SharedHnorm.ipynbOpen in CoCalc
Jupyter notebook Hnorm.ipynb
import numpy as np
from cvxopt import matrix, solvers
def Hnorm(A):
    # Regner ut Hilbert-norm til numpy matrise A
    rad, kol = A.shape
    nullr = np.zeros((rad,rad))
    nullk = np.zeros((kol,kol))
    C = np.bmat([[nullr,A],[A.T,nullk]])

    h0 = [ -0.5*matrix(C) ]

    dim = rad+kol
    c = matrix(np.ones(dim,))
    # Vil lage diagonalmatriser A_i med 1 på plass (i,i), 0 ellers
    diagonal = np.zeros(dim,)
    diagonal[0] = 1
    A0 = np.diag(diagonal)
    G = A0
    for i in xrange(1,dim):
        A0 = np.diag(np.roll(diagonal,i))
        G = np.bmat([[G],[A0]])
    # G0 er nå blokk matrise med A_i'ene stabla nedover i radene.
    G0 = [ matrix(-1.0*G) ]
    solvers.options['show_progress']=False
    sol = solvers.sdp(c, Gs=G0, hs=h0)
    norm = -1
    if sol['status'] == 'optimal':
        norm = sol['primal objective']
    return norm

def ekstrem_ell_infty_recursive(N):
    ekstrem_punkt = np.zeros((2**(N-1),N),dtype=np.int)
    if N == 1:
        ekstrem_punkt[0] = 1
    else:
        ekstrem_punkt[:,0] = np.ones((2**(N-1),),dtype=np.int)
        E = ekstrem_ell_infty_recursive(N-1)
        ekstrem_punkt[:2**(N-2),1:] = E.copy()
        ekstrem_punkt[2**(N-2):,1:] = -1*E.copy()   
    return ekstrem_punkt
    
def ekstrem_ell_infty2(N):
    return ekstrem_ell_infty_recursive(N).transpose()

def Mnorm(A):
    # Regn ut norm max(|Ax|_1, x kolonne i E)
    rad, kol = A.shape
    E = ekstrem_ell_infty2(kol)

    # Ta absolutt verdi av elementene og summer kolonnevis
    return np.max(np.sum(np.abs(A*E),axis=0))
    # Eventuelt 
    # return reduce(max,np.sum(np.abs(A*E),axis=0))

def finnKG(matrise):
    """Tar ei matrise på formen '{{1,1},{1,-1}}' (en streng)
    og returnerer Mnorm, Hnorm og forholdet Hnorm/Mnorm"""
    M = matrise
    M = M.replace('},{',';')
    M = M.replace('{{','[')
    M = M.replace('}}',']')
    M = np.mat(M)
    norm_M = Mnorm(M)
    norm_H = Hnorm(M)
    KG = norm_H/norm_M
    return (norm_M, norm_H, KG)
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be7='{{0,1,0,1,-1,-1,0,0},{-1,0,1,-1,0,0,1,0},{0,1,-1,1,0,1,0,0},{1,-1,0,1,0,0,1,0},{1,1,0,0,0,0,0,0},{0,1,1,0,0,0,0,0},{0,0,1,1,0,0,0,0},{-1,1,0,1,1,0,0,0}}'

be8='{{-1,0,0,1,-1,1,0,0},{-1,0,1,-1,0,0,1,0},{0,1,-1,0,0,1,1,0},{1,-1,1,0,0,1,0,0},{1,1,0,0,0,0,0,0},{0,1,1,0,0,0,0,0},{0,0,1,1,0,0,0,0},{0,0,-1,1,1,1,0,0}}'

be9='{{-1,0,0,1,-1,0,0,1},{-1,0,1,-1,0,1,0,0},{0,1,-1,0,1,0,0,1},{1,-1,1,0,1,0,0,0},{1,1,0,0,0,0,0,0},{0,1,1,0,0,0,0,0},{0,0,1,1,0,0,0,0},{0,0,-1,1,1,1,0,0}}'

be10='{{1,0,0,1,-1,0,-1,0},{0,0,1,-1,0,0,-1,1},{0,1,-1,0,0,0,1,1},{1,-1,1,0,0,0,1,0},{1,1,0,0,0,0,0,0},{0,1,1,0,0,0,0,0},{0,0,1,1,0,0,0,0},{1,0,-1,1,1,0,0,0}}'

