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pythonnumpypivotslice
Granolaboy
Granolaboy

Reputation: 333

Gaussian elimination - pivoting using slicing in python

I'm trying to implement pivoting for the Gaussian elimination in Python and face some problems.

def pivot2(matrix,i):
    # matrix is a N*N matrix
    # i is the column I want to start with

    m = matrix.shape[1]
    for n in range(i,m):
        colMax = np.argmax(abs(matrix[n:,i]), axis=0) #rowindex of highest absolute value in column
        if(colMax == 0): #if max in column is in first row, stop
            break;
        tmpRow = copy.copy(matrix[n,:]) #create new object of same row
        matrix[n,:] = matrix[colMax,:]  #overwrite first row with row of max value
        matrix[colMax,:] = tmpRow       #overwrite old row of max value
    return matrix

The code works for i=0 just fine. However for i=1 I can't search for the index of the maximum value in the whole column because it will obviously always be 0.

When I slice this matrix from a 3x3 matrix:

array([[ 1.,  2.],
       [-3., -2.]])

and use my argmax function, the index is 1. But in my original matrix the index of the same row is 2 and it swaps the wrong rows. How do I fix this?

And is there a simpler way to implement pivoting using slices?

Upvotes: 4

Views: 2308

Answers (1)

roman
roman

Reputation: 117510

You just have to add i to colmax after checking for 0:

...
if(colMax == 0): #if max in column is in first row, stop
    break;
colmax += i   # add this string    
...

Upvotes: 2

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