduct(M, N), (1, 2))
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f = lambdify((M, N), cg, 'numpy')
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assert (f(ma, mb) == np.diagonal(np.einsum(ma, [0, 1], mb, [2, 3]), axis1=1, axis2=2)).all()
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def test_relational():
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if not np:
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skip("NumPy not installed")
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e = Equality(x, 1)
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f = lambdify((x,), e)
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x_ = np.array([0, 1, 2])
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assert np.array_equal(f(x_), [False, True, False])
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e = Unequality(x, 1)
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f = lambdify((x,), e)
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x_ = np.array([0, 1, 2])
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assert np.array_equal(f(x_), [True, False, True])
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e = (x < 1)
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f = lambdify((x,), e)
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x_ = np.array([0, 1, 2])
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assert np.array_equal(f(x_), [True, False, False])
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e = (x <= 1)
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f = lambdify((x,), e)
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x_ = np.array([0, 1, 2])
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assert np.array_equal(f(x_), [True, True, False])
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e = (x > 1)
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f = lambdify((x,), e)
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x_ = np.array([0, 1, 2])
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assert np.array_equal(f(x_), [False, False, True])
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e = (x >= 1)
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f = lambdify((x,), e)
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x_ = np.array([0, 1, 2])
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assert np.array_equal(f(x_), [False, True, True])
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def test_mod():
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if not np:
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skip("NumPy not installed")
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e = Mod(a, b)
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f = lambdify((a, b), e)
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a_ = np.array([0, 1, 2, 3])
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b_ = 2
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assert np.array_equal(f(a_, b_), [0, 1, 0, 1])
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a_ = np.array([0, 1, 2, 3])
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b_ = np.array([2, 2, 2, 2])
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assert np.array_equal(f(a_, b_), [0, 1, 0, 1])
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a_ = np.array([2, 3, 4, 5])
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b_ = np.array([2, 3, 4, 5])
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assert np.array_equal(f(a_, b_), [0, 0, 0, 0])
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def test_pow():
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if not np:
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skip('NumPy not installed')
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expr = Pow(2, -1, evaluate=False)
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f = lambdify([], expr, 'numpy')
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assert f() == 0.5
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def test_expm1():
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if not np:
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skip("NumPy not installed")
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f = lambdify((a,), expm1(a), 'numpy')
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assert abs(f(1e-10) - 1e-10 - 5e-21) <= 1e-10 * NUMPY_DEFAULT_EPSILON
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def test_log1p():
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if not np:
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skip("NumPy not installed")
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f = lambdify((a,), log1p(a), 'numpy')
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assert abs(f(1e-99) - 1e-99) <= 1e-99 * NUMPY_DEFAULT_EPSILON
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def test_hypot():
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if not np:
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skip("NumPy not installed")
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assert abs(lambdify((a, b), hypot(a, b), 'numpy')(3, 4) - 5) <= NUMPY_DEFAULT_EPSILON
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def test_log10():
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if not np:
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skip("NumPy not installed")
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assert abs(lambdify((a,), log10(a), 'numpy')(100) - 2) <= NUMPY_DEFAULT_EPSILON
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def test_exp2():
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if not np:
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skip("NumPy not installed")
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assert abs(lambdify((a,), exp2(a), 'numpy')(5) - 32) <= NUMPY_DEFAULT_EPSILON
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def test_log2():
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if not np:
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skip("NumPy not installed")
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assert abs(lambdify((a,), log2(a), 'numpy')(256) - 8) <= NUMPY_DEFAULT_EPSILON
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def test_Sqrt():
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if not np:
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skip("NumPy not installed")
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assert abs(lambdify((a,), Sqrt(a), 'numpy')(4) - 2) <= NUMPY_DEFAULT_EPSILON
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def test_sqrt():
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if not np:
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skip("NumPy not installed")
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assert abs(lambdify((a,), sqrt(a), 'numpy')(4) - 2) <= NUMPY_DEFAULT_EPSILON
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def test_matsolve():
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if not np:
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skip("NumPy not installed")
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M = MatrixSymbol("M", 3, 3)
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x = MatrixSymbol("x", 3, 1)
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expr = M**(-1) * x + x
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matsolve_expr = MatrixSolve(M, x) + x
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f = lambdify((M, x), expr)
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f_matsolve = lambdify((M, x), matsolve_expr)
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m0 = np.array([[1, 2, 3], [3, 2, 5], [5, 6, 7]])
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assert np.linalg.matrix_rank(m0) == 3
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x0 = np.array([3, 4, 5])
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assert np.allclose(f_matsolve(m0, x0), f(m0, x0))
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def test_16857():
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if not np:
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skip("NumPy not installed")
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a_1 = MatrixSymbol('a_1', 10, 3)
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a_2 = MatrixSymbol('a_2', 10, 3)
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a_3 = MatrixSymbol('a_3', 10, 3)
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a_4 = MatrixSymbol('a_4', 10, 3)
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A = BlockMatrix([[a_1, a_2], [a_3, a_4]])
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assert A.shape == (20, 6)
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printer = NumPyPrinter()
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assert printer.doprint(A) == 'numpy.block([[a_1, a_2], [a_3, a_4]])'
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def test_issue_17006():
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if not np:
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skip("NumPy not installed")
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M = MatrixSymbol("M", 2, 2)
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f = lambdify(M, M + Identity(2))
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ma = np.array([[1, 2], [3, 4]])
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mr = np.array([[2, 2], [3, 5]])
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assert (f(ma) == mr).all()
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from sympy.core.symbol import symbols
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n = symbols('n', integer=True)
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N = MatrixSymbol("M", n, n)
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raises(NotImplementedError, lambda: lambdify(N, N + Identity(n)))
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def test_numpy_array():
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assert NumPyPrinter().doprint(Array(((1, 2), (3, 5)))) == 'numpy.array([[1, 2], [3, 5]])'
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assert NumPyPrinter().doprint(Array((1, 2))) == 'numpy.array((1, 2))'
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def test_numpy_known_funcs_consts():
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assert _numpy_known_constants['NaN'] == 'numpy.nan'
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assert _numpy_known_constants['EulerGamma'] == 'numpy.euler_gamma'
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assert _numpy_known_functions['acos'] == 'numpy.arccos'
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assert _numpy_known_functions['log'] == 'numpy.log'
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def test_scipy_known_funcs_consts():
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assert _scipy_known_constants['GoldenRatio'] == 'scipy.constants.golden_ratio'
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assert _scipy_known_constants['Pi'] == 'scipy.constants.pi'
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assert _scipy_known_functions['erf'] == 'scipy.special.erf'
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assert _scipy_known_functions['factorial'] == 'scipy.special.factorial'
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def test_numpy_print_methods():
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prntr = NumPyPrinter()
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assert hasattr(prntr, '_print_acos')
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assert hasattr(prntr, '_print_log')
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def test_scipy_print_methods():
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prntr = SciPyPrinter()
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assert hasattr(prntr, '_print_acos')
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assert hasattr(prntr, '_print_log')
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assert hasattr(prntr, '_print_erf')
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assert hasattr(prntr, '_print_factorial')
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assert hasattr(prntr, '_print_chebyshevt')
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k = Symbol('k', integer=True, nonnegative=True)
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x = Symbol('x', real=True)
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assert prntr.doprint(polygamma(k, x)) == "scipy.special.polygamma(k, x)"
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assert prntr.doprint(Si(x)) == "scipy.special.sici(x)[0]"
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assert prntr.doprint(Ci(x)) == "scipy.special.sici(x)[1]"
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