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1

$begingroup$

I'm trying to find the intersection of lines $y=a_1x+b_1$ and $y=a_2x+b_2$ using numpy.linalg.solve(). What I can't get my head around is how to correctly make $A$ a square matrix for solve() to work. I'm familiar with solving linear equation systems, but there's something here I don't get.

What I'd like to do is:

def meeting_lines(a1, b1, a2, b2):
 a = np.array([[a1], [a2]])
 b = np.array([b1, b2])
 return np.linalg.solve(a, b)

def main():
 a1=1
 b1=4
 a2=3
 b2=2

 y, x = meeting_lines(a1, b1, a2, b2)

Where I expect $y=-3$ and $x=1$. However, this fails with numpy.linalg.LinAlgError: Last 2 dimensions of the array must be square.

Thank you very much for your help, trying to figure this out has messed up my day already!

numpy linear-algebra

share|improve this question

asked Apr 1 at 12:47

bassebasse

875

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  NB: I must use numpy.linalg.solve().
  $endgroup$
  – basse
  Apr 1 at 12:49
  

  
  
  
  

add a comment | 

1

$begingroup$

I'm trying to find the intersection of lines $y=a_1x+b_1$ and $y=a_2x+b_2$ using numpy.linalg.solve(). What I can't get my head around is how to correctly make $A$ a square matrix for solve() to work. I'm familiar with solving linear equation systems, but there's something here I don't get.

What I'd like to do is:

def meeting_lines(a1, b1, a2, b2):
 a = np.array([[a1], [a2]])
 b = np.array([b1, b2])
 return np.linalg.solve(a, b)

def main():
 a1=1
 b1=4
 a2=3
 b2=2

 y, x = meeting_lines(a1, b1, a2, b2)

Where I expect $y=-3$ and $x=1$. However, this fails with numpy.linalg.LinAlgError: Last 2 dimensions of the array must be square.

Thank you very much for your help, trying to figure this out has messed up my day already!

numpy linear-algebra

share|improve this question

asked Apr 1 at 12:47

bassebasse

875

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  NB: I must use numpy.linalg.solve().
  $endgroup$
  – basse
  Apr 1 at 12:49
  

  
  
  
  

add a comment | 

$begingroup$

I'm trying to find the intersection of lines $y=a_1x+b_1$ and $y=a_2x+b_2$ using numpy.linalg.solve(). What I can't get my head around is how to correctly make $A$ a square matrix for solve() to work. I'm familiar with solving linear equation systems, but there's something here I don't get.

What I'd like to do is:

def meeting_lines(a1, b1, a2, b2):
 a = np.array([[a1], [a2]])
 b = np.array([b1, b2])
 return np.linalg.solve(a, b)

def main():
 a1=1
 b1=4
 a2=3
 b2=2

 y, x = meeting_lines(a1, b1, a2, b2)

Where I expect $y=-3$ and $x=1$. However, this fails with numpy.linalg.LinAlgError: Last 2 dimensions of the array must be square.

Thank you very much for your help, trying to figure this out has messed up my day already!

numpy linear-algebra

share|improve this question

asked Apr 1 at 12:47

bassebasse

875

$endgroup$

def meeting_lines(a1, b1, a2, b2):
 a = np.array([[a1], [a2]])
 b = np.array([b1, b2])
 return np.linalg.solve(a, b)

def main():
 a1=1
 b1=4
 a2=3
 b2=2

 y, x = meeting_lines(a1, b1, a2, b2)

share|improve this question

asked Apr 1 at 12:47

bassebasse

875

share|improve this question

asked Apr 1 at 12:47

bassebasse

875

asked Apr 1 at 12:47

bassebasse

875

asked Apr 1 at 12:47

bassebasse

875

1 Answer
1

active

oldest

votes

1

$begingroup$

You should formulate your lines as follows to have $(x, y)$ as unknowns:
$$beginalign
left.beginmatrix
a_1x-y=-b_1\
a_2x-y=-b_2
endmatrixright}
rightarrow
overbrace
beginbmatrix
a_1& -1\
a_2& -1
endbmatrix
^boldsymbola
overbrace
beginbmatrix
x\
y
endbmatrix
^boldsymbolx
=
overbrace
beginbmatrix
-b_1\
-b_2
endbmatrix
^boldsymbolb
endalign$$
Therefore, the code should be:

import numpy as np

def meeting_lines(a1, b1, a2, b2):
 a = np.array([[a1, -1], [a2, -1]])
 b = np.array([-b1, -b2])
 return np.linalg.solve(a, b)

a1=1
b1=4
a2=3
b2=2
x, y = meeting_lines(a1, b1, a2, b2)
print(x, y)

which outputs:

