def apply(self, z, evaluation):
'%(name)s[z__]'
args = z.numerify(evaluation).get_sequence()
mpmath_function = self.get_mpmath_function(args)
result = None
# if no arguments are inexact attempt to use sympy
if all(not x.is_inexact() for x in args):
result = Expression(self.get_name(), *args).to_sympy()
result = self.prepare_mathics(result)
result = from_sympy(result)
# evaluate leaves to convert e.g. Plus[2, I] -> Complex[2, 1]
return result.evaluate_leaves(evaluation)
elif mpmath_function is None:
return
if not all(isinstance(arg, Number) for arg in args):
return
if any(arg.is_machine_precision() for arg in args):
# if any argument has machine precision then the entire calculation
# is done with machine precision.
float_args = [
arg.round().get_float_value(permit_complex=True)
for arg in args
]
if None in float_args:
return
result = self.call_mpmath(mpmath_function, float_args)
if isinstance(result, (mpmath.mpc, mpmath.mpf)):
if mpmath.isinf(result) and isinstance(result, mpmath.mpc):
result = Symbol('ComplexInfinity')
elif mpmath.isinf(result) and result > 0:
result = Expression('DirectedInfinity', Integer(1))
elif mpmath.isinf(result) and result < 0:
result = Expression('DirectedInfinity', Integer(-1))
elif mpmath.isnan(result):
result = Symbol('Indeterminate')
else:
result = Number.from_mpmath(result)
else:
prec = min_prec(*args)
d = dps(prec)
args = [
Expression('N', arg, Integer(d)).evaluate(evaluation)
for arg in args
]
with mpmath.workprec(prec):
mpmath_args = [x.to_mpmath() for x in args]
if None in mpmath_args:
return
result = self.call_mpmath(mpmath_function, mpmath_args)
if isinstance(result, (mpmath.mpc, mpmath.mpf)):
result = Number.from_mpmath(result, d)
return result
def apply(self, z, evaluation):
'%(name)s[z__]'
args = z.numerify(evaluation).get_sequence()
mpmath_function = self.get_mpmath_function(args)
result = None
# if no arguments are inexact attempt to use sympy
if all(not x.is_inexact() for x in args):
result = Expression(self.get_name(), *args).to_sympy()
result = self.prepare_mathics(result)
result = from_sympy(result)
# evaluate leaves to convert e.g. Plus[2, I] -> Complex[2, 1]
return result.evaluate_leaves(evaluation)
elif mpmath_function is None:
return
if not all(isinstance(arg, Number) for arg in args):
return
if any(arg.is_machine_precision() for arg in args):
# if any argument has machine precision then the entire calculation
# is done with machine precision.
float_args = [arg.round().get_float_value(permit_complex=True) for arg in args]
if None in float_args:
return
result = self.call_mpmath(mpmath_function, float_args)
if isinstance(result, (mpmath.mpc, mpmath.mpf)):
if mpmath.isinf(result) and isinstance(result, mpmath.mpc):
result = Symbol('ComplexInfinity')
elif mpmath.isinf(result) and result > 0:
result = Expression('DirectedInfinity', Integer(1))
elif mpmath.isinf(result) and result < 0:
result = Expression('DirectedInfinity', Integer(-1))
elif mpmath.isnan(result):
result = Symbol('Indeterminate')
else:
result = Number.from_mpmath(result)
else:
prec = min_prec(*args)
d = dps(prec)
args = [Expression('N', arg, Integer(d)).evaluate(evaluation) for arg in args]
with mpmath.workprec(prec):
mpmath_args = [x.to_mpmath() for x in args]
if None in mpmath_args:
return
result = self.call_mpmath(mpmath_function, mpmath_args)
if isinstance(result, (mpmath.mpc, mpmath.mpf)):
result = Number.from_mpmath(result, d)
return result
def __refine_results(self,
intermediate_results: List[Match],
print_results=True):
"""
validate intermediate results to 100 digit precision
:param intermediate_results: list of results from first enumeration
:param print_results: if true print status.
