495 lines
18 KiB
Python
495 lines
18 KiB
Python
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import pytest
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from numpy.f2py.symbolic import (
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Expr,
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Op,
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ArithOp,
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Language,
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as_symbol,
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as_number,
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as_string,
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as_array,
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as_complex,
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as_terms,
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as_factors,
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eliminate_quotes,
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insert_quotes,
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fromstring,
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as_expr,
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as_apply,
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as_numer_denom,
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as_ternary,
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as_ref,
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as_deref,
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normalize,
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as_eq,
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as_ne,
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as_lt,
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as_gt,
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as_le,
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as_ge,
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)
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from . import util
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class TestSymbolic(util.F2PyTest):
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def test_eliminate_quotes(self):
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def worker(s):
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r, d = eliminate_quotes(s)
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s1 = insert_quotes(r, d)
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assert s1 == s
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for kind in ["", "mykind_"]:
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worker(kind + '"1234" // "ABCD"')
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worker(kind + '"1234" // ' + kind + '"ABCD"')
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worker(kind + "\"1234\" // 'ABCD'")
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worker(kind + '"1234" // ' + kind + "'ABCD'")
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worker(kind + '"1\\"2\'AB\'34"')
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worker("a = " + kind + "'1\\'2\"AB\"34'")
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def test_sanity(self):
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x = as_symbol("x")
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y = as_symbol("y")
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z = as_symbol("z")
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assert x.op == Op.SYMBOL
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assert repr(x) == "Expr(Op.SYMBOL, 'x')"
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assert x == x
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assert x != y
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assert hash(x) is not None
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n = as_number(123)
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m = as_number(456)
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assert n.op == Op.INTEGER
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assert repr(n) == "Expr(Op.INTEGER, (123, 4))"
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assert n == n
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assert n != m
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assert hash(n) is not None
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fn = as_number(12.3)
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fm = as_number(45.6)
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assert fn.op == Op.REAL
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assert repr(fn) == "Expr(Op.REAL, (12.3, 4))"
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assert fn == fn
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assert fn != fm
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assert hash(fn) is not None
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c = as_complex(1, 2)
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c2 = as_complex(3, 4)
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assert c.op == Op.COMPLEX
