def generate_symbolic_tfs(stages=4):
import sympy as sp
# construct quad pendulum equation of motion matrix
ksyms = sp.numbered_symbols('k')
msyms = sp.numbered_symbols('m')
w = sp.symbols('w')
k = [next(ksyms) for n in range(stages)]
m = [next(msyms) for n in range(stages)]
A = sp.zeros(stages)
for n in range(stages-1):
# mass and restoring forces (diagonal elements)
A[n, n] = k[n] + k[n+1] - m[n] * w**2
# couplings to stages above and below
A[n, n+1] = -k[n+1]
A[n+1, n] = -k[n+1]
# mass and restoring force of bottom stage
A[-1, -1] = k[-1] - m[-1] * w**2
# want TM equations of motion, so index 4
b = sp.zeros(stages, 1)
b[-1] = 1
# solve linear system
xsyms = sp.numbered_symbols('x')
x = [next(xsyms) for n in range(stages)]
ans = sp.linsolve((A, b), x)
return ans
def __init__(self, n=4, h=4, canonic=True):
if canonic:
x, y = sym.symbols('x, y')
a = tuple(take(n, sym.numbered_symbols('a', start=1)))
else:
x, y = sym.symbols('z_2, z_1', real=True)
a = tuple(-r for r in take(
n, sym.numbered_symbols('r', start=1, real=True)))
super().__init__(x, y, a, h)
def cse2func(funcname,
exprs,
module=math,
auto_import=True,
calc_number=True,
symbols="_tmp"):
import textwrap
printer = CseExprPrinter(settings={
"func_module": module,
"calc_number": calc_number
})
seq, results = cse(exprs, symbols=numbered_symbols(symbols))
codes = ["def %s:" % funcname]
for variable, value in seq:
if calc_number:
value = value.evalf()
codes.append("%s = %s" % (variable, printer._print(value)))
returns = "return (%s)" % ", ".join(
[printer._print(value) for value in results])
codes.append('\n'.join(textwrap.wrap(returns, 80)))
if auto_import and printer.functions:
codes.insert(
1, "from {} import {}".format(module.__name__,
", ".join(printer.functions)))
code = '\n '.join(codes)
return code
def OutputVector_CollectingFactorsNonZero(A,name, mode, initial_tabs = 1, max_index=30, optimizations='basic'):
""" This method collects the constants of the replacement for vectors (only non-zero terms)
Keyword arguments:
A -- The factors
name -- The name of the constant
mode -- The mode of replacement
initial_tabs -- The number of initial tabulations
max_index -- The max number of indexes
optimizations -- The level of optimizations
"""
symbol_name = "c" + name
A_factors, A_collected = sympy.cse(A, sympy.numbered_symbols(symbol_name), optimizations)
A = A_collected[0] # Overwrite lhs with the one with the collected components
aux_dict = {}
Acoefficient_str = ""
for factor in A_factors:
varname = factor[0]
value = factor[1]
output_value = OutputSymbolicVariable(value, mode, varname, aux_dict)
Acoefficient_str += " const double " + varname.__str__() + " = " + output_value
A_out = Acoefficient_str + "\n" + OutputVectorNonZero(A, name, mode, initial_tabs, max_index, aux_dict)
return A_out
def get_cse_code(self, exprs, basename=None,
dummy_groups=(), arrayify_groups=()):
""" Get arrayified code for common subexpression.
Parameters
----------
exprs : list of sympy expressions
basename : str
Stem of variable names (default: cse).
dummy_groups : tuples
"""
if basename is None:
basename = 'cse'
cse_defs, cse_exprs = sympy.cse(
exprs, symbols=sympy.numbered_symbols(basename))
# Let's convert the new expressions into (arrayified) code
cse_defs_code = [
(vname, self.as_arrayified_code(
vexpr, dummy_groups, arrayify_groups))
for vname, vexpr in cse_defs
]
cse_exprs_code = [self.as_arrayified_code(
x, dummy_groups, arrayify_groups) for x in cse_exprs]
return cse_defs_code, cse_exprs_code
def test_satisfiable_all_models():
from sympy.abc import A, B
assert next(satisfiable(False, all_models=True)) is False
assert list(satisfiable((A >> ~A) & A, all_models=True)) == [False]
assert list(satisfiable(True, all_models=True)) == [{true: true}]
models = [{A: True, B: False}, {A: False, B: True}]
result = satisfiable(A ^ B, all_models=True)
models.remove(next(result))
models.remove(next(result))
raises(StopIteration, lambda: next(result))
assert not models
assert list(satisfiable(Equivalent(A, B), all_models=True)) == \
[{A: False, B: False}, {A: True, B: True}]
models = [{A: False, B: False}, {A: False, B: True}, {A: True, B: True}]
for model in satisfiable(A >> B, all_models=True):
models.remove(model)
assert not models
# This is a santiy test to check that only the required number
# of solutions are generated. The expr below has 2**100 - 1 models
# which would time out the test if all are generated at once.
from sympy import numbered_symbols
from sympy.logic.boolalg import Or
sym = numbered_symbols()
X = [next(sym) for i in range(100)]
result = satisfiable(Or(*X), all_models=True)
for i in range(10):
assert next(result)
def Derivatives_CollectingFactors(A,name, mode, initial_tabs = 1, max_index=30, optimizations='basic', postprocess=None, order='canonical'):
""" This method collects the constants of the replacement for derivatives
TODO Think about collecting factors also in the derivatives
Keyword arguments:
A -- The factors
name -- The name of the constant
mode -- The mode of replacement
initial_tabs -- The number of initial tabulations
max_index -- The max number of indexes
optimizations -- The level of optimizations
postprocess -- The type of postprocess
order -- The type of order
"""
symbol_name = "c" + name
A_factors, A_collected = sympy.cse(A, sympy.numbered_symbols(symbol_name), optimizations, postprocess, order)
A = A_collected
Acoefficient_str = ""
for factor in A_factors:
varname = factor[0]
value = factor[1]
Acoefficient_str += " const double " + varname.__str__() + " = " + value
return [A, Acoefficient_str]
def commonsubelim(filename1, filename2):
modifiedlines = []
with open(filename1, 'r') as file:
for line in file:
line = line.strip('\n')
currentline = line + '\n'
flag = False
if ('=' in line):
line = line.strip(';')
lines = line.split('=')
docse = False
lines[1] = lines[1].replace(' ', '')
docse = re.search("[0-9]", lines[1])
if (not docse):
lines[1] = eval(lines[1])
compressedexpr = cse(lines[1], numbered_symbols("help"))
currentline = lines[0] + '='
for helper in compressedexpr[0]:
flag = True
#currentline=currentline+str(ccode(helper[1],helper[0]))+"\n"
modifiedlines.append("int " +
str(ccode(helper[1], helper[0])) +
"\n")
for i, result in enumerate(compressedexpr[1]):
modifiedlines.append("int " +
(ccode(result, "result")))
modifiedlines.append("\n")
if (flag == False):
modifiedlines.append(currentline)
with open(filename2, 'w') as file:
for line in modifiedlines:
file.write(line)
file.write('\n')
file.truncate()
def com_sub_elim():
X1, Y1, Z1, X2, Y2 = symbols('X1 Y1 Z1 X2 Y2')
Q = [X1, Y1, Z1]
P = [X2, Y2]
Rx, Ry, Rz = mixadd_complete(Q, P)
tree = tree_cse([Rx, Ry, Rz], numbered_symbols('e'))
print(tree)
def test_satisfiable_all_models():
from sympy.abc import A, B
assert next(satisfiable(False, all_models=True)) is False
assert list(satisfiable((A >> ~A) & A , all_models=True)) == [False]
assert list(satisfiable(True, all_models=True)) == [{true: true}]
models = [{A: True, B: False}, {A: False, B: True}]
result = satisfiable(A ^ B, all_models=True)
models.remove(next(result))
models.remove(next(result))
raises(StopIteration, lambda: next(result))
assert not models
assert list(satisfiable(Equivalent(A, B), all_models=True)) == \
[{A: False, B: False}, {A: True, B: True}]
models = [{A: False, B: False}, {A: False, B: True}, {A: True, B: True}]
for model in satisfiable(A >> B, all_models=True):
models.remove(model)
assert not models
# This is a santiy test to check that only the required number
# of solutions are generated. The expr below has 2**100 - 1 models
# which would time out the test if all are generated at once.
from sympy import numbered_symbols
from sympy.logic.boolalg import Or
sym = numbered_symbols()
X = [next(sym) for i in range(100)]
result = satisfiable(Or(*X), all_models=True)
for i in range(10):
assert next(result)
def generate_jac_C(self, do_cse=False, chunk_size=100, sparse=True):
"""
translates the symbolic Jacobian to C code using SymPy’s `C-code printer <http://docs.sympy.org/dev/modules/printing.html#module-sympy.printing.ccode>`_. If the symbolic Jacobian has not been generated, it generates it by calling `generate_jac_sym`.
Parameters
----------
do_cse : boolean
Whether SymPy’s `common-subexpression detection <http://docs.sympy.org/dev/modules/rewriting.html#module-sympy.simplify.cse_main>`_ should be applied before translating to C code. It is almost always better to let the compiler do this (unless you want to set the compiler optimisation to `-O2` or lower): For simple differential equations this should not make any difference to the compiler’s optimisations. For large ones, it may make a difference but also take long. As this requires the entire Jacobian at once, it may void advantages gained from using generator functions as an input.
chunk_size : integer
If the number of instructions in the final C code exceeds this number, it will be split into chunks of this size. After the generation of each chunk, SymPy’s cache is cleared. See `large_systems` on why this is useful.
If there is an obvious grouping of your Jacobian, the respective group size suggests itself for `chunk_size`. For example, the derivative of each dynamical variable explicitly depends on 60 others and the Jacobian is sparse, a chunk size of 60 suggests itself.
If smaller than 1, no chunking will happen.
sparse : boolean
Whether a sparse Jacobian should be assumed for optimisation. Note that this does not mean that the Jacobian is stored, parsed or handled as a sparse matrix. This kind of optimisation would require SciPy’s ODE to be able to handle sparse matrices.
"""
self._generate_jac_sym()
jac_sym_wc = self.jac_sym
self.sparse_jac = sparse
if do_cse:
jac_matrix = sympy.Matrix([ [entry for entry in line] for line in jac_sym_wc ])
_cse = sympy.cse(
jac_matrix,
symbols = sympy.numbered_symbols("dummy_jac_")
)
more_helpers = _cse[0]
jac_sym_wc = _cse[1][0].tolist()
else:
more_helpers = []
render_declarations(
(helper[0] for helper in more_helpers),
self._tmpfile("declare_jac_helpers.c")
)
set_dfdy = sympy.Function("set_dfdy")
render_and_write_code(
(
set_dfdy(i,j,entry)
for i,line in enumerate(jac_sym_wc)
for j,entry in enumerate(line)
if ( (entry != 0) or not self.sparse_jac )
),
more_helpers,
self._tmpfile(),
"jac",
{"set_dfdy":"set_dfdy", "y":"y"},
chunk_size = chunk_size
)
self._jac_C_source = True
def generate_predict(self, f, u, Q, dt):
''' Generate a method for doing an EKF prediction step. f(X, u) -> X is
the system dynamics model, X is a symbolic vector of each state
variable name u is the symbolic control input vector. '''
N = self.N
F = f.jacobian(self.X)
U = f.jacobian(u)
vs, es = sp.cse([F - sp.eye(N), f - self.X, Q],
optimizations='basic',
symbols=sp.numbered_symbols("tmp"))
self.generate_predict_cc(f, u, Q, dt, N, F, vs, es)
self.generate_predict_py(f, u, Q, dt, N, F, vs, es)
vs, es = sp.cse([f - self.X, F - sp.eye(N), U],
optimizations='basic',
symbols=sp.numbered_symbols("tmp"))
self.generate_controlstep_py(f, u, dt, N, vs, es)
def _generate_cse(self, prefix='pydy_'):
# NOTE : This assumes the first two items in self.matrices are A and b
# of and Ax=b system. This also ignores cse=False.
gen1 = sm.numbered_symbols(prefix)
subexprs1, mats_simp = sm.cse(self.matrices, symbols=gen1)
A_simp = mats_simp[0]
b_simp = mats_simp[1]
x = A_simp.LUsolve(b_simp)
gen2 = sm.numbered_symbols(prefix, start=len(subexprs1))
subexprs2, x_simp = sm.cse(x, symbols=gen2)
# swap the b matrix with the x result
mats_simp[1] = x_simp[0]
self.subexprs = subexprs1 + subexprs2
self.simplified_matrices = tuple(mats_simp)
def _optimize(expressions):
from sympy import cse, numbered_symbols
commons, outputs = cse(
expressions,
numbered_symbols('t'),
optimizations='basic',
)
for symbol, expr in commons:
print(symbol, '=', expr)
print()
for expr in outputs:
print(expr)
def _optimize(expressions):
from sympy import cse, numbered_symbols
commons, outputs = cse(
expressions,
numbered_symbols('t'),
optimizations='basic',
)
for symbol, expr in commons:
print(symbol, '=', expr)
print()
for expr in outputs:
print(expr)
def cse_codegen(symbols):
cse_results = sympy.cse(symbols, sympy.numbered_symbols("c"))
output = io.StringIO()
for helper in cse_results[0]:
output.write("Scalar const ")
output.write(sympy.printing.ccode(helper[1], helper[0]))
output.write("\n")
assert len(cse_results[1]) == 1
output.write(sympy.printing.ccode(cse_results[1][0], "result"))
output.write("\n")
output.seek(0)
return output
def generate_measurement(self, name, h_x, h_z, z_k, R_k):
H = h_x.jacobian(self.X)
M = h_z.jacobian(z_k) + h_x.jacobian(z_k)
y_k = h_z - h_x
vs, es = sp.cse([y_k, H, M],
optimizations='basic',
symbols=sp.numbered_symbols("tmp"))
self.generate_measurement_cc(name, h_x, h_z, z_k, R_k, H, M, y_k, vs,
es)
self.generate_measurement_py(name, h_x, h_z, z_k, R_k, H, M, y_k, vs,
es)
def generate_f_C(self, simplify=True, do_cse=False, chunk_size=100):
"""
translates the derivative to C code using SymPy’s `C-code printer <http://docs.sympy.org/dev/modules/printing.html#module-sympy.printing.ccode>`_.
