def _call_printer(self, routine):
code_lines = []
for result in routine.result_variables:
if isinstance(result, Result):
assign_to = None
elif isinstance(result, (OutputArgument, InOutArgument)):
assign_to = result.result_var
try:
constants, not_c, c_expr = ccode(
result.expr, assign_to=assign_to, human=False)
except AssignmentError:
assign_to = result.result_var
code_lines.append(
"%s %s;\n" % (result.get_datatype('c'), str(assign_to)))
constants, not_c, c_expr = ccode(
result.expr, assign_to=assign_to, human=False)
for name, value in sorted(constants, key=str):
code_lines.append("double const %s = %s;\n" % (name, value))
if assign_to:
code_lines.append("%s\n" % c_expr)
else:
code_lines.append(" return %s;\n" % c_expr)
return code_lines
def render_and_write_code(
expressions,
helpers,
folder,
name,
user_functions = {},
chunk_size = 100):
helperlines = (
check_code( ccode( helper[1], helper[0], user_functions=user_functions ) ) + "\n"
for helper in helpers
)
codelines = (
check_code( ccode ( expression, user_functions=user_functions ) ) + ";\n"
for expression in expressions
)
with \
open( path.join(folder,name+".c" ), "w" ) as mainfile, \
open( path.join(folder,name+"_definitions.c"), "w" ) as deffile:
if chunk_size < 1:
for line in chain(helperlines, codelines):
mainfile.write(line)
else:
write_in_chunks(helperlines, mainfile, deffile, name+"helpers", chunk_size)
write_in_chunks(codelines , mainfile, deffile, name+"code" , chunk_size)
def test_goto_Label():
s = 'early_exit'
g = goto(s)
assert g.func(*g.args) == g
assert g != goto('foobar')
assert ccode(g) == 'goto early_exit'
l = Label(s)
assert l.is_Atom
assert ccode(l) == 'early_exit:'
assert g.label == l
assert l == Label(s)
assert l != Label('foobar')
def test_create_expand_pow_optimization():
my_opt = create_expand_pow_optimization(4)
x = Symbol('x')
assert ccode(optimize(x**4, [my_opt])) == 'x*x*x*x'
x5x4 = x**5 + x**4
assert ccode(optimize(x5x4, [my_opt])) == 'pow(x, 5) + x*x*x*x'
sin4x = sin(x)**4
assert ccode(optimize(sin4x, [my_opt])) == 'pow(sin(x), 4)'
assert ccode(optimize((x**(-4)), [my_opt])) == 'pow(x, -4)'
def get_prototype(self, routine):
"""Returns a string for the function prototype for the given routine.
If the routine has multiple result objects, an CodeGenError is
raised.
See: http://en.wikipedia.org/wiki/Function_prototype
"""
if len(routine.results) > 1:
raise CodeGenError("C only supports a single or no return value.")
elif len(routine.results) == 1:
ctype = routine.results[0].get_datatype('C')
else:
ctype = "void"
type_args = []
for arg in routine.arguments:
name = ccode(arg.name)
if arg.dimensions:
type_args.append((arg.get_datatype('C'), "*%s" % name))
elif isinstance(arg, ResultBase):
type_args.append((arg.get_datatype('C'), "&%s" % name))
else:
type_args.append((arg.get_datatype('C'), name))
arguments = ", ".join(["%s %s" % t for t in type_args])
return "%s %s(%s)" % (ctype, routine.name, arguments)
def dump_c(self, routines, f, prefix, header=True, empty=True):
"""Write the C code file.
This file contains all the definitions of the routines in c code and
refers to the header file.
Arguments:
routines -- a list of Routine instances
f -- a file-like object to write the file to
prefix -- the filename prefix, used to refer to the proper header
file. Only the basename of the prefix is used.
Optional arguments:
header -- When True, a header comment is included on top of each
source file. [DEFAULT=True]
empty -- When True, empty lines are included to structure the
source files. [DEFAULT=True]
"""
if header:
self._dump_header(f)
if empty: print >> f
print >> f, "#include \"%s.h\"" % os.path.basename(prefix)
print >> f, "#include <math.h>"
if empty: print >> f
for routine in routines:
# function definitions.
prototype, result = self.get_prototype_result(routine)
print >> f, "%s {" % prototype
# return value
if result is not None:
print >> f, " return %s;" % ccode(result.expr)
# curly closing brackets
print >> f, "}"
if empty: print >> f
if empty: print >> f
def get_prototype(self, routine):
"""Returns a string for the function prototype of the routine.
If the routine has multiple result objects, an CodeGenError is
raised.
See: http://en.wikipedia.org/wiki/Function_prototype
"""
if len(routine.results) == 1:
ctype = routine.results[0].get_datatype('C')
else:
ctype = "void"
type_args = []
for arg in routine.arguments:
name = ccode(arg.name)
# Hack to make all double-valued arguments into pointers
if arg.dimensions or isinstance(
arg, ResultBase) or arg.get_datatype('C') == 'double':
type_args.append((arg.get_datatype('C'), "*%s" % name))
else:
type_args.append((arg.get_datatype('C'), name))
arguments = ", ".join(["%s %s" % t for t in type_args])
return "%s %s(%s)" % (ctype, routine.name, arguments)
def test_newtons_method_function__ccode():
x = sp.Symbol("x", real=True)
expr = sp.cos(x) - x**3
func = newtons_method_function(expr, x)
if not cython:
skip("cython not installed.")
if not has_c():
skip("No C compiler found.")
compile_kw = dict(std="c99")
with TemporaryDirectory() as folder:
mod, info = compile_link_import_strings(
[
(
"newton.c",
("#include <math.h>\n"
"#include <stdio.h>\n") + ccode(func),
),
(
"_newton.pyx",
("#cython: language_level={}\n".format("3") +
"cdef extern double newton(double)\n"
"def py_newton(x):\n"
" return newton(x)\n"),
),
],
build_dir=folder,
compile_kwargs=compile_kw,
)
assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12
def get_prototype(self, routine):
"""Returns a string for the function prototype for the given routine.