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assert repr(c) == ("Expr(Op.COMPLEX, (Expr(Op.INTEGER, (1, 4)),"
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" Expr(Op.INTEGER, (2, 4))))")
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assert c == c
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assert c != c2
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assert hash(c) is not None
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s = as_string("'123'")
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s2 = as_string('"ABC"')
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assert s.op == Op.STRING
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assert repr(s) == "Expr(Op.STRING, (\"'123'\", 1))", repr(s)
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assert s == s
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assert s != s2
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a = as_array((n, m))
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b = as_array((n, ))
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assert a.op == Op.ARRAY
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assert repr(a) == ("Expr(Op.ARRAY, (Expr(Op.INTEGER, (123, 4)),"
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" Expr(Op.INTEGER, (456, 4))))")
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assert a == a
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assert a != b
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t = as_terms(x)
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u = as_terms(y)
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assert t.op == Op.TERMS
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assert repr(t) == "Expr(Op.TERMS, {Expr(Op.SYMBOL, 'x'): 1})"
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assert t == t
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assert t != u
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assert hash(t) is not None
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v = as_factors(x)
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w = as_factors(y)
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assert v.op == Op.FACTORS
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assert repr(v) == "Expr(Op.FACTORS, {Expr(Op.SYMBOL, 'x'): 1})"
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assert v == v
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assert w != v
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assert hash(v) is not None
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t = as_ternary(x, y, z)
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u = as_ternary(x, z, y)
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assert t.op == Op.TERNARY
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assert t == t
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assert t != u
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assert hash(t) is not None
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e = as_eq(x, y)
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f = as_lt(x, y)
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assert e.op == Op.RELATIONAL
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assert e == e
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assert e != f
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assert hash(e) is not None
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def test_tostring_fortran(self):
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x = as_symbol("x")
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y = as_symbol("y")
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z = as_symbol("z")
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n = as_number(123)
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m = as_number(456)
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a = as_array((n, m))
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c = as_complex(n, m)
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assert str(x) == "x"
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assert str(n) == "123"
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assert str(a) == "[123, 456]"
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assert str(c) == "(123, 456)"
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assert str(Expr(Op.TERMS, {x: 1})) == "x"
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assert str(Expr(Op.TERMS, {x: 2})) == "2 * x"
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assert str(Expr(Op.TERMS, {x: -1})) == "-x"
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assert str(Expr(Op.TERMS, {x: -2})) == "-2 * x"
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assert str(Expr(Op.TERMS, {x: 1, y: 1})) == "x + y"
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assert str(Expr(Op.TERMS, {x: -1, y: -1})) == "-x - y"
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assert str(Expr(Op.TERMS, {x: 2, y: 3})) == "2 * x + 3 * y"
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assert str(Expr(Op.TERMS, {x: -2, y: 3})) == "-2 * x + 3 * y"
