def _add_splines(c, b1, d, b2, x):
"""Construct c*b1 + d*b2."""
if S.Zero in (b1, c):
rv = piecewise_fold(d * b2)
elif S.Zero in (b2, d):
rv = piecewise_fold(c * b1)
else:
new_args = []
# Just combining the Piecewise without any fancy optimization
p1 = piecewise_fold(c * b1)
p2 = piecewise_fold(d * b2)
# Search all Piecewise arguments except (0, True)
p2args = list(p2.args[:-1])
# This merging algorithm assumes the conditions in
# p1 and p2 are sorted
for arg in p1.args[:-1]:
expr = arg.expr
cond = arg.cond
lower = _ivl(cond, x)[0]
# Check p2 for matching conditions that can be merged
for i, arg2 in enumerate(p2args):
expr2 = arg2.expr
cond2 = arg2.cond
lower_2, upper_2 = _ivl(cond2, x)
if cond2 == cond:
# Conditions match, join expressions
expr += expr2
# Remove matching element
del p2args[i]
# No need to check the rest
break
elif lower_2 < lower and upper_2 <= lower:
# Check if arg2 condition smaller than arg1,
# add to new_args by itself (no match expected
# in p1)
new_args.append(arg2)
del p2args[i]
break
# Checked all, add expr and cond
new_args.append((expr, cond))
# Add remaining items from p2args
new_args.extend(p2args)
# Add final (0, True)
new_args.append((0, True))
rv = Piecewise(*new_args, evaluate=False)
return rv.expand()
def _add_splines(c, b1, d, b2):
"""Construct c*b1 + d*b2."""
if b1 == S.Zero or c == S.Zero:
rv = piecewise_fold(d * b2)
elif b2 == S.Zero or d == S.Zero:
rv = piecewise_fold(c * b1)
else:
new_args = []
n_intervals = len(b1.args)
assert (n_intervals == len(b2.args))
new_args.append((c * b1.args[0].expr, b1.args[0].cond))
for i in range(1, n_intervals - 1):
new_args.append((c * b1.args[i].expr + d * b2.args[i - 1].expr,
b1.args[i].cond))
new_args.append((d * b2.args[-2].expr, b2.args[-2].cond))
new_args.append(b2.args[-1])
rv = Piecewise(*new_args)
return rv.expand()
def _add_splines(c, b1, d, b2):
"""Construct c*b1 + d*b2."""
if b1 == S.Zero or c == S.Zero:
rv = piecewise_fold(d * b2)
elif b2 == S.Zero or d == S.Zero:
rv = piecewise_fold(c * b1)
else:
new_args = []
n_intervals = len(b1.args)
if n_intervals != len(b2.args):
raise ValueError("Args of b1 and b2 are not equal")
new_args.append((c * b1.args[0].expr, b1.args[0].cond))
for i in range(1, n_intervals - 1):
new_args.append((c * b1.args[i].expr + d * b2.args[i - 1].expr,
b1.args[i].cond))
new_args.append((d * b2.args[-2].expr, b2.args[-2].cond))
new_args.append(b2.args[-1])
rv = Piecewise(*new_args)
return rv.expand()
def _add_splines(c, b1, d, b2):
"""Construct c*b1 + d*b2."""
if b1 == S.Zero or c == S.Zero:
rv = piecewise_fold(d*b2)
elif b2 == S.Zero or d == S.Zero:
rv = piecewise_fold(c*b1)
else:
new_args = []
n_intervals = len(b1.args)
assert(n_intervals == len(b2.args))
new_args.append((c*b1.args[0].expr, b1.args[0].cond))
for i in range(1, n_intervals - 1):
new_args.append((
c*b1.args[i].expr + d*b2.args[i - 1].expr,
b1.args[i].cond
))
new_args.append((d*b2.args[-2].expr, b2.args[-2].cond))
new_args.append(b2.args[-1])
rv = Piecewise(*new_args)
return rv.expand()
def _add_splines(c, b1, d, b2):
"""Construct c*b1 + d*b2."""
