高斯消元的Python源码规模排旋转

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''' x = gaussPivot(a,b,tol=1.0e-9).    Solves [a]{x} = {b} by Gauss elimination with    scaled row pivoting'''    from numpy import zeros,argmax,dotimport swap import errordef gaussPivot(a,b,tol=1.0e-12):    n = len(b)  # Set up scale factors    s = zeros(n)    for i in range(n):        s[i] = max(abs(a[i,:]))    for k in range(0,n-1):      # Row interchange, if needed        p = argmax(abs(a[k:n,k])/s[k:n]) + k        if abs(a[p,k]) < tol: error.err('Matrix is singular')        if p != k:            swap.swapRows(b,k,p)            swap.swapRows(s,k,p)            swap.swapRows(a,k,p)      # Elimination        for i in range(k+1,n):            if a[i,k] != 0.0:                lam = a[i,k]/a[k,k]    if abs(a[n-1,n-1]) < tol: error.err('Matrix is singular')  # Back substitution    b[n-1] = b[n-1]/a[n-1,n-1]    for k in range(n-2,-1,-1):        b[k] = (b[k] - dot(a[k,k+1:n],b[k+1:n]))/a[k,k]    return b