be11='{{0,-1,0,1,-1,0,1,0},{1,-1,1,-1,0,0,0,0},{0,1,-1,0,1,0,1,0},{1,-1,0,0,1,0,1,0},{1,1,0,0,0,0,0,0},{0,1,1,0,0,0,0,0},{0,0,1,1,0,0,0,0},{1,0,0,1,1,0,-1,0}}'

be12='{{0,0,-1,1,-1,0,1,0},{1,-1,1,-1,0,0,0,0},{1,1,-1,0,0,0,0,1},{1,-1,1,0,0,0,1,0},{1,1,0,0,0,0,0,0},{0,1,1,0,0,0,0,0},{0,0,1,1,0,0,0,0},{0,-1,0,1,1,0,0,1}}'

be13='{{0,0,-1,1,-1,0,0,1},{-1,0,1,-1,0,0,0,1},{0,1,-1,0,0,0,1,1},{1,-1,1,0,0,0,1,0},{1,1,0,0,0,0,0,0},{0,1,1,0,0,0,0,0},{0,0,1,1,0,0,0,0},{-1,0,0,1,1,0,0,1}}'

be14='{{0,0,0,1,-1,-1,0,1},{1,0,1,-1,0,-1,0,0},{0,1,-1,0,0,1,0,1},{1,-1,1,0,0,1,0,0},{1,1,0,0,0,0,0,0},{0,1,1,0,0,0,0,0},{0,0,1,1,0,0,0,0},{1,0,-1,1,1,0,0,0}}'

be15='{{0,0,-1,1,-1,0,1,0},{0,-1,1,-1,0,1,0,0},{1,1,-1,0,0,1,0,0},{1,-1,1,0,0,0,1,0},{1,1,0,0,0,0,0,0},{0,1,1,0,0,0,0,0},{0,0,1,1,0,0,0,0},{1,-1,0,1,1,0,0,0}}'

be16='{{0,1,0,1,-1,-1,0,0},{-1,0,1,-1,0,0,1,0},{0,1,-1,1,0,1,0,0},{1,-1,0,1,0,0,1,0},{1,1,0,0,0,0,0,0},{0,1,1,0,0,0,0,0},{0,0,1,1,0,0,0,0},{-1,1,0,1,1,0,0,0}}'
map(finnKG,[be1,be2,be3,be4,be5,be6,be7,be8,be9,be10,be11,be12,be13,be14,be15,be16])
[(12, 16.75540629129835, 1.3962838576081957), (12, 16.352672748008796, 1.362722729000733), (12, 16.352672748008796, 1.362722729000733), (12, 16.870701330955377, 1.4058917775796147), (12, 16.676095466115576, 1.3896746221762981), (12, 16.835130176081286, 1.4029275146734406), (12, 16.922638921915073, 1.4102199101595894), (12, 16.67609546611558, 1.3896746221762983), (12, 16.628345570663893, 1.385695464221991), (12, 16.922014929415358, 1.4101679107846132), (12, 16.170047991646275, 1.3475039993038562), (12, 16.768878881354446, 1.3974065734462038), (12, 16.494635678561547, 1.3745529732134623), (12, 16.690282738407543, 1.3908568948672952), (12, 16.835130176081297, 1.4029275146734415), (12, 16.922638921915073, 1.4102199101595894)]