If the routine has multiple result objects, an CodeGenError is
raised.
See: http://en.wikipedia.org/wiki/Function_prototype
"""
if len(routine.results) > 1:
raise CodeGenError("C only supports a single or no return value.")
elif len(routine.results) == 1:
ctype = routine.results[0].get_datatype('C')
else:
ctype = "void"
type_args = []
for arg in routine.arguments:
name = ccode(arg.name)
if arg.dimensions:
type_args.append((arg.get_datatype('C'), "*%s" % name))
elif isinstance(arg, ResultBase):
type_args.append((arg.get_datatype('C'), "&%s" % name))
else:
type_args.append((arg.get_datatype('C'), name))
arguments = ", ".join([ "%s %s" % t for t in type_args])
return "%s %s(%s)" % (ctype, routine.name, arguments)
def test_sizeof():
typename = 'unsigned int'
sz = sizeof(typename)
assert ccode(sz) == 'sizeof(%s)' % typename
assert sz.func(*sz.args) == sz
assert not sz.is_Atom
assert all(atom == typename for atom in sz.atoms())
def test_newtons_method_function__ccode_parameters():
args = x, A, k, p = sp.symbols("x A k p")
expr = A * sp.cos(k * x) - p * x**3
raises(ValueError, lambda: newtons_method_function(expr, x))
use_wurlitzer = wurlitzer
func = newtons_method_function(expr, x, args, debug=use_wurlitzer)
if not has_c():
skip("No C compiler found.")
if not cython:
skip("cython not installed.")
compile_kw = dict(std="c99")
with TemporaryDirectory() as folder:
mod, info = compile_link_import_strings(
[
(
"newton_par.c",
("#include <math.h>\n"
"#include <stdio.h>\n") + ccode(func),
),
(
"_newton_par.pyx",
("#cython: language_level={}\n".format("3") +
"cdef extern double newton(double, double, double, double)\n"
"def py_newton(x, A=1, k=1, p=1):\n"
" return newton(x, A, k, p)\n"),
),
],
compile_kwargs=compile_kw,
build_dir=folder,
)
if use_wurlitzer:
with wurlitzer.pipes() as (out, err):
result = mod.py_newton(0.5)
else:
result = mod.py_newton(0.5)
assert abs(result - 0.865474033102) < 1e-12
if not use_wurlitzer:
skip(
"C-level output only tested when package 'wurlitzer' is available."
)
out, err = out.read(), err.read()
assert err == ""
assert (out == """\
x= 0.5 d_x= 0.61214
x= 1.1121 d_x= -0.20247
x= 0.90967 d_x= -0.042409
x= 0.86726 d_x= -0.0017867
x= 0.86548 d_x= -3.1022e-06
x= 0.86547 d_x= -9.3421e-12
x= 0.86547 d_x= 3.6902e-17
""") # try to run tests with LC_ALL=C if this assertion fails
def _call_printer(self, routine):
code_lines = []
# Compose a list of symbols to be dereferenced in the function
# body. These are the arguments that were passed by a reference
# pointer, excluding arrays.
dereference = []
for arg in routine.arguments:
if isinstance(arg, ResultBase) and not arg.dimensions:
dereference.append(arg.name)
return_val = None
for result in routine.result_variables:
if isinstance(result, Result):
assign_to = routine.name + "_result"
t = result.get_datatype('c')
code_lines.append("{0} {1};\n".format(t, str(assign_to)))
return_val = assign_to
else:
assign_to = result.result_var
try:
constants, not_c, c_expr = ccode(result.expr,
human=False,
assign_to=assign_to,
dereference=dereference)
except AssignmentError:
assign_to = result.result_var
code_lines.append("%s %s;\n" %
(result.get_datatype('c'), str(assign_to)))
constants, not_c, c_expr = ccode(result.expr,
human=False,
assign_to=assign_to,
dereference=dereference)
for name, value in sorted(constants, key=str):
code_lines.append("double const %s = %s;\n" % (name, value))
code_lines.append("%s\n" % c_expr)
if return_val:
code_lines.append(" return %s;\n" % return_val)
return code_lines
def _render_compile_import(funcdef, build_dir):
code_str = render_as_source_file(funcdef, settings=dict(contract=False))
declar = ccode(FunctionPrototype.from_FunctionDefinition(funcdef))
return compile_link_import_strings([
('our_test_func.c', code_str),
('_our_test_func.pyx', ("cdef extern {declar}\n"
"def _{fname}({typ}[:] inp, {typ}[:] out):\n"
" {fname}(inp.size, &inp[0], &out[0])").format(
declar=declar, fname=funcdef.name, typ='double'
))
], build_dir=build_dir)
def _render_compile_import(funcdef, build_dir):
code_str = render_as_source_file(funcdef, settings=dict(contract=False))
declar = ccode(FunctionPrototype.from_FunctionDefinition(funcdef))
return compile_link_import_strings(
[('our_test_func.c', code_str),
('_our_test_func.pyx',
("cdef extern {declar}\n"
"def _{fname}({typ}[:] inp, {typ}[:] out):\n"
" {fname}(inp.size, &inp[0], &out[0])").format(
declar=declar, fname=funcdef.name, typ='double'))],
build_dir=build_dir)
def test_union():
vx, vy = Variable(x, type=float64), Variable(y, type=int64)
u = union("dualuse", [vx, vy])
assert u.func(*u.args) == u
assert u == union("dualuse", (vx, vy))
assert str(u.name) == "dualuse"
assert len(u.declarations) == 2
assert all(isinstance(arg, Declaration) for arg in u.declarations)
assert ccode(u) == ("union dualuse {\n"
" double x;\n"
" int64_t y;\n"
"}")
def _call_printer(self, routine):
code_lines = []
for result in routine.result_variables:
if isinstance(result, Result):
