m = crn.n_complexes

n = crn.n_species

# Y is n by m

Y = np.array(crn.complex_matrix).astype(np.float64)

# Ak is m by m

Ak = np.array(crn.kinetic_matrix).astype(np.float64)

# M is n by m

M = Y.dot(Ak)

print("Input CRN defined by\nY =\n", Y)

print("\nM =\n", M)

print("\nAk =\n", Ak)

print("\nComputing linearly conjugate network with min deficiency ... START\n")

# Ranges for iteration

col_range = range(1, m+1)

row_range = range(1, n+1)

# Set up problem model object

prob = LpProblem("Weakly Reversible Linearly Conjugate Network", LpMaximize)

# Get a list of all off-diagonal entries to use later to greatly

# simplify loops

off_diag = [(i, j) for i,j in product(col_range, repeat=2) if i != j]

# Decision variables for matrix A, only need off-diagonal since A

# has zero-sum columns

A = LpVariable.dicts("A", [(i, j) for i in col_range for j in col_range])

Ah = LpVariable.dicts("Ah", [(i, j) for i in col_range for j in col_range])

# Decision variables for the diagonal of T

T = LpVariable.dicts("T", row_range, eps, ubound)

# Binary variables for counting partitions used and assigning complexes to linkage classes

delta = LpVariable.dicts("delta", off_diag, 0, 1, "Integer")

# Objective

prob += -lpSum(delta[i, j] for (i,j) in off_diag)

# Y*A = T*M

for i in row_range:

for j in col_range:

prob += lpSum( Y[i-1, k-1]*A[k, j] for k in col_range ) == M[i-1, j-1]*T[i]

# A and Ah have zero-sum columns

for j in col_range:

prob += lpSum( A[i,j] for i in col_range ) == 0

prob += lpSum( Ah[i,j] for i in col_range ) == 0

prob += lpSum( Ah[j,i] for i in col_range ) == 0

# Off-diagonal entries are nonnegative and are switch on/off by delta[i,j]

for (i,j) in off_diag:

# A constraints

prob += A[i, j] >= 0

prob += A[i, j] - eps*delta[i, j] >= 0

prob += A[i, j] - ubound*delta[i, j] <= 0

# Ah constraints

prob += Ah[i, j] >= 0

prob += Ah[i, j] - eps*delta[i, j] >= 0

prob += Ah[i, j] - ubound*delta[i, j] <= 0

# Diagonal entries of A, Ah are non-positive

for j in col_range:

prob += A[j, j] <= 0

prob += Ah[j, j] <= 0

status = prob.solve(solver=CPLEX())

#print(prob)

# Problem successfully solved, report results

if status == 1:

# Get solutions to problem

Tsol = np.zeros((n, n))

Asol = np.zeros((m,m))

for i in col_range:

for j in col_range:

Asol[i-1, j-1] = value(A[i, j])

for i in row_range:

Tsol[i-1, i-1] = value(T[i])

print("\nA =\n", Asol)

print("\nT =\n", Tsol)

else: