I have tried executing your code in PyCharm Community Edition but i get no
output in the console. Nothing is printed to the console window.
On Sunday, 29 June 2025 at 15:28:42 UTC+1 peter.st...@gmail.com wrote:
> m = 30 0..2 sec
> m = 40 1.0 sec
> m = 50 1.2 sec
> m = 60 1.6 sec
> m = 70 2.0 sec
>
> This is on my PC, which is a good, average PC
>
>
> stephen.j...@gmail.com schrieb am Sonntag, 29. Juni 2025 um 16:08:15
> UTC+2:
>
> Thanks.
>
> Can you give me a figure for execution time, when m = 30 say?
>
>
>
> Sent from my iPhone.
>
> On 29 Jun 2025, at 13:59, Peter Stahlecker <peter.st...@gmail.com> wrote:
>
> ```
>
> # %%
> import numpy as np
> import sympy as sm
> from scipy.optimize import root
>
> m = 3
>
> w, b = sm.symbols('w, b')
> x = [sm.symbols(f'x_{i}') for i in range(m)]
> y = [sm.symbols(f'y_{i}') for i in range(m)]
>
>
> def f(w, b, x, y):
> """Stephen's function"""
> m = len(x)
> if m != len(y):
> raise ValueError("x and y must have the same length")
>
> summe = sum([sm.sqrt((w**2 * x[i] - w * (y[i] - b))**2) /
> sm.cos(sm.atan((2 * w**2 * b - w * x[i] + y[i] + b) /
> (w**2 * x[i] - w * (y[i] - b))))
> for i in range(m)])
> return summe / m
>
> dfdw = f(w, b, x, y).diff(w)
> dfdb = f(w, b, x, y).diff(b)
>
> gleichung = sm.Matrix([[dfdw, dfdb]])
> gleichung_lam = sm.lambdify((w, b, *x, *y), gleichung, cse=True)
>
> # %%
> # Set values
> x = [1.25, 2.0, 2.4]
> y = [1.75, 1.65, 2.85]
> if len(x) != m or len(y) != m:
> raise ValueError(f"x and y must have length {m}")
>
>
> def func(xx, args):
> w, b = xx[0], xx[1]
> return gleichung_lam(w, b, *args).squeeze()
>
> # Initial guess
> x0 = [1.043, -0.29]
> args = [*x, *y]
> # Iterate. This sometimes improves the result
> for _ in range(3):
> loesung = root(func, x0, args=args)
> x0 = loesung.x
> print("message from root:", loesung.message)
> print('error:', loesung.fun )
> print(f"w: {loesung.x[0]}, b: {loesung.x[1]}")
> ````
>
> This seems to work.
> I tried it for up to m = 75
> NOTE: I replaced abs(a) with sqrt(a**2) as this 'behaves' better
> numerically.
>
> stephen.j...@gmail.com schrieb am Sonntag, 29. Juni 2025 um 14:21:11
> UTC+2:
>
> Let me post a reviewed version of the equations to solve:
>
> [image: Screenshot 2025-06-29 at 13.19.38.png]
>
> On Sunday, 29 June 2025 at 12:25:54 UTC+1 peter.st...@gmail.com wrote:
>
> Clear.
>
> But you only give *one* equation: df(w,b; x, y) /dwdb = 0
>
> *Two* equations are needed to try and solve for w, b.
>
>
>
> *From:* sy...@googlegroups.com <sy...@googlegroups.com> *On Behalf Of
> *Stephen
> Learmonth
> *Sent:* Sunday, June 29, 2025 1:20 PM
> *To:* sympy <sy...@googlegroups.com>
> *Subject:* Re: [sympy] How can I solve this complex math equation using
> SymPy?
>
>
>
> x(i) can be 1.25, 2.0, 2.4 and y(i) can be 1.75, 1.65, 2.85 for i = 1 to 3.
>
> initial guess for w is +1.043 and b = -0.29.
>
>
>
> On Sunday, 29 June 2025 at 11:33:14 UTC+1 peter.st...@gmail.com wrote:
>
>
>
> What woud be the range of x(i), y(i)?
>
> What could be good initial guesses for w, b?
>
> (Needed to solve numerically.)
>
>
>
>
>
> On Sun 29. Jun 2025 at 12:11, <stephen.j...@gmail.com> wrote:
>
> If you can solve for $m = 3$ to start with that would be great.
>
>
>
>
>
> Sent from my iPhone.
>
>
>
> On 29 Jun 2025, at 11:02, stephen.j...@gmail.com wrote:
>
> Yes, it is non-linear
>
>
>
> Closed-form or numerical.
>
>
>
> Thanks.
>
>
>
> Sent from my iPhone.
>
>
>
> On 29 Jun 2025, at 10:47, Peter Stahlecker <peter.st...@gmail.com> wrote:
>
>
>
> At first glance this looks nonlinear in w and in b.
>
> Do you think there exists a closed form solution, or are you looking for a
> numerical solution given the x(i), y(i)?
>
>
>
>
>
> On Sun 29. Jun 2025 at 11:33, Stephen Learmonth <stephen.j...@gmail.com>
> wrote:
>
>
>
> <Screenshot 2025-06-29 at 10.31.04.png>
>
>
>
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