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System of 3 non-linear equations in 3 unknowns (how-to-solve?) - samsonite - Mar-23-2019
This detailed screenshot http://imgbox.com/qFBxoHWd shows how I've solved, in the old past, the system by means of a MatLab function (fsolve), and I'ld like to know if a similar (short) way exists in Python.
Algorithms are listed below:
Output:% ------ system of 3 non linear equations ----------
%
function y=f(x)
y=zeros(3,1);
rad = pi/180;
l1 = 150.210355; s1 = -38.913290; d1 = -11.185833;
l2 = 180.308440; s2 = -14.878290; d2 = 14.545555;
l3 = 223.495977; s3 = 20.492543; d3 = -8.679444;
%---------------------------------------------------
l1 = l1 * rad; s1 = s1 * rad; t1 = tan(d1 * rad);
l2 = l2 * rad; s2 = s2 * rad; t2 = tan(d2 * rad);
l3 = l3 * rad; s3 = s3 * rad; t3 = tan(d3 * rad);
% --------------------------------------------------
y(1)= sin(x(1)+s1)-tan(x(3)+l1)*(cos(x(1)+s1)* sin(x(2))- t1* cos(x(2)));
y(2)= sin(x(1)+s2)-tan(x(3)+l2)*(cos(x(1)+s2)* sin(x(2))- t2* cos(x(2)));
y(3)= sin(x(1)+s3)-tan(x(3)+l3)*(cos(x(1)+s3)* sin(x(2))- t3* cos(x(2)));
endfunction
rad = pi/180;
[x,fval,info]=fsolve(@f,[10*rad;50*rad;0*rad]) % #3 starting values in radians
la= x(1)/rad
fi= x(2)/rad
eps= x(3)/rad
% ---------------- OUTPUT ---------------------
x =
2.6180e-001
6.4577e-001
5.6800e-008
fval =
1.0311e-008
4.9066e-008
5.0822e-008May I have some drifts to reach the goal? Thanks in advance
Edit. For short way I mean the use of an intrinsic function to avoid the classical procedure via an iterative method and related jacobian matrix.
RE: System of 3 non-linear equations in 3 unknowns (how-to-solve?) - scidam - Mar-23-2019
Your code would be almost the same, if you rewrote it in Python.
from math import pi, sin, tan, cos
from scipy.optimize import fsolve
def equations(x):
rad = pi / 180;
l1 = 150.210355; s1 = -38.913290; d1 = -11.185833;
l2 = 180.308440; s2 = -14.878290; d2 = 14.545555;
l3 = 223.495977; s3 = 20.492543; d3 = -8.679444;
l1 = l1 * rad; s1 = s1 * rad; t1 = tan(d1 * rad);
l2 = l2 * rad; s2 = s2 * rad; t2 = tan(d2 * rad);
l3 = l3 * rad; s3 = s3 * rad; t3 = tan(d3 * rad);
return (sin(x[0]+s1)-tan(x[2]+l1)*(cos(x[0]+s1)* sin(x[1])- t1* cos(x[1])),
sin(x[0]+s2)-tan(x[2]+l2)*(cos(x[0]+s2)* sin(x[1])- t2* cos(x[1])),
sin(x[0]+s3)-tan(x[2]+l3)*(cos(x[0]+s3)* sin(x[1])- t3* cos(x[1])))
fsolve(equations, [10 * pi / 180, 50 * pi / 180, 0])Output:array([2.61799394e-01, 6.45771810e-01, 1.20245548e-08]); to separate statements, so, it is desirable to rewrite each assignment in a new line.
RE: System of 3 non-linear equations in 3 unknowns (how-to-solve?) - samsonite - Mar-23-2019
Wonderful solution, scidam! Just added the output of coords in degrees. Thank you very much, and cheers
# ---------- sist_3eq.py -----------
from math import pi, sin, tan, cos
from scipy.optimize import fsolve
def equations(x):
rad = pi / 180;
l1 = 150.210355; s1 = -38.913290; d1 = -11.185833;
l2 = 180.308440; s2 = -14.878290; d2 = 14.545555;
l3 = 223.495977; s3 = 20.492543; d3 = -8.679444;
l1 = l1 * rad; s1 = s1 * rad; t1 = tan(d1 * rad);
l2 = l2 * rad; s2 = s2 * rad; t2 = tan(d2 * rad);
l3 = l3 * rad; s3 = s3 * rad; t3 = tan(d3 * rad);
return (sin(x[0]+s1)-tan(x[2]+l1)*(cos(x[0]+s1)* sin(x[1])- t1* cos(x[1])),
sin(x[0]+s2)-tan(x[2]+l2)*(cos(x[0]+s2)* sin(x[1])- t2* cos(x[1])),
sin(x[0]+s3)-tan(x[2]+l3)*(cos(x[0]+s3)* sin(x[1])- t3* cos(x[1])))
print(fsolve(equations, [10 * pi / 180, 50 * pi / 180, 0]))
a= fsolve(equations, [10 * pi / 180, 50 * pi / 180, 0])
print(a[0]*180/pi,a[1]*180/pi) # coords in degrees
# ------- OUTPUT ----------
# C:\Training>python sist_3eq.py
# [2.61799394e-01 6.45771810e-01 1.20245548e-08]
# 15.00000038215297 36.99999924200017
# -------------------------