:return: final results.
"""
results = []
counter = 0
n_iterations = len(intermediate_results)
constant_vals = [const() for const in self.constants_generator]
for r in intermediate_results:
counter += 1
if (counter % 50) == 0 and print_results:
print(
'passed {} permutations out of {}. found so far {} matches'
.format(counter, n_iterations, len(results)))
try:
val = self.hash_table.evaluate(r.lhs_key, constant_vals)
if mpmath.isinf(val) or mpmath.isnan(val): # safety
continue
except (ZeroDivisionError, KeyError) as e:
continue
# create a_n, b_n with huge length, calculate gcf, and verify result.
an = self.create_an_series(r.rhs_an_poly, g_N_verify_terms)
bn = self.create_bn_series(r.rhs_bn_poly, g_N_verify_terms)
gcf = EfficientGCF(an, bn)
val_str = mpmath.nstr(val, g_N_verify_compare_length)
rhs_str = mpmath.nstr(gcf.evaluate(), g_N_verify_compare_length)
if val_str == rhs_str:
results.append(r)
return results
def compareValues( result1, result2 ):
if isinstance( result1, RPNMeasurement ) != isinstance( result2, RPNMeasurement ):
return False
if isinstance( result1, RPNMeasurement ):
return result1.__eq__( result2 )
else:
if isinf( result1 ):
if isinf( result2 ):
return True
else:
raise ValueError( 'unit test failed' )
print( '**** error in results comparison' )
print( type( result1 ), type( result2 ) )
print( result1, result2, 'are not equal' )
return almosteq( result1, result2 )
def mpf_matrix_fadd(A, B):
"""
Given a m x n matrix A and m x n matrix B either in numpy.matrix
or mpmath.matrix format,
this function computes the sum C = A + B exactly.
The output matrix C is always given in the MPMATH format.
Parameters
----------
A - m x n matrix
B - m x n matrix
Returns
-------
C - m x n matrix
"""
if isinstance(A, numpy.matrix):
try:
A = python2mpf_matrix(A)
except ValueError as e:
raise ValueError('Cannot compute exact sum of two matrices. %s' % e)
else:
if not isinstance(A, mpmath.matrix):
raise ValueError('Cannot compute exact sum of two matrices: unexpected input type, excpected numpy.matrix or mpmath.matrix but got %s') %type(A)
if isinstance(B, numpy.matrix):
try:
B = python2mpf_matrix(B)
except ValueError as e:
raise ValueError('Cannot compute exact sum of two matrices. %s' % e)
else:
if not isinstance(B, mpmath.matrix):
raise ValueError('Cannot compute exact sum of two matrices: unexpected input type, excpected numpy.matrix or mpmath.matrix but got %s') % type(B)
#here both A and B are mpmath matrices
#we consider that A and B are MPF matrices if their first elements are of type mpf, let's test it
if not isinstance(A[0,0], mpmath.mpf) or not isinstance(B[0,0], mpmath.mpf):
raise ValueError('Cannot compute exact product of two matrices: cannot sum complex matrices.')
#test sizes
if A.rows != B.rows or A.cols != B.cols:
raise ValueError('Cannot compute exact sum of two matrices: incorrect sizes.')