1.0 5.0

share|improve this answer

answered Apr 1 at 13:52

EsmailianEsmailian

3,311420

$endgroup$

add a comment | 

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1

$begingroup$

You should formulate your lines as follows to have $(x, y)$ as unknowns:
$$beginalign
left.beginmatrix
a_1x-y=-b_1\
a_2x-y=-b_2
endmatrixright}
rightarrow
overbrace
beginbmatrix
a_1& -1\
a_2& -1
endbmatrix
^boldsymbola
overbrace
beginbmatrix
x\
y
endbmatrix
^boldsymbolx
=
overbrace
beginbmatrix
-b_1\
-b_2
endbmatrix
^boldsymbolb
endalign$$
Therefore, the code should be:

import numpy as np

def meeting_lines(a1, b1, a2, b2):
 a = np.array([[a1, -1], [a2, -1]])
 b = np.array([-b1, -b2])
 return np.linalg.solve(a, b)

a1=1
b1=4
a2=3
b2=2
x, y = meeting_lines(a1, b1, a2, b2)
print(x, y)

which outputs:

1.0 5.0

share|improve this answer

answered Apr 1 at 13:52

EsmailianEsmailian

3,311420

$endgroup$

add a comment | 

1

$begingroup$

You should formulate your lines as follows to have $(x, y)$ as unknowns:
$$beginalign
left.beginmatrix
a_1x-y=-b_1\
a_2x-y=-b_2
endmatrixright}
rightarrow
overbrace
beginbmatrix
a_1& -1\
a_2& -1
endbmatrix
^boldsymbola
overbrace
beginbmatrix
x\
y
endbmatrix
^boldsymbolx
=
overbrace
beginbmatrix
-b_1\
-b_2
endbmatrix
^boldsymbolb
endalign$$
Therefore, the code should be:

import numpy as np

def meeting_lines(a1, b1, a2, b2):
 a = np.array([[a1, -1], [a2, -1]])
 b = np.array([-b1, -b2])
 return np.linalg.solve(a, b)

a1=1
b1=4
a2=3
b2=2
x, y = meeting_lines(a1, b1, a2, b2)
print(x, y)

which outputs:

1.0 5.0

share|improve this answer

answered Apr 1 at 13:52

EsmailianEsmailian

3,311420

$endgroup$

add a comment | 

$begingroup$

You should formulate your lines as follows to have $(x, y)$ as unknowns:
$$beginalign
left.beginmatrix
a_1x-y=-b_1\
a_2x-y=-b_2
endmatrixright}
rightarrow
overbrace
beginbmatrix
a_1& -1\
a_2& -1
endbmatrix
^boldsymbola
overbrace
beginbmatrix
x\
y
endbmatrix
^boldsymbolx
=
overbrace
beginbmatrix
-b_1\
-b_2
endbmatrix
^boldsymbolb
endalign$$
Therefore, the code should be:

import numpy as np

def meeting_lines(a1, b1, a2, b2):
 a = np.array([[a1, -1], [a2, -1]])
 b = np.array([-b1, -b2])
 return np.linalg.solve(a, b)

a1=1
b1=4
a2=3
b2=2
x, y = meeting_lines(a1, b1, a2, b2)
print(x, y)

which outputs:

1.0 5.0

share|improve this answer

answered Apr 1 at 13:52

EsmailianEsmailian

3,311420

$endgroup$

import numpy as np

def meeting_lines(a1, b1, a2, b2):
 a = np.array([[a1, -1], [a2, -1]])
 b = np.array([-b1, -b2])
 return np.linalg.solve(a, b)

a1=1
b1=4
a2=3
b2=2
x, y = meeting_lines(a1, b1, a2, b2)
print(x, y)

1.0 5.0

share|improve this answer

answered Apr 1 at 13:52

EsmailianEsmailian

3,311420

answered Apr 1 at 13:52

EsmailianEsmailian

3,311420

answered Apr 1 at 13:52

EsmailianEsmailian

3,311420