harshadsurdi · October 29, 2012 13:09 · harshadsurdi · Nov 1, 2012
diff --git a/configfile.txt b/configfile.txt
 pdf Nelder-Mead 0 2047
diff --git a/Nelder-Mead.py b/Nelder-Mead.py
 #-------------------------------------------------------------------------------
 # Name:        Nelder-Mead
 # Purpose:
 #
 # Author:      Harshad
 #
 # Created:     25-10-2012
 # Copyright:   (c) Harshad 2012
 # Licence:     <your licence>
 #-------------------------------------------------------------------------------

 ##==============================================================================##

 ##-----------ALL IMPORTS-----------##

 from numpy import  linspace
 from matplotlib import pyplot,legend
 from math import pi,log10,atan2,log
 from scipy import optimize,stats
 from scipy.stats import norm
 from cmath import exp
 ##==============================================================================##

 ##-----------ALL INITIALIZATIONS-----------##

 v1=complex(0.0,0.0)
 v2=complex(0.0,0.0)
 fix_values=-1.0j*2.0*pi*0.01
 global varr_L
 L=400
 c=2.99792458
 delta_f= 0.001953125  #---delta_w = 4THz/2048 = 1953125000
 constant=fix_values*(delta_f*L/c)
 z=complex(0.0,1.0)
 n1=complex(1.0,0.0)
 n3=complex(1.0,0.0)
 global Pwl_omega

 ##==============================================================================##

 ##-----------ALL DEFINITIONS-----------##

 def twopower(x):
    y=int(math.log(x,2))
    return 2**y

 #===========================================
 #======T formulated=========================
 #===========================================

 def Tformulated(n,k,w):
    v3=w*constant
    n2=complex(n,-k)
    v1=1.0/(1.0-(((n2-n1)*(n2-n3)*exp(2*v3*n2))/((n2+n1)*(n2+n3))))
    FP=v1
    v2=((2.0*n2*(n1+n3))/((n2+n1)*(n2+n3)))*((exp((n2-n1)*v3)))*FP
    Tform=v2
    return(Tform)

 #===================================
 #======CONFIG FILE READ=====================
 #===========================================
 fp=open("YOUR PATH\configfile.txt",'r')
 for line in fp:
    var_type,func_type,freq_sel_a,freq_sel_b=map(str,line.split())
    freq_sel_a=int(freq_sel_a)
    freq_sel_b=int(freq_sel_b)
 fp.close()
 #===========================================
 ##==============================================================================##

 ##-----------MAIN ALGORITHM-----------##

 #============= Generating T(w) for given n2,k2 and range of w ==================
 freq=[]
 Tw_read_cmplx=[]
 Tw_read_real=[]
 Tw_read_imag=[]
 Tw_read_abs=[]
 Tw_read_phi=[]
 Tw_abs_log10=[]
 Tw_wrapphi=[]

 if var_type == "fix":
   Tw_read=open("YOUR PATH\Tw_fix.txt",'rt')
 elif var_type == "linear":
     Tw_read = open("YOUR PATH\Tw_lin.txt",'rt')
 elif var_type=="pdf":
     Tw_read=open("YOUR PATH\Tw_norm.txt",'rt')
 else :
     disp("INVALID TYPE OF VARIATION")
     exit()

 for line in Tw_read:
    a,b,c,d,e=map(float,line.split())
    freq.append(a)
    Tw_read_real.append(b)
    Tw_read_imag.append(c)
    Tw_read_abs.append(d)
    Tw_read_phi.append(e)

 n2=4   #the parameters to
 k2=3    #generate Tmeas()
 Tw_abs=Tw_read_abs #Tmeas() is the generation function
 Tw_abs_log10=[log10(i) for i in Tw_abs]
 Tw_phi=Tw_read_phi

 for i in range(len(Tw_read_imag)):
    Tw_wrapphi.append(atan2(Tw_read_imag[i],Tw_read_real[i]))

 pyplot.figure()
 p1,=pyplot.plot(range(len(Tw_abs_log10)),Tw_abs_log10)
 p2,=pyplot.plot(range(len(Tw_phi)),Tw_phi)
 p3,=pyplot.plot(range(len(Tw_wrapphi)),Tw_wrapphi)
 p4,=pyplot.plot(range(len(Tw_abs)),Tw_abs)
 pyplot.title("Formula Generated T(w)")
 pyplot.legend([p1,p2,p3,p4],["Tw_abs_10","Tw_phi","Tw_wrapphi","T_abs"])
 pyplot.show()

 #===========ERROR FUNCTIONS=====================================================

 error=lambda x,w: (log(abs(Tformulated(x[0],x[1],w))) - log(Tw_abs[w]))**2 + (atan2(Tformulated(x[0],x[1],w).imag,Tformulated(x[0],x[1],w).real) - Tw_wrapphi[w])**2

 #========================initial guess vector===================================

 v0_nm=[1,1]
 omega=[500]
 snm_n2=[]
 snm_k2=[]


 #===========================Scipy POWELL========================================

 a=freq_sel_a;b=freq_sel_b
 err_arr=[]
 for w in range(a,b):
    omega[0]=w
    retval2 = optimize.minimize(error,v0_nm,args=(omega),method='Nelder-Mead',options={'gtol':1e-9})
    print w
    #print "minimize Nelder-Mead : ",retval2.x
    #print "VALUE of COUTAZ at (%f,%f) = %s"%(retval2.x[0],retval2.x[1],error([retval2.x[0],retval2.x[1]],omega[0]))
    snm_n2.append(retval2.x[0])
    snm_k2.append(retval2.x[1])
    v0_nm=[retval2.x[0],retval2.x[1]]
    err_arr.append(error(v0_nm,w))

 n=[]
 k=[]