m = A.rows
n = A.cols
C = mp.zeros(m, n)
for i in range(0, m):
for j in range(0, n):
C[i,j] = mpmath.fadd(A[i,j], B[i,j], exact=True)
if mpmath.isnan(C[i,j]) or mpmath.isinf(C[i,j]):
print('WARNING: in matrix sum an abnormal number (NaN/Inf) occured: %f' % C[i,j])
return C
def default_color_function(ctx, z):
if math.isinf(z):
return (1.0, 1.0, 1.0)
if math.isnan(z):
return (0.5, 0.5, 0.5)
pi = 3.1415926535898
a = (float(math.arg(z)) + math.pi) / (2 * math.pi)
a = (a + 0.5) % 1.0
b = 1.0 - float(1 / (1.0 + abs(z)**0.3))
return hls_to_rgb(a, b, 0.8)
def compareValues(result1, result2):
if isinstance(result1, RPNMeasurement) != isinstance(
result2, RPNMeasurement):
return False
if isinstance(result1, RPNMeasurement):
return result1.__eq__(result2)
else:
if isinf(result1):
if isinf(result2):
return True
else:
print('**** error in results comparison')
print(type(result1), type(result2))
print(result1, result2, 'are not equal')
raise ValueError('unit test failed')
return almosteq(result1, result2)
def compareLists(result1, result2):
if len(result1) != len(result2):
raise ValueError('lists are not of equal length:', len(result1),
len(result2))
for i in range(0, len(result1)):
if isinstance(result1[i], RPNGenerator):
return compareLists(list(result1[i].getGenerator()), result2[i])
if isinstance(result2[i], RPNGenerator):
return compareResults(result1[i], list(result2[i].getGenerator()))
if isinstance(result1[i], list) != isinstance(result2[i], list):
raise ValueError('lists are nested to different levels:', result1,
result2)
if isinstance(result1[i], list) and isinstance(result2[i], list):
compareLists(result1[i], result2[i])
else:
if isinf(result1[i]):
if isinf(result2[i]):
return True
else:
print('**** error in results comparison')
print(type(result1[i]), type(result2[i]))
print(result1[i], result2[i], 'are not equal')
raise ValueError('unit test failed')
if not compareValues(result1[i], result2[i]):
digits = max(log10(result1[i]), log10(result2[i])) + 5
mp.dps = digits
print('**** error in results comparison')
print(type(result1[i]), type(result2[i]))
print(result1[i], result2[i], 'are not equal')
print('difference', fsub(result1[i], result2[i]))
print('difference found at index', i)
raise ValueError('unit test failed')
return True
def select():
global lastop, a, listindex, argindex, theFile
if lastop == 0:
print(
'Parse Error: SELECT. came before corresponding EXP. or LOG. at instruction '
+ str(pointer))
print(greporig(pointer))
left = val
middle = a[listindex]
right = val
if listindex > 0:
left = a[listindex - 1]
if listindex < len(a) - 1:
right = a[listindex + 1]
print('Nearby Tape Values: ' + mpmath.nstr(left) + ',' +
mpmath.nstr(middle) + ',' + mpmath.nstr(right))
sys.exit()
elif lastop == 1:
if a[argindex] != 0 or mpmath.im(
a[listindex]) != 0 or a[listindex] >= 0:
try:
a[argindex] = mpmath.power(a[argindex], a[listindex])
except OverflowError:
print(
'Number too large to represent. Try increasing precision or moving default tape value closer to 1.'
)
print(greporig(pointer))
a[argindex] = mpmath.chop(a[argindex], tol)
else:
a[argindex] = mpmath.mpc('inf')
else:
if a[listindex] == 1:
print('Tried to take a log base one at instruction ' +
str(pointer))
print(greporig(pointer))
left = val
middle = a[listindex]
right = val
if listindex > 0:
left = a[listindex - 1]
if listindex < len(a) - 1:
right = a[listindex + 1]
print('Nearby Tape Values: ' + mpmath.nstr(left) + ',' +
mpmath.nstr(middle) + ',' + mpmath.nstr(right))
sys.exit()
a[argindex] = mpmath.log(a[argindex], a[listindex])
#patch up nans when arg is infinite, since we usually want zero for the real part then
if mpmath.isinf(mpmath.im(a[argindex])) and mpmath.isnan(
mpmath.re(a[argindex])):
a[argindex] = mpmath.mpc(0, mpmath.im(a[argindex]))
a[argindex] = mpmath.chop(a[argindex], tol)
oparg = 0
def _ci_upper(table, alpha):
"""
Compute the upper end of the confidence interval.
