name : test_symbolic.py import pytest from numpy.f2py.symbolic import ( Expr, Op, ArithOp, Language, as_symbol, as_number, as_string, as_array, as_complex, as_terms, as_factors, eliminate_quotes, insert_quotes, fromstring, as_expr, as_apply, as_numer_denom, as_ternary, as_ref, as_deref, normalize, as_eq, as_ne, as_lt, as_gt, as_le, as_ge, ) from . import util class TestSymbolic(util.F2PyTest): def test_eliminate_quotes(self): def worker(s): r, d = eliminate_quotes(s) s1 = insert_quotes(r, d) assert s1 == s for kind in ["", "mykind_"]: worker(kind + '"1234" // "ABCD"') worker(kind + '"1234" // ' + kind + '"ABCD"') worker(kind + "\"1234\" // 'ABCD'") worker(kind + '"1234" // ' + kind + "'ABCD'") worker(kind + '"1\\"2\'AB\'34"') worker("a = " + kind + "'1\\'2\"AB\"34'") def test_sanity(self): x = as_symbol("x") y = as_symbol("y") z = as_symbol("z") assert x.op == Op.SYMBOL assert repr(x) == "Expr(Op.SYMBOL, 'x')" assert x == x assert x != y assert hash(x) is not None n = as_number(123) m = as_number(456) assert n.op == Op.INTEGER assert repr(n) == "Expr(Op.INTEGER, (123, 4))" assert n == n assert n != m assert hash(n) is not None fn = as_number(12.3) fm = as_number(45.6) assert fn.op == Op.REAL assert repr(fn) == "Expr(Op.REAL, (12.3, 4))" assert fn == fn assert fn != fm assert hash(fn) is not None c = as_complex(1, 2) c2 = as_complex(3, 4) assert c.op == Op.COMPLEX assert repr(c) == ("Expr(Op.COMPLEX, (Expr(Op.INTEGER, (1, 4))," " Expr(Op.INTEGER, (2, 4))))") assert c == c assert c != c2 assert hash(c) is not None s = as_string("'123'") s2 = as_string('"ABC"') assert s.op == Op.STRING assert repr(s) == "Expr(Op.STRING, (\"'123'\", 1))", repr(s) assert s == s assert s != s2 a = as_array((n, m)) b = as_array((n, )) assert a.op == Op.ARRAY assert repr(a) == ("Expr(Op.ARRAY, (Expr(Op.INTEGER, (123, 4))," " Expr(Op.INTEGER, (456, 4))))") assert a == a assert a != b t = as_terms(x) u = as_terms(y) assert t.op == Op.TERMS assert repr(t) == "Expr(Op.TERMS, {Expr(Op.SYMBOL, 'x'): 1})" assert t == t assert t != u assert hash(t) is not None v = as_factors(x) w = as_factors(y) assert v.op == Op.FACTORS assert repr(v) == "Expr(Op.FACTORS, {Expr(Op.SYMBOL, 'x'): 1})" assert v == v assert w != v assert hash(v) is not None t = as_ternary(x, y, z) u = as_ternary(x, z, y) assert t.op == Op.TERNARY assert t == t assert t != u assert hash(t) is not None e = as_eq(x, y) f = as_lt(x, y) assert e.op == Op.RELATIONAL assert e == e assert e != f assert hash(e) is not None def test_tostring_fortran(self): x = as_symbol("x") y = as_symbol("y") z = as_symbol("z") n = as_number(123) m = as_number(456) a = as_array((n, m)) c = as_complex(n, m) assert str(x) == "x" assert str(n) == "123" assert str(a) == "[123, 456]" assert str(c) == "(123, 456)" assert str(Expr(Op.TERMS, {x: 1})) == "x" assert str(Expr(Op.TERMS, {x: 2})) == "2 * x" assert str(Expr(Op.TERMS, {x: -1})) == "-x" assert str(Expr(Op.TERMS, {x: -2})) == "-2 * x" assert