A=[3,-5,1,0,0,0.5,2,-9,0,0,-1,3,0,0,0,9]
b=[5,22,-8,-18]
x=b
n=4

# think of the dictionary as two dimensional array
# i = \[0..n-1\], j=\[i..n-1\]
# A\[i,j\] (2.dim) \hat{=} A\[i*4+j\] (1.dim)
# to save memory, we calculate it directly in x
# we could save more memory by leaving out x or b :)
# the inner loop is running through:  n < (n(n+1)/2)+1 < n^2
for i in range(n-1,-1,-1):
    for j in range(n-1,i,-1):
        x[i] -= A[i*n+j]*x[j]
    x[i] /= A[i*n+i]

print x

it's a assessement from a lecture about numerics...have to code it in C...but just for trying out my algo, was python just fine.

solving linear equation with triangular matrix

Python