def _var(arg):
if isinstance(arg, Declaration):
return arg.variable
elif isinstance(arg, Variable):
return arg
else:
return Variable.deduced(arg)
def test_Subroutine():
# Code to generate the subroutine in the example from
# http://www.fortran90.org/src/best-practices.html#arrays
r = Symbol("r", real=True)
i = Symbol("i", integer=True)
v_r = Variable.deduced(r, attrs=(dimension(assumed_extent), intent_out))
v_i = Variable.deduced(i)
v_n = Variable("n", integer)
do_loop = Do([Assignment(Element(r, [i]),
literal_dp(1) / i**2)], i, 1, v_n)
sub = Subroutine(
"f",
[v_r],
[
Declaration(v_n),
Declaration(v_i),
Assignment(v_n, size(r)), do_loop
],
)
x = Symbol("x", real=True)
v_x3 = Variable.deduced(x, attrs=[dimension(3)])
mod = Module("mymod", definitions=[sub])
prog = Program(
"foo",
[
use(mod, only=[sub]),
Declaration(v_x3),
SubroutineCall(sub, [v_x3]),
Print([sum_(v_x3), v_x3]),
],
)
if not has_fortran():
skip("No fortran compiler found.")
(stdout, stderr), info = compile_run_strings(
[("a.f90", fcode(mod, standard=90)),
("b.f90", fcode(prog, standard=90))],
clean=True,
)
ref = [1.0 / i**2 for i in range(1, 4)]
assert str(sum(ref))[:-3] in stdout
for _ in ref:
assert str(_)[:-3] in stdout
assert stderr == ""
def test_Subroutine():
# Code to generate the subroutine in the example from
# http://www.fortran90.org/src/best-practices.html#arrays
r = Symbol('r', real=True)
i = Symbol('i', integer=True)
v_r = Variable.deduced(r, attrs=(dimension(assumed_extent), intent_out))
v_i = Variable.deduced(i)
v_n = Variable('n', integer)
do_loop = Do([
Assignment(Element(r, [i]), literal_dp(1)/i**2)
], i, 1, v_n)
sub = Subroutine("f", [v_r], [
Declaration(v_n),
Declaration(v_i),
Assignment(v_n, size(r)),
do_loop
])
x = Symbol('x', real=True)
v_x3 = Variable.deduced(x, attrs=[dimension(3)])
mod = Module('mymod', definitions=[sub])
prog = Program('foo', [
use(mod, only=[sub]),
Declaration(v_x3),
SubroutineCall(sub, [v_x3]),
Print([sum_(v_x3), v_x3])
])
if not has_fortran():
skip("No fortran compiler found.")
(stdout, stderr), info = compile_run_strings([
('a.f90', fcode(mod, standard=90)),
('b.f90', fcode(prog, standard=90))
], clean=True)
ref = [1.0/i**2 for i in range(1, 4)]
assert str(sum(ref))[:-3] in stdout
for _ in ref:
assert str(_)[:-3] in stdout
assert stderr == ''
def test_Program():
x = Symbol('x', real=True)
vx = Variable.deduced(x, 42)
decl = Declaration(vx)
prnt = Print([x, x+1])
prog = Program('foo', [decl, prnt])
if not has_fortran():
skip("No fortran compiler found.")
