#!/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