How to create a tridiagonal matrix in Python?

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Hello, I would like to know how to write a tridiagonal matrix Nxn. I have three vectors that will be updated in a loop.

I’m working with something semlhnante to this: Example

Note: I would just like to know about zeroes and what Python parameters I could use to adjust this. Well, I have two codes here, the first I wrote in Fortran and it’s working fine. The second is what I tried to write in Python.

Fortran:

do i=2,n-1
  do j=2,n-1
    if (i.eq.j) then

      D(i,j+1)=-u_med(i+1)/(delta_r(i)*delta_r(i+1))

      t1 =u_med(i+1)/(delta_r(i)*delta_r(i))

      t2 = u_med(i)/(delta_r(i)*delta_r(i))

      D(i,j)= t1 + t2 + V(i)

      D(i+1,j)=-u_med(i+1)/(delta_r(i)*delta_r(i+1))

    end if

  end do
end do

Python:

for i in range(2,n):
  for j in range(2,n):
    if i == j:
      D[i][j+1] = - u_med[i+1]/(delta_r[i]*delta_r[i+1])
      t1 = u_med[i+1]/(delta_r[i]*delta_r[i])
      t2 = u_med[i]/(delta_r[i]*delta_r[i])
      D[i][j]= t1 + t2 + V[i]
      D[i+1][j]= - u_med[i+1]/(delta_r[i]*delta_r[i+1])

t1 = u_med[2]/(delta_r[1]*delta_r[1])
t2 = 0
D[1][1]= t1 + t2 + V[1]
D[1][2]= - u_med[2]/(delta_r[1]*delta_r[2])
D[2,1]= - u_med[2]/(delta_r[2]*delta_r[1])
t1 = 0
t2 = u_med[n]/(delta_r[n]*delta_r[n])

D[n][n]= t1 + t2 + V[n]

That makes the mistake:

D[i][j+1] = - u_med[i+1]/(delta_r[i]*delta_r[i+1]) Valueerror: Setting an array element with a Sequence.

Definitions of u_med, delta_r, r, n and D in Python:

u_med = np.zeros((n,2))
for i in range(2,n):
  tta1 = r[i]*u[i]
  tta2 = r[i-1]*u[i-1]
  u_med[i] = 0.5*(tta1 + tta2)/(r[i] - r[i-1])

u_med[1] = u_med[2]

delta_r = np.zeros((n-1,2))
for i in range(2,n-1):
  ft1 = r[i+1]*r[i+1]
  ft2 = r[i-1]*r[i-1]
  ft3 = 2*r[i]*(r[i+1] - r[i-1])
  delta_r[i] = math.sqrt(0.125*abs(ft1 - ft2 + ft3))

ri=0
n1 = 51

r1 = ri
r2 = 250
hr1 = (r2-r1)/(n1-1)

r = np.zeros((n1,1))
for i in range(n1):
  r[i] = r1 + i*hr1

u = np.zeros((n+1,1))
for i in range(1,n+1):
  i = 1

D = npm.zeros((n,n))

I suspect the mistake is in:

D = npm.zeros((n,n))

But how could I rewrite it?

python fortran

  • Probably the problem is happening due to u_med and delta_r be bi-dimensional and you try to assign a sub-array (vector) of these variables to a position in the variable D with a Shape incompatible. This works in Fortran, but should be done differently in Python. See: Assigning values to Indexed arrays

  • In fact u_med and delta_r are one-dimensional... D is that it is two-dimensional. Somehow these are defined as two-dimensional?

  • You defined u_med as np.zeros((n,2)) (n rows and 2 columns) and delta_r as np.zeros((n-1,2)) (n-1 rows and 2 columns), therefore, they are two-dimensional

1 answer

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# elementos da diagonal da matriz
for i in range(N):
    for j in range(N):
        if (i == j):
        A[i][j] = 2

# elementos fora da diagonal da matriz
for i in range(N):
    for j in range(N):
        if(i == j and i>=1):
             A[i][j-1] = 1
             A[i-1][j] = 1

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