function [A_coeff,nx_total,B,u,nodes_per_segment, time_matrix_formulation] = matrix_formulation(dx0,lengths0,J_list_norm0,kappa,b)

time_start = tic;

lengths = lengths0;

J_list_norm=J_list_norm0;

dx = dx0;

n_wires = numel(lengths); %number of wire segments in interconnect line

length = 0;

for segment=1:numel(lengths)

length = length + lengths(segment);

nx_total = ceil(length / dx);

nodes_per_segment = zeros(numel(lengths),1);

for i=1:numel(lengths)

nodes_per_segment(i) = ceil(lengths(i)/dx);

B = sparse(nx_total, n_wires);

index = 1;

for i = 1:n_wires

B(index,i)=1;

B(index+nodes_per_segment(i)-1,i)=-1;

index = index + nodes_per_segment(i) -1;

B_coeff = kappa*b/dx;

B = B * B_coeff;

u = J_list_norm;

A_coeff = kappa/(dx*dx);

time_matrix_formulation = toc(time_start);