def trig_replace(self, M, angle, name):
"""Replaces trigonometric expressions cos(x)
and sin(x) by CX and SX
Parameters
==========
M: var or Matrix
Object of substitution
angle: var
symbol that stands for the angle value
name: int or string
brief name X for the angle
Notes
=====
The cos(x) and sin(x) will be replaced by CX and SX,
where X is the name and x is the angle
"""
if not isinstance(angle, Expr) or angle.is_number:
return M
cos_sym, sin_sym = tools.cos_sin_syms(name)
sym_list = [(cos_sym, cos(angle)), (sin_sym, sin(angle))]
subs_dict = {}
for sym, sym_old in sym_list:
if sym_old.has(-1):
subs_dict[-sym_old] = -sym
else:
subs_dict[sym_old] = sym
self.add_to_dict(sym, sym_old)
for i1 in xrange(M.shape[0]):
for i2 in xrange(M.shape[1]):
M[i1, i2] = M[i1, i2].subs(subs_dict)
return M
def trig_replace(self, M, angle, name):
"""Replaces trigonometric expressions cos(x)
and sin(x) by CX and SX
Parameters
==========
M: var or Matrix
Object of substitution
angle: var
symbol that stands for the angle value
name: int or string
brief name X for the angle
Notes
=====
The cos(x) and sin(x) will be replaced by CX and SX,
where X is the name and x is the angle
"""
if not isinstance(angle, Expr) or angle.is_number:
return M
cos_sym, sin_sym = tools.cos_sin_syms(name)
sym_list = [(cos_sym, cos(angle)), (sin_sym, sin(angle))]
subs_dict = {}
for sym, sym_old in sym_list:
if -1 in Mul.make_args(sym_old):
sym_old = -sym_old
subs_dict[sym_old] = sym
self.add_to_dict(sym, sym_old)
for i1 in xrange(M.shape[0]):
for i2 in xrange(M.shape[1]):
M[i1, i2] = M[i1, i2].subs(subs_dict)
return M
def CS12_simp(self, sym, silent=False):
"""
Example
=======
>> print SymbolManager().CS12_simp(sympify("C2*C3 - S2*S3"))
C23 = C2*C3 - S2*S3
C23
>> print SymbolManager().CS12_simp(sympify("C2*S3*R + S2*C3*R"))
S23 = C2*S3 + S2*C3
R*S23
"""
if not sym.is_Add:
repl_dict = {}
for term in sym.atoms(Add):
repl_dict[term] = self.CS12_simp(term)
sym = sym.xreplace(repl_dict)
return sym
names, short_form = tools.trignometric_info(sym)
names = list(names)
if short_form:
names.sort()
sym2 = sym
for n1, n2 in itertools.combinations(names, 2):
if short_form:
C1, S1 = tools.cos_sin_syms(n1)
C2, S2 = tools.cos_sin_syms(n2)
np1, nm1 = tools.get_pos_neg(n1)
np2, nm2 = tools.get_pos_neg(n2)
n12 = tools.ang_sum(np1, np2, nm1, nm2)
nm12 = tools.ang_sum(np1, nm2, nm1, np2)
C12, S12 = tools.cos_sin_syms(n12)
C1m2, S1m2 = tools.cos_sin_syms(nm12)
else:
C1, S1 = cos(n1), sin(n1)
C2, S2 = cos(n2), sin(n2)
C12, S12 = cos(n1+n2), sin(n1+n2)
C1m2, S1m2 = cos(n1-n2), sin(n1-n2)
sym2 = self.try_opt(S12, S1m2, S1*C2, C1*S2, sym2, silent)
sym2 = self.try_opt(C12, C1m2, C1*C2, -S1*S2, sym2, silent)
if sym2 != sym:
return self.CS12_simp(sym2, silent)
else:
return sym
def CS12_simp(self, sym, silent=False):
"""
Example
=======
>> print SymbolManager().CS12_simp(sympify("C2*C3 - S2*S3"))
C23 = C2*C3 - S2*S3
C23
>> print SymbolManager().CS12_simp(sympify("C2*S3*R + S2*C3*R"))
S23 = C2*S3 + S2*C3
R*S23
"""
if not sym.is_Add:
repl_dict = {}
for term in sym.atoms(Add):
repl_dict[term] = self.CS12_simp(term)
sym = sym.xreplace(repl_dict)
return sym
names, short_form = tools.trignometric_info(sym)
names = list(names)
if short_form:
names.sort()
sym2 = sym
for n1, n2 in itertools.combinations(names, 2):
if short_form:
C1, S1 = tools.cos_sin_syms(n1)
C2, S2 = tools.cos_sin_syms(n2)
np1, nm1 = tools.get_pos_neg(n1)
np2, nm2 = tools.get_pos_neg(n2)
n12 = tools.ang_sum(np1, np2, nm1, nm2)
nm12 = tools.ang_sum(np1, nm2, nm1, np2)
C12, S12 = tools.cos_sin_syms(n12)
C1m2, S1m2 = tools.cos_sin_syms(nm12)
else:
C1, S1 = cos(n1), sin(n1)
C2, S2 = cos(n2), sin(n2)
C12, S12 = cos(n1 + n2), sin(n1 + n2)
C1m2, S1m2 = cos(n1 - n2), sin(n1 - n2)
sym2 = self.try_opt(S12, S1m2, S1 * C2, C1 * S2, sym2, silent)
sym2 = self.try_opt(C12, C1m2, C1 * C2, -S1 * S2, sym2, silent)
if sym2 != sym:
return self.CS12_simp(sym2, silent)
else:
return sym
def C2S2_simp(self, sym):
"""
Example
=======
>> print C2S2_simp(sympify("-C**2*RL + S*(D - RL*S)"))
D*S - RL
"""
if not sym.is_Add:
repl_dict = {}
for term in sym.atoms(Add):
repl_dict[term] = self.C2S2_simp(term)
sym = sym.xreplace(repl_dict)
return sym
names, short_form = tools.trignometric_info(sym)
for name in names:
if short_form:
cos_term, sin_term = tools.cos_sin_syms(name)
else:
cos_term, sin_term = cos(name), sin(name)
sym = self.try_opt(tools.ONE, None, sin_term**2, cos_term**2, sym)
return sym
def C2S2_simp(self, sym):
"""
Example
=======
>> print C2S2_simp(sympify("-C**2*RL + S*(D - RL*S)"))
D*S - RL
"""
if not sym.is_Add:
repl_dict = {}
for term in sym.atoms(Add):
repl_dict[term] = self.C2S2_simp(term)
sym = sym.xreplace(repl_dict)
return sym
names, short_form = tools.trignometric_info(sym)
for name in names:
if short_form:
cos_term, sin_term = tools.cos_sin_syms(name)
else:
cos_term, sin_term = cos(name), sin(name)
sym = self.try_opt(
tools.ONE, None, sin_term**2, cos_term**2, sym
)
return sym
