I am trying to solve an overdefined system of equations nummerically with Sympy nsolve, but I keep getting lambdify TypeErrors.
import sympy as sp
f25 = 61900.
f50 = 66200.
f75 = 70700.
f90 = 77700.
#mu = sp.Symbol('mu')
#sigma = sp.Symbol('sigma')
mu = sp.var('mu')
sigma = sp.var('sigma')
def f(x):
f = (1 / sp.sqrt(2 * sp.pi * sp.Pow(sigma,2))) * sp.euler(-1 * (sp.Pow(x - mu,2)) / (2 * sp.Pow(sigma,2)))
return f
f1 = f(f25) - 0.25
f2 = f(f50) - 0.50
f3 = f(f75) - 0.75
f4 = f(f90) - 0.90
sp.nsolve((f1, f2, f3, f4), (mu, sigma), (66000, 10000))
returns
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
File ~\Anaconda3\lib\site-packages\mpmath\calculus\optimization.py:937, in findroot(ctx, f, x0, solver, tol, verbose, verify, **kwargs)
936 try:
--> 937 fx = f(*x0)
938 multidimensional = isinstance(fx, (list, tuple, ctx.matrix))
File <lambdifygenerated-5>:2, in _lambdifygenerated(mu, sigma)
1 def _lambdifygenerated(mu, sigma):
----> 2 return ImmutableDenseMatrix([[mpf((1, 1, -2, 1)) + (mpf(1)/mpf(2))*sqrt(2)*euler(-mpf((0, 239475625, 3, 28))*(1 - mpf((0, 2384070316472963, -67, 52))*mu)**2/sigma**2)/(sqrt(pi)*sqrt(sigma**2))], [mpf((1, 1, -1, 1)) + (mpf(1)/mpf(2))*sqrt(2)*euler(-mpf((0, 68475625, 5, 27))*(1 - mpf((0, 139325861583909, -63, 47))*mu)**2/sigma**2)/(sqrt(pi)*sqrt(sigma**2))], [mpf((1, 3, -2, 2)) + (mpf(1)/mpf(2))*sqrt(2)*euler(-mpf((0, 312405625, 3, 29))*(1 - mpf((0, 8349304248355101, -69, 53))*mu)**2/sigma**2)/(sqrt(pi)*sqrt(sigma**2))], [mpf((1, 8106479329266893, -53, 53)) + (mpf(1)/mpf(2))*sqrt(2)*euler(-mpf((0, 377330625, 3, 29))*(1 - mpf((0, 3798557338215609, -68, 52))*mu)**2/sigma**2)/(sqrt(pi)*sqrt(sigma**2))]])
File ~\Anaconda3\lib\site-packages\mpmath\ctx_mp_python.py:346, in _constant.__call__(self, prec, dps, rounding)
345 if dps: prec = dps_to_prec(dps)
--> 346 return self.context.make_mpf(self.func(prec, rounding))
File ~\Anaconda3\lib\site-packages\mpmath\libmp\libelefun.py:116, in def_mpf_constant.<locals>.f(prec, rnd)
115 wp = prec + 20
--> 116 v = fixed(wp)
117 if rnd in (round_up, round_ceiling):
File ~\Anaconda3\lib\site-packages\mpmath\libmp\libelefun.py:97, in constant_memo.<locals>.g(prec, **kwargs)
96 if prec <= memo_prec:
---> 97 return f.memo_val >> (memo_prec-prec)
98 newprec = int(prec*1.05+10)
TypeError: unsupported operand type(s) for >>: 'int' and 'mpf'
During handling of the above exception, another exception occurred:
TypeError Traceback (most recent call last)
Cell In[3], line 24
21 f3 = f(f75) - 0.75
22 f4 = f(f90) - 0.90
---> 24 sp.nsolve((f1, f2, f3, f4), (mu, sigma), (66000, 10000))
File ~\Anaconda3\lib\site-packages\sympy\utilities\decorator.py:88, in conserve_mpmath_dps.<locals>.func_wrapper(*args, **kwargs)
86 dps = mpmath.mp.dps
87 try:
---> 88 return func(*args, **kwargs)
89 finally:
90 mpmath.mp.dps = dps
File ~\Anaconda3\lib\site-packages\sympy\solvers\solvers.py:3000, in nsolve(dict, *args, **kwargs)
2998 J = lambdify(fargs, J, modules)
2999 # solve the system numerically
-> 3000 x = findroot(f, x0, J=J, **kwargs)
3001 if as_dict:
3002 return [dict(zip(fargs, [sympify(xi) for xi in x]))]
File ~\Anaconda3\lib\site-packages\mpmath\calculus\optimization.py:940, in findroot(ctx, f, x0, solver, tol, verbose, verify, **kwargs)
938 multidimensional = isinstance(fx, (list, tuple, ctx.matrix))
939 except TypeError:
--> 940 fx = f(x0[0])
941 multidimensional = False
942 if 'multidimensional' in kwargs:
TypeError: _lambdifygenerated() missing 1 required positional argument: 'sigma'
I have tried to define my variables as both sp.Symbol and sp.var.
I have tried to bracket the variables to solve for: sp.nsolve((f1, f2, f3, f4), [(mu, sigma)], (66000, 10000)). But that just gives me a new TypeError: TypeError: nsolve expected exactly 1 guess vectors, got 2
Bracketing my input guess values yields yet another TypeError: sp.nsolve((f1, f2, f3, f4), [(mu, sigma)], [(66000, 10000)]). TypeError: cannot create mpf from (66000, 10000).
As I am sure you can tell I have all but given up, and are going at it brute force "monkeys and typewriters" style.
Can anyone offer up any advice?
Looking at your f(x), they appear to be some kind of normal statistical distribution. If so, you might want to replace sp.euler with sp.E ** , where sp.E is Euler's number.