 if var_type == "fix":
   for i in range(a,b):
        n.append(3)
        k.append(1)
 elif var_type == "linear":
    for i in range(a,b):
        n.append(3.5 + 0.2*i/1000)
        k.append(0.1 + 0.1*i/1000)
 elif var_type == "pdf":
    global n2_arr
    global k2_arr
    spread_n2=linspace(1,4,2048)
    spread_k2=linspace(0.01,0.9,2048)
    n2_arr = 1.0+4.0*norm.pdf(spread_n2,2.5,0.5)
    k2_arr= 0.25*norm.pdf(spread_k2,0.5,0.1)
    for i in range(a,b):
        n.append(n2_arr[i])
        k.append(k2_arr[i])

 n_err = [(snm_n2[i] - n[i]) for i in range(len(snm_n2))]
 k_err = [(snm_k2[i] - k[i]) for i in range(len(snm_k2))]


 p4,=pyplot.plot(range(a,b),snm_k2)
 p6,=pyplot.plot(range(len(k)),k,'g+')
 pyplot.legend([p4,p6], ["mini Nelder Mead","k2"])
 pyplot.title("K2")
 pyplot.show()

 p4,=pyplot.plot(range(a,b),snm_n2)
 p6,=pyplot.plot(range(len(n)),n,'g+')
 pyplot.legend([p4,p6], ["mini Nelder Mead_n2","n2"])
 pyplot.title("N2")
 pyplot.show()