Parameters
----------
simplify : boolean
Whether the derivative should be `simplified <http://docs.sympy.org/dev/modules/simplify/simplify.html>`_ (with `ratio=1.0`) before translating to C code. The main reason why you could want to disable this is if your derivative is already optimised and so large that simplifying takes a considerable amount of time.
do_cse : boolean
Whether SymPy’s `common-subexpression detection <http://docs.sympy.org/dev/modules/rewriting.html#module-sympy.simplify.cse_main>`_ should be applied before translating to C code. It is almost always better to let the compiler do this (unless you want to set the compiler optimisation to `-O2` or lower): For simple differential equations this should not make any difference to the compiler’s optimisations. For large ones, it may make a difference but also take long. As this requires all entries of `f` at once, it may void advantages gained from using generator functions as an input.
chunk_size : integer
If the number of instructions in the final C code exceeds this number, it will be split into chunks of this size. After the generation of each chunk, SymPy’s cache is cleared. See `large_systems` on why this is useful.
If there is an obvious grouping of your :math:`f`, the group size suggests itself for `chunk_size`. For example, if you want to simulate the dynamics of three-dimensional oscillators coupled onto a 40×40 lattice and if the differential equations are grouped first by oscillator and then by lattice row, a chunk size of 120 suggests itself.
If smaller than 1, no chunking will happen.
"""
f_sym_wc = self.f_sym()
if simplify:
f_sym_wc = (sympy.simplify(entry,ratio=1) for entry in f_sym_wc)
if do_cse:
_cse = sympy.cse(
sympy.Matrix(list(self.f_sym())),
symbols = sympy.numbered_symbols("dummy_f_")
)
more_helpers = _cse[0]
f_sym_wc = _cse[1][0]
else:
more_helpers = []
render_declarations(
(helper[0] for helper in more_helpers),
self._tmpfile("declare_f_helpers.c")
)
set_dy = sympy.Function("set_dy")
render_and_write_code(
(set_dy(i,entry) for i,entry in enumerate(f_sym_wc)),
more_helpers,
self._tmpfile(),
"f",
{"set_dy":"set_dy", "y":"y"},
chunk_size = chunk_size
)
self._f_C_source = True
def _print_list(self, list_of_exprs):
if all(isinstance(x, sp.Eq) for x in list_of_exprs):
list_of_lhs = [x.lhs for x in list_of_exprs]
list_of_rhs = [x.rhs for x in list_of_exprs]
common_variables, list_of_rhs = sp.cse(
list_of_rhs, symbols=sp.numbered_symbols(prefix='com'))
lines = []
for variable, expression in common_variables:
ass = Assignment(variable, expression)
lines.append('const double ' + self._print(ass))
for i in range(len(list_of_rhs)):
ass = Assignment(list_of_lhs[i], list_of_rhs[i])
lines.append(self._print(ass))
return '\n'.join(lines)
def cse2func(funcname, exprs, module=math, auto_import=True, calc_number=True, symbols="_tmp"):
import textwrap
printer = CseExprPrinter(settings={"func_module": module, "calc_number": calc_number})
seq, results = cse(exprs, symbols=numbered_symbols(symbols))
codes = ["def %s:" % funcname]
for variable, value in seq:
if calc_number:
value = value.evalf()
codes.append("%s = %s" % (variable, printer._print(value)))
returns = "return (%s)" % ", ".join([printer._print(value) for value in results])
codes.append('\n'.join(textwrap.wrap(returns, 80)))
if auto_import and printer.functions:
codes.insert(1, "from {} import {}".format(module.__name__, ", ".join(printer.functions)))
code = '\n '.join(codes)
return code
def test_lsystem_to_matrix_and_ordinate(self):
"""Should make a corresponding matrix from linear equations"""
A = sympy.Matrix([[1, 1, 1], [1, 0, 2], [1, 11, 3]])
a = [-2, 0, 0]
vars_gen = sympy.numbered_symbols("V")
vars_list = [next(vars_gen) for _ in range(0, 3)]
equations = [
vars_list[0] + vars_list[1] + vars_list[2] + 2,
vars_list[0] + 2 * vars_list[2],
vars_list[0] + 11 * vars_list[1] + 3 * vars_list[2],
]
B, b = Equationeer().lsystem_to_matrix_and_ordinate(equations, vars_list)
# print(B)
self.assertEqual(A, B)
self.assertEqual(a, b)
def generate_grid(matrix_dimension, P, frequency=1.02, ed=1, forced_em=None):
grid = Grid()
def choose_conductivity(em, ed):
"""Uses given probability to simulate different concentrations of metallic particles"""
return (em, True) if rnd.random() < P else (ed, False)
def choose_emf(node_from, node_to):
"""Places a battery only in vertical wires"""
return 0 if abs(node_from.id - node_to.id) < matrix_dimension else 1
if forced_em == None:
em = calculate_em(frequency)
else:
em = forced_em
print("Em =", em)
currents_gen = sympy.numbered_symbols('I')
currents = [next(currents_gen) for _ in range(0, 2 * matrix_dimension ** 2)]
currents_iter = iter(currents)
grid.nodes = [Node(number_id) for number_id in range(0, matrix_dimension ** 2)]
i = 0
for node_from in grid.nodes:
for node_to_id in grid.neighborhood_nodes2(node_from):
conductivity, conductor = choose_conductivity(em, ed)
wire = Wire(grid, conductivity, conductor,
choose_emf(node_from, grid.nodes[node_to_id]),
node_from,
grid.nodes[node_to_id],
next(currents_iter))
grid.wires.append(wire)
if wire.horizontal:
grid.nodes[i].wires_from[0] = wire
grid.nodes[node_to_id].wires_to[0] = wire
else:
grid.nodes[i].wires_from[1] = wire
grid.nodes[node_to_id].wires_to[1] = wire
i += 1
grid.dimension = matrix_dimension
return grid, currents
def generate_code(inputs,
exprs,
func_name='generated_function',
printer=None,
simplify=False):
"""Generate code for a Python function from symbolic expression(s)."""
if printer is None:
printer = TupleArrayPrinter()
if not isinstance(exprs, list) and not isinstance(exprs, tuple):
exprs = [exprs]
elif isinstance(exprs, tuple):
exprs = list(exprs)
func_expr_args = {}
ignore_set = set()
for i, expr in enumerate(exprs):
if isinstance(expr, FunctionExpression):
func_expr_args[i] = expr.args
for arg in expr.args:
ignore_set.update((
arg,
) if isinstance(arg, sym.Symbol) else arg.free_symbols)
exprs[i] = expr.return_val
flat_exprs, unflatten = flatten_arrays(exprs)
if simplify:
flat_exprs = [sym.simplify(expr) for expr in flat_exprs]
intermediates, flat_outputs = sym.cse(flat_exprs,
symbols=sym.numbered_symbols('_i'),
optimizations='basic',
ignore=ignore_set)
outputs = unflatten(flat_outputs)
code = f'def {func_name}({generate_input_list_string(inputs)}):\n '
code += '\n '.join([
f'{printer.doprint(i[0])} = {printer.doprint(i[1])}'
for i in intermediates
])
code += '\n return (\n '
code += ',\n '.join([
(f'lambda {generate_input_list_string(func_expr_args[i])}: '
if i in func_expr_args else '') + f'{printer.doprint(output)}'
for i, output in enumerate(outputs)
])
code += '\n )'
return code
def try_solving_moving_endpoints_of_spline():
import sympy as sy
sy.init_printing()
a0, a1, a2, a3, k0, k1, j0, j1, new_t = sy.symbols(
'a0, a1, a2, a3, k0, k1, j0, j1, new_t')
# Q: How much simpler is it if we only move one end?
#j0 = k0 # A: Wow, much simpler! 30+ ops instead of 80+
#j1 = k1 # A: GADS, not much simpler at all, still 80+ operations.
years = new_t * (j1 - j0) + j0
old_t = (years - k0) / (k1 - k0)
d = (((a3 * old_t + a2) * old_t) + a1) * old_t + a0
#d = sy.factor(d)
#d = sy.expand(d)
#d = sy.simplify(d)
d = sy.expand(d)
d = sy.collect(d, new_t)
b0 = d.coeff(new_t, 0)
b1 = d.coeff(new_t, 1)
b2 = d.coeff(new_t, 2)
b3 = d.coeff(new_t, 3)
commons, outputs = sy.cse(
[b0, b1, b2, b3],
sy.numbered_symbols('u'),
#optimizations='basic',
)
n = 0
for symbol, expr in commons:
n += sy.count_ops(expr)
print(symbol, '=', expr)
print()
for i, expr in enumerate(outputs):
n += sy.count_ops(expr)
print('b{} = {}'.format(i, expr))
print('Total operations: {}'.format(n))
def get_cse(matrix):
rows = len(matrix)
cols = len(matrix[0])
expr_list = []
coord_list = {}
for row in range(0, rows):
for col in range(0, cols):
scase = sympy.sympify(matrix[row][col])
coord_list[(row, col)] = len(expr_list)
expr_list.append(scase)
cse = sympy.cse(expr_list, sympy.numbered_symbols('tmp'))
tmp_list = cse[0]
expr_list = cse[1]
expr_mat = []
for row in range(0, rows):
row_list = []
for col in range(0, cols):
i = coord_list[(row, col)]
e = expr_list[i]
row_list.append(expr_list[i])
expr_mat.append(row_list)
return (tmp_list, expr_mat)
def _generate_sub_expressions(self, int_var='z_'):
"""Finds common subexpressions in the mass matrix and forcing vector
expression lists and rewrites them."""
# TODO: make common sub expressions optional
list_of_lists = self.symbols.values()
if None in list_of_lists:
list_of_lists.remove(None)
all_symbols = list(chain.from_iterable(list_of_lists))
while symbols(int_var) in all_symbols:
int_var = random.choice(all_letters) + '_'
sub_expressions, expressions = \
cse([entry[0] for entry in self.expressions['mass_matrix'] +
self.expressions['forcing_vector']],
numbered_symbols(int_var))
self.expressions = \
{'common_sub': sub_expressions,
'mass_matrix': expressions[:self.rows * self.cols],
'forcing_vector': expressions[self.rows * self.cols:]}
def get_cse(matrix):
rows = len(matrix)
cols = len(matrix[0])
expr_list = []
coord_list = {}
for row in range(0, rows):
for col in range(0, cols):
scase = sympy.sympify(matrix[row][col])
coord_list[(row,col)] = len(expr_list)
expr_list.append(scase)
cse = sympy.cse(expr_list, sympy.numbered_symbols('tmp'))
tmp_list = cse[0]
expr_list = cse[1]
expr_mat = []
for row in range(0, rows):
row_list = []
for col in range(0, cols):
i = coord_list[(row,col)]
e = expr_list[i]
row_list.append(expr_list[i])
expr_mat.append(row_list)
return (tmp_list, expr_mat)
def _generate_sub_expressions(self, int_var='z_'):
"""Finds common subexpressions in the mass matrix and forcing vector
expression lists and rewrites them."""
