Find unknown variable in set of equations in numpy

Question

I have six equations and six variables. I am solving it through numpy using np.linalg.solve(a, b). The result gives me 6 values but I don't know which value is x1,x2... unknown variable result satisfies only one equation that is

                          x1+x2+x3+x4+x5+x6=1.

but it does not satisfies other equation. I am considering that x[0] is x1. x[1] is x2 but which is not true because other equation not satisfies when I put according to this format. How can I find which is x1,x2,x3,x4,x5,x6 in returning list? My code is

import numpy as np
a = np.array([[-1,0,0,0.25,1,0.33], [0.33,-1,0,0,0,0.33], [0.33,0.25,-1,0.25,0,0] , [0,0.25,0.5,-1,0,0], [0,0.25,0.5,0.25,-1,0.33], [1,1,1,1,1,1]])
b = np.array([0,0,0,0,0,1])
x = np.linalg.solve(a, b)
print x

answer is:

[ 0.2644666   0.13780854  0.14895903  0.10893165  0.18669913  0.15313504]

thanks. actually i did not know how to do formating. by the way thanks — DANISH TAYYIB, Oct 26 '17 at 10:02
Why do you say it does not satisfy the other equations? I'd say you're wrong there. — Ignacio Vergara Kausel, Oct 26 '17 at 10:05
Then you're doing it wrong or interpreting it wrong. Check my answer below. — Ignacio Vergara Kausel, Oct 26 '17 at 10:14
there is no issue with the float values i put values in equation x1+x2+x3+x4+x5+x6=1. sum of list is 1 which means it is correct but when i put in equation (-1) x1 + (0) x2+ (0) x3+( 0.25) x4+ (1) x5+ (0.33) x6=0 considering that x[0] is x1, x[1] is x2 and so own.... — DANISH TAYYIB, Oct 26 '17 at 10:23
Yes, and `b[0] = 0`.. so what else are you expecting? It's the solution you asked for. — Ignacio Vergara Kausel, Oct 26 '17 at 10:24
I just want to know that which index s x1 value and which value is x2 and so own... — DANISH TAYYIB, Oct 26 '17 at 10:24
i have tried this : eq_1 = (-1 * x[0]) + (.25 * x[3]) + x[4] + (0.33 * x[5] ) print eq_1 — DANISH TAYYIB, Oct 26 '17 at 10:29
And it is! Which number do you get instead? Exactly, will you please see my answer and the referred link please. You have a problem understanding float point arithmetic. — Ignacio Vergara Kausel, Oct 26 '17 at 10:30
i did not understand that question. can you please tell me just that it is zero or not??? — DANISH TAYYIB, Oct 26 '17 at 10:32
For the computer 2.77555756156e-17 is basically 0. Because of how floating point works that's the level of precision you have. — Ignacio Vergara Kausel, Oct 26 '17 at 10:33
if i ma not wront that answer mean this value is very very small and we consider it zero beacuse 2.77555756156e-17 is equal to 0.000000000000000027755 which means zero....??? — DANISH TAYYIB, Oct 26 '17 at 10:34
ok thank you very much . I have spoiled much time to solve understand the hardware problem . actually that is not problem that is a level of precision.:) — DANISH TAYYIB, Oct 26 '17 at 10:36

Ignacio Vergara Kausel · Answer 1 · 2017-10-26T10:13:44.260

0

If you do

for i in range(6):
    (a[i]*x).sum()

You'll get that the first five elements are of the order of e-17 (basically 0 in float representation) and the last one is 1 as specified by the b vector you provided.

I believe your problem is not understanding the issues concerning float arithmetic. You can refer to this question for more information.

edited Oct 26 '17 at 10:13

answered Oct 26 '17 at 10:07

Ignacio Vergara Kausel

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Find unknown variable in set of equations in numpy

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