map(finnKG,[be1,be2,be3,be4,be5,be6,be7,be8,be9,be10,be11,be12,be13,be14,be15,be16,be17,be18,be19,be20,be21,be22,be23,be24,be25,be26,be27,be28,be29,be30,be31,be32,be33,be34,be35,be36,be37,be38,be39,be40,be41])
[(24, 31.034904536673583, 1.2931210223613994), (24, 30.99563100948307, 1.291484625395128), (24, 30.769810449480065, 1.2820754353950028), (24, 30.870610841826384, 1.286275451742766), (24, 31.431308752471345, 1.309637864686306), (24, 29.39387670916724, 1.2247448628819684), (24, 31.355002075588832, 1.3064584198162013), (24, 31.059262443650937, 1.2941359351521224), (24, 30.995631009483056, 1.2914846253951273), (24, 30.365236739120522, 1.2652181974633552), (24, 29.393875880616456, 1.224744828359019), (24, 30.995631009483066, 1.2914846253951278), (24, 30.995631009483052, 1.291484625395127), (24, 30.97258982914021, 1.2905245762141755), (24, 31.355002075588835, 1.3064584198162015), (24, 31.355002075588835, 1.3064584198162015), (24, 30.389646620263996, 1.2662352758443332), (24, 30.769810449480083, 1.2820754353950035), (24, 30.38964662026399, 1.266235275844333), (24, 31.431308752471356, 1.3096378646863065), (24, 31.431308752471345, 1.309637864686306), (24, 30.51374967777216, 1.27140623657384), (24, 29.393875880616463, 1.2247448283590192), (24, 30.769810449480072, 1.282075435395003), (24, 30.513749677772175, 1.2714062365738406), (24, 31.355002075588843, 1.3064584198162017), (24, 29.39387670916723, 1.224744862881968), (24, 31.35500207558884, 1.3064584198162017), (24, 31.431308752471356, 1.3096378646863065), (24, 29.393876820174995, 1.2247448675072914), (24, 31.355002075588843, 1.3064584198162017), (24, 31.133258199616765, 1.2972190916506985), (24, 30.972589829140215, 1.2905245762141757), (24, 30.365236739120533, 1.2652181974633556), (24, 31.35500207558885, 1.3064584198162021), (24, 31.431308752471356, 1.3096378646863065), (24, 29.393875880616452, 1.2247448283590188), (24, 30.365236739120512, 1.2652181974633547), (24, 31.16788407998316, 1.298661836665965), (24, 30.769810449480072, 1.282075435395003), (24, 30.995631009483066, 1.2914846253951278)]
be1='{{-2,2,0,0,-1,1,0,0},{1,1,1,0,1,0,0,0},{0,1,-1,0,0,0,0,0},{1,0,-1,0,0,1,0,1},{0,0,0,0,0,0,0,0},{0,1,1,0,0,-1,0,1},{-1,0,-1,0,3,0,0,1},{1,1,1,0,1,1,0,-1}}'

be2='{{-1,0,0,0,1,1,-1,0},{0,0,0,0,0,0,0,0},{0,0,-1,0,1,0,0,0},{-1,0,-1,0,0,1,2,1},{1,0,0,0,1,0,0,0},{0,0,1,0,1,-1,0,1},{0,0,0,0,0,0,0,0},{1,0,1,0,0,1,1,0}}'

be3='{{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,-1,-1,0,0,1,1},{0,0,-1,1,1,0,0,-1},{0,1,1,1,0,0,1,0},{0,0,0,1,0,0,0,1},{0,-1,1,0,1,0,0,1},{0,0,0,0,0,0,0,0}}'

be4='{{-2,0,0,2,3,0,-2,-1},{0,0,0,0,0,0,0,0},{0,1,-2,-3,2,0,1,1},{0,0,-3,2,1,3,0,1},{1,1,2,0,0,2,1,-1},{2,0,0,2,1,0,-2,1},{0,0,2,-1,4,0,1,2},{-1,0,1,2,-1,1,3,1}}'

be5='{{-1,0,0,0,0,1,0,0},{0,0,0,0,0,0,0,0},{0,0,-1,-1,0,0,1,1},{0,0,-2,1,0,1,0,0},{1,0,1,0,0,1,1,0},{0,0,0,0,0,0,0,0},{-1,0,1,1,0,0,0,1},{1,0,1,1,0,1,0,0}}'

be6='{{-1,1,0,-1,1,1,-2,1},{1,1,0,0,1,0,-1,0},{0,1,-1,-1,1,-1,1,0},{-2,0,-1,1,1,2,2,1},{0,1,1,-1,0,1,1,-1},{0,0,0,0,0,0,0,0},{0,0,1,1,1,0,0,1},{2,0,0,1,1,1,1,0}}'

be7='{{-2,0,0,0,0,1,0,1},{0,0,0,0,0,0,0,0},{0,0,-1,-1,0,0,1,1},{1,0,-2,1,0,1,1,2},{1,1,1,0,0,1,1,1},{0,0,0,0,0,0,-2,2},{0,0,1,0,0,0,0,1},{0,-1,1,0,0,1,1,0}}'

be8='{{0,0,0,0,1,-1,1,-1},{0,0,0,0,0,0,0,0},{0,0,-1,-2,1,0,1,1},{0,0,-1,0,0,1,0,0},{-1,0,1,0,0,1,1,0},{0,0,-1,2,1,0,1,1},{0,0,1,0,1,0,-1,1},{1,0,1,0,0,1,1,0}}'