# TODO: make common sub expressions optional
list_of_lists = self.symbols.values()
if None in list_of_lists:
list_of_lists.remove(None)
all_symbols = list(chain.from_iterable(list_of_lists))
while symbols(int_var) in all_symbols:
int_var = random.choice(all_letters) + '_'
sub_expressions, expressions = \
cse([entry[0] for entry in self.expressions['mass_matrix'] +
self.expressions['forcing_vector']],
numbered_symbols(int_var))
self.expressions = \
{'common_sub': sub_expressions,
'mass_matrix': expressions[:self.rows * self.cols],
'forcing_vector': expressions[self.rows * self.cols:]}
def _generate_cse(self):
# This makes a big long list of every expression in all of the
# matrices.
exprs = []
for matrix in self.matrices:
exprs += matrix[:]
# Compute the common subexpresions.
gen = sm.numbered_symbols('pydy_')
self.subexprs, simplified_exprs = sm.cse(exprs, symbols=gen)
# Turn the expressions back into matrices of the same type.
simplified_matrices = []
idx = 0
for matrix in self.matrices:
num_rows, num_cols = matrix.shape
length = num_rows * num_cols
m = type(matrix)(simplified_exprs[idx:idx + length])
simplified_matrices.append(m.reshape(num_rows, num_cols))
idx += length
self.simplified_matrices = tuple(simplified_matrices)
def _generate_cse(self, prefix='pydy_'):
# This makes a big long list of every expression in all of the
# matrices.
exprs = []
for matrix in self.matrices:
exprs += matrix[:]
# Compute the common subexpresions.
gen = sm.numbered_symbols(prefix)
self.subexprs, simplified_exprs = sm.cse(exprs, symbols=gen)
# Turn the expressions back into matrices of the same type.
simplified_matrices = []
idx = 0
for matrix in self.matrices:
num_rows, num_cols = matrix.shape
length = num_rows * num_cols
m = type(matrix)(simplified_exprs[idx:idx + length])
simplified_matrices.append(m.reshape(num_rows, num_cols))
idx += length
self.simplified_matrices = tuple(simplified_matrices)
def clean_numbers(expr, eps=1e-10):
"""
trys to clean all numbers from numeric noise
"""
if isinstance(expr, (list, tuple)):
return [clean_numbers(elt, eps) for elt in expr]
expr = trunc_small_values(expr)
maxden = int(1/eps)
floats = list(atoms(expr, sp.Float))
rats = []
dummy_symbs = []
symb_gen = sp.numbered_symbols('cde', cls = sp.Dummy)
for f in floats:
rat = sp_fff(f, maxden)
rats.append(rat)
dummy_symbs.append(next(symb_gen))
res1 = expr.subs(list(zip(floats, dummy_symbs)))
res2 = res1.subs(list(zip(dummy_symbs, rats)))
return res2
def clean_numbers(expr, eps=1e-10):
"""
trys to clean all numbers from numeric noise
"""
if isinstance(expr, (list, tuple)):
return [clean_numbers(elt, eps) for elt in expr]
expr = trunc_small_values(expr)
maxden = int(1/eps)
floats = list(atoms(expr, sp.Float))
rats = []
dummy_symbs = []
symb_gen = sp.numbered_symbols('cde', cls = sp.Dummy)
for f in floats:
rat = sp_fff(f, maxden)
rats.append(rat)
dummy_symbs.append(symb_gen.next())
res1 = expr.subs(zip(floats, dummy_symbs))
res2 = res1.subs(zip(dummy_symbs, rats))
return res2
def get_alpha_dot():
"""Use sympy to perform most of the math and use the resulting formulae
to calculate:
inv(I) (\tau - w x (I w))
"""
import sympy as S
ixx, iyy, izz, ixy, ixz, iyz = S.symbols("ixx, iyy, izz, ixy, ixz, iyz")
tx, ty, tz = S.symbols("tx, ty, tz")
wx, wy, wz = S.symbols('wx, wy, wz')
tau = S.Matrix([tx, ty, tz])
I = S.Matrix([[ixx, ixy, ixz], [ixy, iyy, iyz], [ixz, iyz, izz]])
w = S.Matrix([wx, wy, wz])
Iinv = I.inv()
Iinv.simplify()
# inv(I) (\tau - w x (Iw))
res = Iinv * (tau - w.cross(I * w))
res.simplify()
# Now do some awesome sympy magic.
syms, result = S.cse(res, symbols=S.numbered_symbols('tmp'))
for lhs, rhs in syms:
print("%s = %s" % (lhs, rhs))
for i in range(3):
print("omega_dot[%d] =" % i, result[0][i])
def balance_stoichiometry(reactants, products, substances=None,
substance_factory=Substance.from_formula,
parametric_symbols=None, underdetermined=True, allow_duplicates=False):
""" Balances stoichiometric coefficients of a reaction
Parameters
----------
reactants : iterable of reactant keys
products : iterable of product keys
substances : OrderedDict or string or None
Mapping reactant/product keys to instances of :class:`Substance`.
substance_factory : callback
parametric_symbols : generator of symbols
Used to generate symbols for parametric solution for
under-determined system of equations. Default is numbered "x-symbols" starting
from 1.
underdetermined : bool
Allows to find a non-unique solution (in addition to a constant factor
across all terms). Set to ``False`` to disallow (raise ValueError) on
e.g. "C + O2 -> CO + CO2". Set to ``None`` if you want the symbols replaced
so that the coefficients are the smallest possible positive (non-zero) integers.
allow_duplicates : bool
If False: raises an excpetion if keys appear in both ``reactants`` and ``products``.
Examples
--------
>>> ref = {'C2H2': 2, 'O2': 3}, {'CO': 4, 'H2O': 2}
>>> balance_stoichiometry({'C2H2', 'O2'}, {'CO', 'H2O'}) == ref
True
>>> ref2 = {'H2': 1, 'O2': 1}, {'H2O2': 1}
>>> balance_stoichiometry('H2 O2'.split(), ['H2O2'], 'H2 O2 H2O2') == ref2
True
>>> reac, prod = 'CuSCN KIO3 HCl'.split(), 'CuSO4 KCl HCN ICl H2O'.split()
>>> Reaction(*balance_stoichiometry(reac, prod)).string()
'4 CuSCN + 7 KIO3 + 14 HCl -> 4 CuSO4 + 7 KCl + 4 HCN + 7 ICl + 5 H2O'
>>> balance_stoichiometry({'Fe', 'O2'}, {'FeO', 'Fe2O3'}, underdetermined=False)
Traceback (most recent call last):
...
ValueError: The system was under-determined
>>> r, p = balance_stoichiometry({'Fe', 'O2'}, {'FeO', 'Fe2O3'})
>>> list(set.union(*[v.free_symbols for v in r.values()]))
[x1]
>>> b = balance_stoichiometry({'Fe', 'O2'}, {'FeO', 'Fe2O3'}, underdetermined=None)
>>> b == ({'Fe': 3, 'O2': 2}, {'FeO': 1, 'Fe2O3': 1})
True
>>> d = balance_stoichiometry({'C', 'CO'}, {'C', 'CO', 'CO2'}, underdetermined=None, allow_duplicates=True)
>>> d == ({'CO': 2}, {'C': 1, 'CO2': 1})
True
Returns
-------
balanced reactants : dict
balanced products : dict
"""
import sympy
from sympy import (
MutableDenseMatrix, gcd, zeros, linsolve, numbered_symbols, Wild, Symbol,
Integer, Tuple, preorder_traversal as pre
)
_intersect = sorted(set.intersection(*map(set, (reactants, products))))
if _intersect:
if allow_duplicates:
if underdetermined is not None:
raise NotImplementedError("allow_duplicates currently requires underdetermined=None")
if set(reactants) == set(products):
raise ValueError("cannot balance: reactants and products identical")
# For each duplicate, try to drop it completely:
for dupl in _intersect:
try:
result = balance_stoichiometry(
[sp for sp in reactants if sp != dupl],
[sp for sp in products if sp != dupl],
substances=substances, substance_factory=substance_factory,
underdetermined=underdetermined, allow_duplicates=True)
except Exception:
continue
else:
return result
for perm in product(*[(False, True)]*len(_intersect)): # brute force (naive)
r = set(reactants)
p = set(products)
for remove_reac, dupl in zip(perm, _intersect):
if remove_reac:
r.remove(dupl)
else:
p.remove(dupl)
try:
result = balance_stoichiometry(
r, p, substances=substances, substance_factory=substance_factory,
parametric_symbols=parametric_symbols, underdetermined=underdetermined,
allow_duplicates=False)
except ValueError:
continue
else:
return result
else:
raise ValueError("Failed to remove duplicate keys: %s" % _intersect)
else:
raise ValueError("Substances on both sides: %s" % str(_intersect))
if substances is None:
substances = OrderedDict([(k, substance_factory(k)) for k in chain(reactants, products)])
if isinstance(substances, str):
substances = OrderedDict([(k, substance_factory(k)) for k in substances.split()])
if type(reactants) == set: # we don't want isinstance since it might be "OrderedSet"
reactants = sorted(reactants)
if type(products) == set:
products = sorted(products)
subst_keys = list(reactants) + list(products)
cks = Substance.composition_keys(substances.values())
if parametric_symbols is None:
parametric_symbols = numbered_symbols('x', start=1, integer=True, positive=True)
# ?C2H2 + ?O2 -> ?CO + ?H2O
# Ax = 0
# A: x:
#
# C2H2 O2 CO H2O
# C -2 0 1 0 x0 = 0
# H -2 0 0 2 x1 0
# O 0 -2 1 1 x2 0
# x3
def _get(ck, sk):
return substances[sk].composition.get(ck, 0) * (-1 if sk in reactants else 1)
for ck in cks: # check that all components are present on reactant & product sides
for rk in reactants:
if substances[rk].composition.get(ck, 0) != 0:
break
else:
any_pos = any(substances[pk].composition.get(ck, 0) > 0 for pk in products)
any_neg = any(substances[pk].composition.get(ck, 0) < 0 for pk in products)
if any_pos and any_neg:
pass # negative and positive parts among products, no worries
else:
raise ValueError("Component '%s' not among reactants" % ck)
for pk in products:
if substances[pk].composition.get(ck, 0) != 0:
break
else:
any_pos = any(substances[pk].composition.get(ck, 0) > 0 for pk in reactants)
any_neg = any(substances[pk].composition.get(ck, 0) < 0 for pk in reactants)
if any_pos and any_neg:
pass # negative and positive parts among reactants, no worries
else:
raise ValueError("Component '%s' not among products" % ck)
A = MutableDenseMatrix([[_get(ck, sk) for sk in subst_keys] for ck in cks])
symbs = list(reversed([next(parametric_symbols) for _ in range(len(subst_keys))]))
sol, = linsolve((A, zeros(len(cks), 1)), symbs)
wi = Wild('wi', properties=[lambda k: not k.has(Symbol)])
cd = reduce(gcd, [1] + [1/m[wi] for m in map(
lambda n: n.match(symbs[-1]/wi), pre(sol)) if m is not None])
sol = sol.func(*[arg/cd for arg in sol.args])
def remove(cont, symb, remaining):
subsd = dict(zip(remaining/symb, remaining))
cont = cont.func(*[(arg/symb).expand().subs(subsd) for arg in cont.args])
if cont.has(symb):
raise ValueError("Bug, please report an issue at https://github.com/bjodah/chempy")
return cont
done = False
for idx, symb in enumerate(symbs):
for expr in sol:
iterable = expr.args if expr.is_Add else [expr]
for term in iterable:
if term.is_number:
done = True
break
if done:
break
if done:
break
for expr in sol:
if (expr/symb).is_number:
sol = remove(sol, symb, MutableDenseMatrix(symbs[idx+1:]))
break
for symb in symbs:
cd = 1
for expr in sol:
iterable = expr.args if expr.is_Add else [expr]
for term in iterable:
if term.is_Mul and term.args[0].is_number and term.args[1] == symb:
cd = gcd(cd, term.args[0])
if cd != 1:
sol = sol.func(*[arg.subs(symb, symb/cd) for arg in sol.args])
integer_one = 1 # need 'is' check, SyntaxWarning when checking against literal
if underdetermined is integer_one:
from ._release import __version__
if int(__version__.split('.')[1]) > 6:
warnings.warn( # deprecated because comparison with ``1`` problematic (True==1)
("Pass underdetermined == None instead of ``1`` (depreacted since 0.7.0,"
" will_be_missing_in='0.9.0')"), ChemPyDeprecationWarning)
underdetermined = None
if underdetermined is None:
sol = Tuple(*[Integer(x) for x in _solve_balancing_ilp_pulp(A)])
fact = gcd(sol)
sol = MutableDenseMatrix([e/fact for e in sol]).reshape(len(sol), 1)
sol /= reduce(gcd, sol)
if 0 in sol:
raise ValueError("Superfluous species given.")
if underdetermined:
if any(x == sympy.nan for x in sol):
raise ValueError("Failed to balance reaction")
else:
for x in sol:
if len(x.free_symbols) != 0:
raise ValueError("The system was under-determined")
if not all(residual == 0 for residual in A * sol):
raise ValueError("Failed to balance reaction")
def _x(k):
coeff = sol[subst_keys.index(k)]
return int(coeff) if underdetermined is None else coeff
return (
OrderedDict([(k, _x(k)) for k in reactants]),
OrderedDict([(k, _x(k)) for k in products])
)
def generate_mass_forcing_cython_code(filename_prefix, mass_matrix,
forcing_vector, constants,
coordinates, speeds, specified=None):
"""Generates a Cython shared object module with a function that
evaluates the mass_matrix and the forcing vector.
Parameters
----------
filename_prefix : string
The desired name of the created module.
mass_matrix : sympy.matrices.dense.MutableDenseMatrix, shape(n,n)
The symbolic mass matrix of the system.
forcing_vector : sympy.matrices.dense.MutableDenseMatrix, shape(n,1)
The symbolic forcing vector of the system.
constants : list of sympy.core.symbol.Symbol
The constants in the equations of motion.
coordinates : list of sympy.core.function.Function
The generalized coordinates of the system.
speeds : list of sympy.core.function.Function
The generalized speeds of the system.
specified : list of sympy.core.function.Function, optional, default=None
The specifed quantities of the system.