(stdout, stderr), info = compile_run_strings([('main.f90', fcode(prog, standard=90))], clean=True)
assert '42' in stdout
assert '43' in stdout
assert stderr == ''
assert info['exit_status'] == os.EX_OK
def array(symbol, dim, intent=None, **kwargs):
""" Convenience function for creating a Variable instance for a Fortran array
Parameters
==========
symbol : symbol
dim : Attribute or iterable
If dim is an ``Attribute`` it need to have the name 'dimension'. If it is
not an ``Attribute``, then it is passsed to :func:`dimension` as ``*dim``
intent : str
One of: 'in', 'out', 'inout' or None
\\*\\*kwargs:
Keyword arguments for ``Variable`` ('type' & 'value')
Examples
========
>>> from sympy.printing import fcode
>>> from sympy.codegen.ast import integer, real
>>> from sympy.codegen.fnodes import array
>>> arr = array('a', '*', 'in', type=integer)
>>> print(fcode(arr.as_Declaration(), source_format='free', standard=2003))
integer*4, dimension(*), intent(in) :: a
>>> x = array('x', [3, ':', ':'], intent='out', type=real)
>>> print(fcode(x.as_Declaration(value=1), source_format='free', standard=2003))
real*8, dimension(3, :, :), intent(out) :: x = 1
"""
if isinstance(dim, Attribute):
if str(dim.name) != 'dimension':
raise ValueError(
"Got an unexpected Attribute argument as dim: %s" % str(dim))
else:
dim = dimension(*dim)
attrs = list(kwargs.pop('attrs', [])) + [dim]
if intent is not None:
if intent not in (intent_in, intent_out, intent_inout):
intent = {
'in': intent_in,
'out': intent_out,
'inout': intent_inout
}[intent]
attrs.append(intent)
value = kwargs.pop('value', None)
type_ = kwargs.pop('type', None)
if type_ is None:
return Variable.deduced(symbol, value=value, attrs=attrs)
else:
return Variable(symbol, type_, value=value, attrs=attrs)
def test_Program():
x = Symbol('x', real=True)
vx = Variable.deduced(x, 42)
decl = Declaration(vx)
prnt = Print([x, x+1])
prog = Program('foo', [decl, prnt])
if not has_fortran():
skip("No fortran compiler found.")
(stdout, stderr), info = compile_run_strings([('main.f90', fcode(prog, standard=90))], clean=True)
assert '42' in stdout
assert '43' in stdout
assert stderr == ''
assert info['exit_status'] == os.EX_OK
def test_Program():
x = Symbol("x", real=True)
vx = Variable.deduced(x, 42)
decl = Declaration(vx)
prnt = Print([x, x + 1])
prog = Program("foo", [decl, prnt])
if not has_fortran():
skip("No fortran compiler found.")
(stdout, stderr), info = compile_run_strings(
[("main.f90", fcode(prog, standard=90))], clean=True)
assert "42" in stdout
assert "43" in stdout
assert stderr == ""
assert info["exit_status"] == os.EX_OK
def test_Variable():
v = Variable(x, type_=Type('real'))
assert v.symbol == x
assert v.type == real
assert v.value_const == False
w = Variable(y, {value_const}, f32)
assert w.symbol == y
assert w.type == f32
assert w.value_const
v_n = Variable(n, type_=Type.from_expr(n))
assert v_n.type == integer
v_i = Variable(i, type_=Type.from_expr(n))
assert v_i.type == integer
a_i = Variable.deduced(i)
assert a_i.type == integer
def array(symbol, dim, intent=None, **kwargs):
""" Convenience function for creating a Variable instance for a Fortran array
Parameters
==========
symbol : symbol
dim : Attribute or iterable
If dim is an ``Attribute`` it need to have the name 'dimension'. If it is
not an ``Attribute``, then it is passsed to :func:`dimension` as ``*dim``
intent : str
One of: 'in', 'out', 'inout' or None
\\*\\*kwargs:
Keyword arguments for ``Variable`` ('type' & 'value')
Examples
========
>>> from sympy.printing import fcode
>>> from sympy.codegen.ast import integer, real
>>> from sympy.codegen.fnodes import array
>>> arr = array('a', '*', 'in', type=integer)
>>> print(fcode(arr.as_Declaration(), source_format='free', standard=2003))
integer*4, dimension(*), intent(in) :: a
>>> x = array('x', [3, ':', ':'], intent='out', type=real)
>>> print(fcode(x.as_Declaration(value=1), source_format='free', standard=2003))
real*8, dimension(3, :, :), intent(out) :: x = 1
"""
if isinstance(dim, Attribute):
if str(dim.name) != 'dimension':
raise ValueError("Got an unexpected Attribute argument as dim: %s" % str(dim))
else:
dim = dimension(*dim)
attrs = list(kwargs.pop('attrs', [])) + [dim]
if intent is not None:
if intent not in (intent_in, intent_out, intent_inout):
intent = {'in': intent_in, 'out': intent_out, 'inout': intent_inout}[intent]
attrs.append(intent)
value = kwargs.pop('value', None)
type_ = kwargs.pop('type', None)
if type_ is None:
return Variable.deduced(symbol, value=value, attrs=attrs)
else:
return Variable(symbol, type_, value=value, attrs=attrs)
def test_Module():
x = Symbol('x', real=True)
v_x = Variable.deduced(x)
sq = FunctionDefinition(real, 'sqr', [v_x], [Return(x**2)])
mod_sq = Module('mod_sq', [], [sq])
sq_call = FunctionCall('sqr', [42.])