"""
if mpmath.isinf(_sample_odds_ratio(table)):
return mpmath.mp.inf
x, total, ngood, nsample = _hypergeom_params_from_table(table)
# fnch.cdf is a decreasing function of nc, so we negate
# it in the lambda expression.
nc = _solve(lambda nc: -fnch.cdf(x, nc, total, ngood, nsample) + alpha)
return nc
def _refine_results(self,
intermediate_results: List[Match],
print_results=True):
"""
validate intermediate results to 100 digit precision
:param intermediate_results: list of results from first enumeration
:param print_results: if true print status.
:return: final results.
"""
results = []
counter = 0
n_iterations = len(intermediate_results)
constant_vals = [const() for const in self.constants_generator]
for res in intermediate_results:
counter += 1
if (counter % 50) == 0 and print_results:
print(
'passed {} permutations out of {}. found so far {} matches'
.format(counter, n_iterations, len(results)))
try:
all_matches = self.hash_table.evaluate(res.lhs_key)
# check if all values encountered are not inf or nan
if not all([
not (mpmath.isinf(val) or mpmath.isnan(val))
for val, _, _ in all_matches
]): # safety
print('Something wicked happened!')
print(
f'Encountered a NAN or inf in LHS db, at {res.lhs_key}, {constant_vals}'
)
continue
except (ZeroDivisionError, KeyError):
# if there was an exeption here, there is no need to halt the entire execution, but only note it to the
# user
continue
# create a_n, b_n with huge length, calculate gcf, and verify result.
an = self.create_an_series(res.rhs_an_poly, g_N_verify_terms)
bn = self.create_bn_series(res.rhs_bn_poly, g_N_verify_terms)
gcf = EfficientGCF(an, bn)
rhs_str = mpmath.nstr(gcf.evaluate(), g_N_verify_compare_length)
for i, match in enumerate(all_matches):
val_str = mpmath.nstr(match[0], g_N_verify_compare_length)
if val_str == rhs_str:
# This patch is ment to allow support for multiple matches for an
# LHS key, i will later be used to determind which item in the LHS dict
# was matched
results.append(RefinedMatch(*res, i, match[1], match[2]))
return results
def _refine_results(self, precise_intermediate_results, verbose=True):
"""
validate intermediate results to 100 digit precision
:param precise_intermediate_results: list of results from first enumeration
:param verbose: if true print status.
:return: final results.
"""
results = []
counter = 0
n_iterations = len(precise_intermediate_results)
constant_vals = [const() for const in self.constants_generator]
for res, rhs_str in precise_intermediate_results:
counter += 1
if (counter % 10_000 == 0 or counter == n_iterations) and verbose:
print(
'Passed {} permutations out of {}. Found so far {} matches'
.format(counter, n_iterations, len(results)))
try:
all_matches = self.hash_table.evaluate(res.lhs_key)
# check if all values encountered are not inf or nan
if not all([
not (mpmath.isinf(val) or mpmath.isnan(val))
for val, _, _ in all_matches
]): # safety
print('Something wicked happened!')
print(
f'Encountered a NAN or inf in LHS db, at {res.lhs_key}, {constant_vals}'
)
continue
except (ZeroDivisionError, KeyError):
# if there was an exception here, there is no need to halt the entire execution,
# but only note it to the user
continue
for i, match in enumerate(all_matches):
val_str = mpmath.nstr(match[0], g_N_verify_compare_length)
if val_str == rhs_str:
# This patch is meant to allow support for multiple matches for an
# LHS key, it will later be used to determine which item in the LHS dict
# was matched
results.append(RefinedMatch(*res, i, match[1], match[2]))
def mpf_get_representation(a):
"""
Given a MP floating-point number of type mpmath.mpf
this function returns a tuple (y, n) of python long integers
such that
a = y * 2**n
exactly.