 p1,=pyplot.plot(range(len(snm_n2)),n_err)
 p2,=pyplot.plot(range(len(snm_k2)),k_err)
 p3,=pyplot.plot(range(len(err_arr)),err_arr)
 pyplot.legend([p1,p2,p3],["n_err","k_err","err_arr"])
 pyplot.title("error in n and k and total error")
 pyplot.show()
diff --git a/Tw_norm.txt b/Tw_norm.txt
 0	1.0	1.32348898008e-23	1.0	1.32348898008e-23
 1	0.999999539017	-0.000596125501776	0.999999716699	-0.000596125705966
 2	0.999998337324	-0.00120293853116	0.999999060855	-0.00120293995102
 3	0.999996356043	-0.00182055552504	0.999998013259	-0.0018205601477
 4	0.999993555463	-0.00244909317018	0.999996554507	-0.00244910405687
 5	0.999989895045	-0.0030886683852	0.999994665018	-0.0030886897743
 6	0.999985333434	-0.00373939830297	0.999992325062	-0.00373943571782
 7	0.999979828472	-0.00440140025344	0.999989514783	-0.00440146061503
 8	0.999973337209	-0.00507479174712	0.999986214225	-0.00507488349146
 9	0.999965815916	-0.00575969045911	0.999982403362	-0.0057598236596
 10	0.9999572201	-0.00645621421385	0.999978062125	-0.00645640070845
 11	0.999947504521	-0.00716448097062	0.999973170433	-0.00716473449393
 12	0.999936623208	-0.00788460880983	0.999967708223	-0.0078849451301
 13	0.999924529473	-0.00861671592028	0.999961655483	-0.00861715298129
 14	0.999911175937	-0.00936092058732	0.999954992286	-0.00936147865508
 15	0.999896514542	-0.0101173411821	0.999947698826	-0.0101180429965
 16	0.999880496579	-0.0108860961518	0.999939755449	-0.0108869670829
 17	0.999863072702	-0.0116673040114	0.999931142697	-0.0116683722206
 18	0.999844192957	-0.0124610833363	0.999921841339	-0.0124623799421
 19	0.999823806803	-0.0132675527564	0.999911832416	-0.0132691120048
 20	0.999801863136	-0.0140868309521	0.999901097278	-0.0140886903914
 21	0.999778310315	-0.0149190366509	0.999889617623	-0.0149212373109
 22	0.999753096187	-0.0157642886264	0.999877375548	-0.0157668752019
 23	0.999726168116	-0.0166227056986	0.99986435358	-0.0166257267372
 24	0.999697473006	-0.0174944067361	0.999850534731	-0.0174979148294
 25	0.999666957336	-0.0183795106597	0.999835902537	-0.0183835626389
 26	0.99963456718	-0.0192781364489	0.999820441103	-0.0192827935837
 27	0.999600248245	-0.0201904031491	0.999804135154	-0.0201957313499
 28	0.999563945894	-0.021116429882	0.99978697008	-0.0211224999059
 29	0.999525605178	-0.0220563358575	0.999768931983	-0.0220632235165
 30	0.999485170867	-0.0230102403883	0.999750007725	-0.0230180267604
 31	0.99944258748	-0.0239782629061	0.99973018498	-0.0239870345495
 32	0.999397799316	-0.0249605229811	0.999709452283	-0.0249703721498
 33	0.999350750481	-0.0259571403432	0.999687799077	-0.0259681652051
 34	0.999301384926	-0.0269682349063	0.999665215764	-0.0269805397625
 35	0.999249646468	-0.0279939267948	0.99964169376	-0.0280076223005
 36	0.999195478827	-0.0290343363731	0.99961722554	-0.0290495397591
 37	0.999138825651	-0.0300895842774	0.999591804691	-0.030106419573
 38	0.999079630548	-0.0311597914509	0.999565425962	-0.0311783897061
 39	0.999017837112	-0.0322450791815	0.999538085317	-0.03226557869
 40	0.998953388953	-0.0333455691423	0.999509779983	-0.0333681156636
 41	0.998886229719	-0.0344613834354	0.999480508499	-0.0344861304164
 42	0.998816303124	-0.0355926446386	0.999450270768	-0.0356197534337
 43	0.998743552975	-0.0367394758551	0.999419068107	-0.0367691159451
 44	0.998667923188	-0.0379020007662	0.999386903289	-0.0379343499751
 45	0.998589357813	-0.0390803436874	0.9993537806	-0.0391155883969
 46	0.998507801054	-0.0402746296278	0.999319705878	-0.0403129649889
 47	0.998423197283	-0.0414849843517	0.999284686563	-0.0415266144936
 48	0.998335491059	-0.0427115344449	0.999248731739	-0.0427566726802
 49	0.998244627136	-0.043954407383	0.999211852179	-0.0440032764088
 50	0.99815055048	-0.0452137316032	0.999174060386	-0.0452665636984
 51	0.998053206269	-0.04648963658	0.999135370635	-0.0465466737976
 52	0.997952539905	-0.0477822529029	0.999095799008	-0.0478437472578
 53	0.997848497009	-0.0490917123581	0.999055363434	-0.049157926009
 54	0.997741023426	-0.0504181480132	0.999014083723	-0.0504893534397
 55	0.997630065215	-0.0517616943051	0.998971981599	-0.051838174478
 56	0.997515568643	-0.0531224871302	0.998929080728	-0.0532045356765
 57	0.997397480169	-0.0545006639387	0.99888540675	-0.0545885852993
 58	0.997275746433	-0.055896363831	0.998840987301	-0.0559904734128
 59	0.997150314227	-0.0573097276575	0.998795852037	-0.0574103519776
 60	0.997021130475	-0.0587408981204	0.998750032654	-0.0588483749442
 61	0.996888142202	-0.0601900198793	0.998703562903	-0.0603046983509
 62	0.996751296493	-0.0616572396582	0.998656478607	-0.0617794804243
 63	0.99661054046	-0.0631427063555	0.998608817666	-0.0632728816815
 64	0.996465821186	-0.0646465711566	0.99856062007	-0.0647850650361
 65	0.996317085681	-0.0661689876477	0.998511927894	-0.0663161959046
 66	0.996164280819	-0.0677101119327	0.998462785304	-0.0678664423169
 67	0.996007353274	-0.069270102751	0.998413238549	-0.0694359750269
 68	0.995846249449	-0.0708491215976	0.998363335952	-0.0710249676267
 69	0.9956809154	-0.072447332844	0.998313127895	-0.0726335966615
 70	0.995511296747	-0.0740649038612	0.998262666805	-0.0742620417467
 71	0.995337338589	-0.0757020051424	0.998212007126	-0.0759104856861
 72	0.995158985395	-0.0773588104282	0.998161205298	-0.0775791145923