prg_sq = Program('foobar', [
use('mod_sq', only=['sqr']),
Print(['"Square of 42 = "', sq_call])
])
if not has_fortran():
skip("No fortran compiler found.")
(stdout, stderr), info = compile_run_strings([
('mod_sq.f90', fcode(mod_sq, standard=90)),
('main.f90', fcode(prg_sq, standard=90))
], clean=True)
assert '42' in stdout
assert str(42**2) in stdout
assert stderr == ''
def test_Module():
x = Symbol('x', real=True)
v_x = Variable.deduced(x)
sq = FunctionDefinition(real, 'sqr', [v_x], [Return(x**2)])
mod_sq = Module('mod_sq', [], [sq])
sq_call = FunctionCall('sqr', [42.])
prg_sq = Program(
'foobar',
[use('mod_sq', only=['sqr']),
Print(['"Square of 42 = "', sq_call])])
if not has_fortran():
skip("No fortran compiler found.")
(stdout, stderr), info = compile_run_strings(
[('mod_sq.f90', fcode(mod_sq, standard=90)),
('main.f90', fcode(prg_sq, standard=90))],
clean=True)
assert '42' in stdout
assert str(42**2) in stdout
assert stderr == ''
def test_Variable():
v = Variable(x, type=real)
assert v == Variable(v)
assert v == Variable('x', type=real)
assert v.symbol == x
assert v.type == real
assert value_const not in v.attrs
assert v.func(*v.args) == v
assert str(v) == 'Variable(x, type=real)'
w = Variable(y, f32, attrs={value_const})
assert w.symbol == y
assert w.type == f32
assert value_const in w.attrs
assert w.func(*w.args) == w
v_n = Variable(n, type=Type.from_expr(n))
assert v_n.type == integer
assert v_n.func(*v_n.args) == v_n
v_i = Variable(i, type=Type.from_expr(n))
assert v_i.type == integer
assert v_i != v_n
a_i = Variable.deduced(i)
assert a_i.type == integer
assert Variable.deduced(Symbol('x', real=True)).type == real
assert a_i.func(*a_i.args) == a_i
v_n2 = Variable.deduced(n, value=3.5, cast_check=False)
assert v_n2.func(*v_n2.args) == v_n2
assert abs(v_n2.value - 3.5) < 1e-15
raises(ValueError, lambda: Variable.deduced(n, value=3.5, cast_check=True))
v_n3 = Variable.deduced(n)
assert v_n3.type == integer
assert str(v_n3) == 'Variable(n, type=integer)'
assert Variable.deduced(z, value=3).type == integer
assert Variable.deduced(z, value=3.0).type == real
assert Variable.deduced(z, value=3.0 + 1j).type == complex_
def test_Variable():
v = Variable(x, type=real)
assert v == Variable(v)
assert v == Variable('x', type=real)
assert v.symbol == x
assert v.type == real
assert value_const not in v.attrs
assert v.func(*v.args) == v
assert str(v) == 'Variable(x, type=real)'
w = Variable(y, f32, attrs={value_const})
assert w.symbol == y
assert w.type == f32
assert value_const in w.attrs
assert w.func(*w.args) == w
v_n = Variable(n, type=Type.from_expr(n))
assert v_n.type == integer
assert v_n.func(*v_n.args) == v_n
v_i = Variable(i, type=Type.from_expr(n))
assert v_i.type == integer
assert v_i != v_n
a_i = Variable.deduced(i)
assert a_i.type == integer
assert Variable.deduced(Symbol('x', real=True)).type == real
assert a_i.func(*a_i.args) == a_i
v_n2 = Variable.deduced(n, value=3.5, cast_check=False)
assert v_n2.func(*v_n2.args) == v_n2