assign_to = None
elif isinstance(result, (OutputArgument, InOutArgument)):
assign_to = result.result_var
try:
constants, not_c, c_expr = ccode(result.expr, assign_to=assign_to, human=False)
except AssignmentError:
assign_to = result.result_var
code_lines.append("%s %s;\n" % (result.get_datatype('c'), str(assign_to)))
constants, not_c, c_expr = ccode(result.expr, assign_to=assign_to, human=False)
for name, value in sorted(constants, key=str):
code_lines.append("double const %s = %s;\n" % (name, value))
if assign_to:
code_lines.append("%s\n" % c_expr)
else:
code_lines.append(" return %s;\n" % c_expr)
return code_lines
def test_union():
vx, vy = Variable(x, type=float64), Variable(y, type=int64)
u = union('dualuse', [vx, vy])
assert u.func(*u.args) == u
assert u == union('dualuse', (vx, vy))
assert str(u.name) == 'dualuse'
assert len(u.declarations) == 2
assert all(isinstance(arg, Declaration) for arg in u.declarations)
assert ccode(u) == (
"union dualuse {\n"
" double x;\n"
" int64_t y;\n"
"}")
def test_struct():
vx, vy = Variable(x, type=float64), Variable(y, type=float64)
s = struct("vec2", [vx, vy])
assert s.func(*s.args) == s
assert s == struct("vec2", (vx, vy))
assert s != struct("vec2", (vy, vx))
assert str(s.name) == "vec2"
assert len(s.declarations) == 2
assert all(isinstance(arg, Declaration) for arg in s.declarations)
assert ccode(s) == ("struct vec2 {\n"
" double x;\n"
" double y;\n"
"}")
def _call_printer(self, routine):
code_lines = []
# Compose a list of symbols to be dereferenced in the function
# body. These are the arguments that were passed by a reference
# pointer, excluding arrays.
dereference = []
for arg in routine.arguments:
if isinstance(arg, ResultBase) and not arg.dimensions:
dereference.append(arg.name)
return_val = None
for result in routine.result_variables:
if isinstance(result, Result):
assign_to = routine.name + "_result"
t = result.get_datatype('c')
code_lines.append("{0} {1};\n".format(t, str(assign_to)))
return_val = assign_to
else:
assign_to = result.result_var
try:
constants, not_c, c_expr = ccode(result.expr, human=False,
assign_to=assign_to, dereference=dereference)
except AssignmentError:
assign_to = result.result_var
code_lines.append(
"%s %s;\n" % (result.get_datatype('c'), str(assign_to)))
constants, not_c, c_expr = ccode(result.expr, human=False,
assign_to=assign_to, dereference=dereference)
for name, value in sorted(constants, key=str):
code_lines.append("double const %s = %s;\n" % (name, value))
code_lines.append("%s\n" % c_expr)
if return_val:
code_lines.append(" return %s;\n" % return_val)
return code_lines
def test_struct():
vx, vy = Variable(x, type=float64), Variable(y, type=float64)
s = struct('vec2', [vx, vy])
assert s.func(*s.args) == s
assert s == struct('vec2', (vx, vy))
assert s != struct('vec2', (vy, vx))
assert str(s.name) == 'vec2'
assert len(s.declarations) == 2
assert all(isinstance(arg, Declaration) for arg in s.declarations)
assert ccode(s) == (
"struct vec2 {\n"
" double x;\n"
" double y;\n"
"}")
def test_create_expand_pow_optimization():
cc = lambda x: ccode(optimize(x, [create_expand_pow_optimization(4)]))
x = Symbol('x')
assert cc(x**4) == 'x*x*x*x'
assert cc(x**4 + x**2) == 'x*x + x*x*x*x'
assert cc(x**5 + x**4) == 'pow(x, 5) + x*x*x*x'
assert cc(sin(x)**4) == 'pow(sin(x), 4)'
# gh issue 15335
assert cc(x**(-4)) == '1.0/(x*x*x*x)'
assert cc(x**(-5)) == 'pow(x, -5)'
assert cc(-x**4) == '-x*x*x*x'
assert cc(x**4 - x**2) == '-x*x + x*x*x*x'
i = Symbol('i', integer=True)
assert cc(x**i - x**2) == 'pow(x, i) - x*x'
def test_create_expand_pow_optimization():
cc = lambda x: ccode(optimize(x, [create_expand_pow_optimization(4)]))
x = Symbol("x")
assert cc(x**4) == "x*x*x*x"
assert cc(x**4 + x**2) == "x*x + x*x*x*x"
assert cc(x**5 + x**4) == "pow(x, 5) + x*x*x*x"
assert cc(sin(x)**4) == "pow(sin(x), 4)"
# gh issue 15335
assert cc(x**(-4)) == "1.0/(x*x*x*x)"
assert cc(x**(-5)) == "pow(x, -5)"
assert cc(-(x**4)) == "-x*x*x*x"
assert cc(x**4 - x**2) == "-x*x + x*x*x*x"
i = Symbol("i", integer=True)
assert cc(x**i - x**2) == "pow(x, i) - x*x"
def _render_compile_import(funcdef, build_dir):
code_str = render_as_source_file(funcdef, settings=dict(contract=False))
declar = ccode(FunctionPrototype.from_FunctionDefinition(funcdef))
return compile_link_import_strings(
[
("our_test_func.c", code_str),
(
"_our_test_func.pyx",
("#cython: language_level={}\n".format("3") +
"cdef extern {declar}\n"
"def _{fname}({typ}[:] inp, {typ}[:] out):\n"
" {fname}(inp.size, &inp[0], &out[0])").format(
declar=declar, fname=funcdef.name, typ="double"),
),
],
build_dir=build_dir,
)
def test_newtons_method_function__ccode_parameters():
args = x, A, k, p = sp.symbols('x A k p')
expr = A * sp.cos(k * x) - p * x**3
raises(ValueError, lambda: newtons_method_function(expr, x))
use_wurlitzer = wurlitzer
func = newtons_method_function(expr, x, args, debug=use_wurlitzer)
if not has_c():
skip("No C compiler found.")
