Solve for an equation of a plane in Python (like in Matlab)

Question

I have a data set, and I'm trying to get the equation of a plane from it. That is: a*x + b*y + c = z In my case, dT = x, dTa = y, Constant = c, and dV = z.

I'm able to do this quite easily in Matlab, code:

dT = [8.5; 3.5; .4; 12.9]

dT =

    8.5000
    3.5000
    0.4000
   12.9000

dTa = [8.5; 18; 22; 34.9]

dTa =

    8.5000
   18.0000
   22.0000
   34.9000

dV = [3; 1; .5; 3]

dV =

    3.0000
    1.0000
    0.5000
    3.0000

Constant = ones(size(dT))

Constant =

     1
     1
     1
     1

coefficients = [dT dTa Constant]\dV

coefficients =

    0.2535
   -0.0392
    1.0895

so, here, coefficients = (a, b, c).

Is there an equivalent way to do this in Python? I've been trying to use the numpy module (numpy.linalg), but its not working out so well. For one, the matrix MUST be square, and even so, it doesn't give very nice answers. For example:

Error:

>>> dT
[8.5, 3.5, 0.4, 12.9]
>>> dTa
[8.5, 18, 22, 34.9]
>>> dV
[3, 1, 0.5, 3]
>>> Constant
array([ 1.,  1.,  1.,  1.])
>>> numpy.linalg.solve([dT, dTa, Constant], dV)

Traceback (most recent call last):
  File "<pyshell#45>", line 1, in <module>
    numpy.linalg.solve([dT, dTa, Constant], dV)
  File "C:\Python27\lib\site-packages\numpy\linalg\linalg.py", line 312, in solve
    _assertSquareness(a)
  File "C:\Python27\lib\site-packages\numpy\linalg\linalg.py", line 160, in _assertSquareness
    raise LinAlgError, 'Array must be square'
LinAlgError: Array must be square

Wokrking with square matrix:

>>> dT
array([  8.5,   3.5,  12.9])
>>> dTa
array([  8.5,  18. ,  34.9])
>>> dV
array([3, 1, 3])
>>> Constant
array([ 1.,  1.,  1.])
>>> numpy.linalg.solve([dT, dTa, Constant], dV)
array([ 2.1372267 ,  2.79746835, -1.93469505])

These are not even close to the values I got before!!

Any ideas guys? Any advice appreciated.

Answer 1

So, I found this picture

and adapted it to include a constant. Here's my solved code:

    X = 0
    XX = 0
    XY = 0
    XZ = 0

    Y = 0
    YY = 0
    YZ = 0

    Z = 0

    for j in range(0, len(dTemp)):
        X = X + dTemp[j]
        XX = XX + (dTemp[j] * dTemp[j])
        XY = XY + (dTemp[j] * dTempA[j])
        XZ = XZ + (dTemp[j] * Applied[j])

        Y = Y + dTempA[j]
        YY = YY + (dTempA[j] * dTempA[j])
        YZ = YZ + (dTempA[j] * Applied[j])

        Z = Z + Applied[j]


    lhs = numpy.array([[XX, XY, X], [XY, YY, Y], [X, Y, 1]]) 
    rhs = numpy.array([XZ,  YZ, Z])

    coefficients = numpy.linalg (lhs, rhs)

    a = coefficients[0]
    b = coefficients[1]
    c = coefficients[2]

I think that did the trick! still, values a little off, but maybe that's because Matlab was using a different algorithm?

Answer 2

In the first example, you need to use numpy.linalg.lstsq. Either way, you appear to have mixed up the rows and columns of your matrix. Fix it using something like numpy.linalg.solve(zip(dT, dTa, Constant), dV).