If the number is +Inf, -Inf or NaN
WARNING: we get into the internal structure of MPF class.
a._mpf_ yeilds a tuple of four variables:
_mpf_[0] - sign
_mpf_[1] - mantissa
_mpf_[2] - exponent
_mpf_[3] - size of mantissa with which the number was created
Parameters
----------
a - MP number
Returns
-------
y - long
n - int or long
"""
if not isinstance(a, mpmath.mpf):
raise ValueError('Expected mpmath.mpf but got %s' % type(a))
if mpmath.isinf(a) or mpmath.isnan(a):
raise ValueError(
'Cannot get a representation of number: an Inf or NaN occured')
t = a._mpf_
if len(t) != 4:
raise ValueError(
'Something is wrong, could not get mpf number structure')
n = t[2]
y = -t[1] if t[0] else t[1]
return y, n
def drawbox():
global a, listindex, centerx, centery, pixdict, z, red, green, blue, canv, verbose
if verbose:
print('Outputting: ' + mpmath.nstr(mpmath.chop(a[listindex])))
if mpmath.isnan(a[listindex]) or mpmath.isinf(a[listindex]):
return
try:
x = int(mpmath.nint(mpmath.re(a[listindex]))) + centerx
y = int(mpmath.nint(mpmath.im(a[listindex]))) + centery
if (x, y) in pixdict:
canv.delete(pixdict[(x, y)])
del pixdict[(x, y)]
pixdict[(x, y)] = canv.create_rectangle(x * z - z + 1,
y * z - z + 1,
x * z + 1,
y * z + 1,
fill=rgb(red, green, blue),
width=0)
except OverflowError:
#the number is so huge it's not going to be displayed anyway, so just suppress the error and move on
pass
def pmean(x, p):
"""
Power (or generalized) mean of the values in the sequence x.
"""
# Special cases
if p == 0:
return gmean(x)
elif p == 1:
return mean(x)
elif p == -1:
return hmean(x)
elif mpmath.isinf(p):
with mpmath.extraprec(16):
if p > 0:
return max(mpmath.mpf(t) for t in x)
else:
return min(mpmath.mpf(t) for t in x)
with mpmath.extraprec(16):
p = mpmath.mpf(p)
return mpmath.power(mean([mpmath.mpf(t)**p for t in x]), 1/p)
def impulse_response(self,
Ts: float,
Tmax: float,
Tstart: float = 0,
K: float = 1.0,
N: int = 200,
P=20,
plot=False,
verbose=False):
'''
This function returns FDL's exp(-(L*s)^alpha) time response for the time vector t=[Tstart:Ts:Tmax].
Parameters:
-----------
: L: the dead time [s]
: alpha: the fractional power ]0,1[
: Ts: sampling time [s]
: Tmax: the end value of the time vector [s]
: Tstart: the start value [s] (default: Ts)
: K: the size of the input impulse (default: 1.0)
: N: Quality of the output (The number of summation terms) (default: 200)
: P: Estimated peak size (default: 20)
: plot: Bool, plot the impulse response (default: False)
: verbose: Bool, write to terminal (default: False)
Returns:
--------
: t: time vector [s]
: I: impulse response vector
'''
# Produce time axis: the time power will converge as t > 1
if Tstart == 0:
Tstart = Ts
t = np.arange(Tstart, Tmax, Ts)
# Prepare alpha vector
diff_start_idx = [0]
diff_stop_idx = []
type_alpha = [] # 0: cst| 1: var
if isinstance(self.alpha, float):
alpha = len(t) * [self.alpha]
diff_stop_idx.append(len(alpha))
type_alpha.append(0)
else:
alpha = self.alpha
diff_alpha = [
1 if not math.isclose(a_diff, 0.0) else 0
for a_diff in np.diff(alpha, prepend=alpha[0])
]
add_idx_bool = True
for idx, el in enumerate(diff_alpha):
if not math.isclose(el, 0.0):
if (not add_idx_bool) and (idx + 1 is not len(alpha)) and (
math.isclose(diff_alpha[idx + 1], 0)):
add_idx_bool = True
if add_idx_bool:
diff_stop_idx.append(idx)
diff_start_idx.append(idx)
add_idx_bool = False
elif not add_idx_bool:
add_idx_bool = True
diff_stop_idx.append(len(alpha))
for k in range(len(diff_start_idx)):