if b1 == S.Zero or c == S.Zero:
rv = piecewise_fold(d*b2)
elif b2 == S.Zero or d == S.Zero:
rv = piecewise_fold(c*b1)
else:
new_args = []
n_intervals = len(b1.args)
if n_intervals != len(b2.args):
raise ValueError("Args of b1 and b2 are not equal")
new_args.append((c*b1.args[0].expr, b1.args[0].cond))
for i in range(1, n_intervals - 1):
new_args.append((
c*b1.args[i].expr + d*b2.args[i - 1].expr,
b1.args[i].cond
))
new_args.append((d*b2.args[-2].expr, b2.args[-2].cond))
new_args.append(b2.args[-1])
rv = Piecewise(*new_args)
return rv.expand()
def _add_splines(c, b1, d, b2):
"""Construct c*b1 + d*b2."""
if b1 == S.Zero or c == S.Zero:
rv = piecewise_fold(d * b2)
elif b2 == S.Zero or d == S.Zero:
rv = piecewise_fold(c * b1)
else:
new_args = []
# Just combining the Piecewise without any fancy optimization
p1 = piecewise_fold(c * b1)
p2 = piecewise_fold(d * b2)
# Search all Piecewise arguments except (0, True)
p2args = list(p2.args[:-1])
# This merging algorithm assumes the conditions in
# p1 and p2 are sorted
for arg in p1.args[:-1]:
# Conditional of Piecewise are And objects
# the args of the And object is a tuple of two
# Relational objects the numerical value is in the .rhs
# of the Relational object
expr = arg.expr
cond = arg.cond
lower = cond.args[0].rhs
# Check p2 for matching conditions that can be merged
for i, arg2 in enumerate(p2args):
expr2 = arg2.expr
cond2 = arg2.cond
lower_2 = cond2.args[0].rhs
upper_2 = cond2.args[1].rhs
if cond2 == cond:
# Conditions match, join expressions
expr += expr2
# Remove matching element
del p2args[i]
# No need to check the rest
break
elif lower_2 < lower and upper_2 <= lower:
# Check if arg2 condition smaller than arg1,
# add to new_args by itself (no match expected
# in p1)
new_args.append(arg2)
del p2args[i]
break
# Checked all, add expr and cond
new_args.append((expr, cond))
# Add remaining items from p2args
new_args.extend(p2args)
# Add final (0, True)
new_args.append((0, True))
rv = Piecewise(*new_args)
return rv.expand()
def _add_splines(c, b1, d, b2):
"""Construct c*b1 + d*b2."""
if b1 == S.Zero or c == S.Zero:
rv = piecewise_fold(d*b2)
elif b2 == S.Zero or d == S.Zero:
rv = piecewise_fold(c*b1)
else:
new_args = []
n_intervals = len(b1.args)
if n_intervals != len(b2.args):
# Args of b1 and b2 are not equal. Just combining the Piecewise without any fancy optimisation
p1 = piecewise_fold(c*b1)
p2 = piecewise_fold(d*b2)
# Search all Piecewise arguments except (0, True)
p2args = list(p2.args[:-1])
# This merging algorithm assume the conditions in p1 and p2 are sorted
for arg in p1.args[:-1]:
# Conditional of Piecewise are And objects
# the args of the And object is a tuple of two Relational objects
# the numerical value is in the .rhs of the Relational object
expr = arg.expr
cond = arg.cond
lower = cond.args[0].rhs
# Check p2 for matching conditions that can be merged
for i, arg2 in enumerate(p2args):
expr2 = arg2.expr
cond2 = arg2.cond
lower_2 = cond2.args[0].rhs
upper_2 = cond2.args[1].rhs
if cond2 == cond:
# Conditions match, join expressions
expr += expr2
# Remove matching element
del p2args[i]
# No need to check the rest
break
elif lower_2 < lower and upper_2 <= lower:
# Check if arg2 condition smaller than arg1, add to new_args by itself (no match expected in p1)
new_args.append(arg2)
del p2args[i]
break
# Checked all, add expr and cond
new_args.append((expr, cond))
# Add remaining items from p2args
new_args.extend(p2args)
# Add final (0, True)
new_args.append((0, True))
else:
new_args.append((c*b1.args[0].expr, b1.args[0].cond))
for i in range(1, n_intervals - 1):
new_args.append((
c*b1.args[i].expr + d*b2.args[i - 1].expr,
b1.args[i].cond
))
new_args.append((d*b2.args[-2].expr, b2.args[-2].cond))
new_args.append(b2.args[-1])
rv = Piecewise(*new_args)
return rv.expand()