624.sagews

#example of swamping
#taken from Timothy Sauer's Numerical Analysis page 98

#a swamping problem
#using double precision arithmetic
m = matrix([[10.0^-20,1.0],[1.0,2.0]])
b = vector([1.0,4.0])
x = m.solve_right(b)
#answer should be close to (2,1)
#"swamping" problem occurs due to very small numbers used for pivot in Gaussian Elimination
#10^20 + 1 ~= 10^20 in Gaussian Elimination
print x

(0.000000000000000, 1.00000000000000)

#now first swap rows, then calculate
m = matrix([[1.0,2.0],[10.0^-20,1.0]])
b = vector([4.0,1.0])
x = m.solve_right(b)
#answer should be close to (2,1)
print x
print "ta dah"

(2.00000000000000, 1.00000000000000) ta dah