"""
# TODO : Maybe, allow expressions to be passed in for the specified
# quantities for computation inside the c file. Would need the value of
# time in the mass_forcing function.
c_filename = filename_prefix + '_c.c'
header_filename = filename_prefix + '_c.h'
pyx_filename = filename_prefix + '.pyx'
setup_py_filename = filename_prefix + '_setup.py'
# Comma separated lists of the input variables to the arrays, so that
# you know which order you should supply them. These are used in the
# comments in the C and header file.
# TODO: Add these to the doc string of the imported cythonized function.
comma_lists = {}
for list_name, sym_list in zip(['constants', 'coordinates', 'speeds',
'specified'],
[constants, coordinates, speeds,
specified]):
if sym_list is not None:
comma_lists[list_name] = ', '.join([str(s).split('(')[0] for s
in sym_list])
else:
comma_lists[list_name] = ['None Supplied']
rows, cols = mass_matrix.shape
mass_matrix_list = mass_matrix.reshape(rows * cols, 1).tolist()
forcing_vector_list = forcing_vector.tolist()
# TODO: make common sub expressions optional
sub_expressions, expressions = cse([entry[0] for entry in
mass_matrix_list +
forcing_vector_list],
numbered_symbols('z_'))
expressions = {'common_sub': sub_expressions,
'mass_matrix': expressions[:rows * cols],
'forcing_vector': expressions[rows * cols:]}
PyDyCCodePrinter = pydy_c_printer(constants, coordinates, speeds,
specified)
code_blocks = {}
for exp_type, expression_list in expressions.items():
c_lines = []
for i, exp in enumerate(expression_list):
if exp_type == 'common_sub':
code_str = PyDyCCodePrinter().doprint(exp[1])
c_lines.append('double {} = {};'.format(str(exp[0]),
code_str))
else:
code_str = PyDyCCodePrinter().doprint(exp)
c_lines.append('{} = {};'.format('{}[{}]'.format(exp_type,
i),
code_str))
code_blocks[exp_type] = '\n '.join(c_lines)
template_values = {
'header_filename': header_filename,
'constants_len': len(constants),
'mass_matrix_len': rows * cols,
'forcing_vector_len': len(forcing_vector),
'coordinates_len': len(coordinates),
'speeds_len': len(speeds),
'specified_len': len(specified) if specified is not None else 0,
'constants_list': comma_lists['constants'],
'coordinates_list': comma_lists['coordinates'],
'speeds_list': comma_lists['speeds'],
'specified_list': comma_lists['specified'],
'sub_expression_block': code_blocks['common_sub'],
'mass_matrix_block': code_blocks['mass_matrix'],
'forcing_vector_block': code_blocks['forcing_vector'],
'prefix': filename_prefix,
'c_filename': c_filename,
'pyx_filename': pyx_filename,
}
if specified is not None:
specified_template = {
'specified_double': " " * 18 + "double specified[{specified_len}], // specified = [{specified_list}]".format(**template_values) + '\n',
'specified_assert': "\n assert len(specified) == {specified_len}\n".format(**template_values),
'def_specified_arg': ",\n np.ndarray[np.double_t, ndim=1, mode='c'] specified",
'cdef_specified_arg': "\n" + ' ' * 22 + "double* specified,",
'call_specified_arg': "\n" + ' ' * 17 + "<double*> specified.data,"
}
else:
specified_template = {
'specified_double': "",
'specified_assert': "",
'def_specified_arg': "",
'cdef_specified_arg': "",
'call_specified_arg': ""
}
template_values.update(specified_template)
files = {c_filename: c_template,
header_filename: h_template,
pyx_filename: pyx_template,
setup_py_filename: setup_template}
for filename, template in files.items():
code = template.format(**template_values)
with open(filename, 'w') as f:
f.write(code)
# This prevents output to stdout and waits till it is done.
p = subprocess.Popen(['python', setup_py_filename, 'build_ext',
'--inplace'], stderr=subprocess.STDOUT,
stdout=subprocess.PIPE)
p.wait()
def balance_stoichiometry(reactants, products, substances=None,
substance_factory=Substance.from_formula,
parametric_symbols=None, underdetermined=True, allow_duplicates=False):
""" Balances stoichiometric coefficients of a reaction
Parameters
----------
reactants : iterable of reactant keys
products : iterable of product keys
substances : OrderedDict or string or None
Mapping reactant/product keys to instances of :class:`Substance`.
substance_factory : callback
parametric_symbols : generator of symbols
Used to generate symbols for parametric solution for
under-determined system of equations. Default is numbered "x-symbols" starting
from 1.
underdetermined : bool
Allows to find a non-unique solution (in addition to a constant factor
across all terms). Set to ``False`` to disallow (raise ValueError) on
e.g. "C + O2 -> CO + CO2". Set to ``None`` if you want the symbols replaced
so that the coefficients are the smallest possible positive (non-zero) integers.
allow_duplicates : bool
If False: raises an excpetion if keys appear in both ``reactants`` and ``products``.
Examples
--------
>>> ref = {'C2H2': 2, 'O2': 3}, {'CO': 4, 'H2O': 2}
>>> balance_stoichiometry({'C2H2', 'O2'}, {'CO', 'H2O'}) == ref
True
>>> ref2 = {'H2': 1, 'O2': 1}, {'H2O2': 1}
>>> balance_stoichiometry('H2 O2'.split(), ['H2O2'], 'H2 O2 H2O2') == ref2
True
>>> reac, prod = 'CuSCN KIO3 HCl'.split(), 'CuSO4 KCl HCN ICl H2O'.split()
>>> Reaction(*balance_stoichiometry(reac, prod)).string()
'4 CuSCN + 7 KIO3 + 14 HCl -> 4 CuSO4 + 7 KCl + 4 HCN + 7 ICl + 5 H2O'
>>> balance_stoichiometry({'Fe', 'O2'}, {'FeO', 'Fe2O3'}, underdetermined=False)
Traceback (most recent call last):
...
ValueError: The system was under-determined
>>> r, p = balance_stoichiometry({'Fe', 'O2'}, {'FeO', 'Fe2O3'})
>>> list(set.union(*[v.free_symbols for v in r.values()]))
[x1]
>>> b = balance_stoichiometry({'Fe', 'O2'}, {'FeO', 'Fe2O3'}, underdetermined=None)
>>> b == ({'Fe': 3, 'O2': 2}, {'FeO': 1, 'Fe2O3': 1})
True
>>> d = balance_stoichiometry({'C', 'CO'}, {'C', 'CO', 'CO2'}, underdetermined=None, allow_duplicates=True)
>>> d == ({'CO': 2}, {'C': 1, 'CO2': 1})
True
Returns
-------
balanced reactants : dict
balanced products : dict
"""
import sympy
from sympy import (
MutableDenseMatrix, gcd, zeros, linsolve, numbered_symbols, Wild, Symbol,
Integer, Tuple, preorder_traversal as pre
)
_intersect = sorted(set.intersection(*map(set, (reactants, products))))
if _intersect:
if allow_duplicates:
if underdetermined is not None:
raise NotImplementedError("allow_duplicates currently requires underdetermined=None")
if set(reactants) == set(products):
raise ValueError("cannot balance: reactants and products identical")
# For each duplicate, try to drop it completely:
for dupl in _intersect:
try:
result = balance_stoichiometry(
[sp for sp in reactants if sp != dupl],
[sp for sp in products if sp != dupl],
substances=substances, substance_factory=substance_factory,
underdetermined=underdetermined, allow_duplicates=True)
except Exception:
continue
else:
return result
for perm in product(*[(False, True)]*len(_intersect)): # brute force (naive)
r = set(reactants)
p = set(products)
for remove_reac, dupl in zip(perm, _intersect):
if remove_reac:
r.remove(dupl)
else:
p.remove(dupl)
try:
result = balance_stoichiometry(
r, p, substances=substances, substance_factory=substance_factory,
parametric_symbols=parametric_symbols, underdetermined=underdetermined,
allow_duplicates=False)
except Exception:
continue
else:
return result
else:
raise ValueError("Failed to remove duplicate keys: %s" % _intersect)
else:
raise ValueError("Substances on both sides: %s" % str(_intersect))
if substances is None:
substances = OrderedDict([(k, substance_factory(k)) for k in chain(reactants, products)])
if isinstance(substances, str):
substances = OrderedDict([(k, substance_factory(k)) for k in substances.split()])
if type(reactants) == set: # we don't want isinstance since it might be "OrderedSet"
reactants = sorted(reactants)
if type(products) == set:
products = sorted(products)
subst_keys = list(reactants) + list(products)
cks = Substance.composition_keys(substances.values())
if parametric_symbols is None:
parametric_symbols = numbered_symbols('x', start=1, integer=True, positive=True)
# ?C2H2 + ?O2 -> ?CO + ?H2O
# Ax = 0
# A: x:
#
# C2H2 O2 CO H2O
# C -2 0 1 0 x0 = 0
# H -2 0 0 2 x1 0
# O 0 -2 1 1 x2 0
# x3
def _get(ck, sk):
return substances[sk].composition.get(ck, 0) * (-1 if sk in reactants else 1)
for ck in cks: # check that all components are present on reactant & product sides
for rk in reactants:
if substances[rk].composition.get(ck, 0) != 0:
break
else:
raise ValueError("Component '%s' not among reactants" % ck)
for pk in products:
if substances[pk].composition.get(ck, 0) != 0:
break
else:
raise ValueError("Component '%s' not among products" % ck)
A = MutableDenseMatrix([[_get(ck, sk) for sk in subst_keys] for ck in cks])
symbs = list(reversed([next(parametric_symbols) for _ in range(len(subst_keys))]))
sol, = linsolve((A, zeros(len(cks), 1)), symbs)
wi = Wild('wi', properties=[lambda k: not k.has(Symbol)])
cd = reduce(gcd, [1] + [1/m[wi] for m in map(
lambda n: n.match(symbs[-1]/wi), pre(sol)) if m is not None])
sol = sol.func(*[arg/cd for arg in sol.args])
def remove(cont, symb, remaining):
subsd = dict(zip(remaining/symb, remaining))
cont = cont.func(*[(arg/symb).expand().subs(subsd) for arg in cont.args])
if cont.has(symb):
raise ValueError("Bug, please report an issue at https://github.com/bjodah/chempy")
return cont
done = False
for idx, symb in enumerate(symbs):
for expr in sol:
iterable = expr.args if expr.is_Add else [expr]
for term in iterable:
if term.is_number:
done = True
break
if done:
break
if done:
break
for expr in sol:
if (expr/symb).is_number:
sol = remove(sol, symb, MutableDenseMatrix(symbs[idx+1:]))
break
for symb in symbs:
cd = 1
for expr in sol:
iterable = expr.args if expr.is_Add else [expr]
for term in iterable:
if term.is_Mul and term.args[0].is_number and term.args[1] == symb:
cd = gcd(cd, term.args[0])
if cd != 1:
sol = sol.func(*[arg.subs(symb, symb/cd) for arg in sol.args])
if underdetermined is 1:
from ._release import __version__
if int(__version__.split('.')[1]) > 6:
warnings.warn( # deprecated because comparison with ``1`` problematic (True==1)
("Pass underdetermined == None instead of ``1`` (depreacted since 0.7.0,"
" will_be_missing_in='0.9.0')"), ChemPyDeprecationWarning)
underdetermined = None
if underdetermined is None:
sol = Tuple(*[Integer(x) for x in _solve_balancing_ilp_pulp(A)])
fact = gcd(sol)
sol = MutableDenseMatrix([e/fact for e in sol]).reshape(len(sol), 1)
sol /= reduce(gcd, sol)
if 0 in sol:
raise ValueError("Superfluous species given.")