 73	0.994976180906	-0.0790354968304	0.998110319719	-0.0792681180071
 74	0.994788868017	-0.0807322449577	0.99805941071	-0.0809776890242
 75	0.994596988651	-0.0824492390399	0.998008540471	-0.0827080244118
 76	0.994400483635	-0.0841866670532	0.997957773036	-0.0844593247365
 77	0.994199292552	-0.0859447208436	0.997907174216	-0.0862317944872
 78	0.993993353601	-0.0877235962498	0.997856811542	-0.0880256421998
 79	0.993782603433	-0.0895234932252	0.997806754199	-0.0898410805816
 80	0.993566976991	-0.0913446159569	0.997757072955	-0.0916783266356
 81	0.993346407331	-0.0931871729845	0.997707840085	-0.0935376017843
 82	0.993120825439	-0.0950513773144	0.997659129287	-0.0954191319932
 83	0.992890160036	-0.0969374465328	0.997611015596	-0.0973231478929
 84	0.992654337377	-0.0988456029145	0.997563575281	-0.0992498849005
 85	0.992413281032	-0.100776073528	0.997516885754	-0.101199583339
 86	0.992166911671	-0.102729090337	0.997471025452	-0.103172488556
 87	0.991915146824	-0.104704890297	0.997426073727	-0.105168851038
 88	0.99165790064	-0.106703715446	0.997382110724	-0.107188926526
 89	0.991395083636	-0.108725812988	0.997339217251	-0.109232976126
 90	0.991126602428	-0.110771435376	0.997297474647	-0.111301266414
 91	0.990852359465	-0.112840840383	0.997256964637	-0.113394069546
 92	0.990572252739	-0.114934291166	0.997217769187	-0.115511663354
 93	0.990286175492	-0.117052056323	0.997179970346	-0.117654331446
 94	0.989994015916	-0.119194409944	0.997143650088	-0.119822363296
 95	0.989695656833	-0.121361631648	0.997108890137	-0.122016054334
 96	0.989390975375	-0.123554006616	0.997075771797	-0.124235706028
 97	0.98907984265	-0.125771825607	0.997044375769	-0.126481625961
 98	0.988762123395	-0.128015384967	0.997014781961	-0.1287541279
 99	0.988437675625	-0.130284986631	0.996987069292	-0.131053531866
 100	0.988106350269	-0.132580938098	0.996961315493	-0.133380164187
 101	0.987767990802	-0.134903552414	0.996937596897	-0.135734357551
 102	0.987422432857	-0.137253148118	0.996915988224	-0.138116451049
 103	0.987069503842	-0.139630049195	0.996896562364	-0.140526790214
 104	0.986709022539	-0.142034584999	0.996879390145	-0.14296572704
 105	0.986340798701	-0.144467090165	0.996864540108	-0.145433620008
 106	0.985964632637	-0.146927904509	0.996852078262	-0.14793083409
 107	0.985580314791	-0.149417372902	0.996842067847	-0.150457740752
 108	0.985187625319	-0.151935845131	0.996834569082	-0.153014717937
 109	0.984786333654	-0.154483675743	0.996829638916	-0.155602150049
 110	0.984376198067	-0.157061223863	0.996827330766	-0.158220427918
 111	0.98395696523	-0.159668852999	0.996827694259	-0.160869948752
 112	0.983528369761	-0.16230693082	0.996830774965	-0.163551116088
 113	0.983090133783	-0.164975828917	0.996836614129	-0.166264339715
 114	0.982641966465	-0.167675922536	0.9968452484	-0.169010035597
 115	0.982183563572	-0.170407590292	0.996856709552	-0.171788625778
 116	0.981714607006	-0.17317121386	0.996871024215	-0.174600538271
 117	0.98123476436	-0.175967177635	0.996888213589	-0.177446206934
 118	0.980743688453	-0.178795868375	0.996908293169	-0.180326071336
 119	0.980241016893	-0.181657674812	0.996931272464	-0.183240576602
 120	0.979726371618	-0.184552987236	0.996957154718	-0.186190173244
 121	0.979199358463	-0.187482197059	0.996985936625	-0.18917531698
 122	0.978659566718	-0.190445696342	0.997017608061	-0.19219646853
 123	0.978106568704	-0.193443877301	0.997052151798	-0.195254093404
 124	0.97753991935	-0.196477131778	0.997089543238	-0.198348661666
 125	0.97695915579	-0.199545850692	0.997129750138	-0.201480647683
 126	0.976363796959	-0.202650423448	0.997172732347	-0.20465052986
 127	0.975753343218	-0.205791237328	0.997218441547	-0.207858790353
 128	0.975127275979	-0.208968676846	0.997266820997	-0.211105914764
 129	0.974485057362	-0.212183123073	0.997317805285	-0.214392391825
 130	0.973826129861	-0.215434952932	0.997371320094	-0.217718713051
 131	0.973149916035	-0.218724538469	0.997427281965	-0.22108537239
 132	0.972455818222	-0.222052246079	0.997485598083	-0.224492865841
 133	0.971743218278	-0.225418435723	0.997546166066	-0.227941691065
 134	0.971011477343	-0.228823460095	0.997608873769	-0.231432346965
 135	0.97025993564	-0.232267663775	0.997673599101	-0.234965333262
 136	0.969487912297	-0.235751382345	0.997740209858	-0.238541150043
 137	0.968694705217	-0.239274941485	0.997808563572	-0.24216029729
 138	0.96787959097	-0.24283865603	0.997878507374	-0.245823274401
 139	0.967041824734	-0.246442829016	0.997949877878	-0.249530579685
 140	0.966180640274	-0.250087750689	0.998022501091	-0.253282709841
 141	0.965295249963	-0.253773697502	0.998096192331	-0.257080159425
 142	0.964384844854	-0.257500931078	0.998170756178	-0.260923420295
 143	0.963448594794	-0.261269697165	0.998245986452	-0.264812981045
 144	0.962485648595	-0.265080224565	0.998321666201	-0.268749326423
 145	0.961495134256	-0.268932724052	0.998397567737	-0.272732936735
 146	0.960476159241	-0.272827387271	0.998473452684	-0.276764287233
 147	0.959427810815	-0.276764385636	0.998549072065	-0.2808438475
 148	0.958349156441	-0.280743869208	0.998624166415	-0.28497208081
 149	0.95723924424	-0.284765965578	0.998698465936	-0.289149443491