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assert str(Expr(Op.TERMS, {x: 2, y: -3})) == "2 * x - 3 * y"
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assert str(Expr(Op.FACTORS, {x: 1})) == "x"
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assert str(Expr(Op.FACTORS, {x: 2})) == "x ** 2"
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assert str(Expr(Op.FACTORS, {x: -1})) == "x ** -1"
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assert str(Expr(Op.FACTORS, {x: -2})) == "x ** -2"
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assert str(Expr(Op.FACTORS, {x: 1, y: 1})) == "x * y"
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assert str(Expr(Op.FACTORS, {x: 2, y: 3})) == "x ** 2 * y ** 3"
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v = Expr(Op.FACTORS, {x: 2, Expr(Op.TERMS, {x: 1, y: 1}): 3})
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assert str(v) == "x ** 2 * (x + y) ** 3", str(v)
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v = Expr(Op.FACTORS, {x: 2, Expr(Op.FACTORS, {x: 1, y: 1}): 3})
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assert str(v) == "x ** 2 * (x * y) ** 3", str(v)
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assert str(Expr(Op.APPLY, ("f", (), {}))) == "f()"
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assert str(Expr(Op.APPLY, ("f", (x, ), {}))) == "f(x)"
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assert str(Expr(Op.APPLY, ("f", (x, y), {}))) == "f(x, y)"
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assert str(Expr(Op.INDEXING, ("f", x))) == "f[x]"
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assert str(as_ternary(x, y, z)) == "merge(y, z, x)"
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assert str(as_eq(x, y)) == "x .eq. y"
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assert str(as_ne(x, y)) == "x .ne. y"
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assert str(as_lt(x, y)) == "x .lt. y"
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assert str(as_le(x, y)) == "x .le. y"
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assert str(as_gt(x, y)) == "x .gt. y"
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assert str(as_ge(x, y)) == "x .ge. y"
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def test_tostring_c(self):
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language = Language.C
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x = as_symbol("x")
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y = as_symbol("y")
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z = as_symbol("z")
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n = as_number(123)
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assert Expr(Op.FACTORS, {x: 2}).tostring(language=language) == "x * x"
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assert (Expr(Op.FACTORS, {
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x + y: 2
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}).tostring(language=language) == "(x + y) * (x + y)")
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assert Expr(Op.FACTORS, {
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x: 12
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}).tostring(language=language) == "pow(x, 12)"
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assert as_apply(ArithOp.DIV, x,
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y).tostring(language=language) == "x / y"
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assert (as_apply(ArithOp.DIV, x,
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x + y).tostring(language=language) == "x / (x + y)")
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assert (as_apply(ArithOp.DIV, x - y, x +
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y).tostring(language=language) == "(x - y) / (x + y)")
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assert (x + (x - y) / (x + y) +
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n).tostring(language=language) == "123 + x + (x - y) / (x + y)"
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assert as_ternary(x, y, z).tostring(language=language) == "(x?y:z)"
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assert as_eq(x, y).tostring(language=language) == "x == y"
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assert as_ne(x, y).tostring(language=language) == "x != y"
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assert as_lt(x, y).tostring(language=language) == "x < y"
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assert as_le(x, y).tostring(language=language) == "x <= y"
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assert as_gt(x, y).tostring(language=language) == "x > y"
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assert as_ge(x, y).tostring(language=language) == "x >= y"
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def test_operations(self):
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x = as_symbol("x")
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y = as_symbol("y")
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z = as_symbol("z")