be9='{{0,-2,0,-2,2,2,0,0},{-1,1,1,0,1,0,0,0},{0,1,-1,-2,1,-1,1,1},{-1,1,-1,1,1,1,-1,1},{1,1,0,1,0,1,0,0},{0,0,0,1,-1,0,1,1},{1,0,1,1,2,0,0,1},{0,0,0,0,0,1,1,0}}'

be10='{{-2,0,0,1,0,0,0,1},{0,1,1,0,0,0,0,0},{0,1,-2,-1,0,0,1,1},{1,0,-2,1,0,2,-1,1},{1,1,1,1,0,1,1,0},{0,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,1},{0,-1,1,0,0,1,1,0}}'

be11='{{-2,1,0,0,1,0,0,0},{1,1,1,0,1,0,0,0},{0,1,-2,-1,1,0,1,0},{1,0,-1,0,1,1,0,0},{0,0,0,0,0,0,0,0},{0,1,0,1,-1,0,0,1},{0,0,1,-1,1,0,0,1},{0,0,1,1,0,1,1,0}}'

be12='{{0,0,0,-1,0,2,-2,1},{-3,0,0,1,0,1,1,0},{0,0,-1,-2,1,0,1,1},{1,0,-3,2,0,1,1,0},{1,0,2,2,-1,1,1,0},{0,0,0,2,1,0,0,1},{0,0,1,0,1,0,0,0},{1,0,1,0,0,1,2,1}}'

be13='{{0,0,0,0,0,0,0,0},{-2,0,0,1,1,0,0,0},{0,0,-1,-2,1,0,1,1},{1,0,-1,1,0,0,0,1},{1,0,1,1,0,0,1,0},{0,1,0,1,1,0,0,1},{0,-1,1,0,1,0,0,1},{0,0,0,0,0,0,0,0}}'

be14='{{0,0,0,0,0,0,-1,1},{0,0,1,0,2,0,0,-1},{0,1,-2,-2,1,0,1,1},{0,0,-3,3,1,0,0,1},{1,1,1,1,0,0,0,0},{-1,0,1,1,1,0,1,1},{0,0,1,0,0,0,0,1},{0,0,1,1,-1,0,1,0}}'

be15='{{0,0,0,0,0,0,0,0},{-1,1,1,0,1,0,0,0},{0,1,-1,-1,1,0,0,0},{0,0,-1,1,0,0,0,0},{1,1,1,1,0,0,0,0},{0,0,0,1,1,0,0,0},{0,-1,0,0,1,0,0,0},{0,0,0,0,0,0,0,0}}'

be16='{{-2,0,0,0,1,1,0,0},{0,0,0,0,0,0,0,0},{0,0,-1,-1,1,0,1,0},{1,0,-1,1,1,1,0,1},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,1,0,1,-1,0,1},{1,0,1,0,0,1,1,0}}'

be17='{{-1,0,0,-1,2,0,-1,1},{0,0,1,1,1,0,0,-1},{0,0,-1,-1,1,0,1,0},{0,-1,-3,2,0,2,0,0},{0,1,1,0,0,1,1,0},{0,0,0,0,0,0,0,0},{0,-2,1,2,1,0,1,1},{1,2,1,1,1,1,0,1}}'

be18='{{0,-1,0,0,3,0,-4,2},{0,1,1,-1,1,0,0,0},{0,1,-2,-2,1,0,1,1},{0,0,-2,1,-1,1,0,1},{2,0,1,0,0,0,1,2},{-1,0,0,3,1,0,1,2},{-2,0,1,-1,1,0,2,3},{1,1,1,2,2,1,1,-1}}'

be19='{{0,0,0,1,0,-1,0,0},{0,1,1,-1,0,0,0,1},{0,1,-1,-1,1,-1,1,0},{0,0,-2,2,1,2,0,1},{0,1,1,1,-1,1,0,1},{0,0,-1,0,0,0,0,1},{0,-1,1,-1,1,1,0,1},{0,0,1,1,0,2,1,-1}}'
map(finnKG,[be1,be2,be3,be4,be5,be6,be7,be8,be9,be10,be11,be12,be13,be14,be15,be16,be17,be18,be19])
[(14, 18.52427743526463, 1.3231626739474736), (10, 13.889221864024767, 1.3889221864024768), (8, 11.262193612766497, 1.4077742015958121), (28, 36.796166309716384, 1.3141487967755852), (10, 13.927382345028443, 1.3927382345028443), (18, 23.833860667116777, 1.3241033703953766), (14, 19.4226359178549, 1.3873311369896357), (12, 16.456451797538342, 1.3713709831281953), (18, 24.34163342775525, 1.352312968208625), (14, 18.93173628326298, 1.352266877375927), (14, 19.24179388093499, 1.3744138486382134), (20, 26.9060337319048, 1.3453016865952399), (12, 16.28190537861783, 1.3568254482181523), (16, 21.734447543098085, 1.3584029714436303), (8, 11.262193612766499, 1.4077742015958123), (10, 13.746545829433064, 1.3746545829433063), (18, 24.673625377971682, 1.3707569654428713), (26, 34.52417328607499, 1.327852818695192), (16, 21.589622798862724, 1.3493514249289202)]