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 1750	-0.473269302979	0.0236920325355	0.473861947774	-9.47479656758
 1751	-0.477977658028	-0.00178334513586	0.477980984867	-9.42104695613
 1752	-0.48129973108	-0.027601069711	0.482090499997	-9.36749375607
 1753	-0.483216364708	-0.0536822235727	0.486189095157	-9.31413808208
 1754	-0.483713212332	-0.0799469333863	0.490275416417	-9.26098116255
 1755	-0.482780788988	-0.106314693129	0.494348160906	-9.20802432579
 1756	-0.480414496903	-0.132704691037	0.498406083287	-9.15526898596
 1757	-0.476614625457	-0.159036138034	0.502448001688	-9.10271662858
 1758	-0.471386325359	-0.18522859518	0.506472803029	-9.05036879599
 1759	-0.464739557186	-0.211202297632	0.510479447714	-8.99822707282
 1760	-0.456689014729	-0.236878472669	0.514466973661	-8.94629307149
 1761	-0.447254023867	-0.262179649384	0.51843449964	-8.89456841804
 1762	-0.436458417964	-0.287029957773	0.522381227908	-8.8430547383
 1763	-0.424330391035	-0.311355415072	0.526306446142	-8.79175364449
 1764	-0.410902330179	-0.335084197386	0.530209528662	-8.74066672243
 1765	-0.396210628931	-0.358146894842	0.534089936961	-8.68979551935
 1766	-0.380295483408	-0.380476748734	0.537947219556	-8.63914153247
 1767	-0.363200673218	-0.402009869353	0.541781011187	-8.58870619837
 1768	-0.344973329228	-0.422685433465	0.545591031398	-8.53849088318
 1769	-0.325663690346	-0.44244586063	0.549377082521	-8.48849687369
 1770	-0.305324851497	-0.461236967853	0.553139047126	-8.4387253694
 1771	-0.284012504976	-0.479008102257	0.556876884967	-8.38917747547
 1772	-0.261784677332	-0.495712251783	0.560590629473	-8.33985419671
 1773	-0.238701463863	-0.511306134073	0.564280383844	-8.29075643247
 1774	-0.214824762721	-0.525750263984	0.567946316791	-8.2418849725
 1775	-0.1902180105	-0.539009000323	0.571588657994	-8.19324049378
 1776	-0.164945921067	-0.551050572595	0.575207693302	-8.14482355827
 1777	-0.139074229236	-0.561847088689	0.578803759754	-8.09663461147
 1778	-0.112669440726	-0.571374524579	0.582377240465	-8.04867398194
 1779	-0.085798589676	-0.579612697194	0.585928559416	-8.00094188153
 1780	-0.058529004829	-0.586545221698	0.589458176212	-7.95343840642
 1781	-0.0309280853158	-0.592159454485	0.592966580843	-7.90616353886
 1782	-0.0030630867981	-0.596446423213	0.596454288495	-7.85911714951
 1783	0.0249990814266	-0.599400745217	0.599921834441	-7.81229900045
 1784	0.0531920479197	-0.601020535637	0.603369769063	-7.76570874868
 1785	0.0814501589014	-0.601307306565	0.606798653025	-7.71934595008
 1786	0.109708646203	-0.600265858475	0.610209052623	-7.67321006385
 1787	0.137903783336	-0.597904165167	0.613601535348	-7.62730045723
 1788	0.165973029771	-0.594233253345	0.616976665679	-7.58161641058
 1789	0.193855163587	-0.589267077947	0.620335001109	-7.5361571227
 1790	0.221490402785	-0.583022394189	0.623677088446	-7.49092171633
 1791	0.248820515579	-0.575518627278	0.627003460371	-7.4459092438
 1792	0.27578892007	-0.566777740597	0.630314632283	-7.40111869276
 1793	0.302340773756	-0.556824103138	0.633611099422	-7.35654899201
 1794	0.32842305334	-0.545684356823	0.636893334277	-7.31219901729
 1795	0.353984625346	-0.533387284321	0.640161784283	-7.26806759705
 1796	0.378976308056	-0.519963677835	0.643416869794	-7.2241535182
 1797	0.40335092529	-0.505446209314	0.646658982341	-7.18045553166
 1798	0.427063352539	-0.489869302425	0.649888483157	-7.13697235791
 1799	0.450070555973	-0.473269006585	0.653105701971	-7.09370269229
 1800	0.472331624786	-0.455682873292	0.656310936055	-7.05064521019
 1801	0.493807797391	-0.437149834912	0.659504449513	-7.00779857199
 1802	0.514462481863	-0.417710086077	0.662686472817	-6.96516142782
 1803	0.534261271091	-0.397404967763	0.665857202552	-6.92273242209
 1804	0.553171953001	-0.37627685411	0.669016801378	-6.88051019779
 1805	0.57116451623	-0.354369042002	0.672165398194	-6.83849340051
 1806	0.588211151554	-0.331725643409	0.675303088478	-6.79668068226
 1807	0.604286249404	-0.308391480466	0.678429934807	-6.75507070496
 1808	0.619366393697	-0.284411983251	0.681545967531	-6.71366214376
 1809	0.633430352258	-0.259833090217	0.684651185592	-6.67245369
 1810	0.646459064014	-0.234701151219	0.687745557477	-6.631444054
 1811	0.658435623166	-0.209062833092	0.690829022287	-6.59063196753
 1812	0.669345260485	-0.182965027702	0.693901490916	-6.55001618602
 1813	0.679175321885	-0.156454762427	0.696962847319	-6.50959549059
 1814	0.687915244377	-0.129579113026	0.700012949865	-6.46936868978
 1815	0.695556529522	-0.102385118828	0.703051632754	-6.42933462103
 1816	0.702092714467	-0.0749197002259	0.706078707503	-6.38949215197
 1817	0.707519340627	-0.0472295784405	0.709093964465	-6.34984018149
 1818	0.711833920108	-0.0193611975306	0.712097174399	-6.31037764055
 1819	0.715035899898	0.00863935135007	0.715088090052	-6.27110349285
 1820	0.717126623903	0.036726403454	0.718066447776	-6.23201673527
 1821	0.718109292874	0.0648547916857	0.721031969137	-6.19311639814
 1822	0.717988922263	0.0929799155732	0.723984362533	-6.15440154533
 1823	0.716772298072	0.121057807936	0.726923324805	-6.11587127418
 1824	0.714467930744	0.149045199211	0.729848542829	-6.07752471532
 1825	0.711086007138	0.176899579401	0.732759695085	-6.03936103226
 1826	0.706638340671	0.204579257582	0.735656453203	-6.00137942096
