Singular matrix error as a single function but not when run piece wise-CodePudding

Why am I getting a singular error when I run it as a function, but when it was done piece wise before it worked correctly? Using the same matrices for both. Following along from a video and I am not able to see what I did different when looking though what he did.

#Artificial data for learning purpose provided by Alex
X= [
    [148, 24,1385],
    [132,25,2031],
    [453,11,86],
    [158,24,185],
    [172,25,201],
    [413,11,86],
    [38,54,185],
    [142,25,431],
    [453,31,86]
]
    
X = np.array(X)

# Add in the bias (default) value of car before calculating features. 
ones = np.ones(X.shape[0])
X = np.column_stack([ones, X])

# y values provided by Alex
y = [10000,20000,15000,20050,10000,20000,15000,25000,12000]

XTX = X.T.dot(X)
XTX_inv = np.linalg.inv(XTX)
w_full = XTX_inv.dot(X.T).dot(y)

# bias value
w0 = w_full[0]
# features
w = w_full[1:]
print(w0, w)
#Output: 25844.754055766753, array([ -16.08906468, -199.47254894,   -1.22802883])

At this point the code runs as expected. However, this function gives an error:

# Error in function
def train_linear_regression(X, y):
    ones = np.ones(X.shape[0])
    X = np.column_stack([ones, X])

    XTX = X.T.dot(X)
    XTX_inv = np.linalg.inv(XTX)
    w = XTX_inv.dot(X.T).dot(y)
    
    return w[0], w[1:]

w0, w = train_linear_regression(X, y)
print(w0, w)
---------------------------------------------------------------------------
LinAlgError                               Traceback (most recent call last)
<ipython-input-48-ed5d7ddc40b1> in <module>
----> 1 train_linear_regression(X,y)

2 frames
<__array_function__ internals> in inv(*args, **kwargs)

/usr/local/lib/python3.7/dist-packages/numpy/linalg/linalg.py in _raise_linalgerror_singular(err, flag)
     86 
     87 def _raise_linalgerror_singular(err, flag):
---> 88     raise LinAlgError("Singular matrix")
     89 
     90 def _raise_linalgerror_nonposdef(err, flag):

LinAlgError: Singular matrix

CodePudding user response：

It looks like you are adding/stacking bias (ones) to X twice. First with in the normal flow and second time within the function, that is leading to determinant of 0 for the matrix XTX in the function.

So you need to remove the addition of ones from one of them.

def train_linear_regression(X, y):
    ones = np.ones(X.shape[0]) 
    X = np.column_stack([ones, X]) # stacking ones here again - REMOVE
....

CodePudding user response：

Try below code, there is no error:

X= [
    [148, 24,1385],
    [132,25,2031],
    [453,11,86],
    [158,24,185],
    [172,25,201],
    [413,11,86],
    [38,54,185],
    [142,25,431],
    [453,31,86]
]
X = np.array(X)    #maintain this as input

def train_linear_regression(X, y):    #this is your code, no change
    ones = np.ones(X.shape[0])
    X = np.column_stack([ones, X])

    XTX = X.T.dot(X)
    XTX_inv = np.linalg.inv(XTX)
    w = XTX_inv.dot(X.T).dot(y)
    
    return w[0], w[1:]

w0, w = train_linear_regression(X, y)
print(w0, w)

Output:

25844.754055766753 [ -16.08906468 -199.47254894   -1.22802883]

The reason is that you have converted X with this code:

ones = np.ones(X.shape[0])
X = np.column_stack([ones, X])

So the original X with shape (9, 3):

array([[ 148,   24, 1385],
       [ 132,   25, 2031],
       [ 453,   11,   86],
       [ 158,   24,  185],
       [ 172,   25,  201],
       [ 413,   11,   86],
       [  38,   54,  185],
       [ 142,   25,  431],
       [ 453,   31,   86]])

has become this with shape (9, 4):

array([[1.000e 00, 1.480e 02, 2.400e 01, 1.385e 03],
       [1.000e 00, 1.320e 02, 2.500e 01, 2.031e 03],
       [1.000e 00, 4.530e 02, 1.100e 01, 8.600e 01],
       [1.000e 00, 1.580e 02, 2.400e 01, 1.850e 02],
       [1.000e 00, 1.720e 02, 2.500e 01, 2.010e 02],
       [1.000e 00, 4.130e 02, 1.100e 01, 8.600e 01],
       [1.000e 00, 3.800e 01, 5.400e 01, 1.850e 02],
       [1.000e 00, 1.420e 02, 2.500e 01, 4.310e 02],
       [1.000e 00, 4.530e 02, 3.100e 01, 8.600e 01]])