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assert x + x == Expr(Op.TERMS, {x: 2})
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assert x - x == Expr(Op.INTEGER, (0, 4))
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assert x + y == Expr(Op.TERMS, {x: 1, y: 1})
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assert x - y == Expr(Op.TERMS, {x: 1, y: -1})
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assert x * x == Expr(Op.FACTORS, {x: 2})
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assert x * y == Expr(Op.FACTORS, {x: 1, y: 1})
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assert +x == x
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assert -x == Expr(Op.TERMS, {x: -1}), repr(-x)
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assert 2 * x == Expr(Op.TERMS, {x: 2})
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assert 2 + x == Expr(Op.TERMS, {x: 1, as_number(1): 2})
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assert 2 * x + 3 * y == Expr(Op.TERMS, {x: 2, y: 3})
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assert (x + y) * 2 == Expr(Op.TERMS, {x: 2, y: 2})
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assert x**2 == Expr(Op.FACTORS, {x: 2})
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assert (x + y)**2 == Expr(
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Op.TERMS,
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{
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Expr(Op.FACTORS, {x: 2}): 1,
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Expr(Op.FACTORS, {y: 2}): 1,
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Expr(Op.FACTORS, {
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x: 1,
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y: 1
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}): 2,
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},
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)
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assert (x + y) * x == x**2 + x * y
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assert (x + y)**2 == x**2 + 2 * x * y + y**2
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assert (x + y)**2 + (x - y)**2 == 2 * x**2 + 2 * y**2
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assert (x + y) * z == x * z + y * z
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assert z * (x + y) == x * z + y * z
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assert (x / 2) == as_apply(ArithOp.DIV, x, as_number(2))
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assert (2 * x / 2) == x
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assert (3 * x / 2) == as_apply(ArithOp.DIV, 3 * x, as_number(2))
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assert (4 * x / 2) == 2 * x
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assert (5 * x / 2) == as_apply(ArithOp.DIV, 5 * x, as_number(2))
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assert (6 * x / 2) == 3 * x
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assert ((3 * 5) * x / 6) == as_apply(ArithOp.DIV, 5 * x, as_number(2))
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assert (30 * x**2 * y**4 / (24 * x**3 * y**3)) == as_apply(
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ArithOp.DIV, 5 * y, 4 * x)
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assert ((15 * x / 6) / 5) == as_apply(ArithOp.DIV, x,
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as_number(2)), (15 * x / 6) / 5
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assert (x / (5 / x)) == as_apply(ArithOp.DIV, x**2, as_number(5))
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assert (x / 2.0) == Expr(Op.TERMS, {x: 0.5})
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s = as_string('"ABC"')
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t = as_string('"123"')
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assert s // t == Expr(Op.STRING, ('"ABC123"', 1))
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assert s // x == Expr(Op.CONCAT, (s, x))
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assert x // s == Expr(Op.CONCAT, (x, s))
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c = as_complex(1.0, 2.0)
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assert -c == as_complex(-1.0, -2.0)
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assert c + c == as_expr((1 + 2j) * 2)
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assert c * c == as_expr((1 + 2j)**2)
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def test_substitute(self):
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x = as_symbol("x")
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y = as_symbol("y")
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z = as_symbol("z")
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a = as_array((x, y))
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assert x.substitute({x: y}) == y
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assert (x + y).substitute({x: z}) == y + z
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assert (x * y).substitute({x: z}) == y * z
