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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") |
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assert fromstring("(/x, y/)") == a, fromstring("(/x, y/)") |
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assert fromstring("f((/x, y/))") == f(a) |
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assert fromstring("(/(x+y)*z/)") == as_array(((x + y) * z, )) |
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assert fromstring("123") == as_number(123) |
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assert fromstring("123_2") == as_number(123, 2) |
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assert fromstring("123_myintkind") == as_number(123, "myintkind") |
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assert fromstring("123.0") == as_number(123.0, 4) |
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assert fromstring("123.0_4") == as_number(123.0, 4) |
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assert fromstring("123.0_8") == as_number(123.0, 8) |
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assert fromstring("123.0e0") == as_number(123.0, 4) |
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assert fromstring("123.0d0") == as_number(123.0, 8) |
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assert fromstring("123d0") == as_number(123.0, 8) |
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assert fromstring("123e-0") == as_number(123.0, 4) |
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assert fromstring("123d+0") == as_number(123.0, 8) |
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assert fromstring("123.0_myrealkind") == as_number(123.0, "myrealkind") |
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assert fromstring("3E4") == as_number(30000.0, 4) |
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assert fromstring("(1, 2)") == as_complex(1, 2) |
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assert fromstring("(1e2, PI)") == as_complex(as_number(100.0), |
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as_symbol("PI")) |
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assert fromstring("[1, 2]") == as_array((as_number(1), as_number(2))) |
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assert fromstring("POINT(x, y=1)") == as_apply(as_symbol("POINT"), |
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x, |
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y=as_number(1)) |
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assert fromstring( |
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'PERSON(name="John", age=50, shape=(/34, 23/))') == as_apply( |
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as_symbol("PERSON"), |
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name=as_string('"John"'), |
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age=as_number(50), |
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shape=as_array((as_number(34), as_number(23))), |
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) |
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assert fromstring("x?y:z") == as_ternary(x, y, z) |
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assert fromstring("*x") == as_deref(x) |
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assert fromstring("**x") == as_deref(as_deref(x)) |
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assert fromstring("&x") == as_ref(x) |
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assert fromstring("(*x) * (*y)") == as_deref(x) * as_deref(y) |
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assert fromstring("(*x) * *y") == as_deref(x) * as_deref(y) |
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assert fromstring("*x * *y") == as_deref(x) * as_deref(y) |
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assert fromstring("*x**y") == as_deref(x) * as_deref(y) |
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assert fromstring("x == y") == as_eq(x, y) |
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assert fromstring("x != y") == as_ne(x, y) |
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assert fromstring("x < y") == as_lt(x, y) |
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assert fromstring("x > y") == as_gt(x, y) |
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assert fromstring("x <= y") == as_le(x, y) |
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assert fromstring("x >= y") == as_ge(x, y) |
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assert fromstring("x .eq. y", language=Language.Fortran) == as_eq(x, y) |
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assert fromstring("x .ne. y", language=Language.Fortran) == as_ne(x, y) |
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assert fromstring("x .lt. y", language=Language.Fortran) == as_lt(x, y) |
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assert fromstring("x .gt. y", language=Language.Fortran) == as_gt(x, y) |
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assert fromstring("x .le. y", language=Language.Fortran) == as_le(x, y) |
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assert fromstring("x .ge. y", language=Language.Fortran) == as_ge(x, y) |
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def test_traverse(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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def replace_visit(s, r=z): |
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if s == x: |
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return r |
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assert x.traverse(replace_visit) == z |
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assert y.traverse(replace_visit) == y |
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assert z.traverse(replace_visit) == z |
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assert (f(y)).traverse(replace_visit) == f(y) |
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assert (f(x)).traverse(replace_visit) == f(z) |
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assert (f[y]).traverse(replace_visit) == f[y] |
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assert (f[z]).traverse(replace_visit) == f[z] |
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assert (x + y + z).traverse(replace_visit) == (2 * z + y) |
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assert (x + |
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f(y, x - z)).traverse(replace_visit) == (z + |
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f(y, as_number(0))) |
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assert as_eq(x, y).traverse(replace_visit) == as_eq(z, y) |
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function_symbols = set() |
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symbols = set() |
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|
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def collect_symbols(s): |
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if s.op is Op.APPLY: |
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oper = s.data[0] |
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function_symbols.add(oper) |
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if oper in symbols: |
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symbols.remove(oper) |
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elif s.op is Op.SYMBOL and s not in function_symbols: |
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symbols.add(s) |
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|
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(x + f(y, x - z)).traverse(collect_symbols) |
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assert function_symbols == {f} |
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assert symbols == {x, y, z} |
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|
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def collect_symbols2(expr, symbols): |
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if expr.op is Op.SYMBOL: |
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symbols.add(expr) |
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|
|
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symbols = set() |
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(x + f(y, x - z)).traverse(collect_symbols2, symbols) |
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assert symbols == {x, y, z, f} |
|
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|
|
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|
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def collect_symbols3(expr, symbols): |
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if expr.op is Op.APPLY: |
|
|
|
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|
return expr |
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if expr.op is Op.SYMBOL: |
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symbols.add(expr) |
|
|
|
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symbols = set() |
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(x + f(y, x - z)).traverse(collect_symbols3, symbols) |
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assert symbols == {x} |
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|
|
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|
def test_linear_solve(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.linear_solve(x) == (as_number(1), as_number(0)) |
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assert (x + 1).linear_solve(x) == (as_number(1), as_number(1)) |
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assert (2 * x).linear_solve(x) == (as_number(2), as_number(0)) |
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assert (2 * x + 3).linear_solve(x) == (as_number(2), as_number(3)) |
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assert as_number(3).linear_solve(x) == (as_number(0), as_number(3)) |
|
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assert y.linear_solve(x) == (as_number(0), y) |
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assert (y * z).linear_solve(x) == (as_number(0), y * z) |
|
|
|
|
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assert (x + y).linear_solve(x) == (as_number(1), y) |
|
|
assert (z * x + y).linear_solve(x) == (z, y) |
|
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assert ((z + y) * x + y).linear_solve(x) == (z + y, y) |
|
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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)} |
|
|
|
