I am just learning python and want to define a function that returns a nxn square matrix, with predefined values for the main diagonal(i=j), upper diagonal (j=i+1)and lower diagonal (j=i-1) and all other elements to be equal 0.
Any help would be appreciated,
thanks
import numpy as np
import scipy as sp
n=6
m=np.zeros((n,n))
for i in range(n):
m[i-1,i]=-1
m[i,i]=2
m[i,i-1]=1
m[0,n-1]=0
m[n-1,0]=0
print m
If a,b,c are your three list for the upper diagonal, main diagonal, and lower diagonal respectively, you can write it as follows:
import numpy as np
a=[1,2,3,4]
b=[5,6,7,8,9]
c=[10,11,12,13]
n=len(b)
m=np.zeros((n,n))
for i in range(0,n-1):
m[i,i+1]=a[i]
m[i,i]=b[i]
m[i+1,i]=c[i]
m[n-1,n-1]=b[n-1]
print(m)
In the code above you initialize a zero matrix, and then update only the upper,lower, and main diagonal entries according to your lists. The output is
[[ 5. 1. 0. 0. 0.]
[ 10. 6. 2. 0. 0.]
[ 0. 11. 7. 3. 0.]
[ 0. 0. 12. 8. 4.]
[ 0. 0. 0. 13. 9.]]
Edit: A shorter way, suggested by @hpaulj would be
m=np.diag(a,1)+np.diag(b,0)+np.diag(c,-1)
np.diag(r,k) create a matrix in which the k'th diagonal above the main diagonal (below if k is negative) is r and the rest of the entries are 0.
See documentation here: https://docs.scipy.org/doc/numpy/reference/generated/numpy.diag.html
Here's a method that takes in a list of items to add on the diagonal, using numpy.diag and taking advantage of the k parameter to specify which diagonal we want to modify.
import numpy as np
def create_diag(n, l):
arr = np.zeros((n, n))
# check that l contains an odd number of elements
if len(l) % 2 != 1:
return arr
# check that we have at most the number of diagonals in the matrix
if len(l) >= 2*n:
return arr
# set limits of diagonals to set. setting 3 diagonals means limits=[-1,0,1]. setting 1 diagonal means limits=[0]
limit = int((len(l) - 1) / 2)
limits = range(-limit, limit + 1)
# maps k-->list of values on the diagonal
diag_map = dict(zip(limits, l))
for k, v in diag_map.items():
diag = [v] * (n - abs(k))
arr += np.diag(diag, k=k)
return arr
# elements to put on the diagonal, centered about the main diagonal (i=j)
l = [-1,1,2]
n = 6
diag_arr = create_diag(n, l)
# [[ 1. 2. 0. 0. 0. 0.]
# [-1. 1. 2. 0. 0. 0.]
# [ 0. -1. 1. 2. 0. 0.]
# [ 0. 0. -1. 1. 2. 0.]
# [ 0. 0. 0. -1. 1. 2.]
# [ 0. 0. 0. 0. -1. 1.]]
scipy.sparsehas a couple of ways of setting multiple diagonals at once. Thenumpy.diagsets one diagonal at a time, but otherwise is easy to use.