problem trying to solve an equation

[nicolas playe]

Hi all,

I try to solve a non linear equation but it conitnue runiing since 48 hours now.

``

import sympy as sp

X = sp.MatrixSymbol('X',2,2)
W = sp.MatrixSymbol('W',2,2)
Y = sp.MatrixSymbol('Y',1,2)
W_X = sp.MatMul(W,X.T)

liste = []
for i in range(W_X.shape[0]):
    row = []
    for j in range(W_X.shape[1]):
        row.append(1/(1+sp.exp(-W_X[i,j])))
       
    liste.append(row)
sigmoid = sp.Matrix(liste)

liste = []
for i in range(Y.shape[0]):
    row = []
    for j in range(Y.shape[1]):
        row.append(sp.log(Y[i,j]/(1-Y[i,j])))
    liste.append(row)
log_Y = sp.Matrix(liste)

test = sigmoid.inv()

W2 = sp.MatMul(log_Y,test).as_explicit()

liste = []
for index in range(W2.shape[1]):
    for i in range(W.shape[0]):
        for j in range(W.shape[1]):
            liste.append(W2[index].diff(W[i,j]))
           
           

p = sp.solve(liste,list(W),check=False,manual=True)

```

Do someone have an idea where i am wrong or if it is from sympy ?

Thanks a lot

[Md Affan]

I think you should   simplifythe equation and reduce the computational complexity as much as possible. It may also be helpful to check the implementation for errors or potential issues with the input parameters.

[Chris Smith]

An answer is given in https://github.com/sympy/sympy/issues/24824

[emanuel.c...@gmail.com]

I have a couple problems with this “answer”, which roughly replace the transcendental function calls (which are indeed bijections) with symbols and solving for these symbols.

The most serious is that the transformed expressions are rational functions, and he proposed solution solves for their numerators. The author failed to note that for each proposed solution, the denominators are zero, meaning that the expressions are undefined at these points. Using those propôsed solutions require serious justifications (e. g. computing the limits of the (transformed) expressions at these points).

See my answer.

​

[Alan Bromborsky]

Do you have the equations written out in LaTeX so I could understand the system better?

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[emanuel.c...@gmail.com]

This slight modification of the original answer’s code will leave you à symliste variable which can be displayed as formatted LaTeX in the Jupyter notebook. I do not know (yet) how to display a list of such expressions.

from sympy import * X = MatrixSymbol('X',2,2) W = MatrixSymbol('W',2,2) Y = MatrixSymbol('Y',1,2) W_X = MatMul(W,X.T) n = list(symbols('n:8')) reps = {} xreps = {} liste = [] k=-1 for i in range(W_X.shape[0]): row = [] for j in range(W_X.shape[1]): k += 1 row.append(n[k]) y = exp(-W_X[i,j]) reps[n[k]]=1/(1+y) xreps[exp(-W_X[i,j])] = solve(n[k] - reps[n[k]], y)[0].simplify() liste.append(row) sigmoid = Matrix(liste) k=-1 liste = [] for i in range(Y.shape[0]): row = [] for j in range(Y.shape[1]): k+=1 reps[Symbol('l%s'%k)]=log(Y[i,j]/(1-Y[i,j])) row.append(Symbol('l%s'%k)) liste.append(row) log_Y = Matrix(liste) test = sigmoid.inv() W2 = MatMul(log_Y,test).as_explicit() ireps = {v:k for k,v in reps.items()} symliste = [] for index in range(W2.shape[1]): for i in range(W.shape[0]): for j in range(W.shape[1]): # liste.append(W2[index].subs(reps).diff(W[i,j]).subs(ireps).subs(xreps)) # Defer symbolification symliste.append(W2[index].subs(reps).diff(W[i,j])) # Symboilification liste=[u.subs(ireps).subs(xreps) for u in symliste] # List of list of symbolic factors xx = dict(list(zip(list(X), symbols('x:4')))) liste = [factor(i.as_numer_denom()[0].subs(xx)).args for i in liste] # (*) liste = [[i for i in j if i not in n and i not in (-1,)+symbols('l:2')] for j in liste] print(liste)

HTH,

​