assert abs(v_n2.value - 3.5) < 1e-15
raises(ValueError, lambda: Variable.deduced(n, value=3.5, cast_check=True))
v_n3 = Variable.deduced(n)
assert v_n3.type == integer
assert str(v_n3) == 'Variable(n, type=integer)'
assert Variable.deduced(z, value=3).type == integer
assert Variable.deduced(z, value=3.0).type == real
assert Variable.deduced(z, value=3.0+1j).type == complex_
def test_fcode_Declaration():
def check(expr, ref, **kwargs):
assert fcode(expr, standard=95, source_format='free', **kwargs) == ref
i = symbols('i', integer=True)
var1 = Variable.deduced(i)
dcl1 = Declaration(var1)
check(dcl1, "integer*4 :: i")
x, y = symbols('x y')
var2 = Variable(x, float32, value=42, attrs={value_const})
dcl2b = Declaration(var2)
check(dcl2b, 'real*4, parameter :: x = 42')
var3 = Variable(y, type=bool_)
dcl3 = Declaration(var3)
check(dcl3, 'logical :: y')
check(float32, "real*4")
check(float64, "real*8")
check(real, "real*4", type_aliases={real: float32})
check(real, "real*8", type_aliases={real: float64})
def test_Module():
x = Symbol("x", real=True)
v_x = Variable.deduced(x)
sq = FunctionDefinition(real, "sqr", [v_x], [Return(x**2)])
mod_sq = Module("mod_sq", [], [sq])
sq_call = FunctionCall("sqr", [42.0])
prg_sq = Program(
"foobar",
[use("mod_sq", only=["sqr"]),
Print(['"Square of 42 = "', sq_call])])
if not has_fortran():
skip("No fortran compiler found.")
(stdout, stderr), info = compile_run_strings(
[
("mod_sq.f90", fcode(mod_sq, standard=90)),
("main.f90", fcode(prg_sq, standard=90)),
],
clean=True,
)
assert "42" in stdout
assert str(42**2) in stdout
assert stderr == ""
def test_fcode_Declaration():
def check(expr, ref, **kwargs):
assert fcode(expr, standard=95, source_format='free', **kwargs) == ref
i = symbols('i', integer=True)
var1 = Variable.deduced(i)
dcl1 = Declaration(var1)
check(dcl1, "integer*4 :: i")
x, y = symbols('x y')
var2 = Variable(x, float32, value=42, attrs={value_const})
dcl2b = Declaration(var2)
check(dcl2b, 'real*4, parameter :: x = 42')
var3 = Variable(y, type=bool_)
dcl3 = Declaration(var3)
check(dcl3, 'logical :: y')
check(float32, "real*4")
check(float64, "real*8")
check(real, "real*4", type_aliases={real: float32})
check(real, "real*8", type_aliases={real: float64})
def test_Variable__deduced():
v_i = Variable.deduced(i)
assert v_i.type == integer
def newtons_method(expr,
wrt,
atol=1e-12,
delta=None,
debug=False,
itermax=None,
counter=None):
""" Generates an AST for Newton-Raphson method (a root-finding algorithm).
Returns an abstract syntax tree (AST) based on ``sympy.codegen.ast`` for Netwon's
method of root-finding.
Parameters
==========
expr : expression
wrt : Symbol
With respect to, i.e. what is the variable.
atol : number or expr
Absolute tolerance (stopping criterion)
delta : Symbol
Will be a ``Dummy`` if ``None``.
debug : bool
Whether to print convergence information during iterations
itermax : number or expr
Maximum number of iterations.
counter : Symbol
Will be a ``Dummy`` if ``None``.