if sum(diff_alpha[diff_start_idx[k]:diff_stop_idx[k]]
) == diff_stop_idx[k] - diff_start_idx[k]:
type_alpha.append(1)
else:
type_alpha.append(0)
# Init parameters of loop
i = 0
summed_terms = len(t) * [0]
# Set precisions
mp.dps = 65
mp.prec = 100
while i < N:
# Init one term vector
single_term = len(t) * [0]
for k in range(len(diff_start_idx)):
if type_alpha[k]:
single_term[diff_start_idx[k]:diff_stop_idx[
k]] = self.__calculate_single_term_var_alpha__(
t[diff_start_idx[k]:diff_stop_idx[k]], i,
alpha[diff_start_idx[k]:diff_stop_idx[k]])
else:
single_term[diff_start_idx[k]:diff_stop_idx[
k]] = self.__calculate_single_term_cst_alpha__(
t[diff_start_idx[k]:diff_stop_idx[k]], i,
alpha[diff_start_idx[k]])
# Add the current iteration to the previous iterations
with warnings.catch_warnings():
warnings.filterwarnings('error')
try:
summed_terms = [
sum_el +
single_el if not math.isinf(sum_el + single_el) else
sys.float_info.min
for sum_el, single_el in zip(summed_terms, single_term)
]
except:
summed_terms = [
fsum([sum_el, single_el])
if not isinf(fsum([sum_el, single_el])) else
sys.float_info.min
for sum_el, single_el in zip(summed_terms, single_term)
]
# Update iteration counter
i += 1
if verbose and (i % 5 == 0):
# Print progress
print('Progress: {:d}%'.format(math.floor(i / N * 100)),
end='\r',
flush=True)
if verbose:
print('', end='\n', flush=True)
# Polish off the error due to cutting of the summation
q1 = [i for i, val in enumerate(summed_terms) if abs(val) > P]
q2 = [i for i, val in enumerate(summed_terms) if val < 0]
I_norm = summed_terms
if len(q1) is not 0:
#TODO: improve cleaning, no magic number 10, look at derivative?
if q1[-1] + 10 < len(I_norm):
I_norm[0:(q1[-1] + 10)] = (q1[-1] + 10) * [0]
if len(q2) is not 0:
I_norm[0:q2[-1] + 1] = (q2[-1] + 1) * [0]
I = [float(K * I_norm_el) for I_norm_el in I_norm]
if plot:
plt.figure()
plt.plot(t, I)
plt.show()
return t, I
def impulse_response(self,
Ts: float,
Tmax: float,
K=1.0,
N: int = 200,
P=20,
plot=False,
verbose=False):
'''
This function returns FDL's exp(-(L*s)^alpha) time response for the time vector t=[Ts:Ts:Tmax].
Parameters:
-----------
: L: the dead time [s]
: alpha: the fractional power ]0,1[
: Ts: sampling time [s]
: Tmax: the end value of the time vector [s]
: N: Quality of the output (The number of summation terms)
: P: Estimated peak size
Returns:
--------
: t: time vector [s]
: I: impulse response vector
'''
# Produce time axis: the time power will converge as t > 1
t = np.arange(Ts, Tmax, Ts)
if isinstance(self.alpha, float):
alpha = self.alpha
else:
alpha = self.alpha[0]
# Init parameters of loop
i = 0
summed_terms = len(t) * [0]
while i < N:
# Gamma-function of integer argument is infinite
arg = i * alpha
if arg.is_integer():
single_term = len(t) * [0]
else:
try:
# Calculate the different terms of the single_term
factorial_i = math.factorial(i)
gamma_ia = math.gamma(-i * alpha)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
time_power = [t_el**(-i * alpha - 1) for t_el in t]
L_ai = (-1)**i * self.L**(i * alpha)
const = L_ai / (factorial_i * gamma_ia)
if math.isinf(const):
raise OverflowError
single_term = [tp * const for tp in time_power]
except OverflowError:
# Check if there are any overflows
mp.dps = 65
mp.prec = 100
factorial_i_hp = factorial(i)
gamma_ia_hp = gamma(-i * alpha)
with warnings.catch_warnings():
warnings.filterwarnings('error')
try:
L_ai_hp = mpf((-1)**i * self.L**(i * alpha))
except:
if verbose:
print('Overflow stop at {}%, due to large L'.
