Data update

Task/Resistor-mesh/Julia/resistor-mesh.jl

@@ -1,7 +1,27 @@
-N = 10
-D1 = speye(N-1,N) - spdiagm(ones(N-1),1,N-1,N)
-D = [ kron(D1, speye(N)); kron(speye(N), D1) ]
-i, j = N*1 + 2, N*7+7
-b = zeros(N^2); b[i], b[j] = 1, -1
+using SparseArrays, LinearAlgebra
+
+const N = 10
+
+# Build an (N-1) x N discrete forward-difference operator:
+# each row k has +1 at column k and -1 at column k+1
+const rows = vcat(1:(N-1), 1:(N-1))
+const cols = vcat(1:(N-1), 2:N)
+const vals = vcat(ones(N-1), -ones(N-1))
+const D1 = sparse(rows, cols, vals, N-1, N)   # (N-1) x N
+
+# Identity as a sparse NxN
+const I_N = spdiagm(0 => ones(N))
+
+# Build 2D difference operator with Kronecker products
+const D = [kron(D1, I_N); kron(I_N, D1)]      # (2*N*(N-1)) x (N^2)
+
+# indices and right-hand side
+const i, j = N*1 + 2, N*7 + 7
+const b = zeros(N^2)
+b[i], b[j] = 1.0, -1.0
+
+# Solve normal equations (least-squares / Poisson-style)
 v = (D' * D) \ b
-v[i] - v[j]
+
+# potential difference
+println(v[i] - v[j])