if not cython:
skip("cython not installed.")
compile_kw = dict(std='c99')
with tempfile.TemporaryDirectory() as folder:
mod, info = compile_link_import_strings(
[('newton_par.c', ('#include <math.h>\n'
'#include <stdio.h>\n') + ccode(func)),
('_newton_par.pyx',
("#cython: language_level={}\n".format("3") +
"cdef extern double newton(double, double, double, double)\n"
"def py_newton(x, A=1, k=1, p=1):\n"
" return newton(x, A, k, p)\n"))],
compile_kwargs=compile_kw,
build_dir=folder)
if use_wurlitzer:
with wurlitzer.pipes() as (out, err):
result = mod.py_newton(0.5)
else:
result = mod.py_newton(0.5)
assert abs(result - 0.865474033102) < 1e-12
if not use_wurlitzer:
skip(
"C-level output only tested when package 'wurlitzer' is available."
)
out, err = out.read(), err.read()
assert err == ''
assert out == """\
def test_newtons_method_function__ccode():
x = sp.Symbol('x', real=True)
expr = sp.cos(x) - x**3
func = newtons_method_function(expr, x)
if not cython:
skip("cython not installed.")
if not has_c():
skip("No C compiler found.")
compile_kw = dict(std='c99')
with TemporaryDirectory() as folder:
mod, info = compile_link_import_strings([
('newton.c', ('#include <math.h>\n'
'#include <stdio.h>\n') + ccode(func)),
('_newton.pyx', ("cdef extern double newton(double)\n"
"def py_newton(x):\n"
" return newton(x)\n"))
], build_dir=folder, compile_kwargs=compile_kw)
assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12
def test_newtons_method_function__ccode():
x = sp.Symbol('x', real=True)
expr = sp.cos(x) - x**3
func = newtons_method_function(expr, x)
if not cython:
skip("cython not installed.")
if not has_c():
skip("No C compiler found.")
compile_kw = dict(std='c99')
with TemporaryDirectory() as folder:
mod, info = compile_link_import_strings(
[('newton.c', ('#include <math.h>\n'
'#include <stdio.h>\n') + ccode(func)),
('_newton.pyx', ("cdef extern double newton(double)\n"
"def py_newton(x):\n"
" return newton(x)\n"))],
build_dir=folder,
compile_kwargs=compile_kw)
assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12
def print_cpp(self):
# Print imports necessary.
print("#include <cmath> \nusing namespace std;\n")
# Generate code for input structures.
moment_state_struct = "struct MomentState {\n"
for m, _ in self._moment_state_dynamics.items():
moment_state_struct += "double " + str(m) + ";\n"
moment_state_struct += "};\n"
print(moment_state_struct)
disturbance_moment_struct = "struct DisturbanceMoments{\n"
for dist_moment in self._disturbance_moments:
disturbance_moment_struct += "double " + str(dist_moment) + ";\n"
disturbance_moment_struct += "};\n"
print(disturbance_moment_struct)
controls_struct = "struct Controls{\n"
for control_var in self._control_variables:
controls_struct += "double " + str(control_var) + ";\n"
controls_struct += "};\n"
print(controls_struct)
# Generate code for the function.
print("void PropagateMoments(const MomentState *prev_moment_state, const DisturbanceMoments *disturbance_moments, const Controls *control_inputs, MomentState *moment_state){")
print("// Aliases for the required inputs.")
for m, dynamics in self._moment_state_dynamics.items():
print("const double &" + str(m) + " = prev_moment_state->" + str(m) + ";")
print("\n")
for dist_moment in self._disturbance_moments:
print("const double &" + str(dist_moment) + " = disturbance_moments->" + str(dist_moment) + ";")
if self._control_variables:
print("\n")
for control_var in self._control_variables:
print("const double &" + str(control_var) + " = control_inputs->" + str(control_var) + ";")
print("\n// Dynamics updates.")
for m, dynamics in self._moment_state_dynamics.items():
print("moment_state->" + str(m) + " = " + str(ccode(dynamics)) + ";\n")
print("return; \n }")
def test_newtons_method_function__ccode_parameters():
args = x, A, k, p = sp.symbols('x A k p')
expr = A*sp.cos(k*x) - p*x**3
raises(ValueError, lambda: newtons_method_function(expr, x))
use_wurlitzer = wurlitzer
func = newtons_method_function(expr, x, args, debug=use_wurlitzer)
if not has_c():
skip("No C compiler found.")