str(Expr(Op.TERMS, {x: 1, y: 1})) == "x + y" assert str(Expr(Op.TERMS, {x: -1, y: -1})) == "-x - y" assert str(Expr(Op.TERMS, {x: 2, y: 3})) == "2 * x + 3 * y" assert str(Expr(Op.TERMS, {x: -2, y: 3})) == "-2 * x + 3 * y" assert str(Expr(Op.TERMS, {x: 2, y: -3})) == "2 * x - 3 * y" assert str(Expr(Op.FACTORS, {x: 1})) == "x" assert str(Expr(Op.FACTORS, {x: 2})) == "x ** 2" assert str(Expr(Op.FACTORS, {x: -1})) == "x ** -1" assert str(Expr(Op.FACTORS, {x: -2})) == "x ** -2" assert str(Expr(Op.FACTORS, {x: 1, y: 1})) == "x * y" assert str(Expr(Op.FACTORS, {x: 2, y: 3})) == "x ** 2 * y ** 3" v = Expr(Op.FACTORS, {x: 2, Expr(Op.TERMS, {x: 1, y: 1}): 3}) assert str(v) == "x ** 2 * (x + y) ** 3", str(v) v = Expr(Op.FACTORS, {x: 2, Expr(Op.FACTORS, {x: 1, y: 1}): 3}) assert str(v) == "x ** 2 * (x * y) ** 3", str(v) assert str(Expr(Op.APPLY, ("f", (), {}))) == "f()" assert str(Expr(Op.APPLY, ("f", (x, ), {}))) == "f(x)" assert str(Expr(Op.APPLY, ("f", (x, y), {}))) == "f(x, y)" assert str(Expr(Op.INDEXING, ("f", x))) == "f[x]" assert str(as_ternary(x, y, z)) == "merge(y, z, x)" assert str(as_eq(x, y)) == "x .eq. y" assert str(as_ne(x, y)) == "x .ne. y" assert str(as_lt(x, y)) == "x .lt. y" assert str(as_le(x, y)) == "x .le. y" assert str(as_gt(x, y)) == "x .gt. y" assert str(as_ge(x, y)) == "x .ge. y" def test_tostring_c(self): language = Language.C x = as_symbol("x") y = as_symbol("y") z = as_symbol("z") n = as_number(123) assert Expr(Op.FACTORS, {x: 2}).tostring(language=language) == "x * x" assert (Expr(Op.FACTORS, { x + y: 2 }).tostring(language=language) == "(x + y) * (x + y)") assert Expr(Op.FACTORS, { x: 12 }).tostring(language=language) == "pow(x, 12)" assert as_apply(ArithOp.DIV, x, y).tostring(language=language) == "x / y" assert (as_apply(ArithOp.DIV, x, x + y).tostring(language=language) == "x / (x + y)") assert (as_apply(ArithOp.DIV, x - y, x + y).tostring(language=language) == "(x - y) / (x + y)") assert (x + (x - y) / (x + y) + n).tostring(language=language) == "123 + x + (x - y) / (x + y)" assert as_ternary(x, y, z).tostring(language=language) == "(x?y:z)" assert as_eq(x, y).tostring(language=language) == "x == y" assert as_ne(x, y).tostring(language=language) == "x != y" assert as_lt(x, y).tostring(language=language) == "x < y" assert as_le(x, y).tostring(language=language) == "x <= y" assert as_gt(x, y).tostring(language=language) == "x > y" assert as_ge(x, y).tostring(language=language) == "x >= y" def test_operations(self): x = as_symbol("x") y = as_symbol("y") z = as_symbol("z") assert x + x == Expr(Op.TERMS, {x: 2}) assert x - x == Expr(Op.INTEGER, (0, 4)) assert x + y == Expr(Op.TERMS, {x: 1, y: 1}) assert x - y == Expr(Op.TERMS, {x: 1, y: -1}) assert x * x == Expr(Op.FACTORS, {x: 2}) assert x * y == Expr(Op.FACTORS, {x: 1, y: 1}) assert +x == x assert -x == Expr(Op.TERMS, {x: -1}), repr(-x) assert 2 * x == Expr(Op.TERMS, {x: 2}) assert 2 + x == Expr(Op.TERMS, {x: 1, as_number(1): 