def row_proper(A):
"""
Reduction of a polynomial matrix to row proper polynomial matrix
Implementation of the algorithm as shown in page 7 of
Vardulakis, A.I.G. (Antonis I.G). Linear Multivariable Control: Algebraic Analysis and Synthesis Methods.
Chichester,New York,Brisbane,Toronto,Singapore: John Wiley & Sons, 1991.
INPUT:
Polynomial Matrix A
OUTPUT:
T:An equivalent matrix in row proper form
TL the unimodular transformation matrix
Christos Tsolakis
Example: TODO
T=Matrix([[1, s**2, 0], [0, s, 1]])
is_row_proper(T)
see also Wolovich Linear Multivariable Systems Springer
"""
T=A.copy()
Transfomation_Matrix=eye(T.rows) #initialize transformation matrix
while not is_row_proper(T):
#for i in range(3):
Thr=mc.highest_row_degree_matrix(T,s)
#pprint(Thr)
x=symbols('x0:%d'%(Thr.rows+1))
Thr=Thr.transpose()
Thr0=Thr.col_insert(Thr.cols,zeros(Thr.rows,1))
SOL=solve_linear_system(Thr0,*x) # solve the system
a=Matrix(x)
D={var:1 for var in x if var not in SOL.keys()} # put free variables equal to 1
D.update({var:SOL[var].subs(D) for var in x if var in SOL.keys()})
a=a.subs(D)
r0=mc.find_degree(T,s)
row_degrees=mc.row_degrees(T,s)
i0=row_degrees.index(max(row_degrees))
ast=Matrix(1,T.rows,[a[i]*s**(r0-row_degrees[i]) for i in range(T.rows)])
#pprint (ast)
TL=eye(T.rows)
TL[i0*TL.cols]=ast
#pprint (TL)
T=TL*T
T.simplify()
Transfomation_Matrix=TL*Transfomation_Matrix
Transfomation_Matrix.simplify()
#pprint (T)
#print('----------------------------')
return Transfomation_Matrix,T
def test_Matrix2():
m = Matrix([[x, x**2], [5, 2/x]])
assert (matrix(m.subs(x, 2)) == matrix([[2, 4], [5, 1]])).all()
m = Matrix([[sin(x), x**2], [5, 2/x]])
assert (matrix(m.subs(x, 2)) == matrix([[sin(2), 4], [5, 1]])).all()
def test_Matrix1():
m = Matrix([[x, x**2], [5, 2/x]])
assert (array(m.subs(x, 2)) == array([[2, 4], [5, 1]])).all()
m = Matrix([[sin(x), x**2], [5, 2/x]])
assert (array(m.subs(x, 2)) == array([[sin(2), 4], [5, 1]])).all()