 1827	0.701138319665	0.232043418928	0.738538483473	-5.96357910922
 1828	0.694600853995	0.259252179196	0.741405448313	-5.92595935595
 1829	0.687042320094	0.286166636599	0.744257007695	-5.88851945038
 1830	0.678480504421	0.312748921018	0.747092820523	-5.85125871119
 1831	0.66893454546	0.33896224049	0.74991254596	-5.8141764855
 1832	0.658424874376	0.364770924907	0.752715844695	-5.77727214789
 1833	0.64697315441	0.390140466874	0.755502380155	-5.74054509923
 1834	0.634602219149	0.415037559672	0.758271819658	-5.70399476562
 1835	0.621336009774	0.439430132281	0.761023835499	-5.66762059715
 1836	0.607199511425	0.463287381403	0.763758105975	-5.63142206668
 1837	0.592218688811	0.486579800476	0.76647431634	-5.59539866866
 1838	0.5764204212	0.509279205624	0.7691721597	-5.55954991776
 1839	0.559832436939	0.531358758534	0.771851337836	-5.52387534771
 1840	0.54248324764	0.55279298625	0.774511561964	-5.48837450995
 1841	0.524402082188	0.573557797863	0.777152553423	-5.45304697236
 1842	0.505618820715	0.593630498127	0.779774044302	-5.41789231803
 1843	0.486163928696	0.612989797985	0.782375777999	-5.38291014396
 1844	0.466068391307	0.631615822065	0.784957509715	-5.34810005983
 1845	0.445363648213	0.649490113137	0.78751900689	-5.3134616868
 1846	0.424081528914	0.666595633618	0.790060049569	-5.2789946563
 1847	0.402254188801	0.682916764141	0.792580430715	-5.24469860886
 1848	0.379914046077	0.698439299269	0.795079956463	-5.21057319298
 1849	0.357093719652	0.713150440423	0.797558446316	-5.17661806404
 1850	0.33382596817	0.72703878609	0.800015733285	-5.14283288325
 1851	0.310143630286	0.740094319416	0.802451663989	-5.10921731659
 1852	0.286079566301	0.752308393258	0.804866098691	-5.07577103386
 1853	0.261666601291	0.76367371281	0.807258911297	-5.04249370776
 1854	0.236937469817	0.774184315902	0.809629989311	-5.00938501294
 1855	0.211924762321	0.783835551088	0.811979233746	-4.97644462522
 1856	0.186660873303	0.792624053635	0.814306558995	-4.94367222074
 1857	0.161177951352	0.800547719533	0.816611892671	-4.91106747524
 1858	0.135507851112	0.807605677665	0.81889517541	-4.8786300633
 1859	0.109682087244	0.813798260238	0.821156360646	-4.84635965774
 1860	0.0837317904395	0.819126971627	0.823395414353	-4.81425592897
 1861	0.0576876655396	0.823594455752	0.82561231477	-4.78231854439
 1862	0.031579951788	0.827204462117	0.827807052097	-4.75054716792
 1863	0.0054383852586	0.829961810653	0.829979628169	-4.71894145949
 1864	-0.020707836526	0.831872355476	0.83213005612	-4.68750107459
 1865	-0.0468300877688	0.832942947714	0.834258360022	-4.65622566387
 1866	-0.0729003453605	0.833181397512	0.836364574521	-4.6251148728
 1867	-0.0988912176296	0.832596435343	0.83844874445	-4.59416834135
 1868	-0.124775970889	0.831197672756	0.840510924442	-4.5633857037
 1869	-0.150528553797	0.82899556268	0.842551178536	-4.53276658798
 1870	-0.17612361955	0.826001359384	0.844569579767	-4.50231061611
 1871	-0.201536545939	0.822227078229	0.846566209769	-4.47201740356
 1872	-0.226743453301	0.817685455306	0.848541158361	-4.44188655927
 1873	-0.25172122041	0.81238990706	0.850494523144	-4.41191768548
 1874	-0.276447498339	0.806354490019	0.852426409089	-4.3821103777
 1875	-0.300900722357	0.7995938607	0.85433692814	-4.3524642246
 1876	-0.325060121899	0.792123235789	0.856226198809	-4.32297880803
 1877	-0.348905728676	0.783958352695	0.858094345782	-4.29365370297
 1878	-0.372418382975	0.775115430527	0.859941499532	-4.26448847756
 1879	-0.395579738217	0.765611131596	0.861767795936	-4.23548269315
 1880	-0.418372263836	0.755462523499	0.863573375897	-4.20663590434
 1881	-0.440779246536	0.744687041845	0.865358384988	-4.17794765904
 1882	-0.462784790012	0.733302453688	0.867122973084	-4.14941749859
 1883	-0.484373813181	0.72132682172	0.868867294026	-4.12104495784
 1884	-0.505532047012	0.708778469274	0.870591505278	-4.09282956529
 1885	-0.526246030013	0.695675946167	0.872295767604	-4.06477084318
 1886	-0.546503102449	0.682037995449	0.873980244755	-4.03686830768
 1887	-0.566291399366	0.667883521059	0.875645103166	-4.009121469
 1888	-0.585599842476	0.65323155645	0.877290511661	-3.98152983157
 1889	-0.604418130995	0.638101234183	0.878916641179	-3.95409289421
 1890	-0.622736731481	0.622511756528	0.880523664504	-3.92681015027
 1891	-0.640546866755	0.606482367078	0.882111756007	-3.89968108787
 1892	-0.657840503962	0.590032323402	0.883681091408	-3.87270519
 1893	-0.674610341838	0.573180870734	0.885231847535	-3.84588193479
 1894	-0.69084979726	0.555947216718	0.886764202114	-3.81921079563
 1895	-0.70655299112	0.538350507195	0.888278333552	-3.79269124141
 1896	-0.721714733597	0.520409803057	0.889774420743	-3.76632273668
 1897	-0.736330508885	0.502144058142	0.891252642881	-3.74010474186
 1898	-0.750396459435	0.48357209818	0.892713179286	-3.71403671342
 1899	-0.763909369752	0.464712600779	0.894156209237	-3.68811810409
 1900	-0.776866649821	0.445584076438	0.89558191182	-3.66234836303
 1901	-0.789266318199	0.426204850583	0.896990465782	-3.63672693603
 1902	-0.801106984826	0.406593046604	0.8983820494	-3.61125326568
 1903	-0.812387833596	0.386766569886	0.89975684035	-3.5859267916
 1904	-0.823108604751	0.366743092812	0.9011150156	-3.56074695056
 1905	-0.833269577109	0.346540040722	0.902456751296	-3.5357131767
