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