format(math.ceil(i / N * 100)))
break
const_hp = mpf(L_ai_hp / (factorial_i_hp * gamma_ia_hp))
single_term = [tp * float(const_hp) for tp in time_power]
# Check if time power is not infinite at t < 1
q = [
i for i, val in enumerate(time_power)
if math.isinf(val)
]
for j in range(len(q)):
time_power_temp = power(t[q[j]], (-alpha * i - 1))
quotient_hp = time_power_temp * const_hp
if math.isinf(float(quotient_hp)):
single_term[q[j]] = sys.float_info.max
else:
single_term[q[j]] = float(quotient_hp)
# Add the current iteration to the previous iterations
with warnings.catch_warnings():
warnings.filterwarnings('error')
try:
summed_terms = [
sum_el +
single_el if not math.isinf(sum_el + single_el) else
sys.float_info.min
for sum_el, single_el in zip(summed_terms, single_term)
]
except:
summed_terms = [
fsum([sum_el, single_el])
if not isinf(fsum([sum_el, single_el])) else
sys.float_info.min
for sum_el, single_el in zip(summed_terms, single_term)
]
# Update iteration counter
i += 1
if verbose and (i % 5 == 0):
# Print progress
print('Progress: {:d}%'.format(math.floor(i / N * 100)),
end='\r',
flush=True)
if verbose:
print('', end='\n', flush=True)
# Polish off the error due to cutting of the summation
q1 = [i for i, val in enumerate(summed_terms) if abs(val) > P]
q2 = [i for i, val in enumerate(summed_terms) if val < 0]
I_norm = summed_terms
if len(q1) is not 0:
#TODO: improve cleaning, no magic number 10, look at derivative?
if q1[-1] + 10 < len(I_norm):
I_norm[0:(q1[-1] + 10)] = (q1[-1] + 10) * [0]
if len(q2) is not 0:
I_norm[0:q2[-1] + 1] = (q2[-1] + 1) * [0]
I = [K * I_norm_el for I_norm_el in I_norm]
if plot:
plt.figure()
plt.plot(t, I)
plt.show()
return t, I
def run_quadmath_conversions(self):
import pybind11_test_01 as p
if not p.has_quadmath():
return
try:
from mpmath import mpf, mp, workprec, isnan, isinf
except ImportError:
return
# Default precision is 53, so the conversion will fail.
self.assertRaises(TypeError, lambda: p.test_real128_conversion(mpf()))
self.assertRaises(TypeError,
lambda: p.test_real128_conversion(mpf("inf")))
self.assertRaises(TypeError,
lambda: p.test_real128_conversion(mpf("nan")))
# Set precision to quadruple.
mp.prec = 113
self.assertTrue(p.test_real128_conversion(mpf()) == 0)
self.assertTrue(p.test_real128_conversion(mpf(1)) == 1)
self.assertTrue(p.test_real128_conversion(mpf(-1)) == -1)
self.assertTrue(p.test_real128_conversion(mpf("inf")) == mpf("inf"))
self.assertTrue(p.test_real128_conversion(-mpf("inf")) == -mpf("inf"))
self.assertTrue(isnan(p.test_real128_conversion(mpf("nan"))))
self.assertTrue(
p.test_real128_conversion(
mpf("1.32321321001020301293838201938121203")) == mpf(
"1.32321321001020301293838201938121203"))
self.assertTrue(
p.test_real128_conversion(
-mpf("1.32321321001020301293838201938121203")) ==
-mpf("1.32321321001020301293838201938121203"))
self.assertTrue(
p.test_real128_conversion(mpf(2)**-16382) == mpf(2)**-16382)
self.assertTrue(
p.test_real128_conversion(-(mpf(2)**-16382)) == -(mpf(2)**-16382))