if not cython:
skip("cython not installed.")
compile_kw = dict(std='c99')
with TemporaryDirectory() as folder:
mod, info = compile_link_import_strings([
('newton_par.c', ('#include <math.h>\n'
'#include <stdio.h>\n') + ccode(func)),
('_newton_par.pyx', ("cdef extern double newton(double, double, double, double)\n"
"def py_newton(x, A=1, k=1, p=1):\n"
" return newton(x, A, k, p)\n"))
], compile_kwargs=compile_kw, build_dir=folder)
if use_wurlitzer:
with wurlitzer.pipes() as (out, err):
result = mod.py_newton(0.5)
else:
result = mod.py_newton(0.5)
assert abs(result - 0.865474033102) < 1e-12
if not use_wurlitzer:
skip("C-level output only tested when package 'wurlitzer' is available.")
out, err = out.read(), err.read()
assert err == ''
assert out == """\
def get_prototype(self, routine):
"""Returns a string for the function prototype of the routine.
If the routine has multiple result objects, an CodeGenError is
raised.
See: http://en.wikipedia.org/wiki/Function_prototype
"""
if len(routine.results) == 1:
ctype = routine.results[0].get_datatype('C')
else:
ctype = "void"
type_args = []
for arg in routine.arguments:
name = ccode(arg.name)
# Hack to make all double-valued arguments into pointers
if arg.dimensions or isinstance(arg, ResultBase) or arg.get_datatype('C') == 'double':
type_args.append((arg.get_datatype('C'), "*%s" % name))
else:
type_args.append((arg.get_datatype('C'), name))
arguments = ", ".join([ "%s %s" % t for t in type_args])
return "%s %s(%s)" % (ctype, routine.name, arguments)
def print_in_c(expr, standard='C99'):
return ccode(expr, standard=standard)
dudy=diff(u_an,y);
dudz=diff(u_an,z);
dvdx=diff(v_an,x);
dvdy=diff(v_an,y);
dvdz=diff(v_an,z);
dwdx=diff(w_an,x);
dwdy=diff(w_an,y);
dwdz=diff(w_an,z);
from sympy.printing.ccode import ccode, CCodePrinter
ccode(u_an)
from sympy.utilities.codegen import codegen,Routine
codegen((
("u_an", u_an),
("v_an", v_an),
("w_an", w_an),
("du_dx",dudx),
("du_dy",dudy),
("du_dz",dudz),
("dv_dx",dvdx),
("dv_dy",dvdy),
("dv_dz",dvdz),
def codelines():
for expression in expressions:
codeline = ccode(expression, user_functions=user_functions)
yield check_code(codeline) + ";\n"
Bi = Symbol("Bi")
z1r = Symbol("z1r")
z1i = Symbol("z1i")
f1r = Symbol("f1r")
f1i = Symbol("f1i")
solution = solve([Br*( f1r*z1r - f1i*z1i - 1) + Bi*(f1i*z1r + f1r*z1i) + (f1r - z1r),
Bi*(-f1r*z1r + f1i*z1i - 1) + Br*(f1i*z1r + f1r*z1i) + (f1i - z1i)], [Br, Bi])
print solution[Br]
# (-fi**2*zr - fr**2*zr + fr*zi**2 + fr*zr**2 - fr + zr)/(fi**2*zi**2 + fi**2*zr**2 + fr**2*zi**2 + fr**2*zr**2 - 1)
print solution[Bi]
# (-fi**2*zi + fi*zi**2 + fi*zr**2 - fi - fr**2*zi + zi)/(fi**2*zi**2 + fi**2*zr**2 + fr**2*zi**2 + fr**2*zr**2 - 1)
print ccode(solution[Br])
# (-fi*fi*zr - fr*fr*zr + fr*zi*zi + fr*zr*zr - fr + zr)/(fi*fi*zi*zi + fi*fi*zr*zr + fr*fr*zi*zi + fr*fr*zr*zr - 1)
print ccode(solution[Bi])
# (-fi*fi*zi + fi*zi*zi + fi*zr*zr - fi - fr*fr*zi + zi)/(fi*fi*zi*zi + fi*fi*zr*zr + fr*fr*zi*zi + fr*fr*zr*zr - 1)
Br = Symbol("Br")
Bi = Symbol("Bi")
Rr = Symbol("Rr")
Ri = Symbol("Ri")
z1r = Symbol("z1r")
z1i = Symbol("z1i")
f1r = Symbol("f1r")
f1i = Symbol("f1i")
z2r = Symbol("z2r")
z2i = Symbol("z2i")
def test_CommaOperator():
expr = CommaOperator(PreIncrement(x), 2*x)
assert ccode(expr) == '(++(x), 2*x)'
assert expr.func(*expr.args) == expr
def test_PreDecrement():
p = PreDecrement(x)
assert p.func(*p.args) == p
assert ccode(p) == "--(x)"
def test_alignof():
ax = alignof(x)
assert ccode(ax) == "alignof(x)"
assert ax.func(*ax.args) == ax
def test_print_Mul():
x, y = symbols("x y")
s = ccode(x ** (-3) * y ** (-2))
def test_PreIncrement():
p = PreIncrement(x)
assert p.func(*p.args) == p
assert ccode(p) == '++(x)'
Br = Symbol("Br", "real")
Bi = Symbol("Bi", "real")
dBr = Symbol("dBr", "real")
dBi = Symbol("dBi", "real")