if underdetermined:
if any(x == sympy.nan for x in sol):
raise ValueError("Failed to balance reaction")
else:
for x in sol:
if len(x.free_symbols) != 0:
raise ValueError("The system was under-determined")
if not all(residual == 0 for residual in A * sol):
raise ValueError("Failed to balance reaction")
def _x(k):
coeff = sol[subst_keys.index(k)]
return int(coeff) if underdetermined is None else coeff
return (
OrderedDict([(k, _x(k)) for k in reactants]),
OrderedDict([(k, _x(k)) for k in products])
)
# Form expressions for derivatives of the g's w.r.t. lean and pitch
dh = [0] * 8
for i in range(4):
for j in range(2):
dh[2 * i + j] = h[i].diff(q[j + 1])
# Subsitution dictionary to replace dynamic symbols with regular symbols
symbol_dict = {q[1]: Symbol('q1'), q[2]: Symbol('q2'), qd[0]: Symbol('qd0')}
for i in range(4):
h[i] = h[i].subs(symbol_dict)
for i in range(8):
dh[i] = dh[i].subs(symbol_dict)
# CSE on g's
z, h_red = cse(h, numbered_symbols('z'))
# Form output code for g's
output_code = " // Intermediate variables for h's\n"
for zi_lhs, zi_rhs in z:
output_code += " {0} = {1};\n".format(zi_lhs, ccode(zi_rhs))
output_code += "\n // h's\n"
for i in range(4):
output_code += " h[{0}] = {1};\n".format(i, ccode(h_red[i]))
# CSE on dh's
z, dh_red = cse(dh, numbered_symbols('z'))
# Form output code for dg's
output_code += "\n // Intermediate variables for dh's\n"
qd[0]: Symbol('qd0'), qd[1]: Symbol('qd1'), qd[2]: Symbol('qd2'),
u[0]: Symbol('u0'), u[1]: Symbol('u1'), u[2]: Symbol('u2'),
ud[0]: Symbol('ud0'), ud[1]: Symbol('ud1'), ud[2]: Symbol('ud2')}
for i in range(len(exp_ode)):
exp_ode[i] = exp_ode[i].subs(subs_dict)
for i in range(len(exp_output)):
exp_output[i] = exp_output[i].subs(subs_dict)
for i in range(len(exp_jac)):
exp_jac[i] = exp_jac[i].subs(subs_dict)
# CSE on all quantities needed for numerical integration of ordinary
# differential equations: qd_rhs (5), M_dyn (9), f_dyn (3)
z, exp_ode_red = cse(exp_ode, numbered_symbols('z'))
output_code = " // Intermediate variables for ODE function\n"
for zi_lhs, zi_rhs in z:
output_code += " {0} = {1};\n".format(zi_lhs, ccode(zi_rhs))
output_code += "\n // Kinematic differential equations\n"
for i in range(5):
output_code += " dxdt[{0}] = {1};\n".format(i, ccode(exp_ode_red[i]))
output_code += "\n // Mass matrix\n"
for i in range(3):
for j in range(3):
output_code += " M_dyn({0}, {1}) = {2};\n".format(i, j,
ccode(exp_ode_red[5 + 3*i + j]))
def sparse_solve_for_commuting_term(cvector, psi_lower, order, orders,
matrixrows, subspace, norm = False,
fvarname = 'A', iofvars = None, subs_rules = None, split_orders = None):
fvar_gen = sympy.numbered_symbols('fvar')
fvars = [next(fvar_gen) for i in range(len(subspace))]
psi_order = [Ncproduct(-fvars[subspace[key]], list(key))
for i,key in enumerate(subspace)]
if norm:
psi_total = psi_lower + psi_order
new_orders = orders.copy()
new_orders.update(dict(zip(fvars, [order]*len(fvars))))
sparse_normalise(psi_total, order, new_orders, fvars, cvector, matrixrows, split_orders, start_ind = len(fvars))
sub_sub_spaces = find_sub_subspaces(matrixrows)
print(sub_sub_spaces)
solutions = {}
if subs_rules is None:
subs_rules = {}
#deal with empty rows
# for i, row in matrixrows.items():
# if not row:
# if sympy.simplify(cvector[i]) != 0:
# poss = False
# for iofvar in iofvars:
# if iofvar in cvector[i].atoms(sympy.Symbol):
# sub_sub_spaces.append([i])
# print('Warning, new sspace: ' + str(i))
# poss = True
# if not poss:
# print(matrixrows)
# print(cvector)
# raise ValueError('Error term to cancel in null')
length_ss = len(sub_sub_spaces)
fvargen = sympy.numbered_symbols(fvarname)
tempgen = sympy.numbered_symbols('temp')
tempvars = []
newfvars = []
for i, ss_space in enumerate(sub_sub_spaces):
#if i == 4:
#ipdb.set_trace()
solutions.update(solve_for_sub_subspace(matrixrows, ss_space,
fvars, cvector, iofvars,
subs_rules, fvargen, newfvars, tempgen, tempvars))
print_progress(i, length_ss)
solvector = []
for fvar in fvars:
try:
solvector.append(solutions[fvar])
except KeyError:
newfvars.append(next(fvargen))
solvector.append(newfvars[-1])
for tempvar in tempvars:
if tempvar not in subs_rules:
newfvars.append(next(fvargen))
subs_rules[tempvar] = newfvars[-1]
if newfvars:
if iofvars is not None:
iofvars[:] = newfvars
if not subs_rules:
return simplify_group([Ncproduct(-solvector[i], list(key))
for i,key in enumerate(subspace)])
else:
ret = simplify_group([Ncproduct(-solvector[i].xreplace(subs_rules), list(key))
for i,key in enumerate(subspace)])
for tempvar in tempvars:
subs_rules.pop(tempvar, None)
return ret
# Form expressions for derivatives of the g's w.r.t. lean and pitch
dh = [0]*8
for i in range(4):
for j in range(2):
dh[2*i + j] = h[i].diff(q[j+1])
# Subsitution dictionary to replace dynamic symbols with regular symbols
symbol_dict = {q[1]: Symbol('q1'), q[2]: Symbol('q2'), qd[0]: Symbol('qd0')}
for i in range(4):
h[i] = h[i].subs(symbol_dict)
for i in range(8):
dh[i] = dh[i].subs(symbol_dict)
# CSE on g's
z, h_red = cse(h, numbered_symbols('z'))
# Form output code for g's
output_code = " // Intermediate variables for h's\n"
for zi_lhs, zi_rhs in z:
output_code += " {0} = {1};\n".format(zi_lhs, ccode(zi_rhs))
output_code += "\n // h's\n"
for i in range(4):
output_code += " h[{0}] = {1};\n".format(i, ccode(h_red[i]))
# CSE on dh's
z, dh_red = cse(dh, numbered_symbols('z'))
# Form output code for dg's
output_code += "\n // Intermediate variables for dh's\n"
def cse_lambdify(args, expr, **kwargs):
'''
Wrapper for sympy.lambdify which makes use of common subexpressions.
'''
# Note:
# This was expected to speed up the evaluation of the created functions.
# However performance gain is only at ca. 5%
# check input expression
if type(expr) == str:
raise TypeError('Not implemented for string input expression!')
# check given expression
try:
check_expression(expr)
except TypeError as err:
raise NotImplementedError("Only sympy expressions are allowed, yet")
# get sequence of symbols from input arguments
if type(args) == str:
args = sp.symbols(args, seq=True)
elif hasattr(args, '__iter__'):
# this may kill assumptions
args = [sp.Symbol(str(a)) for a in args]
if not hasattr(args, '__iter__'):
args = (args, )
# get the common subexpressions
cse_pairs, red_exprs = sp.cse(expr, symbols=sp.numbered_symbols('r'))
if len(red_exprs) == 1:
red_exprs = red_exprs[0]
# check if sympy found any common subexpressions
if not cse_pairs:
# if not, use standard lambdify
return sp.lambdify(args, expr, **kwargs)
# now we are looking for those arguments that are part of the reduced expression(s)
shortcuts = zip(*cse_pairs)[0]
atoms = sp.Set(red_exprs).atoms()
cse_args = [arg for arg in tuple(args) + tuple(shortcuts) if arg in atoms]
# next, we create a function that evaluates the reduced expression
cse_expr = red_exprs
# if dummify is set to False then sympy.lambdify still returns a numpy.matrix
# regardless of the possibly passed module dictionary {'ImmutableMatrix' : numpy.array}
if kwargs.get('dummify') == False:
kwargs['dummify'] = True
reduced_exprs_fnc = sp.lambdify(args=cse_args, expr=cse_expr, **kwargs)
# get the function that evaluates the replacement pairs
modules = kwargs.get('modules')
if modules is None:
modules = ['math', 'numpy', 'sympy']
namespaces = []
if isinstance(modules, (dict, str)) or not hasattr(modules, '__iter__'):
namespaces.append(modules)
else:
namespaces += list(modules)
nspace = {}
for m in namespaces[::-1]:
nspace.update(_get_namespace(m))
eval_pairs_fnc = make_cse_eval_function(input_args=args,
replacement_pairs=cse_pairs,
ret_filter=cse_args,
namespace=nspace)
# now we can wrap things together
def cse_fnc(*args):
cse_args_evaluated = eval_pairs_fnc(args)
return reduced_exprs_fnc(*cse_args_evaluated)
return cse_fnc
qd[0]: Symbol('qd0'), qd[1]: Symbol('qd1'), qd[2]: Symbol('qd2'),
u[0]: Symbol('u0'), u[1]: Symbol('u1'), u[2]: Symbol('u2'),
ud[0]: Symbol('ud0'), ud[1]: Symbol('ud1'), ud[2]: Symbol('ud2')}
for i in range(len(exp_ode)):
exp_ode[i] = exp_ode[i].subs(subs_dict)
for i in range(len(exp_output)):
exp_output[i] = exp_output[i].subs(subs_dict)
for i in range(len(exp_jac)):
exp_jac[i] = exp_jac[i].subs(subs_dict)
# CSE on all quantities needed for numerical integration of ordinary
# differential equations: qd_rhs (5), M_dyn (9), f_dyn (3)
z, exp_ode_red = cse(exp_ode, numbered_symbols('z'))
output_code = " // Intermediate variables for ODE function\n"
for zi_lhs, zi_rhs in z:
output_code += " {0} = {1};\n".format(zi_lhs, ccode(zi_rhs))
output_code += "\n // Kinematic differential equations\n"
for i in range(5):
output_code += " dxdt[{0}] = {1};\n".format(i, ccode(exp_ode_red[i]))
output_code += "\n // Mass matrix\n"
for i in range(3):
for j in range(3):
output_code += " M_dyn({0}, {1}) = {2};\n".format(i, j,
ccode(exp_ode_red[5 + 3*i + j]))
def variables(self):
dummy_groups = (
DummyGroup('depvdummies', self._fo_odesys.na_depv),
DummyGroup('paramdummies', self._fo_odesys.param_and_sol_symbs),
)
arrayify_groups = (
ArrayifyGroup('depvdummies', self.depv_tok, self.depv_offset),
ArrayifyGroup('paramdummies', self.param_tok, self.param_offset)
)
code_func_cse, code_func_exprs = self.get_cse_code(
self._fo_odesys.na_f.values(), 'csefunc', dummy_groups, arrayify_groups)
y0 = ', '.join(['1.0'] * self.NY)
y0_names = ', '.join(map(str, self._fo_odesys.na_depv))
params = ', '.join(['1.0'] * len(self.prog_param_symbs))
param_names = ', '.join(map(str, self.prog_param_symbs))
indepv = self._fo_odesys.indepv
# TODO: this is inefficient, implement linear scaling algo in
# FirstOrderODESystem
sparse_jac = OrderedDict(reduce(add, [
[((i, j), expr) for j, expr in enumerate(row) if expr != 0]\
for i, row in enumerate(self._fo_odesys.na_jac.tolist())
]))
dfdt = self._fo_odesys.na_dfdt.values()
code_jac_cse, code_jac_exprs = self.get_cse_code(
sparse_jac.values() + dfdt, 'csejac', dummy_groups, arrayify_groups)
code_pure_dfdt_cse, code_pure_dfdt_exprs = self.get_cse_code(
dfdt, 'csedfdt', dummy_groups, arrayify_groups)
code_dfdt_exprs = code_jac_exprs[len(sparse_jac):]
code_jac_exprs = zip(sparse_jac.keys(),
code_jac_exprs[:len(sparse_jac)])
# Populate ia, ja (sparse index specifiers using fortran indexing)
# see documentation of LSODES in ODEPACK for definition
# (Yale sparse matrix)
# ja contains row indices of nonzero elements
# ia contains index in ja where row i starts
ia, ja = [1], []
k = 1 # <--- index starts at 1 in fortran, not at 0 as in C/Python
code_yale_jac_exprs = []
code_yale_jac_cse = []
for ci in range(self.NY):
col_exprs = []
cur_ja = []
for ri in [sri for sri, sci in sparse_jac.keys() if sci == ci]:
cur_ja.append(ri+1) # Fortran index
k += 1
col_exprs.append(sparse_jac[(ri,ci)])
# Store indices in ja
ja.extend(cur_ja)
# Store indicies in ia
ia.append(k)
# Extract common subexpressions for this column
cse_defs, cse_exprs = sympy.cse(
col_exprs, symbols = sympy.numbered_symbols(
'csejaccol{}'.format(ci)))
# Format code: expressions in cse terms
code_exprs = zip(cur_ja, [
self.as_arrayified_code(x, dummy_groups, arrayify_groups) for x \
in cse_exprs
])
code_yale_jac_exprs.append(code_exprs)
# Format code: CSE definitions
code_cse_defs=[]
for var_name, var_expr in cse_defs:
code_var_expr = self.as_arrayified_code(
var_expr, dummy_groups, arrayify_groups)
code_cse_defs.append((var_name, code_var_expr))
code_yale_jac_cse.append(code_cse_defs)
ia = ia [:-1]
return {'NY': self.NY,
'NNZ': len(sparse_jac),
'IA': ia,
'JA': ja,
'NPARAM': len(self.prog_param_symbs),
'y0_comma_sep_str': y0,
'y0_names': y0_names,
'param_vals_comma_sep_str': params,
'param_names': param_names,
'cse_func': code_func_cse, 'f': code_func_exprs,
'cse_jac': code_jac_cse, 'jac': code_jac_exprs,
'yale_jac_exprs': code_yale_jac_exprs,
'yale_jac_cse': code_yale_jac_cse,
'dfdt': code_dfdt_exprs,
'pure_dfdt_exprs': code_pure_dfdt_exprs,
'pure_dfdt_cse': code_pure_dfdt_cse,
}
# substitute the algabrain equations in the ode system to generate the complete ode_subs a1.gen_ode_subs() # finding all the parameters a1.eq_all_params(Zone = 'algebraic') a1.eq_all_params(Zone = 'ode') a1.eq_all_params(Zone = 'ode_subs') # eample how to use the method replace_singe_var() # a1.eq['algebraic']['delta_L1'] = a1.replace_singe_var(a1.eq['algebraic']['delta_L1'], 'x_1', 'x_11') x_vec = a1.eq['ode_subs'].keys() # fixme: the code below is not working as 'm_1' and 'm_2' are strings, but they should be sympy objects # todo: change eq_all_params() to store and the sympy objects par_vec = [a1.all_params_ode_subs['m1'], a1.all_params_ode_subs['m2']] sens_sys_list = a1.sys_dict_to_list(a1.eq['ode_subs']) sens_sys = a1.sens_ext_sys(sens_sys_list, x_vec, par_vec) print sens_sys sens_sys_list = a1.sys_dict_to_list(sens_sys) from sympy import cse, numbered_symbols a4=cse(sens_sys_list, symbols=numbered_symbols(prefix='t', start=0)) a1.print_Sys_optim(a4, func_name = 'r1')
def ufuncify_matrix(args, expr, const=None, tmp_dir=None, parallel=False):
"""Returns a function that evaluates a matrix of expressions in a tight
loop.
Parameters
----------
args : iterable of sympy.Symbol
A list of all symbols in expr in the desired order for the output
function.
expr : sympy.Matrix
A matrix of expressions.
const : tuple, optional
This should include any of the symbols in args that should be
constant with respect to the loop.
tmp_dir : string, optional
The path to a directory in which to store the generated files. If
None then the files will be not be retained after the function is
compiled.
parallel : boolean, optional
If True and openmp is installed, the generated code will be
parallelized across threads. This is only useful when expr are
extremely large.