 1906	-0.842871550207	0.326174578808	0.903782222667	-3.51082490168
 1907	-0.851915826353	0.305663599929	0.905091603934	-3.48608155489
 1908	-0.860404192667	0.285023713315	0.90638506823	-3.46148256356
 1909	-0.868338903108	0.264271234151	0.907662787521	-3.43702735298
 1910	-0.87572266055	0.243422174004	0.908924932542	-3.41271534659
 1911	-0.882558598911	0.222492232081	0.910171672734	-3.38854596622
 1912	-0.888850265389	0.20149678729	0.91140317619	-3.36451863218
 1913	-0.894601602809	0.180450891074	0.912619609607	-3.3406327634
 1914	-0.899816932126	0.15936926101	0.91382113824	-3.31688777762
 1915	-0.904500935087	0.138266275119	0.915007925872	-3.29328309148
 1916	-0.908658637098	0.117155966898	0.916180134773	-3.26981812067
 1917	-0.91229539029	0.0960520210184	0.917337925678	-3.24649228005
 1918	-0.915416856826	0.0749677696831	0.918481457762	-3.22330498379
 1919	-0.918028992448	0.0539161896093	0.919610888625	-3.20025564546
 1920	-0.920138030287	0.0329098996168	0.920726374269	-3.17734367815
 1921	-0.921750464959	0.0119611587942	0.921828069095	-3.15456849459
 1922	-0.922873036936	-0.00891813478025	0.922916125892	-3.13192950726
 1923	-0.923512717233	-0.0297164447888	0.923990695831	-3.10942612846
 1924	-0.923676692397	-0.0504225969171	0.925051928466	-3.08705777042
 1925	-0.92337234982	-0.0710257786147	0.926099971731	-3.0648238454
 1926	-0.922607263381	-0.0915155383971	0.927134971949	-3.04272376577
 1927	-0.921389179422	-0.11188178471	0.928157073832	-3.02075694407
 1928	-0.919726003068	-0.132114784379	0.929166420493	-2.99892279313
 1929	-0.917625784894	-0.152205160671	0.93016315345	-2.97722072611
 1930	-0.915096707935	-0.172143890976	0.931147412644	-2.95565015661
 1931	-0.912147075065	-0.191922304147	0.932119336447	-2.93421049867
 1932	-0.908785296714	-0.211532077509	0.933079061676	-2.91290116691
 1933	-0.905019878958	-0.230965233552	0.93402672361	-2.89172157655
 1934	-0.900859411961	-0.25021413634	0.934962456007	-2.87067114345
 1935	-0.896312558775	-0.269271487646	0.935886391116	-2.84974928423
 1936	-0.891388044503	-0.288130322833	0.936798659702	-2.82895541625
 1937	-0.886094645818	-0.306784006501	0.937699391059	-2.8082889577
 1938	-0.880441180833	-0.325226227912	0.93858871303	-2.78774932761
 1939	-0.874436499336	-0.343450996217	0.939466752031	-2.76733594596
 1940	-0.868089473366	-0.361452635495	0.940333633066	-2.74704823364
 1941	-0.861408988144	-0.379225779623	0.941189479746	-2.72688561254
 1942	-0.854403933346	-0.396765366988	0.942034414318	-2.70684750557
 1943	-0.847083194721	-0.414066635061	0.942868557674	-2.68693333671
 1944	-0.839455646039	-0.431125114846	0.943692029382	-2.66714253099
 1945	-0.831530141382	-0.447936625206	0.944504947699	-2.64747451459
 1946	-0.823315507753	-0.464497267102	0.945307429597	-2.62792871482
 1947	-0.814820538015	-0.480803417733	0.94609959078	-2.60850456016
 1948	-0.806053984146	-0.496851724602	0.946881545706	-2.58920148029
 1949	-0.797024550803	-0.512639099525	0.947653407605	-2.5700189061
 1950	-0.787740889198	-0.528162712571	0.948415288503	-2.55095626972
 1951	-0.778211591269	-0.543419985974	0.949167299237	-2.53201300452
 1952	-0.768445184148	-0.558408587998	0.949909549479	-2.51318854519
 1953	-0.758450124922	-0.573126426789	0.950642147749	-2.49448232766
 1954	-0.748234795665	-0.587571644201	0.951365201441	-2.47589378921
 1955	-0.73780749876	-0.601742609626	0.952078816835	-2.45742236841
 1956	-0.727176452476	-0.615637913818	0.952783099118	-2.4390675052
 1957	-0.716349786819	-0.629256362727	0.953478152402	-2.42082864084
 1958	-0.705335539635	-0.642596971355	0.95416407974	-2.40270521796
 1959	-0.694141652956	-0.65565895763	0.954840983143	-2.38469668057
 1960	-0.682775969604	-0.668441736311	0.955508963595	-2.36680247405
 1961	-0.671246230015	-0.680944912932	0.956168121073	-2.34902204519
 1962	-0.659560069302	-0.693168277786	0.956818554558	-2.33135484216
 1963	-0.64772501454	-0.70511179996	0.957460362054	-2.31380031455
 1964	-0.635748482262	-0.716775621415	0.958093640597	-2.29635791336
 1965	-0.623637776171	-0.728160051131	0.958718486278	-2.27902709102
 1966	-0.611400085051	-0.739265559315	0.959334994248	-2.26180730137
 1967	-0.599042480873	-0.750092771666	0.959943258738	-2.24469799971
 1968	-0.586571917098	-0.76064246372	0.960543373067	-2.22769864276
 1969	-0.573995227153	-0.770915555267	0.96113542966	-2.2108086887
 1970	-0.561319123093	-0.780913104835	0.961719520054	-2.19402759715
 1971	-0.548550194429	-0.790636304271	0.962295734917	-2.17735482918
 1972	-0.535694907123	-0.800086473389	0.962864164053	-2.16078984734
 1973	-0.522759602739	-0.809265054714	0.963424896417	-2.14433211561
 1974	-0.509750497748	-0.818173608308	0.963978020126	-2.12798109947
 1975	-0.49667368298	-0.826813806687	0.964523622465	-2.11173626584
 1976	-0.483535123215	-0.835187429831	0.965061789903	-2.09559708314
 1977	-0.47034065691	-0.843296360288	0.9655926081	-2.07956302123
 1978	-0.457095996053	-0.851142578366	0.966116161916	-2.06363355149
 1979	-0.443806726145	-0.85872815743	0.966632535421	-2.04780814674
 1980	-0.430478306295	-0.866055259288	0.967141811903	-2.03208628131
 1981	-0.417116069434	-0.873126129681	0.967644073878	-2.016467431
 1982	-0.403725222627	-0.879943093868	0.968139403098	-2.00095107312
