Initial commit.
#!/usr/bin/python
# Contains all the polynomial functions
import pylab as pl
def polsize(Q, degQ):
""" Determines dimensions of a polynomial matrix. """
rQ, cQ = pl.atleast_2d(Q).shape
cQ = cQ/float(degQ+1)
if abs(round(cQ)-cQ) > 1e-6:
print "Degree of input inconsistent with number of columns"
return
else:
cQ = int(round(cQ))
return rQ, cQ
def polmul(A, degA, B, degB):
A = pl.atleast_2d(A)
B = pl.atleast_2d(B)
rA, cA = polsize(A, degA)
rB, cB = polsize(B, degB)
if cA != rB:
print "polmul: Inconsistent dimensions of input matrices"
return
degC = degA + degB
C = []
for k in range(0, degC+1):
mi = 0
if k-degB > mi:
mi = k-degB
ma = degA
if k < ma:
ma = k
Ck = pl.zeros((rA,cB))
for i in range(mi, ma+1):
Ck = Ck + pl.dot(A[..., i*cA:(i+1)*cA], B[..., (k-i)*cB:(k-i+1)*cB])
Ck = pl.squeeze(Ck)
C = pl.hstack((C, Ck))
return C, degC
def poladd(A, degA, B, degB):
A = pl.atleast_2d(A)
B = pl.atleast_2d(B)
rA, cA = polsize(A, degA)
rB, cB = polsize(B, degB)
if cA != rB:
print "polmul: Inconsistent dimensions of input matrices"
return
degC = max(degA, degB)
if degC >= degA:
A = pl.hstack((A, pl.zeros((rA,(degC-degA)*cA))))
if degC >= degB:
B = pl.hstack((B, pl.zeros((rB,(degC-degB)*cB))))
C = A + B
return C, degC
def polsplit2(fac, a=1-1e-5):
fac = pl.atleast_1d(fac)
if a>1:
print "good polynomial also is unstable"
return
roots = pl.roots(fac)
# extract good and bad roots
badindex = pl.find(pl.absolute(roots)>=a-1.0e-5)
badpoly = pl.poly(roots[badindex])
goodindex = pl.find(pl.absolute(roots)<a-1.0e-5)
goodpoly = pl.poly(roots[goodindex])
# scale by equating the largest terms
index = pl.absolute(fac).argmax()
goodbad = pl.convolve(goodpoly, badpoly)
factor = fac[index]/goodbad[index]
goodpoly = goodpoly * factor
badpoly = pl.atleast_1d(badpoly)
goodpoly = pl.atleast_1d(goodpoly)
return goodpoly, badpoly
def polsplit3(fac, a=1):
fac = pl.atleast_1d(fac)
if a>1:
print "good polynomial also is unstable"
return
roots = pl.roots(fac)
# extract good and bad roots
badindex = pl.find((pl.absolute(roots)>=a-1.0e-5) + (pl.real(roots)<-0.05))
badpoly = pl.poly(roots[badindex])
goodindex = pl.find((pl.absolute(roots)<a-1.0e-5) * (pl.real(roots)>=-0.05))
goodpoly = pl.poly(roots[goodindex])
# scale by equating the largest terms
index = pl.absolute(fac).argmax()
goodbad = pl.convolve(goodpoly, badpoly)
factor = fac[index]/goodbad[index]
goodpoly = goodpoly * factor
badpoly = pl.atleast_1d(badpoly)
goodpoly = pl.atleast_1d(goodpoly)
return goodpoly, badpoly
def putin(A, degA, B, degB, i, j):
from clcoef import clcoef
A = pl.atleast_2d(A)
B = pl.atleast_2d(B)
rA, cA = polsize(A,degA)
if degB > degA:
A = pl.hstack((A, pl.zeros((rA,(degB-degA)*cA))))
degA = degB
for k in range(degB+1):
A[i,(k*cA)+j] = B[0,k]
if degA > degB:
for k in range(degB+1,degA+1):
A[i,(k*cA)+j] = 0
A, degA = clcoef(A,degA)
return A, degA
def ext(A, degA, k, l):
from clcoef import clcoef
rA, cA = polsize(A, degA)
degB = degA
B = pl.zeros((1, degB+1))
for m in range(degB+1):
B[0, m] = A[k, (m*cA)+l]
B,degB = clcoef(B, degB)
return B, degB
def transp(Q, degQ):
""" Function to transpose a polynomial matrix. """
rQ, cQ = polsize(Q, degQ)
rP = cQ
cP = rQ
degP = degQ
P = pl.zeros((rP, (degP+1)*cP))
for i in range(degP+1):
P[:, i*cP:(i+1)*cP] = Q[:, i*cQ:(i+1)*cQ].T
return P, degP
if __name__== "__main__":
# print "Test for polsize"
# print polsize([1, 2, 1],4)
# print "Test for polmul"
# C = pl.array([[1, 0, 0.5, 2], [0, 1, -4.71, 2.8]])
# A = pl.array([0.5, 3.5])
# print polmul(A, 0, C, 1)
# print "Test for polsplit3"
# print polsplit3([1, -0.37])
print "Test for putin"
A = pl.array([0,0])
B = pl.array([0.44, -1.6, 1.6, -0.44])
print putin(A, 0, B, 3, 0, 0)
pass