"""
# TODO : This is my first ever global variable in Python. It'd probably
# be better if this was a class attribute of a Ufuncifier class. And I'm
# not sure if this current version counts sequentially.
global module_counter
matrix_size = expr.shape[0] * expr.shape[1]
file_prefix_base = 'ufuncify_matrix'
file_prefix = '{}_{}'.format(file_prefix_base, module_counter)
if tmp_dir is None:
codedir = tempfile.mkdtemp(".ufuncify_compile")
else:
codedir = os.path.abspath(tmp_dir)
if not os.path.exists(codedir):
os.makedirs(codedir)
taken = False
while not taken:
try:
open(os.path.join(codedir, file_prefix + '.pyx'), 'r')
except IOError:
taken = True
else:
file_prefix = '{}_{}'.format(file_prefix_base, module_counter)
module_counter += 1
d = {
'routine_name': 'eval_matrix',
'file_prefix': file_prefix,
'matrix_output_size': matrix_size,
'num_rows': expr.shape[0],
'num_cols': expr.shape[1]
}
if parallel:
if openmp_installed():
openmp = True
else:
openmp = False
msg = ('openmp is not installed or not working properly, request '
'for parallel execution ignored.')
warnings.warn(msg)
if parallel and openmp:
d['loop_sig'] = "prange(n, nogil=True)"
d['head_gil'] = " nogil"
d['compile_args'] = "'-fopenmp'"
d['link_args'] = "'-fopenmp'"
else:
d['loop_sig'] = "range(n)"
d['head_gil'] = ""
d['compile_args'] = ""
d['link_args'] = ""
matrix_sym = sm.MatrixSymbol('matrix', expr.shape[0], expr.shape[1])
sub_exprs, simple_mat = sm.cse(expr, sm.numbered_symbols('z_'))
sub_expr_code = '\n'.join([
'double ' + sm.ccode(sub_expr[1], sub_expr[0])
for sub_expr in sub_exprs
])
matrix_code = sm.ccode(simple_mat[0], matrix_sym)
d['eval_code'] = ' ' + '\n '.join(
(sub_expr_code + '\n' + matrix_code).split('\n'))
c_indent = len('void {routine_name}('.format(**d))
c_arg_spacer = ',\n' + ' ' * c_indent
input_args = ['double {}'.format(sm.ccode(a)) for a in args]
d['input_args'] = c_arg_spacer.join(input_args)
cython_input_args = []
indexed_input_args = []
for a in args:
if const is not None and a in const:
typ = 'double'
idexy = '{}'
else:
typ = 'np.ndarray[np.double_t, ndim=1]'
idexy = '{}[i]'
cython_input_args.append('{} {}'.format(typ, sm.ccode(a)))
indexed_input_args.append(idexy.format(sm.ccode(a)))
cython_indent = len('def {routine_name}_loop('.format(**d))
cython_arg_spacer = ',\n' + ' ' * cython_indent
d['numpy_typed_input_args'] = cython_arg_spacer.join(cython_input_args)
d['indexed_input_args'] = ',\n'.join(indexed_input_args)
files = {}
files[d['file_prefix'] + '_c.c'] = _c_template.format(**d)
files[d['file_prefix'] + '_h.h'] = _h_template.format(**d)
files[d['file_prefix'] + '.pyx'] = _cython_template.format(**d)
files[d['file_prefix'] + '_setup.py'] = _setup_template.format(**d)
workingdir = os.getcwd()
os.chdir(codedir)
try:
sys.path.append(codedir)
for filename, code in files.items():
with open(filename, 'w') as f:
f.write(code)
cmd = [
sys.executable, d['file_prefix'] + '_setup.py', 'build_ext',
'--inplace'
]
subprocess.call(cmd, stderr=subprocess.STDOUT, stdout=subprocess.PIPE)
cython_module = importlib.import_module(d['file_prefix'])
finally:
module_counter += 1
sys.path.remove(codedir)
os.chdir(workingdir)
if tmp_dir is None:
shutil.rmtree(codedir)
return getattr(cython_module, d['routine_name'] + '_loop')
def ufuncify_matrix(args, expr, const=None, tmp_dir=None):
"""Returns a function that evaluates a matrix of expressions in a tight
loop.
Parameters
----------
args : iterable of sympy.Symbol
A list of all symbols in expr in the desired order for the output
function.
expr : sympy.Matrix
A matrix of expressions.
const : tuple, optional
This should include any of the symbols in args that should be
constant with respect to the loop.
tmp_dir : string, optional
The path to a directory in which to store the generated files. If
None then the files will be not be retained after the function is
compiled.
"""
# TODO : This is my first ever global variable in Python. It'd probably
# be better if this was a class attribute of a Ufuncifier class. And I'm
# not sure if this current version counts sequentially.
global module_counter
matrix_size = expr.shape[0] * expr.shape[1]
file_prefix_base = 'ufuncify_matrix'
file_prefix = '{}_{}'.format(file_prefix_base, module_counter)
if tmp_dir is None:
codedir = tempfile.mkdtemp(".ufuncify_compile")
else:
codedir = os.path.abspath(tmp_dir)
if not os.path.exists(codedir):
os.makedirs(codedir)
taken = False
while not taken:
try:
open(os.path.join(codedir, file_prefix + '.pyx'), 'r')
except IOError:
taken = True
else:
file_prefix = '{}_{}'.format(file_prefix_base, module_counter)
module_counter += 1
d = {'routine_name': 'eval_matrix',
'file_prefix': file_prefix,
'matrix_output_size': matrix_size,
'num_rows': expr.shape[0],
'num_cols': expr.shape[1]}
matrix_sym = sy.MatrixSymbol('matrix', expr.shape[0], expr.shape[1])
sub_exprs, simple_mat = sy.cse(expr, sy.numbered_symbols('z_'))
sub_expr_code = '\n'.join(['double ' + sy.ccode(sub_expr[1], sub_expr[0])
for sub_expr in sub_exprs])
matrix_code = sy.ccode(simple_mat[0], matrix_sym)
d['eval_code'] = ' ' + '\n '.join((sub_expr_code + '\n' + matrix_code).split('\n'))
c_indent = len('void {routine_name}('.format(**d))
c_arg_spacer = ',\n' + ' ' * c_indent
input_args = ['double {}'.format(sy.ccode(a)) for a in args]
d['input_args'] = c_arg_spacer.join(input_args)
cython_input_args = []
indexed_input_args = []
for a in args:
if const is not None and a in const:
typ = 'double'
idexy = '{}'
else:
typ = 'np.ndarray[np.double_t, ndim=1]'
idexy = '{}[i]'
cython_input_args.append('{} {}'.format(typ, sy.ccode(a)))
indexed_input_args.append(idexy.format(sy.ccode(a)))
cython_indent = len('def {routine_name}_loop('.format(**d))
cython_arg_spacer = ',\n' + ' ' * cython_indent
d['numpy_typed_input_args'] = cython_arg_spacer.join(cython_input_args)
d['indexed_input_args'] = ',\n'.join(indexed_input_args)
files = {}
files[d['file_prefix'] + '_c.c'] = _c_template.format(**d)
files[d['file_prefix'] + '_h.h'] = _h_template.format(**d)
files[d['file_prefix'] + '.pyx'] = _cython_template.format(**d)
files[d['file_prefix'] + '_setup.py'] = _setup_template.format(**d)
workingdir = os.getcwd()
os.chdir(codedir)
try:
sys.path.append(codedir)
for filename, code in files.items():
with open(filename, 'w') as f:
f.write(code)
cmd = [sys.executable, d['file_prefix'] + '_setup.py', 'build_ext',
'--inplace']
subprocess.call(cmd, stderr=subprocess.STDOUT, stdout=subprocess.PIPE)
cython_module = importlib.import_module(d['file_prefix'])
finally:
module_counter += 1
sys.path.remove(codedir)
os.chdir(workingdir)
if tmp_dir is None:
shutil.rmtree(codedir)
return getattr(cython_module, d['routine_name'] + '_loop')
def outputC(sympyexpr, output_varname_str, filename = "stdout", params = "", prestring = "", poststring = ""):
outCparams = parse_outCparams_string(params)
preindent = outCparams.preindent
TYPE = par.parval_from_str("PRECISION")
if outCparams.enable_TYPE == "False":
TYPE = ""
# Step 0: Initialize
# commentblock: comment block containing the input SymPy string,
# set only if outCverbose==True
# outstring: the output C code string
commentblock = ""
outstring = ""
# Step 1: If enable_SIMD==True, then check if TYPE=="double". If not, error out.
# Otherwise set TYPE="REAL_SIMD_ARRAY", which should be #define'd
# within the C code. For example for AVX-256, the C code should have
# #define REAL_SIMD_ARRAY __m256d
if outCparams.enable_SIMD == "True":
if TYPE not in ('double', ''):
print("SIMD output currently only supports double precision or typeless. Sorry!")
sys.exit(1)
if TYPE == "double":
TYPE = "REAL_SIMD_ARRAY"
# Step 2a: Apply sanity checks when either sympyexpr or
# output_varname_str is a list.
if isinstance(output_varname_str, list) and not isinstance(sympyexpr, list):
print("Error: Provided a list of output variable names, but only one SymPy expression.")
sys.exit(1)
if isinstance(sympyexpr, list):
if not isinstance(output_varname_str, list):
print("Error: Provided a list of SymPy expressions, but no corresponding list of output variable names")
sys.exit(1)
elif len(output_varname_str) != len(sympyexpr):
print("Error: Length of SymPy expressions list ("+str(len(sympyexpr))+
") != Length of corresponding output variable name list ("+str(len(output_varname_str))+")")
sys.exit(1)
# Step 2b: If sympyexpr and output_varname_str are not lists,
# convert them to lists of one element each, to
# simplify proceeding code.
if not isinstance(output_varname_str, list) and not isinstance(sympyexpr, list):
output_varname_strtmp = [output_varname_str]
output_varname_str = output_varname_strtmp
sympyexprtmp = [sympyexpr]
sympyexpr = sympyexprtmp
sympyexpr = sympyexpr[:] # pass-by-value (copy list)
# Step 3: If outCparams.verbose = True, then output the original SymPy
# expression(s) in code comments prior to actual C code
if outCparams.outCverbose == "True":
commentblock += preindent+"/*\n"+preindent+" * Original SymPy expression"
if len(output_varname_str)>1:
commentblock += "s"
commentblock += ":\n"
for i, varname in enumerate(output_varname_str):
if i == 0:
if len(output_varname_str) != 1:
commentblock += preindent+" * \"["
else:
commentblock += preindent+" * \""
else:
commentblock += preindent+" * "
commentblock += varname + " = " + str(sympyexpr[i])
if i == len(output_varname_str)-1:
if len(output_varname_str) != 1:
commentblock += "]\"\n"
else:
commentblock += "\"\n"
else:
commentblock += ",\n"
commentblock += preindent+" */\n"
# Step 4: Add proper indentation of C code:
if outCparams.includebraces == "True":
indent = outCparams.preindent+" "
else:
indent = outCparams.preindent+""
# Step 5: Should the output variable, e.g., outvar, be declared?
# If so, start output line with e.g., "double outvar "
outtypestring = ""
if outCparams.declareoutputvars == "True":
outtypestring = indent+TYPE + " "
else:
outtypestring = indent
# Step 6a: If common subexpression elimination (CSE) disabled, then
# just output the SymPy string in the most boring way,
# nearly consistent with SymPy's ccode() function,
# though with support for float & long double types
# as well.
SIMD_RATIONAL_decls = RATIONAL_decls = ""
if outCparams.CSE_enable == "False":
# If CSE is disabled:
for i in range(len(sympyexpr)):
outstring += outtypestring + ccode_postproc(sp.ccode(sympyexpr[i], output_varname_str[i],
user_functions=custom_functions_for_SymPy_ccode))+"\n"
# Step 6b: If CSE enabled, then perform CSE using SymPy and then
# resulting C code.
else:
# If CSE is enabled:
SIMD_const_varnms = []
SIMD_const_values = []
varprefix = '' if outCparams.CSE_varprefix == 'tmp' else outCparams.CSE_varprefix
if outCparams.CSE_preprocess == "True" or outCparams.enable_SIMD == "True":
# If CSE_preprocess == True, then perform partial factorization
# If enable_SIMD == True, then declare _NegativeOne_ in preprocessing
factor_negative = eval(outCparams.enable_SIMD) and eval(outCparams.SIMD_find_more_subs)
sympyexpr, map_sym_to_rat = cse_preprocess(sympyexpr, prefix=varprefix,
declare=eval(outCparams.enable_SIMD), negative=factor_negative, factor=eval(outCparams.CSE_preprocess))
for v in map_sym_to_rat:
p, q = float(map_sym_to_rat[v].p), float(map_sym_to_rat[v].q)
if outCparams.enable_SIMD == "False":
RATIONAL_decls += indent + 'const double ' + str(v) + ' = '
# Since Integer is a subclass of Rational in SymPy, we need only check whether
# the denominator q = 1 to determine if a rational is an integer.
if q != 1: RATIONAL_decls += str(p) + '/' + str(q) + ';\n'
else: RATIONAL_decls += str(p) + ';\n'
sympy_version = sp.__version__.replace('rc', '...').replace('b', '...')
sympy_major_version = int(sympy_version.split(".")[0])
sympy_minor_version = int(sympy_version.split(".")[1])
if sympy_major_version < 1 or (sympy_major_version == 1 and sympy_minor_version < 3):
print('Warning: SymPy version', sympy_version, 'does not support CSE postprocessing.')
