''' x = gaussPivot(a,b,tol=1.0e-9).
Solves [a]{x} = {b} by Gauss elimination with
scaled row pivoting
'''
from numpy import zeros,argmax,dot
import swap
import error
def 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]
a[i,k+1:n] = a [i,k+1:n] - lam*a[k,k+1:n]
b[i] = b[i] - lam*b[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
#//python/7427