Examples
========
>>> from sympy import symbols, cos
>>> from sympy.codegen.ast import Assignment
>>> from sympy.codegen.algorithms import newtons_method
>>> x, dx, atol = symbols('x dx atol')
>>> expr = cos(x) - x**3
>>> algo = newtons_method(expr, x, atol, dx)
>>> algo.has(Assignment(dx, -expr/expr.diff(x)))
True
References
==========
.. [1] https://en.wikipedia.org/wiki/Newton%27s_method
"""
if delta is None:
delta = Dummy()
Wrapper = Scope
name_d = 'delta'
else:
Wrapper = lambda x: x
name_d = delta.name
delta_expr = -expr / expr.diff(wrt)
whl_bdy = [
Assignment(delta, delta_expr),
AddAugmentedAssignment(wrt, delta)
]
if debug:
prnt = Print([wrt, delta],
r"{}=%12.5g {}=%12.5g\n".format(wrt.name, name_d))
whl_bdy = [whl_bdy[0], prnt] + whl_bdy[1:]
req = Gt(Abs(delta), atol)
declars = [Declaration(Variable(delta, type=real, value=oo))]
if itermax is not None:
counter = counter or Dummy(integer=True)
v_counter = Variable.deduced(counter, 0)
declars.append(Declaration(v_counter))
whl_bdy.append(AddAugmentedAssignment(counter, 1))
req = And(req, Lt(counter, itermax))
whl = While(req, CodeBlock(*whl_bdy))
blck = declars + [whl]
return Wrapper(CodeBlock(*blck))
def newtons_method(expr, wrt, atol=1e-12, delta=None, debug=False,
itermax=None, counter=None):
""" Generates an AST for Newton-Raphson method (a root-finding algorithm).
Returns an abstract syntax tree (AST) based on ``sympy.codegen.ast`` for Netwon's
method of root-finding.
Parameters
==========
expr : expression
wrt : Symbol
With respect to, i.e. what is the variable.
atol : number or expr
Absolute tolerance (stopping criterion)
delta : Symbol
Will be a ``Dummy`` if ``None``.
debug : bool
Whether to print convergence information during iterations
itermax : number or expr
Maximum number of iterations.
counter : Symbol
Will be a ``Dummy`` if ``None``.
Examples
========
>>> from sympy import symbols, cos
>>> from sympy.codegen.ast import Assignment
>>> from sympy.codegen.algorithms import newtons_method
>>> x, dx, atol = symbols('x dx atol')
>>> expr = cos(x) - x**3
>>> algo = newtons_method(expr, x, atol, dx)
>>> algo.has(Assignment(dx, -expr/expr.diff(x)))
True
References
==========
.. [1] https://en.wikipedia.org/wiki/Newton%27s_method
"""
if delta is None:
delta = Dummy()
Wrapper = Scope
name_d = 'delta'
else:
Wrapper = lambda x: x
name_d = delta.name
delta_expr = -expr/expr.diff(wrt)
whl_bdy = [Assignment(delta, delta_expr), AddAugmentedAssignment(wrt, delta)]
if debug:
prnt = Print([wrt, delta], r"{0}=%12.5g {1}=%12.5g\n".format(wrt.name, name_d))
whl_bdy = [whl_bdy[0], prnt] + whl_bdy[1:]
req = Gt(Abs(delta), atol)
declars = [Declaration(Variable(delta, type=real, value=oo))]
if itermax is not None:
counter = counter or Dummy(integer=True)
v_counter = Variable.deduced(counter, 0)
declars.append(Declaration(v_counter))
whl_bdy.append(AddAugmentedAssignment(counter, 1))
req = And(req, Lt(counter, itermax))
whl = While(req, CodeBlock(*whl_bdy))
blck = declars + [whl]
return Wrapper(CodeBlock(*blck))