Pr = Symbol("Pr", "real")
Pi = Symbol("Pi", "real")
Fr = Symbol("Fr", "real")
Fi = Symbol("Fi", "real")
Rr = Symbol("Rr", "real")
Ri = Symbol("Ri", "real")
# print re(((Pr + I*Pi) + (Br + I*Bi)*pone) / ((Br - I*Bi)*(Pr + I*Pi) + pone)).simplify()
# numerator
print ccode(
(((Pr + I * Pi) + (Br + I * Bi) * sqrt(Pr * Pr + Pi * Pi + 1)) *
((Br + I * Bi) * (Pr - I * Pi) + sqrt(Pr * Pr + Pi * Pi + 1))).expand())
# I*Bi*Bi*Pi*pone - Bi*Bi*Pr*pone + 2*Bi*Br*Pi*pone + 2*I*Bi*Br*Pr*pone + I*Bi*Pi*Pi + I*Bi*Pr*Pr + I*Bi*(Pi*Pi + Pr*Pr + 1) - I*Br*Br*Pi*pone + Br*Br*Pr*pone + Br*Pi*Pi + Br*Pr*Pr + Br*(Pi*Pi + Pr*Pr + 1) + I*Pi*pone + Pr*pone
# Real part: -Bi*Bi*Pr*pone + 2*Bi*Br*Pi*pone + Br*Br*Pr*pone + Br*Pi*Pi + Br*Pr*Pr + Br*(Pi*Pi + Pr*Pr + 1) + Pr*pone
# Imag part: I*Bi*Bi*Pi*pone + 2*I*Bi*Br*Pr*pone + I*Bi*Pi*Pi + I*Bi*Pr*Pr + I*Bi*(Pi*Pi + Pr*Pr + 1) - I*Br*Br*Pi*pone + I*Pi*pone
# denominator
print ccode(
(((Br - I * Bi) * (Pr + I * Pi) + sqrt(Pr * Pr + Pi * Pi + 1)) *
((Br + I * Bi) * (Pr - I * Pi) + sqrt(Pr * Pr + Pi * Pi + 1))).expand())
# Bi*Bi*Pi*Pi + Bi*Bi*Pr*Pr + 2*Bi*Pi*pone + Br*Br*Pi*Pi + Br*Br*Pr*Pr + 2*Br*Pr*pone + Pi*Pi + Pr*Pr + 1
### START EXTENDING B TO THE WHOLE PLANE
# numerator
def _call_printer(self, routine):
prototype, result = self.get_prototype_result(routine)
if result is not None:
return [" return %s;\n" % ccode(result.expr)]
else:
return []
def test_PreDecrement():
p = PreDecrement(x)
assert p.func(*p.args) == p
assert ccode(p) == '--(x)'
def test_alignof():
ax = alignof(x)
assert ccode(ax) == 'alignof(x)'
assert ax.func(*ax.args) == ax
def test_PostDecrement():
p = PostDecrement(x)
assert p.func(*p.args) == p
assert ccode(p) == '(x)--'
def test_PostIncrement():
p = PostIncrement(x)
assert p.func(*p.args) == p
assert ccode(p) == "(x)++"
toHalfPlane = (toDisk + I)/(I*toDisk + 1) twiceImag = toHalfPlane - toHalfPlane.conjugate() highPoint = toHalfPlane + twiceImag/2 # highPoint = toHalfPlane + I backToDisk = (-highPoint + I)/(I*highPoint - 1) # backToScreen = R.conjugate()*(backToDisk - B)/(-B.conjugate()*backToDisk + 1) backToScreen = (backToDisk - B)/(-B.conjugate()*backToDisk + 1) tmp = backToScreen.simplify() print ccode(tmp) # (-B + (-2*(B*R + I)/(I*B*R + 1) + (conjugate(B)*conjugate(R) - I)/(-I*conjugate(B)*conjugate(R) + 1) + I)/(I*(2*(B*R + I)/(I*B*R + 1) - (conjugate(B)*conjugate(R) - I)/(-I*conjugate(B)*conjugate(R) + 1)) - 1))*conjugate(R)/(1 - (-2*(B*R + I)/(I*B*R + 1) + (conjugate(B)*conjugate(R) - I)/(-I*conjugate(B)*conjugate(R) + 1) + I)*conjugate(B)/(I*(2*(B*R + I)/(I*B*R + 1) - (conjugate(B)*conjugate(R) - I)/(-I*conjugate(B)*conjugate(R) + 1)) - 1)) # other sign: (B + (-2*(B + I)/(I*B + 1) + I + (conjugate(B) - I)/(-I*conjugate(B) + 1))/(I*(2*(B + I)/(I*B + 1) - (conjugate(B) - I)/(-I*conjugate(B) + 1)) - 1))/(1 + (-2*(B + I)/(I*B + 1) + I + (conjugate(B) - I)/(-I*conjugate(B) + 1))*conjugate(B)/(I*(2*(B + I)/(I*B + 1) - (conjugate(B) - I)/(-I*conjugate(B) + 1)) - 1)) # just I: (B - (B + I)/((I*B + 1)*(I*((B + I)/(I*B + 1) + I) - 1)))/(-(B + I)*conjugate(B)/((I*B + 1)*(I*((B + I)/(I*B + 1) + I) - 1)) + 1) # numer = (-B + (-2*(B*R + I)/(I*B*R + 1) + (conjugate(B)*conjugate(R) - I)/(-I*conjugate(B)*conjugate(R) + 1) + I)/(I*(2*(B*R + I)/(I*B*R + 1) - (conjugate(B)*conjugate(R) - I)/(-I*conjugate(B)*conjugate(R) + 1)) - 1))*conjugate(R) # denom = (1 - (-2*(B*R + I)/(I*B*R + 1) + (conjugate(B)*conjugate(R) - I)/(-I*conjugate(B)*conjugate(R) + 1) + I)*conjugate(B)/(I*(2*(B*R + I)/(I*B*R + 1) - (conjugate(B)*conjugate(R) - I)/(-I*conjugate(B)*conjugate(R) + 1)) - 1)) # numer = (-B + (-2*(B + I)/(I*B + 1) + I + (conjugate(B) - I)/(-I*conjugate(B) + 1))/(I*(2*(B + I)/(I*B + 1) - (conjugate(B) - I)/(-I*conjugate(B) + 1)) - 1)) # denom = (1 - (-2*(B + I)/(I*B + 1) + I + (conjugate(B) - I)/(-I*conjugate(B) + 