CSE_results = sp.cse(sympyexpr, sp.numbered_symbols(outCparams.CSE_varprefix + '_'),
order=outCparams.CSE_sorting)
else:
CSE_results = cse_postprocess(sp.cse(sympyexpr, sp.numbered_symbols(outCparams.CSE_varprefix + '_'),
order=outCparams.CSE_sorting))
for commonsubexpression in CSE_results[0]:
FULLTYPESTRING = "const " + TYPE + " "
if outCparams.enable_TYPE == "False":
FULLTYPESTRING = ""
if outCparams.enable_SIMD == "True":
outstring += indent + FULLTYPESTRING + str(commonsubexpression[0]) + " = " + \
str(expr_convert_to_SIMD_intrins(commonsubexpression[1],map_sym_to_rat,varprefix,outCparams.SIMD_find_more_FMAsFMSs)) + ";\n"
else:
outstring += indent + FULLTYPESTRING + ccode_postproc(sp.ccode(commonsubexpression[1], commonsubexpression[0],
user_functions=custom_functions_for_SymPy_ccode)) + "\n"
for i, result in enumerate(CSE_results[1]):
if outCparams.enable_SIMD == "True":
outstring += outtypestring + output_varname_str[i] + " = " + \
str(expr_convert_to_SIMD_intrins(result,map_sym_to_rat,varprefix,outCparams.SIMD_find_more_FMAsFMSs)) + ";\n"
else:
outstring += outtypestring+ccode_postproc(sp.ccode(result,output_varname_str[i],
user_functions=custom_functions_for_SymPy_ccode))+"\n"
# Complication: SIMD functions require numerical constants to be stored in SIMD arrays
# Resolution: This function extends lists "SIMD_const_varnms" and "SIMD_const_values",
# which store the name of each constant SIMD array (e.g., _Integer_1) and
# the value of each variable (e.g., 1.0).
if outCparams.enable_SIMD == "True":
for v in map_sym_to_rat:
p, q = float(map_sym_to_rat[v].p), float(map_sym_to_rat[v].q)
SIMD_const_varnms.extend([str(v)])
if q != 1: SIMD_const_values.extend([str(p) + '/' + str(q)])
else: SIMD_const_values.extend([str(p)])
# Step 6b.i: If enable_SIMD == True , and
# there is at least one SIMD const variable,
# then declare the SIMD_const_varnms and SIMD_const_values arrays
if outCparams.enable_SIMD == "True" and len(SIMD_const_varnms) != 0:
# Step 6a) Sort the list of definitions. Idea from:
# https://stackoverflow.com/questions/9764298/is-it-possible-to-sort-two-listswhich-reference-each-other-in-the-exact-same-w
SIMD_const_varnms, SIMD_const_values = \
(list(t) for t in zip(*sorted(zip(SIMD_const_varnms, SIMD_const_values))))
# Step 6b) Remove duplicates
uniq_varnms = superfast_uniq(SIMD_const_varnms)
uniq_values = superfast_uniq(SIMD_const_values)
SIMD_const_varnms = uniq_varnms
SIMD_const_values = uniq_values
if len(SIMD_const_varnms) != len(SIMD_const_values):
print("Error: SIMD constant declaration arrays SIMD_const_varnms[] and SIMD_const_values[] have inconsistent sizes!")
sys.exit(1)
for i in range(len(SIMD_const_varnms)):
if outCparams.enable_TYPE == "False":
SIMD_RATIONAL_decls += indent + SIMD_const_varnms[i] + " = " + SIMD_const_values[i]+";"
else:
SIMD_RATIONAL_decls += indent + "const double " + "tmp" + SIMD_const_varnms[i] + " = " + SIMD_const_values[i] + ";\n"
SIMD_RATIONAL_decls += indent + "const REAL_SIMD_ARRAY " + SIMD_const_varnms[i] + " = ConstSIMD(" + "tmp" + SIMD_const_varnms[i] + ");\n"
SIMD_RATIONAL_decls += "\n"
# Step 7: Construct final output string
final_Ccode_output_str = commentblock
# Step 7a: Output C code in indented curly brackets if
# outCparams.includebraces = True
if outCparams.includebraces == "True": final_Ccode_output_str += outCparams.preindent+"{\n"
final_Ccode_output_str += prestring + RATIONAL_decls + SIMD_RATIONAL_decls + outstring + poststring
if outCparams.includebraces == "True": final_Ccode_output_str += outCparams.preindent+"}\n"
# Step 8: If filename == "stdout", then output
# C code to standard out (useful for copy-paste or interactive
# mode). Otherwise output to file specified in variable name.
if filename == "stdout":
# Output to standard out (stdout; "the screen")
print(final_Ccode_output_str)
elif filename == "returnstring":
return final_Ccode_output_str
else:
# Output to the file specified by the function input parameter string 'filename':
with open(filename, outCparams.outCfileaccess) as file:
file.write(final_Ccode_output_str)
successstr = ""
if outCparams.outCfileaccess == "a":
successstr = "Appended "
elif outCparams.outCfileaccess == "w":
successstr = "Wrote "
print(successstr + "to file \"" + filename + "\"")
def generate(self, expressions, functionname, const_function=True, callbacks=None):
"""Given a numpy nd-array of sympy expressions, return a function which
will generate a C-style function that will compute the entries of the
array. The array is flattened out into a contiguous array with the
last index varying fastest (row-major for matrices).
"""
orig_shape = expressions.shape
s = "\n/** Computes the n-d array of shape ("
for d in expressions.shape[:-1]:
s += "{0}, ".format(d)
s += "{0})\n *\n".format(expressions.shape[-1])
s += " * @param[out] ar a C-array of with {0}".format(expressions.size)
s += " elements\n */\n"
expressions_flat = np.zeros((expressions.size,), dtype=object)
for i, ai in enumerate(expressions.flat):
if isinstance(ai, int):
expressions_flat[i] = S(0)
else:
expressions_flat[i] = ai.subs(self.subs_dict)
if self._class_name != "":
member_function_name = self._class_name + "::" + functionname
function_signature = "void {0}(double ar[{1}])".format(member_function_name, expressions_flat.size)
else:
function_signature = "void {0}(double ar[{1}])".format(functionname, expressions_flat.size)
if const_function:
function_signature += " const"
s += "// " + function_signature + ";\n"
s += function_signature + "\n{\n"
repl, redu = cse(expressions_flat, symbols=numbered_symbols("z"))
if len(repl):
s += " double z[{0}];\n\n".format(len(repl))
if callbacks is not None:
for c in callbacks:
cname, symbolname = c
s += " " + cname + "(" + symbolname + ");\n"
for i, r in enumerate(repl):
s += " " + re.sub(r'z(\d+)', r'z[\1]', str(r[0])) + " = "
tmp = re.sub(r'z(\d+)', r'z[\1]', ccode(r[1])) + ";\n"
if self.state_prefix:
tmp = re.sub(self.state_prefix + r'(\d+)',
self.state_prefix + r'[\1]', tmp)
for p, r in self.regex_list:
test = re.compile(p)
tmp = test.sub(r, tmp)
s += tmp
s += "\n"
for i, red_i in enumerate(redu):
s += " ar[{0}] = ".format(i)
tmp = re.sub(r'z(\d+)', r'z[\1]', ccode(red_i))
if self.state_prefix:
tmp = re.sub(self.state_prefix + r'(\d+)',
self.state_prefix + r'[\1]', tmp)
for p, r in self.regex_list:
test = re.compile(p)
tmp = test.sub(r, tmp)
s += tmp
s += ";\n"
self.s += s + "}\n"
return s
def dse_cse(expr):
"""
Perform common subexpression elimination on sympy expressions.
:param expr: sympy equation or list of equations on which CSE is performed.
:return: A list of the resulting equations after performing CSE
"""
expr = expr if isinstance(expr, list) else [expr]
temps, stencils = cse(expr, numbered_symbols("temp"))
# Restores the LHS
for i in range(len(expr)):
stencils[i] = Eq(expr[i].lhs, stencils[i].rhs)
to_revert = {}
to_keep = []
# Restores IndexedBases if they are collected by CSE and
# reverts changes to simple index operations (eg: t - 1)
for temp, value in temps:
if isinstance(value, IndexedBase):
to_revert[temp] = value
elif isinstance(value, Indexed):
to_revert[temp] = value
elif isinstance(value, Add) and not \
set([t, x, y, z]).isdisjoint(set(value.args)):
to_revert[temp] = value
else:
to_keep.append((temp, value))
# Restores the IndexedBases and the Indexes in the assignments to revert
for temp, value in to_revert.items():
s_dict = {}
for arg in preorder_traversal(value):
if isinstance(arg, Indexed):
new_indices = []
for index in arg.indices:
if index in to_revert:
new_indices.append(to_revert[index])
else:
new_indices.append(index)
if arg.base.label in to_revert:
s_dict[arg] = Indexed(to_revert[value.base.label],
*new_indices)
to_revert[temp] = value.xreplace(s_dict)
subs_dict = {}
# Builds a dictionary of the replacements
for expr in stencils + [assign for temp, assign in to_keep]:
for arg in preorder_traversal(expr):
if isinstance(arg, Indexed):
new_indices = []
for index in arg.indices:
if index in to_revert:
new_indices.append(to_revert[index])
else:
new_indices.append(index)
if arg.base.label in to_revert:
subs_dict[arg] = Indexed(to_revert[arg.base.label],
*new_indices)
elif tuple(new_indices) != arg.indices:
subs_dict[arg] = Indexed(arg.base, *new_indices)
if arg in to_revert:
subs_dict[arg] = to_revert[arg]
stencils = [stencil.xreplace(subs_dict) for stencil in stencils]
to_keep = [Eq(temp[0], temp[1].xreplace(subs_dict)) for temp in to_keep]
# If the RHS of a temporary variable is the LHS of a stencil,
# update the value of the temporary variable after the stencil
new_stencils = []
for stencil in stencils:
new_stencils.append(stencil)
for temp in to_keep:
if stencil.lhs in preorder_traversal(temp.rhs):
new_stencils.append(temp)
break
return to_keep + new_stencils
def solve_motion_equations(M, B, state_vars=[], input_vars=[], parameters_values=dict()):
'''
Solves the motion equations given by the mass matrix and right hand side
to define a callable function for the vector field of the respective
control system.
Parameters
----------
M : sympy.Matrix
A sympy.Matrix containing sympy expressions and symbols that represents
the mass matrix of the control system.
B : sympy.Matrix
A sympy.Matrix containing sympy expressions and symbols that represents
the right hand site of the motion equations.
state_vars : list
A list with sympy.Symbols's for each state variable.
input_vars : list
A list with sympy.Symbols's for each input variable.
parameter_values : dict
A dictionary with a key:value pair for each system parameter.
Returns
-------
callable
'''
M_shape = M.shape
B_shape = B.shape
assert(M_shape[0] == B_shape[0])
# at first we create a buffer for the string that we complete and execute
# to dynamically define a function and return it
fnc_str_buffer ='''
def f(x, u):
# System variables
%s # x_str
%s # u_str
# Parameters
%s # par_str
# Sympy Common Expressions
%s # cse_str
# Vectorfield
%s # ff_str
return ff
'''
#################################
# handle system state variables #
#################################
# --> leads to x_str which shows how to unpack the state variables
x_str = ''
for var in state_vars:
x_str += '%s, '%str(var)
# as a last we remove the trailing '; ' to avoid syntax erros
x_str = x_str + '= x'
##########################
# handle input variables #
##########################
# --> leads to u_str which will show how to unpack the inputs of the control system
u_str = ''
for var in input_vars:
u_str += '%s, '%str(var)
# after we remove the trailing '; ' to avoid syntax errors x_str will look like:
# 'u1, u2, ... , um = u'
u_str = u_str + '= u'
############################
# handle system parameters #
############################
# --> leads to par_str
par_str = ''
for k, v in parameters_values.items():
# 'k' is the name of a system parameter such as mass or gravitational acceleration
# 'v' is its value in SI units
par_str += '%s = %s; '%(str(k), str(v))
# as a last we remove the trailing '; ' from par_str to avoid syntax errors
par_str = par_str[:-2]
# now solve the motion equations w.r.t. the accelerations
sol = M.solve(B)
# use SymPy's Common Subexpression Elimination
cse_list, cse_res = sp.cse(sol, symbols=sp.numbered_symbols('q'))
################################
# handle common subexpressions #
################################
# --> leads to cse_str
cse_str = ''
#cse_list = [(str(l), str(r)) for l, r in cse_list]
for cse_pair in cse_list:
cse_str += '%s = %s; '%(str(cse_pair[0]), str(cse_pair[1]))
# add result of cse
for i in xrange(M_shape[0]):
cse_str += 'q%d_dd = %s; '%(i, str(cse_res[0][i]))
cse_str = cse_str[:-2]
######################
# create vectorfield #
######################
# --> leads to ff_str
ff_str = 'ff = ['
for i in xrange(M_shape[0]):
ff_str += '%s, '%str(state_vars[2*i+1])
ff_str += 'q%s_dd, '%(i)
# remove trailing ',' and add closing brackets
ff_str = ff_str[:-2] + ']'
############################
# Create callable function #
############################
# now we can replace all placeholders in the function string buffer
fnc_str = fnc_str_buffer%(x_str, u_str, par_str, cse_str, ff_str)
# and finally execute it which will create a python function 'f'
exec(fnc_str)
# now we have defined a callable function that can be used within PyTrajectory
return f
def outputC(sympyexpr,
output_varname_str,
filename="stdout",
params="",
prestring="",
poststring=""):
outCparams = parse_outCparams_string(params)
preindent = outCparams.preindent
TYPE = par.parval_from_str("PRECISION")
if outCparams.enable_TYPE == "False":
TYPE = ""
# Step 0: Initialize
# commentblock: comment block containing the input SymPy string,
# set only if outCverbose==True
# outstring: the output C code string
commentblock = ""
outstring = ""
# Step 1: If SIMD_enable==True, then check if TYPE=="double". If not, error out.
# Otherwise set TYPE="REAL_SIMD_ARRAY", which should be #define'd
# within the C code. For example for AVX-256, the C code should have
# #define REAL_SIMD_ARRAY __m256d
if outCparams.SIMD_enable == "True":
if not (TYPE == "double" or TYPE == ""):
print(
"SIMD output currently only supports double precision or typeless. Sorry!"
