I have a function:
def euler(a, b, R, r, time, h): # Euler Method
a0 = a
b0 = b
R0 = R
r0 = r
for i in range(3):
a[0][i] = a[0][i] + h * fai_1(a0, b0, R0, r0, i)
a[1][i] = a[1][i] + h * fai_2(a0, b0, R0, r0, i)
a[2][i] = a[2][i] + h * fai_3(a0, b0, R0, r0, i)
b[0][i] = b[0][i] + h * fbi_1(a0, b0, R0, r0, i)
b[1][i] = b[1][i] + h * fbi_2(a0, b0, R0, r0, i)
b[2][i] = b[2][i] + h * fbi_3(a0, b0, R0, r0, i)
r[i] = r[i] + h * fr(a0, b0, R0, r0, i)
for i in range(3):
R[0][i] = R[0][i] + h * fR(a0, b0, R0, r0)[0][i]
R[1][i] = R[1][i] + h * fR(a0, b0, R0, r0)[1][i]
R[2][i] = R[2][i] + h * fR(a0, b0, R0, r0)[2][i]
time = time + h
return [a, b, R, r, time]
where the h is a constant prescribed value, a, b, r, and R are 3x3 matrices (2D arrays), and the functions fai_1, fai_2,... also prescribed.
I would like to run the above function for 100 steps, where the elements are appended to an empty array at each step. The trouble I am having is that this function updates the values at each step and overwrite the elements in my array so I end with 100 identical elements.
For example, I am starting with
a = [[0.0, 0.0, 0.0], [1.0, -1.0, 0.0], [-0.5, 1.0, 1.0]]
b = [[0.0, 0.0, 0.0], [1.0, 1.0, 0.5], [-1.0, 0.5, 1.0]]
R = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
r = [-1.0, 1.0, 0.0]
time = 0.0
and tried executing (to extract the first array in b)
barr = []
for i in range(3):
u = euler(a, b, R, r, time, h)
barr.append( u[1][0] )
print( barr )
This prints:
[0.27195, 0.3172665, 0.175097505], [0.27195, 0.3172665, 0.175097505],
[0.27195, 0.3172665, 0.175097505]
And I would like to get:
[0.1, 0.1, 0.05], [0.19, 0.205, 0.11], [0.27195, 0.3172665, 0.175097505]
I believe I know what is happening here. The function is updating the value u[1][0] each time it is called, which in turn rewrites the value in barr. However, I have no idea how to fix this issue. I have tried many different way to write this, but it always ends in the same issue.
What's most frustrating to me, is that I have written code extremely similar to this before:
def euler(theta, x, y, h):
theta0 = theta
x0 = x
y0 = y
for i in range(5):
theta[i] = theta[i] + h * ftheta[i](theta0,x0,y0)
x[i] = x[i] + h * fx[i](theta0,x0,y0)
y[i] = y[i] + h * fy[i](theta0,x0,y0)
return [theta, x, y]
with
x = [-1.39, 6.05, 1.0 , 0, 0]
y = [-3.33, -1.82, -2.0, 2.0, 0]
theta = [-3.98, 0.0, 1.0, np.pi / 4, 0]
Then, executing
xarr = []
for i in range(p):
u1 = euler(theta, x, y, h)
xarr.append( u1[1][3] )
yarr1.append( u1[2][3] )
thetaarr1.append( u1[0][3] )
print(xarr)
This works as I would like it to, and doesn't update all of the values in xarr at each iteration. The only difference I can see here is the introduction of 2D arrays, as opposed to 1D.
Can anyone help me see what's happening here?
Unfortunately, the code I am working on is too long to include in its entirety, but if anyone would like me to add a part that may be relevant, please let me know.