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assert (x**4).substitute({x: z}) == z**4
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assert (x / y).substitute({x: z}) == z / y
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assert x.substitute({x: y + z}) == y + z
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assert a.substitute({x: y + z}) == as_array((y + z, y))
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assert as_ternary(x, y,
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z).substitute({x: y + z}) == as_ternary(y + z, y, z)
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assert as_eq(x, y).substitute({x: y + z}) == as_eq(y + z, y)
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def test_fromstring(self):
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x = as_symbol("x")
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y = as_symbol("y")
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z = as_symbol("z")
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f = as_symbol("f")
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s = as_string('"ABC"')
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t = as_string('"123"')
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a = as_array((x, y))
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assert fromstring("x") == x
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assert fromstring("+ x") == x
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assert fromstring("- x") == -x
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assert fromstring("x + y") == x + y
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assert fromstring("x + 1") == x + 1
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assert fromstring("x * y") == x * y
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assert fromstring("x * 2") == x * 2
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assert fromstring("x / y") == x / y
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assert fromstring("x ** 2", language=Language.Python) == x**2
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assert fromstring("x ** 2 ** 3", language=Language.Python) == x**2**3
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assert fromstring("(x + y) * z") == (x + y) * z
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assert fromstring("f(x)") == f(x)
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assert fromstring("f(x,y)") == f(x, y)
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assert fromstring("f[x]") == f[x]
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assert fromstring("f[x][y]") == f[x][y]
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assert fromstring('"ABC"') == s
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assert (normalize(
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fromstring('"ABC" // "123" ',
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language=Language.Fortran)) == s // t)
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assert fromstring('f("ABC")') == f(s)
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|
assert fromstring('MYSTRKIND_"ABC"') == as_string('"ABC"', "MYSTRKIND")
|
||
|
|
|
||
|
|
assert fromstring("(/x, y/)") == a, fromstring("(/x, y/)")
|
||
|
|
assert fromstring("f((/x, y/))") == f(a)
|
||
|
|
assert fromstring("(/(x+y)*z/)") == as_array(((x + y) * z, ))
|
||
|
|
|
||
|
|
assert fromstring("123") == as_number(123)
|
||
|
|
assert fromstring("123_2") == as_number(123, 2)
|
||
|
|
assert fromstring("123_myintkind") == as_number(123, "myintkind")
|
||
|
|
|
||
|
|
assert fromstring("123.0") == as_number(123.0, 4)
|
||
|
|
assert fromstring("123.0_4") == as_number(123.0, 4)
|
||
|
|
assert fromstring("123.0_8") == as_number(123.0, 8)
|
||
|
|
assert fromstring("123.0e0") == as_number(123.0, 4)
|
||
|
|
assert fromstring("123.0d0") == as_number(123.0, 8)
|
||
|
|
assert fromstring("123d0") == as_number(123.0, 8)
|
||
|
|
assert fromstring("123e-0") == as_number(123.0, 4)
|
||
|
|
assert fromstring("123d+0") == as_number(123.0, 8)
|
||
|
|
assert fromstring("123.0_myrealkind") == as_number(123.0, "myrealkind")
|
||
|
|
assert fromstring("3E4") == as_number(30000.0, 4)
|
||
|
|
|
||
|
|
assert fromstring("(1, 2)") == as_complex(1, 2)
|
||
|
|
assert fromstring("(1e2, PI)") == as_complex(as_number(100.0),
|
||
|
|
as_symbol("PI"))
|
||
|
|
|
||
|
|
assert fromstring("[1, 2]") == as_array((as_number(1), as_number(2)))
|
||
|
|
|
||
|
|
assert fromstring("POINT(x, y=1)") == as_apply(as_symbol("POINT"),
|
||
|
|
x,
|
||
|
|
y=as_number(1))
|
||
|
|
assert fromstring(
|
||
|
|
'PERSON(name="John", age=50, shape=(/34, 23/))') == as_apply(
|
||
|
|
as_symbol("PERSON"),
|
||
|
|
name=as_string('"John"'),
|
||
|
|
age=as_number(50),
|
||
|
|
shape=as_array((as_number(34), as_number(23))),
|
||
|
|
)
|
||
|
|
|
||
|
|
assert fromstring("x?y:z") == as_ternary(x, y, z)
|
||
|
|
|
||
|
|
assert fromstring("*x") == as_deref(x)
|
||
|
|
assert fromstring("**x") == as_deref(as_deref(x))
|
||
|
|
assert fromstring("&x") == as_ref(x)
|
||
|
|
assert fromstring("(*x) * (*y)") == as_deref(x) * as_deref(y)