2}) assert 2 * x + 3 * y == Expr(Op.TERMS, {x: 2, y: 3}) assert (x + y) * 2 == Expr(Op.TERMS, {x: 2, y: 2}) assert x**2 == Expr(Op.FACTORS, {x: 2}) assert (x + y)**2 == Expr( Op.TERMS, { Expr(Op.FACTORS, {x: 2}): 1, Expr(Op.FACTORS, {y: 2}): 1, Expr(Op.FACTORS, { x: 1, y: 1 }): 2, }, ) assert (x + y) * x == x**2 + x * y assert (x + y)**2 == x**2 + 2 * x * y + y**2 assert (x + y)**2 + (x - y)**2 == 2 * x**2 + 2 * y**2 assert (x + y) * z == x * z + y * z assert z * (x + y) == x * z + y * z assert (x / 2) == as_apply(ArithOp.DIV, x, as_number(2)) assert (2 * x / 2) == x assert (3 * x / 2) == as_apply(ArithOp.DIV, 3 * x, as_number(2)) assert (4 * x / 2) == 2 * x assert (5 * x / 2) == as_apply(ArithOp.DIV, 5 * x, as_number(2)) assert (6 * x / 2) == 3 * x assert ((3 * 5) * x / 6) == as_apply(ArithOp.DIV, 5 * x, as_number(2)) assert (30 * x**2 * y**4 / (24 * x**3 * y**3)) == as_apply( ArithOp.DIV, 5 * y, 4 * x) assert ((15 * x / 6) / 5) == as_apply(ArithOp.DIV, x, as_number(2)), (15 * x / 6) / 5 assert (x / (5 / x)) == as_apply(ArithOp.DIV, x**2, as_number(5)) assert (x / 2.0) == Expr(Op.TERMS, {x: 0.5}) s = as_string('"ABC"') t = as_string('"123"') assert s // t == Expr(Op.STRING, ('"ABC123"', 1)) assert s // x == Expr(Op.CONCAT, (s, x)) assert x // s == Expr(Op.CONCAT, (x, s)) c = as_complex(1.0, 2.0) assert -c == as_complex(-1.0, -2.0) assert c + c == as_expr((1 + 2j) * 2) assert c * c == as_expr((1 + 2j)**2) def test_substitute(self): x = as_symbol("x") y = as_symbol("y") z = as_symbol("z") a = as_array((x, y)) assert x.substitute({x: y}) == y assert (x + y).substitute({x: z}) == y + z assert (x * y).substitute({x: z}) == y * z assert (x**4).substitute({x: z}) == z**4 assert (x / y).substitute({x: z}) == z / y assert x.substitute({x: y + z}) == y + z assert a.substitute({x: y + z}) == as_array((y + z, y)) assert as_ternary(x, y, z).substitute({x: y + z}) == as_ternary(y + z, y, z) assert as_eq(x, y).substitute({x: y + z}) == as_eq(y + z, y) def test_fromstring(self): x = as_symbol("x") y = as_symbol("y") z = as_symbol("z") f = as_symbol("f") s = as_string('"ABC"') t = as_string('"123"') a = as_array((x, y)) assert fromstring("x") == x assert fromstring("+ x") == x assert fromstring("- x") == -x assert fromstring("x + y") == x + y assert fromstring("x + 1") == x + 1 assert fromstring("x * y") == x * y assert fromstring("x * 2") == x * 2 assert fromstring("x / y") == x / y assert fromstring("x ** 2", language=Language.Python) == x**2 assert fromstring("x ** 2 ** 3", language=Language.Python) == x**2**3 assert fromstring("(x + y) * z") == (x + y) * z assert fromstring("f(x)") == f(x) assert fromstring("f(x,y)") == f(x, y) assert fromstring("f[x]") == f[x] assert fromstring("f[x][y]") == f[x][y] assert fromstring('"ABC"') == s assert (normalize( fromstring('"ABC" // "123" ', language=Language.Fortran)) == s // t) assert fromstring('f("ABC")') == f(s) 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)}