)
exit(1)
if TYPE == "double":
TYPE = "REAL_SIMD_ARRAY"
else:
TYPE = ""
# Step 2a: Apply sanity checks when either sympyexpr or
# output_varname_str is a list.
if type(output_varname_str) is list and type(sympyexpr) is not list:
print(
"Error: Provided a list of output variable names, but only one SymPy expression."
)
exit(1)
if type(sympyexpr) is list:
if type(output_varname_str) is not list:
print(
"Error: Provided a list of SymPy expressions, but no corresponding list of output variable names"
)
exit(1)
elif len(output_varname_str) != len(sympyexpr):
print("Error: Length of SymPy expressions list (" +
str(len(sympyexpr)) +
") != Length of corresponding output variable name list (" +
str(len(output_varname_str)) + ")")
exit(1)
# Step 2b: If sympyexpr and output_varname_str are not lists,
# convert them to lists of one element each, to
# simplify proceeding code.
if type(output_varname_str) is not list and type(sympyexpr) is not list:
output_varname_strtmp = [output_varname_str]
output_varname_str = output_varname_strtmp
sympyexprtmp = [sympyexpr]
sympyexpr = sympyexprtmp
# Step 3: If outCparams.verbose = True, then output the original SymPy
# expression(s) in code comments prior to actual C code
if outCparams.outCverbose == "True":
commentblock += preindent + "/*\n" + preindent + " * Original SymPy expression"
if len(output_varname_str) > 1:
commentblock += "s"
commentblock += ":\n"
for i in range(len(output_varname_str)):
if i == 0:
if len(output_varname_str) != 1:
commentblock += preindent + " * \"["
else:
commentblock += preindent + " * \""
else:
commentblock += preindent + " * "
commentblock += output_varname_str[i] + " = " + str(sympyexpr[i])
if i == len(output_varname_str) - 1:
if len(output_varname_str) != 1:
commentblock += "]\"\n"
else:
commentblock += "\"\n"
else:
commentblock += ",\n"
commentblock += preindent + " */\n"
# Step 4: Add proper indentation of C code:
if outCparams.includebraces == "True":
indent = outCparams.preindent + " "
else:
indent = outCparams.preindent + ""
# Step 5: Should the output variable, e.g., outvar, be declared?
# If so, start output line with e.g., "double outvar "
outtypestring = ""
if outCparams.declareoutputvars == "True":
outtypestring = outCparams.preindent + indent + TYPE + " "
else:
outtypestring = outCparams.preindent + indent
# Step 6a: If common subexpression elimination (CSE) disabled, then
# just output the SymPy string in the most boring way,
# nearly consistent with SymPy's ccode() function,
# though with support for float & long double types
# as well.
SIMD_decls = ""
if outCparams.CSE_enable == "False":
# If CSE is disabled:
for i in range(len(sympyexpr)):
outstring += outtypestring + ccode_postproc(
sp.ccode(sympyexpr[i], output_varname_str[i])) + "\n"
# Step 6b: If CSE enabled, then perform CSE using SymPy and then
# resulting C code.
else:
# If CSE is enabled:
SIMD_const_varnms = []
SIMD_const_values = []
CSE_results = sp.cse(sympyexpr,
sp.numbered_symbols(outCparams.CSE_varprefix),
order='canonical')
for commonsubexpression in CSE_results[0]:
FULLTYPESTRING = "const " + TYPE + " "
if outCparams.enable_TYPE == "False":
FULLTYPESTRING = ""
if outCparams.SIMD_enable == "True":
outstring += outCparams.preindent + indent + FULLTYPESTRING + str(commonsubexpression[0]) + " = " + \
str(expr_convert_to_SIMD_intrins(commonsubexpression[1],SIMD_const_varnms,SIMD_const_values,outCparams.SIMD_debug)) + ";\n"
else:
outstring += outCparams.preindent + indent + FULLTYPESTRING + ccode_postproc(
sp.ccode(commonsubexpression[1],
commonsubexpression[0])) + "\n"
for i, result in enumerate(CSE_results[1]):
if outCparams.SIMD_enable == "True":
outstring += outtypestring + output_varname_str[i] + " = " + \
str(expr_convert_to_SIMD_intrins(result,SIMD_const_varnms,SIMD_const_values,outCparams.SIMD_debug)) + ";\n"
else:
outstring += outtypestring + ccode_postproc(
sp.ccode(result, output_varname_str[i])) + "\n"
# Step 6b.i: If SIMD_enable == True , and
# there is at least one SIMD const variable,
# then declare the SIMD_const_varnms and SIMD_const_values arrays
if outCparams.SIMD_enable == "True" and len(SIMD_const_varnms) != 0:
# Step 6a) Sort the list of definitions. Idea from:
# https://stackoverflow.com/questions/9764298/is-it-possible-to-sort-two-listswhich-reference-each-other-in-the-exact-same-w
SIMD_const_varnms, SIMD_const_values = \
(list(t) for t in zip(*sorted(zip(SIMD_const_varnms, SIMD_const_values))))
# Step 6b) Remove duplicates
uniq_varnms = superfast_uniq(SIMD_const_varnms)
uniq_values = superfast_uniq(SIMD_const_values)
SIMD_const_varnms = uniq_varnms
SIMD_const_values = uniq_values
if len(SIMD_const_varnms) != len(SIMD_const_values):
print(
"Error: SIMD constant declaration arrays SIMD_const_varnms[] and SIMD_const_values[] have inconsistent sizes!"
)
exit(1)
for i in range(len(SIMD_const_varnms)):
if outCparams.enable_TYPE == "False":
SIMD_decls += outCparams.preindent + indent + SIMD_const_varnms[
i] + " = " + SIMD_const_values[i] + ";"
else:
SIMD_decls += outCparams.preindent + indent + "const double " + outCparams.CSE_varprefix + SIMD_const_varnms[
i] + " = " + SIMD_const_values[i] + ";\n"
SIMD_decls += outCparams.preindent + indent + "const REAL_SIMD_ARRAY " + SIMD_const_varnms[
i] + " = ConstSIMD(" + outCparams.CSE_varprefix + SIMD_const_varnms[
i] + ");\n"
SIMD_decls += "\n"
# Step 7: Construct final output string
final_Ccode_output_str = commentblock
# Step 7a: Output C code in indented curly brackets if
# outCparams.includebraces = True
if outCparams.includebraces == "True":
final_Ccode_output_str += outCparams.preindent + "{\n"
final_Ccode_output_str += prestring + SIMD_decls + outstring + poststring
if outCparams.includebraces == "True":
final_Ccode_output_str += outCparams.preindent + "}\n"
# Step 8: If filename == "stdout", then output
# C code to standard out (useful for copy-paste or interactive
# mode). Otherwise output to file specified in variable name.
if filename == "stdout":
# Output to standard out (stdout; "the screen")
print(final_Ccode_output_str)
elif filename == "returnstring":
return final_Ccode_output_str
else:
# Output to the file specified by the function input parameter string 'filename':
with open(filename, outCparams.outCfileaccess) as file:
file.write(final_Ccode_output_str)
successstr = ""
if outCparams.outCfileaccess == "a":
successstr = "Appended "
elif outCparams.outCfileaccess == "w":
successstr = "Wrote "
print(successstr + "to file \"" + filename + "\"")
import commutator as comm
from sympy import I, symbols, latex, numbered_symbols
p = comm.print_group
c = comm.calculate_commutator
N = comm.Ncproduct
X_gen = numbered_symbols('X')
Y_gen = numbered_symbols('Y')
L = 20
X = [next(X_gen) for i in range(L+1)]
Y = [next(Y_gen) for i in range(L+1)]
orders = dict(zip(X+Y,[1]*2*(L+1)))
p.orders = orders
Ypart = [N(I*Y[j+1], [2*j+1,2*j+4]) for j in range(L-2)]
Xpart = [N(-X[j+1], [2*j+1,2*j+2,2*j+3,2*j+4]) for j in range(L-2)]
small = Xpart+Ypart
Zpart = [N(-I, [2*j+2,2*j+3]) for j in range(L-1)]
Jpart = Zpart
H = small +Jpart
START_ORDER = 1
END_ORDER = 8
START_PSI = N(1, 'a1')
START_IOFVARS = []
START_SPLIT_ORDERS = [0, 1]
START_NORMDICT = {}
def cse_lambdify(args, expr, **kwargs):
'''
Wrapper for sympy.lambdify which makes use of common subexpressions.
'''
# Note:
# This was expected to speed up the evaluation of the created functions.
# However performance gain is only at ca. 5%
# check input expression
if type(expr) == str:
raise TypeError('Not implemented for string input expression!')
# check given expression
try:
check_expression(expr)
except TypeError as err:
raise NotImplementedError("Only sympy expressions are allowed, yet")
# get sequence of symbols from input arguments
if type(args) == str:
args = sp.symbols(args, seq=True)
elif hasattr(args, '__iter__'):
# this may kill assumptions
args = [sp.Symbol(str(a)) for a in args]
if not hasattr(args, '__iter__'):
args = (args,)
# get the common subexpressions
cse_pairs, red_exprs = sp.cse(expr, symbols=sp.numbered_symbols('r'))
if len(red_exprs) == 1:
red_exprs = red_exprs[0]
# check if sympy found any common subexpressions
if not cse_pairs:
# if not, use standard lambdify
return sp.lambdify(args, expr, **kwargs)
# now we are looking for those arguments that are part of the reduced expression(s)
shortcuts = zip(*cse_pairs)[0]
atoms = sp.Set(red_exprs).atoms()
cse_args = [arg for arg in tuple(args) + tuple(shortcuts) if arg in atoms]
# next, we create a function that evaluates the reduced expression
cse_expr = red_exprs
# if dummify is set to False then sympy.lambdify still returns a numpy.matrix
# regardless of the possibly passed module dictionary {'ImmutableMatrix' : numpy.array}
if kwargs.get('dummify') == False:
kwargs['dummify'] = True
reduced_exprs_fnc = sp.lambdify(args=cse_args, expr=cse_expr, **kwargs)
# get the function that evaluates the replacement pairs
modules = kwargs.get('modules')
if modules is None:
modules = ['math', 'numpy', 'sympy']
namespaces = []
if isinstance(modules, (dict, str)) or not hasattr(modules, '__iter__'):
namespaces.append(modules)
else:
namespaces += list(modules)
nspace = {}
for m in namespaces[::-1]:
nspace.update(_get_namespace(m))
eval_pairs_fnc = make_cse_eval_function(input_args=args,
replacement_pairs=cse_pairs,
ret_filter=cse_args,
namespace=nspace)
# now we can wrap things together
def cse_fnc(*args):
cse_args_evaluated = eval_pairs_fnc(args)
return reduced_exprs_fnc(*cse_args_evaluated)
return cse_fnc
from sympy import I, symbols, numbered_symbols, S
import commutator as comm
p = comm.print_group
N = comm.SigmaProduct
L = 20
V, J, J2, f = symbols('V J J2 f', real=True)
h_gen = numbered_symbols('h', real=True)
hs = [next(h_gen) for i in range(L + 1)]
vardict = {'J2': J2, 'f': f, 'V': V, 'J': J}
vardict.update(zip([str(h) for h in hs], hs))
orders = {f: 1}
Js = [J, J2]
p.orders = orders
fpart = [N(-f, ("x", [j])) for j in range(1, L + 1)]
hpart = [N(-hs[j], ("z", [j])) for j in range(1, L + 1)]
Jpart = [N(-J, ("zz", [j, j + 1])) for j in range(1, L)]
small = fpart
large = Jpart + hpart
H = large + small
zeroth_order = [N(1, "z10")]
print("Hamiltonian:")
p(H, breaks=False)
("rear_.c", ((w + c)*N.x + ((rR + tR)*N.z & R.x)*R.x) & R.x),
("front_.Ixx", R.x & IFront & R.x),
("front_.Iyy", R.y & IFront & R.y),
("front_.Izz", R.z & IFront & R.z),
("front_.Ixz", R.x & IFront & R.z),
("front_.J", IFyy),
("front_.m", mH + mF),
("front_.R", rF),
("front_.r", tF),
("front_.a", FO_HO_mc.pos_from(FO) & R.x),
("front_.b", FO_HO_mc.pos_from(FO) & R.z),
("front_.c", (c*N.x + (rF + tF)*N.z) & R.x),
("ls_", ((rR + tR)*N.z + w * N.x - (rF + tF)*N.z) & R.z)]
eqns_to_cse = [rhs for lhs, rhs in expressions]
repl, redu = cse(eqns_to_cse, symbols=numbered_symbols("z"))
s = '#include "bicycle.h"\n'
s += '#include "whipple.h"\n\n'
s += 'namespace bicycle {\n\n'
s += 'void Bicycle::set_parameters(const Whipple & w)\n{\n'
s += ' double * z = new double[{0}];\n\n'.format(len(repl))
for i, r in enumerate(repl):
s += " " + re.sub(r'z(\d+)', r'z[\1]', str(r[0])) + " = "
s += re.sub(r'z(\d+)', r'z[\1]', ccode(r[1])) + ";\n"
s += "\n"
for i, (ex_i, red_i) in enumerate(zip(expressions, redu)):
s += " " + ex_i[0] + " = "
s += re.sub(r'z(\d+)', r'z[\1]', ccode(red_i))
s += ";\n"