map(finnKG,[be1])
[(16, 20.86748137203552, 1.30421758575222)]
map(finnKG,[be1,be2,be3,be4,be5,be6,be7,be8,be9,be10,be11,be12,be13,be14,be15,be16,be17,be18,be19,be20,be21,be22,be23,be24,be25,be26,be27,be28,be29,be30,be31,be32,be33,be34,be35,be36,be37,be38,be39,be40,be41,be42,be43,be44,be45,be46,be47,be48,be49,be50,be51,be52,be53,be54,be55,be56,be57,be58,be59,be60,be61,be62,be63,be64,be65,be66,be67,be68,be69,be70,be71,be72,be73,be74,be75,be76,be77,be78,be79,be80,be81,be82,be83,be84,be85,be86,be87,be88,be89,be90,be91,be92,be93,be94,be95,be96,be97,be98,be99,be100,be101,be102,be103,be104,be105,be106,be107,be108,be109,be110,be111,be112,be113,be114,be115,be116,be117,be118,be119,be120,be121,be122,be123,be124,be125,be126,be127,be128,be129,be130,be131,be132,be133,be134,be135,be136,be137,be138,be139,be140,be141,be142,be143,be144,be145,be146,be147,be148,be149,be150,be151,be152,be153,be154,be155,be156,be157,be158,be159,be160,be161,be162,be163,be164,be165,be166,be167,be168,be169,be170,be171,be172,be173,be174,be175])
--------------------------------------------------------------------------- NameError Traceback (most recent call last) <ipython-input-6-f6c148c6a058> in <module>() ----> 1 map(finnKG,[be1,be2,be3,be4,be5,be6,be7,be8,be9,be10,be11,be12,be13,be14,be15,be16,be17,be18,be19,be20,be21,be22,be23,be24,be25,be26,be27,be28,be29,be30,be31,be32,be33,be34,be35,be36,be37,be38,be39,be40,be41,be42,be43,be44,be45,be46,be47,be48,be49,be50,be51,be52,be53,be54,be55,be56,be57,be58,be59,be60,be61,be62,be63,be64,be65,be66,be67,be68,be69,be70,be71,be72,be73,be74,be75,be76,be77,be78,be79,be80,be81,be82,be83,be84,be85,be86,be87,be88,be89,be90,be91,be92,be93,be94,be95,be96,be97,be98,be99,be100,be101,be102,be103,be104,be105,be106,be107,be108,be109,be110,be111,be112,be113,be114,be115,be116,be117,be118,be119,be120,be121,be122,be123,be124,be125,be126,be127,be128,be129,be130,be131,be132,be133,be134,be135,be136,be137,be138,be139,be140,be141,be142,be143,be144,be145,be146,be147,be148,be149,be150,be151,be152,be153,be154,be155,be156,be157,be158,be159,be160,be161,be162,be163,be164,be165,be166,be167,be168,be169,be170,be171,be172,be173,be174,be175]) NameError: name 'finnKG' is not defined



















map(finnKG,[be14])

map(finnKG,[be1])
WARNING: Some output was deleted.
























map(finnKG,[be1])
[(8, 11.262193104312297, 1.4077741380390372)]












be180='{{0,0,0,0,0,0,0,0},{1,1,0,0,1,1,0,0},{0,0,-1,0,1,0,0,0},{0,0,0,-1,0,1,0,0},{1,0,0,1,-1,0,0,1},{0,1,1,0,0,-1,1,0},{0,0,1,1,1,0,-1,0},{0,0,1,1,0,1,0,-1}}'
map(finnKG,[be180])
[(12, 16.9705624961966, 1.4142135413497166)]