def ALGO11(As, Bs, Cs, Ds, do_test):
# =======================STEP 1======================================
r = As.rows
m = Bs.cols
p = Cs.rows
Ps = BlockMatrix([[As, Bs], [-Cs, Ds]]).as_mutable()
List_P = mc.matrix_coeffs(Ps, s)
List_P.reverse()
q = len(List_P)
k = List_P[0].rows
l = List_P[0].cols
Zero_Mat = zeros(List_P[0].rows, List_P[0].cols) # list of zeroes
# ==================END==STEP 1======================================
# =======================STEP 2======================================
# Haskel matrices #wikipedia ???
# PiE
A = []
for i in range(2, q):
A.append([List_P[j] for j in range(i, q)])
for i in range(1, len(A)):
A[i] = A[i] + [Zero_Mat] * i
PiE = BlockMatrix(A).as_mutable()
A = []
for i in range(3, q + 1):
A.append([List_P[j] for j in range(i, q)])
A[i - 3] = A[i - 3] + [Zero_Mat] * (i - 2)
PiA = BlockMatrix(A)
PiB = BlockMatrix((q - 2), 1, List_P[2:])
PiC = BlockMatrix(1, q - 2, List_P[2:])
rE = PiE.rank()
# ===================END=====STEP 2==================================
# =======================STEP 3======================================
J = PiE.rref()[1] # pivot columns
I = (PiE.transpose()).rref()[1] # pivot rows
PE = Matrix(mat(PiE)[ix_(I, J)]) # mat and ix are Numpy functions
PA = Matrix(mat(PiA)[ix_(I, J)])
PB = Matrix(mat(PiB)[ix_(I, range(l))])
PC = Matrix(mat(PiC)[ix_(range(k), J)])
# ===================END=STEP 3======================================
# =======================STEP 4======================================
Lambda = r + rE + p + m
E = BlockMatrix(
[[List_P[1], PC], [PB, PA], [zeros(Lambda - k - PB.rows, PB.cols), zeros(Lambda - k - PB.rows, PA.cols)]]
).as_mutable()
E = E.row_join(zeros(Lambda, Lambda - l - PC.cols))
A = BlockMatrix(
[
[-List_P[0], zeros(k, PE.cols), zeros(k - p, Lambda - l - PE.cols).col_join(-eye(p))],
[zeros(PE.rows, l), PE, zeros(PE.rows, p)],
[zeros(m, l - m).row_join(eye(m)), zeros(m, PE.cols), zeros(m, p)],
]
).as_mutable()
B = BlockMatrix([[zeros(r + p + rE, m)], [eye(m)]]).as_mutable()
C = BlockMatrix([[zeros(p, r + m + rE), eye(p)]]).as_mutable()
D = zeros(p, m)
# ===============END==STEP 4=========================================
if do_test == True:
test_result = test(rE, r, p, m, PE, PA, PC, As, Bs, Cs, Ds, E, A, B, C, D)
else:
test_result = "not done"
return E, A, B, C, D, test_result
