def compile_function_matlab(equations, symbols, arg_names, output_names=None, funname='anonymous'):
from function_compiler_ast import std_date_symbol
from function_compiler_ast import StandardizeDates
from collections import OrderedDict
table = OrderedDict()
aa = arg_names
# if output_names is not None:
# aa = arg_names + [output_names]
for a in aa:
symbol_group = a[0]
date = a[1]
an = a[2]
for b in symbols[symbol_group]:
index = symbols[symbol_group].index(b)
table[(b,date)] = (an, index)
table_symbols = { k: (std_date_symbol(*k)) for k in table.keys() }
code_preamble = ""
for k,v in table.iteritems():
std_name = table_symbols[k]
if v[0] != 'p':
code_preamble += "{} = {}(:,{});\n".format(std_name, v[0], v[1]+1)
else:
code_preamble += "{} = {}({});\n".format(std_name, v[0], v[1]+1)
if output_names:
out_group, out_time, out_s = output_names
else:
out_s = 'out'
expressions = []
code_expr = ""
import sympy
for i,eq in enumerate(equations):
expr = str_to_expr(eq)
sd = StandardizeDates(symbols, arg_names)
sexpr = sd.visit(expr)
expressions.append(sexpr)
eq_string = (print_matlab(sexpr))
if output_names is None:
code_expr += "out(:,{}) = {} ;\n".format(i+1, eq_string)
else:
out_symbol = symbols[out_group][i]
out_name = std_date_symbol(out_symbol, out_time)
code_expr += "{} = {} ;\n".format(out_name, eq_string)
code_expr += "{}(:,{}) = {} ;\n".format(out_s,i+1, out_name)
## temporary code to differentiate equations using sympy
if output_names:
# solve triangular system
sympy_names = [sympy.Symbol(e) for e in symbols[out_group]]
eq_dict = OrderedDict()
for i,name in enumerate(sympy_names):
eq = sympy.sympify(codegen.to_source(expressions[i]))
eq_dict[name] = eq.subs(eq_dict)
sympy_equations = eq_dict.values()
else:
sympy_equations = [sympy.sympify(codegen.to_source(expr)) for expr in expressions]
all_derivatives = OrderedDict()
for agn in arg_names:
sym_group = agn[0]
date = agn[1]
short_sym_group = agn[2]
sym_names = [std_date_symbol(s, date) for s in symbols[sym_group]]
dvals = []
for eq in sympy_equations:
deq = []
for s in sym_names:
sym = sympy.Symbol(s)
ddif = (eq.diff(sym))
deq.append(ast.parse(str(ddif)).body[0])
dvals.append(deq)
all_derivatives[short_sym_group] = dvals
## end of temporary code
code_dexpr = ""
for k,derivs in all_derivatives.iteritems():
code_dexpr += '\n%derivatives w.r.t {}\n'.format(k)
assign_name = "d_{}".format(k)
code_dexpr += '{} = zeros(N,{},{});\n'.format(assign_name, len(derivs), len(derivs[0]))
for i in range(len(derivs)):
for j in range(len(derivs[0])):
eq = derivs[i][j]
ss = print_matlab(eq)
if ss != '0':
code_dexpr += "{}(:,{},{}) = {};\n".format(assign_name, i+1, j+1, ss)
code_dexpr += '\n'
code = """\
function [{out_s}, {dout_s}] = {funname}({args_list})
%% preamble
{preamble}
N = size({first_arg},1);
out = zeros(N,{n_out});
%% equations
{equations}
%% derivatives
if nargout > 1
{dequations}
end
end
""".format(
out_s = out_s,
dout_s = str.join(', ', ["d_{}".format(e[2]) for e in arg_names]),
preamble = code_preamble,
funname = funname,
args_list = str.join(', ', [e[2] for e in arg_names]),
n_out = len(equations),
first_arg = arg_names[0][2],
equations = code_expr,
dequations = code_dexpr
)
return code
def compile_function_matlab(equations,
symbols,
arg_names,
output_names=None,
funname='anonymous'):
from function_compiler_ast import std_date_symbol
from function_compiler_ast import StandardizeDates
from collections import OrderedDict
table = OrderedDict()
aa = arg_names
# if output_names is not None:
# aa = arg_names + [output_names]
for a in aa:
symbol_group = a[0]
date = a[1]
an = a[2]
for b in symbols[symbol_group]:
index = symbols[symbol_group].index(b)
table[(b, date)] = (an, index)
table_symbols = {k: (std_date_symbol(*k)) for k in table.keys()}
code_preamble = ""
for k, v in table.iteritems():
std_name = table_symbols[k]
if v[0] != 'p':
code_preamble += "{} = {}(:,{});\n".format(std_name, v[0],
v[1] + 1)
else:
code_preamble += "{} = {}({});\n".format(std_name, v[0], v[1] + 1)
if output_names:
out_group, out_time, out_s = output_names
else:
out_s = 'out'
code_expr = ""
for i, eq in enumerate(equations):
expr = str_to_expr(eq)
sd = StandardizeDates(symbols, arg_names)
sexpr = sd.visit(expr)
eq_string = (print_matlab(sexpr))
if output_names is None:
code_expr += "out(:,{}) = {} ;\n".format(i + 1, eq_string)
else:
out_symbol = symbols[out_group][i]
out_name = std_date_symbol(out_symbol, out_time)
code_expr += "{} = {} ;\n".format(out_name, eq_string)
code_expr += "{}(:,{}) = {} ;\n".format(out_s, i + 1, out_name)
code = """\
function [{out_s}] = {funname}({args_list})
{preamble}
N = size({first_arg},1);
out = zeros(N,{n_out});
{equations}
end
""".format(out_s=out_s,
preamble=code_preamble,
funname=funname,
args_list=str.join(', ', [e[2] for e in arg_names]),
n_out=len(equations),
first_arg=arg_names[0][2],
equations=code_expr)
return code
def compile_higher_order_function(eqs, syms, params, order=2, funname='anonymous',
return_code=False, compile=False):
'''From a list of equations and variables, define a multivariate functions with higher order derivatives.'''
from function_compiler_ast import StandardizeDatesSimple, std_date_symbol
all_vars = syms + [(p,0) for p in params]
sds = StandardizeDatesSimple(all_vars)
if isinstance(eqs[0], str):
# elif not isinstance(eqs[0], sympy.Basic):
# assume we have ASTs
eqs = [ast.parse(eq).body[0] for eq in eqs]
eqs_std = [sds.visit(eq) for eq in eqs]
eqs_sym = [ast_to_sympy(eq) for eq in eqs_std]
else:
eqs_sym = eqs
symsd = [std_date_symbol(a,b) for a,b in syms]
paramsd = [std_date_symbol(a,0) for a in params]
D = higher_order_diff(eqs_sym, symsd, order=order)
txt = """def {funname}(x, p, order=1):
import numpy
from numpy import log, exp, tan
""".format(funname=funname)
for i in range(len(syms)):
txt += " {} = x[{}]\n".format(symsd[i], i)
txt += "\n"
for i in range(len(params)):
txt += " {} = p[{}]\n".format(paramsd[i], i)
txt += "\n out = numpy.zeros({})".format(len(eqs))
for i in range(len(eqs)):
txt += "\n out[{}] = {}".format(i, D[0][i])
txt += """
if order == 0:
return out
"""
if order >= 1:
# Jacobian
txt += " out_1 = numpy.zeros(({},{}))\n".format(len(eqs), len(syms))
for i in range(len(eqs)):
for j in range(len(syms)):
val = D[1][i,j]
if val != 0:
txt += " out_1[{},{}] = {}\n".format(i,j,D[1][i,j])
txt += """
if order == 1:
return [out, out_1]
"""
if order >= 2:
# Hessian
txt += " out_2 = numpy.zeros(({},{},{}))\n".format(len(eqs), len(syms), len(syms))
for n in range(len(eqs)):
for i in range(len(syms)):
for j in range(len(syms)):
val = D[2][n,i,j]
if val is not None:
if val != 0:
txt += " out_2[{},{},{}] = {}\n".format(n,i,j,D[2][n,i,j])
else:
i1, j1 = sorted( (i,j) )
if D[2][n,i1,j1] != 0:
txt += " out_2[{},{},{}] = out_2[{},{},{}]\n".format(n,i,j,n,i1,j1)
txt += """
if order == 2:
return [out, out_1, out_2]
"""
if order >= 3:
# Hessian
txt += " out_3 = numpy.zeros(({},{},{},{}))\n".format(len(eqs), len(syms), len(syms), len(syms))
for n in range(len(eqs)):
for i in range(len(syms)):
for j in range(len(syms)):
for k in range(len(syms)):
val = D[3][n,i,j,k]
if val is not None:
if val != 0:
txt += " out_3[{},{},{},{}] = {}\n".format(n,i,j,k,D[3][n,i,j,k])
else:
i1, j1, k1 = sorted( (i,j,k) )
if D[3][n,i1,j1,k1] != 0:
txt += " out_3[{},{},{},{}] = out_3[{},{},{},{}]\n".format(n,i,j,k,n,i1,j1,k1)
txt += """
if order == 3:
return [out, out_1, out_2, out_3]
"""
if return_code:
return txt
else:
d = {}
d['division'] = division
exec(txt, d)
fun = d[funname]
if compile:
raise Exception("Not implemented.")
return fun
def compile_function_matlab(equations, symbols, arg_names, output_names=None, funname='anonymous'):
from function_compiler_ast import std_date_symbol
from function_compiler_ast import StandardizeDates
from collections import OrderedDict
table = OrderedDict()
aa = arg_names
# if output_names is not None:
# aa = arg_names + [output_names]
for a in aa:
symbol_group = a[0]
date = a[1]
an = a[2]
for b in symbols[symbol_group]:
index = symbols[symbol_group].index(b)
table[(b,date)] = (an, index)
table_symbols = { k: (std_date_symbol(*k)) for k in table.keys() }
code_preamble = ""
for k,v in table.iteritems():
std_name = table_symbols[k]
if v[0] != 'p':
code_preamble += "{} = {}(:,{});\n".format(std_name, v[0], v[1]+1)
else:
code_preamble += "{} = {}({});\n".format(std_name, v[0], v[1]+1)
if output_names:
out_group, out_time, out_s = output_names
else:
out_s = 'out'
code_expr = ""
for i,eq in enumerate(equations):
expr = str_to_expr(eq)
sd = StandardizeDates(symbols, arg_names)
sexpr = sd.visit(expr)
eq_string = (print_matlab(sexpr))
if output_names is None:
code_expr += "out(:,{}) = {} ;\n".format(i+1, eq_string)
else:
out_symbol = symbols[out_group][i]
out_name = std_date_symbol(out_symbol, out_time)
code_expr += "{} = {} ;\n".format(out_name, eq_string)
code_expr += "{}(:,{}) = {} ;\n".format(out_s,i+1, out_name)
code = """\
function [{out_s}] = {funname}({args_list})
{preamble}
N = size({first_arg},1);
out = zeros(N,{n_out});
{equations}
end
""".format(
out_s = out_s,
preamble = code_preamble,
funname = funname,
args_list = str.join(', ', [e[2] for e in arg_names]),
n_out = len(equations),
first_arg = arg_names[0][2],
equations = code_expr
)
return code