1))*conjugate(B)/(I*(2*(B + I)/(I*B + 1) - (conjugate(B) - I)/(-I*conjugate(B) + 1)) - 1)) # numer = (B + (-2*(B + I)/(I*B + 1) + I + (conjugate(B) - I)/(-I*conjugate(B) + 1))/(I*(2*(B + I)/(I*B + 1) - (conjugate(B) - I)/(-I*conjugate(B) + 1)) - 1)) # denom = (1 + (-2*(B + I)/(I*B + 1) + I + (conjugate(B) - I)/(-I*conjugate(B) + 1))*conjugate(B)/(I*(2*(B + I)/(I*B + 1) - (conjugate(B) - I)/(-I*conjugate(B) + 1)) - 1)) # numer = (B - (B + I)/((I*B + 1)*(I*((B + I)/(I*B + 1) + I) - 1))) # denom = (-(B + I)*conjugate(B)/((I*B + 1)*(I*((B + I)/(I*B + 1) + I) - 1)) + 1) # numer = (-B - (B + I)/((I*B + 1)*(I*((B + I)/(I*B + 1) + I) - 1))) # denom = ((B + I)*conjugate(B)/((I*B + 1)*(I*((B + I)/(I*B + 1) + I) - 1)) + 1) numer = (-B + (-3*(B + I)/(2*(I*B + 1)) + I + (conjugate(B) - I)/(2*(-I*conjugate(B) + 1)))/(I*(3*(B + I)/(2*(I*B + 1)) - (conjugate(B) - I)/(2*(-I*conjugate(B) + 1))) - 1))
# Writing u_an,v_an, and w_an and their gradients in a C file ------------------------------------------
dudx = diff(u_an, x)
dudy = diff(u_an, y)
dudz = diff(u_an, z)
dvdx = diff(v_an, x)
dvdy = diff(v_an, y)
dvdz = diff(v_an, z)
dwdx = diff(w_an, x)
dwdy = diff(w_an, y)
dwdz = diff(w_an, z)
from sympy.printing.ccode import ccode, CCodePrinter
ccode(u_an)
from sympy.utilities.codegen import codegen, Routine
codegen((
("u_an", u_an),
("v_an", v_an),
("w_an", w_an),
("du_dx", dudx),
("du_dy", dudy),
("du_dz", dudz),
("dv_dx", dvdx),
("dv_dy", dvdy),
("dv_dz", dvdz),
("dw_dx", dwdx),
("dw_dy", dwdy),
("dw_dz", dwdz),
def test_CommaOperator():
expr = CommaOperator(PreIncrement(x), 2 * x)
assert ccode(expr) == "(++(x), 2*x)"
assert expr.func(*expr.args) == expr
fout.write("<li>%s</li>\n" % _mathml(sol))
# ccode(sol, assign_to='sol%d' % (i+1))
fout.write("</ul>")
fout.write("<p>Points in cartesian coordinates (x, y, z)</p>\n")
fout.write("<ul>")
for i, sol in enumerate(solutions):
fout.write("<li><ul>")
for k, v in ai:
fout.write("<li>%s: %s</li>\n" % (k, _mathml(v.subs(t, sol))))
fout.write("</ul></li>")
fout.write("</ul>")
fout.write("<h5>C Code</h5>\n")
for i, sol in enumerate(solutions):
for k, v in ai:
fout.write("<pre>%s</pre>\n" % ccode(v.subs(t, sol), assign_to=k))
if len(solutions) == 2:
sola, solb = solutions
# compute distance inside
distance = _simplify(Abs(sola - solb))
fout.write("<h4>Distance inside</h4>\n")
fout.write("<p>Distance between crossing points.</p>\n")
fout.write("%s\n" % _mathml(distance))
fout.write("<h4>C Code</h4>\n")
for i, sol in enumerate(solutions):
fout.write("<pre>%s</pre>" % ccode(sol, assign_to='sol%d' % (i+1)))
fout.write("<pre>%s</pre>" % ccode(distance, assign_to="distance"))
if len(solutions) == 1:
def test_PreIncrement():
p = PreIncrement(x)
assert p.func(*p.args) == p
assert ccode(p) == "++(x)"
solution = solve(
[
Br * (f1r * z1r - f1i * z1i - 1) + Bi * (f1i * z1r + f1r * z1i) + (f1r - z1r),
Bi * (-f1r * z1r + f1i * z1i - 1) + Br * (f1i * z1r + f1r * z1i) + (f1i - z1i),
],
[Br, Bi],
)
print solution[Br]
# (-fi**2*zr - fr**2*zr + fr*zi**2 + fr*zr**2 - fr + zr)/(fi**2*zi**2 + fi**2*zr**2 + fr**2*zi**2 + fr**2*zr**2 - 1)
print solution[Bi]
# (-fi**2*zi + fi*zi**2 + fi*zr**2 - fi - fr**2*zi + zi)/(fi**2*zi**2 + fi**2*zr**2 + fr**2*zi**2 + fr**2*zr**2 - 1)
print ccode(solution[Br])
# (-fi*fi*zr - fr*fr*zr + fr*zi*zi + fr*zr*zr - fr + zr)/(fi*fi*zi*zi + fi*fi*zr*zr + fr*fr*zi*zi + fr*fr*zr*zr - 1)
print ccode(solution[Bi])
# (-fi*fi*zi + fi*zi*zi + fi*zr*zr - fi - fr*fr*zi + zi)/(fi*fi*zi*zi + fi*fi*zr*zr + fr*fr*zi*zi + fr*fr*zr*zr - 1)
Br = Symbol("Br")
Bi = Symbol("Bi")
Rr = Symbol("Rr")
Ri = Symbol("Ri")
z1r = Symbol("z1r")
z1i = Symbol("z1i")
f1r = Symbol("f1r")
f1i = Symbol("f1i")
z2r = Symbol("z2r")
z2i = Symbol("z2i")
def qasm(self, prec=15):
"""Return the corresponding OPENQASM string."""