|
||
|
|
assert fromstring("(*x) * *y") == as_deref(x) * as_deref(y)
|
||
|
|
assert fromstring("*x * *y") == as_deref(x) * as_deref(y)
|
||
|
|
assert fromstring("*x**y") == as_deref(x) * as_deref(y)
|
||
|
|
|
||
|
|
assert fromstring("x == y") == as_eq(x, y)
|
||
|
|
assert fromstring("x != y") == as_ne(x, y)
|
||
|
|
assert fromstring("x < y") == as_lt(x, y)
|
||
|
|
assert fromstring("x > y") == as_gt(x, y)
|
||
|
|
assert fromstring("x <= y") == as_le(x, y)
|
||
|
|
assert fromstring("x >= y") == as_ge(x, y)
|
||
|
|
|
||
|
|
assert fromstring("x .eq. y", language=Language.Fortran) == as_eq(x, y)
|
||
|
|
assert fromstring("x .ne. y", language=Language.Fortran) == as_ne(x, y)
|
||
|
|
assert fromstring("x .lt. y", language=Language.Fortran) == as_lt(x, y)
|
||
|
|
assert fromstring("x .gt. y", language=Language.Fortran) == as_gt(x, y)
|
||
|
|
assert fromstring("x .le. y", language=Language.Fortran) == as_le(x, y)
|
||
|
|
assert fromstring("x .ge. y", language=Language.Fortran) == as_ge(x, y)
|
||
|
|
|
||
|
|
def test_traverse(self):
|
||
|
|
x = as_symbol("x")
|
||
|
|
y = as_symbol("y")
|
||
|
|
z = as_symbol("z")
|
||
|
|
f = as_symbol("f")
|
||
|
|
|
||
|
|
# Use traverse to substitute a symbol
|
||
|
|
def replace_visit(s, r=z):
|
||
|
|
if s == x:
|
||
|
|
return r
|
||
|
|
|
||
|
|
assert x.traverse(replace_visit) == z
|
||
|
|
assert y.traverse(replace_visit) == y
|
||
|
|
assert z.traverse(replace_visit) == z
|
||
|
|
assert (f(y)).traverse(replace_visit) == f(y)
|
||
|
|
assert (f(x)).traverse(replace_visit) == f(z)
|
||
|
|
assert (f[y]).traverse(replace_visit) == f[y]
|
||
|
|
assert (f[z]).traverse(replace_visit) == f[z]
|
||
|
|
assert (x + y + z).traverse(replace_visit) == (2 * z + y)
|
||
|
|
assert (x +
|
||
|
|
f(y, x - z)).traverse(replace_visit) == (z +
|
||
|
|
f(y, as_number(0)))
|
||
|
|
assert as_eq(x, y).traverse(replace_visit) == as_eq(z, y)
|
||
|
|
|
||
|
|
# Use traverse to collect symbols, method 1
|
||
|
|
function_symbols = set()
|
||
|
|
symbols = set()
|
||
|
|
|
||
|
|
def collect_symbols(s):
|
||
|
|
if s.op is Op.APPLY:
|
||
|
|
oper = s.data[0]
|
||
|
|
function_symbols.add(oper)
|
||
|
|
if oper in symbols:
|
||
|
|
symbols.remove(oper)
|
||
|
|
elif s.op is Op.SYMBOL and s not in function_symbols:
|
||
|
|
symbols.add(s)
|
||
|
|
|
||
|
|
(x + f(y, x - z)).traverse(collect_symbols)
|
||
|
|
assert function_symbols == {f}
|
||
|
|
assert symbols == {x, y, z}
|
||
|
|
|
||
|
|
# Use traverse to collect symbols, method 2
|
||
|
|
def collect_symbols2(expr, symbols):
|
||
|
|
if expr.op is Op.SYMBOL:
|
||
|
|
symbols.add(expr)
|
||
|
|
|
||
|
|
symbols = set()
|
||
|
|
(x + f(y, x - z)).traverse(collect_symbols2, symbols)
|
||
|
|
assert symbols == {x, y, z, f}
|
||
|
|
|
||
|
|
# Use traverse to partially collect symbols
|
||
|
|
def collect_symbols3(expr, symbols):
|
||
|
|
if expr.op is Op.APPLY:
|
||
|
|
# skip traversing function calls
|
||
|
|
return expr
|
||
|
|
if expr.op is Op.SYMBOL:
|
||
|
|
symbols.add(expr)
|
||
|
|
|
||
|
|
symbols = set()
|
||
|
|
(x + f(y, x - z)).traverse(collect_symbols3, symbols)
|
||
|
|
assert symbols == {x}
|
||
|
|
|
||
|
|
def test_linear_solve(self):
|
||
|
|
x = as_symbol("x")
|
||
|
|
y = as_symbol("y")
|
||
|
|
z = as_symbol("z")
|
||
|
|
|
||
|
|
assert x.linear_solve(x) == (as_number(1), as_number(0))
|
||
|
|
assert (x + 1).linear_solve(x) == (as_number(1), as_number(1))
|
||
|
|
assert (2 * x).linear_solve(x) == (as_number(2), as_number(0))
|
||
|
|
assert (2 * x + 3).linear_solve(x) == (as_number(2), as_number(3))
|
||
|
|
assert as_number(3).linear_solve(x) == (as_number(0), as_number(3))
|
||
|
|
assert y.linear_solve(x) == (as_number(0), y)
|
||
|
|
assert (y * z).linear_solve(x) == (as_number(0), y * z)
|
||
|
|
|
||
|
|
assert (x + y).linear_solve(x) == (as_number(1), y)
|
||
|
|
assert (z * x + y).linear_solve(x) == (z, y)
|
||
|
|
assert ((z + y) * x + y).linear_solve(x) == (z + y, y)
|
||
|
|
assert (z * y * x + y).linear_solve(x) == (z * y, y)
|
||
|
|
|
||
|
|
pytest.raises(RuntimeError, lambda: (x * x).linear_solve(x))
|
||
|
|
|
||
|
|
def test_as_numer_denom(self):
|
||
|
|
x = as_symbol("x")
|
||
|
|
y = as_symbol("y")
|
||
|
|
n = as_number(123)
|
||
|
|
|
||
|
|
assert as_numer_denom(x) == (x, as_number(1))
|
||
|
|
assert as_numer_denom(x / n) == (x, n)
|
||
|
|
assert as_numer_denom(n / x) == (n, x)
|
||
|
|
assert as_numer_denom(x / y) == (x, y)
|
||
|
|
assert as_numer_denom(x * y) == (x * y, as_number(1))
|
||
|
|
assert as_numer_denom(n + x / y) == (x + n * y, y)
|
||
|
|
assert as_numer_denom(n + x / (y - x / n)) == (y * n**2, y * n - x)
|
||
|
|
|
||
|
|
def test_polynomial_atoms(self):
|
||
|
|
x = as_symbol("x")
|
||
|
|
y = as_symbol("y")
|
||
|
|
n = as_number(123)
|
||
|
|
|
||
|
|
assert x.polynomial_atoms() == {x}
|
||
|
|
assert n.polynomial_atoms() == set()
|
||
|
|
assert (y[x]).polynomial_atoms() == {y[x]}
|
||
|
|
assert (y(x)).polynomial_atoms() == {y(x)}
|
||
|
|
assert (y(x) + x).polynomial_atoms() == {y(x), x}
|
||
|
|
assert (y(x) * x[y]).polynomial_atoms() == {y(x), x[y]}
|
||
|
|
assert (y(x)**x).polynomial_atoms() == {y(x)}
|