追赶法求解过程
import numpy as np
## Tri Diagonal Matrix Algorithm(a.k.a Thomas algorithm) solver
def TDMAsolver(a, b, c, d):
'''
TDMA solver, a b c d can be NumPy array type or Python list type.
refer to http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm
and to http://www.cfd-online.com/Wiki/Tridiagonal_matrix_algorithm_-_TDMA_(Thomas_algorithm)
'''
nf = len(d) # number of equations
ac, bc, cc, dc = map(np.array, (a, b, c, d)) # copy arrays
for it in range(1, nf):
mc = ac[it-1]/bc[it-1]
bc[it] = bc[it] - mc*cc[it-1]
dc[it] = dc[it] - mc*dc[it-1]
xc = bc
xc[-1] = dc[-1]/bc[-1]
for il in range(nf-2, -1, -1):
xc[il] = (dc[il]-cc[il]*xc[il+1])/bc[il]
return xc
例如：
A = np.array([[10,2,0,0],[3,10,4,0],[0,1,7,5],[0,0,3,4]],dtype=float)
a = np.array([3.,1,3])
b = np.array([10.,10.,7.,4.])
c = np.array([2.,4.,5.])
d = np.array([3,4,5,6.])
print(TDMAsolver(a, b, c, d))
>> [ 0.14877589 0.75612053 -1.00188324 2.25141243]
#compare against numpy linear algebra library
print(np.linalg.solve(A, d))
>> [ 0.14877589 0.75612053 -1.00188324 2.25141243]