if self.value == pi:
return "pi"
return ccode(self.value, precision=prec)
def get_c_function(scalar, couplings):
args_replace = dict(zip([str(el) for el in couplings],
['args['+str(i)+']' for i in range(len(couplings))]))
return multiple_replace(ccode(scalar), args_replace)
def render_declarations(expressions, filename):
with open(filename, "w") as output:
for expression in expressions:
output.write("double " + ccode(expression) + ";\n")
pone = Symbol("pone", "real") # it doesn't really belive that they're real...
Br = Symbol("Br", "real")
Bi = Symbol("Bi", "real")
dBr = Symbol("dBr", "real")
dBi = Symbol("dBi", "real")
Pr = Symbol("Pr", "real")
Pi = Symbol("Pi", "real")
Fr = Symbol("Fr", "real")
Fi = Symbol("Fi", "real")
Rr = Symbol("Rr", "real")
Ri = Symbol("Ri", "real")
# print re(((Pr + I*Pi) + (Br + I*Bi)*pone) / ((Br - I*Bi)*(Pr + I*Pi) + pone)).simplify()
# numerator
print ccode((((Pr + I*Pi) + (Br + I*Bi)*sqrt(Pr*Pr + Pi*Pi + 1)) * ((Br + I*Bi)*(Pr - I*Pi) + sqrt(Pr*Pr + Pi*Pi + 1))).expand())
# I*Bi*Bi*Pi*pone - Bi*Bi*Pr*pone + 2*Bi*Br*Pi*pone + 2*I*Bi*Br*Pr*pone + I*Bi*Pi*Pi + I*Bi*Pr*Pr + I*Bi*(Pi*Pi + Pr*Pr + 1) - I*Br*Br*Pi*pone + Br*Br*Pr*pone + Br*Pi*Pi + Br*Pr*Pr + Br*(Pi*Pi + Pr*Pr + 1) + I*Pi*pone + Pr*pone
# Real part: -Bi*Bi*Pr*pone + 2*Bi*Br*Pi*pone + Br*Br*Pr*pone + Br*Pi*Pi + Br*Pr*Pr + Br*(Pi*Pi + Pr*Pr + 1) + Pr*pone
# Imag part: I*Bi*Bi*Pi*pone + 2*I*Bi*Br*Pr*pone + I*Bi*Pi*Pi + I*Bi*Pr*Pr + I*Bi*(Pi*Pi + Pr*Pr + 1) - I*Br*Br*Pi*pone + I*Pi*pone
# denominator
print ccode((((Br - I*Bi)*(Pr + I*Pi) + sqrt(Pr*Pr + Pi*Pi + 1)) * ((Br + I*Bi)*(Pr - I*Pi) + sqrt(Pr*Pr + Pi*Pi + 1))).expand())
# Bi*Bi*Pi*Pi + Bi*Bi*Pr*Pr + 2*Bi*Pi*pone + Br*Br*Pi*Pi + Br*Br*Pr*Pr + 2*Br*Pr*pone + Pi*Pi + Pr*Pr + 1
### START EXTENDING B TO THE WHOLE PLANE
# numerator
print ccode(((sqrt(1 + Br*Br + Bi*Bi)*(Pr + I*Pi) + (Br + I*Bi)*sqrt(Pr*Pr + Pi*Pi + 1)) * ((Br + I*Bi)*(Pr - I*Pi) + sqrt(1 + Br*Br + Bi*Bi)*sqrt(Pr*Pr + Pi*Pi + 1))).expand())
# I*Bi*Bi*Pi*pone - Bi*Bi*Pr*pone + 2*Bi*Br*Pi*pone + 2*I*Bi*Br*Pr*pone + I*Bi*Pi*Pi*bone + I*Bi*Pr*Pr*bone + I*Bi*bone*(Pi*Pi + Pr*Pr + 1) - I*Br*Br*Pi*pone + Br*Br*Pr*pone + Br*Pi*Pi*bone + Br*Pr*Pr*bone + Br*bone*(Pi*Pi + Pr*Pr + 1) + I*Pi*(Bi*Bi + Br*Br + 1)*pone + Pr*(Bi*Bi + Br*Br + 1)*pone
def qasm(self, prec=15):
"""Return the corresponding OPENQASM string."""
if self.value == pi:
return "pi"
return ccode(self.value, precision=prec)
def test_PostIncrement():
p = PostIncrement(x)
assert p.func(*p.args) == p
assert ccode(p) == '(x)++'