# Try subnormal numbers behaviour.
self.assertTrue(mpf(2)**-16495 != 0)
self.assertTrue(p.test_real128_conversion(mpf(2)**-16495) == mpf(0))
# Try the workprec construct.
with workprec(2000):
self.assertRaises(TypeError,
lambda: p.test_real128_conversion(mpf()))
self.assertRaises(TypeError,
lambda: p.test_real128_conversion(mpf("inf")))
self.assertRaises(TypeError,
lambda: p.test_real128_conversion(mpf("nan")))
# Test that the real128 overload is picked before the real one,
# if instantiated before.
self.assertTrue(p.test_overload(mpf(2)**-16495) == 0)
if not p.has_mpfr():
with workprec(2000):
self.assertTrue(p.test_overload(mpf(2)**-16495) != 0)
# Test we don't end up to inf if the significand has more than 113 bits.
mp.prec = 40000
foo = mpf("1.1")
with workprec(113):
self.assertFalse(isinf(p.test_real128_conversion(foo)))
# Restore prec on exit.
mp.prec = 53
def compareResults( result1, result2 ):
'''Compares two RPN expressions to make sure they produce the same result.
Does nothing if the results compare successfully, otherwise raises an
exception.'''
if isinstance( result1, RPNGenerator ):
return compareResults( list( result1.getGenerator( ) ), result2 )
if isinstance( result2, RPNGenerator ):
return compareResults( result1, list( result2.getGenerator( ) ) )
if isinstance( result1, list ) != isinstance( result2, list ):
print( '**** error in results comparison' )
print( ' result 1: ', result1 )
print( ' result 2: ', result2 )
raise ValueError( 'one result is a list, the other isn\'t' )
if isinstance( result1, str ) != isinstance( result2, str ):
print( '**** error in results comparison' )
print( ' result 1: ', result1 )
print( ' result 2: ', result2 )
raise ValueError( 'one result is a string, the other isn\'t' )
if isinstance( result1, str ) and isinstance( result2, str ):
if result1 != result2:
print( '**** error in results comparison' )
print( type( result1 ), type( result2 ) )
print( result1, result2, 'are not equal' )
raise ValueError( 'unit test failed' )
else:
return
if isinstance( result1, RPNMeasurement ) and isinstance( result2, RPNMeasurement ):
if result1 != result2:
print( '**** error in results comparison' )
print( type( result1 ), type( result2 ) )
with workdps( 50 ):
print( result1.value, result1.units, result2.value, result2.units, 'are not equal' )
raise ValueError( 'unit test failed' )
else:
return True
if isinstance( result1, list ) and isinstance( result2, list ):
if len( result1 ) != len( result2 ):
raise ValueError( 'lists are not of equal length:', len( result1 ), len( result2 ) )
for i in range( 0, len( result1 ) ):
if isinf( result1[ i ] ):
if isinf( result2[ i ] ):
return True
else:
print( '**** error in results comparison' )
print( type( result1[ i ] ), type( result2[ i ] ) )
print( result1[ i ], result2[ i ], 'are not equal' )
raise ValueError( 'unit test failed' )
if not compareValues( result1[ i ], result2[ i ] ):
digits = max( log10( result1[ i ] ), log10( result2[ i ] ) ) + 5
mp.dps = digits
print( '**** error in results comparison' )
print( type( result1[ i ] ), type( result2[ i ] ) )
print( result1[ i ], result2[ i ], 'are not equal' )
print( 'difference', fsub( result1[ i ], result2[ i ] ) )
print( 'difference found at index', i )
raise ValueError( 'unit test failed' )
else:
if not compareValues( result1, result2 ):
print( '**** error in results comparison' )
print( ' result 1: ', result1 )
print( ' result 2: ', result2 )
raise ValueError( 'unit test failed' )