 1983	-0.390310847501	-0.886508552308	0.968627880557	-1.98553668645
 1984	-0.376877900759	-0.892824976449	0.969109586502	-1.97022375126
 1985	-0.36343121479	-0.898894904604	0.969584600439	-1.95501174933
 1986	-0.349975498374	-0.904720937944	0.970053001137	-1.93990016393
 1987	-0.336515337458	-0.91030573657	0.970514866644	-1.92488847984
 1988	-0.32305519602	-0.915652015705	0.970970274283	-1.90997618331
 1989	-0.309599417007	-0.92076254197	0.971419300666	-1.89516276212
 1990	-0.296152223338	-0.925640129766	0.971862021699	-1.88044770555
 1991	-0.282717718978	-0.930287637752	0.972298512587	-1.86583050438
 1992	-0.269299890072	-0.934707965423	0.972728847839	-1.85131065092
 1993	-0.255902606138	-0.938904049783	0.973153101278	-1.83688763895
 1994	-0.242529621313	-0.942878862115	0.973571346044	-1.82256096381
 1995	-0.229184575653	-0.946635404846	0.973983654598	-1.80833012231
 1996	-0.215870996474	-0.950176708507	0.974390098732	-1.79419461282
 1997	-0.202592299744	-0.953505828788	0.97479074957	-1.7801539352
 1998	-0.189351791511	-0.956625843682	0.975185677575	-1.76620759085
 1999	-0.176152669367	-0.959539850724	0.975574952555	-1.75235508266
 2000	-0.162998023953	-0.96225096432	0.975958643666	-1.73859591509
 2001	-0.149890840484	-0.964762313158	0.976336819418	-1.72492959409
 2002	-0.136834000312	-0.96707703772	0.976709547679	-1.71135562717
 2003	-0.123830282511	-0.969198287868	0.977076895681	-1.69787352335
 2004	-0.110882365484	-0.97112922052	0.977438930022	-1.68448279319
 2005	-0.0979928285872	-0.97287299741	0.977795716673	-1.67118294879
 2006	-0.0851641537801	-0.974432782934	0.978147320983	-1.65797350377
 2007	-0.0723987272827	-0.975811742064	0.978493807677	-1.64485397333
 2008	-0.0596988412497	-0.977013038358	0.97883524087	-1.63182387417
 2009	-0.0470666954541	-0.978039832035	0.979171684061	-1.61888272456
 2010	-0.0345043989804	-0.978895278131	0.979503200146	-1.60603004431
 2011	-0.0220139719237	-0.979582524735	0.979829851416	-1.59326535478
 2012	-0.00959734709343	-0.980104711286	0.980151699563	-1.58058817888
 2013	0.00274362827906	-0.980464966951	0.980468805682	-1.56799804107
 2014	0.015007190833	-0.980666409077	0.980781230279	-1.55549446739
 2015	0.0271916593704	-0.980712141695	0.981089033272	-1.5430769854
 2016	0.0392954331506	-0.98060525411	0.981392273993	-1.53074512425
 2017	0.0513169901884	-0.980348819544	0.981691011196	-1.51849841464
 2018	0.0632548855577	-0.979945893849	0.981985303056	-1.50633638886
 2019	0.0751077497007	-0.979399514278	0.982275207176	-1.49425858072
 2020	0.0868742867454	-0.978712698321	0.982560780589	-1.48226452565
 2021	0.0985532728322	-0.977888442598	0.982842079763	-1.47035376062
 2022	0.11014355445	-0.976929721809	0.983119160601	-1.45852582419
 2023	0.121644046784	-0.975839487743	0.983392078449	-1.44678025649
 2024	0.133053732074	-0.974620668338	0.983660888097	-1.43511659923
 2025	0.144371657992	-0.973276166799	0.983925643781	-1.42353439571
 2026	0.155596936021	-0.971808860759	0.98418639919	-1.4120331908
 2027	0.166728739866	-0.970221601505	0.984443207466	-1.40061253096
 2028	0.177766303864	-0.968517213236	0.984696121209	-1.38927196425
 2029	0.188708921423	-0.966698492378	0.984945192481	-1.3780110403
 2030	0.199555943471	-0.964768206947	0.985190472807	-1.36682931035
 2031	0.210306776923	-0.962729095946	0.98543201318	-1.35572632722
 2032	0.220960883172	-0.960583868817	0.985669864064	-1.34470164533
 2033	0.231517776593	-0.958335204929	0.985904075397	-1.33375482071
 2034	0.241977023068	-0.955985753102	0.986134696594	-1.32288541097
 2035	0.252338238529	-0.953538131181	0.98636177655	-1.31209297534
 2036	0.262601087528	-0.950994925637	0.986585363645	-1.30137707463
 2037	0.272765281821	-0.948358691214	0.986805505745	-1.29073727129
 2038	0.282830578973	-0.945631950602	0.987022250206	-1.28017312935
 2039	0.292796780986	-0.94281719415	0.987235643877	-1.26968421446
 2040	0.30266373295	-0.939916879612	0.987445733103	-1.25927009386
 2041	0.312431321716	-0.936933431922	0.98765256373	-1.24893033644
 2042	0.322099474583	-0.933869242999	0.987856181105	-1.23866451268
 2043	0.331668158018	-0.930726671587	0.988056630081	-1.22847219466
 2044	0.341137376391	-0.927508043113	0.988253955019	-1.21835295612
 2045	0.350507170735	-0.924215649585	0.988448199794	-1.20830637237
 2046	0.359777617526	-0.920851749506	0.988639407793	-1.19833202037
 2047	0.36894882749	-0.917418567816	0.988827621924	-1.18842947868
	#-------------------------------------------------------------------------------
	# Name: Nelder-Mead
	# Purpose:
	#
	# Author: Harshad
	#
	# Created: 25-10-2012
	# Copyright: (c) Harshad 2012
	# Licence: <your licence>
	#-------------------------------------------------------------------------------

	##==============================================================================##

	##-----------ALL IMPORTS-----------##

	from numpy import linspace
	from matplotlib import pyplot,legend
	from math import pi,log10,atan2,log
	from scipy import optimize,stats
	from scipy.stats import norm
	from cmath import exp
	##==============================================================================##

	##-----------ALL INITIALIZATIONS-----------##

	v1=complex(0.0,0.0)
	v2=complex(0.0,0.0)
	fix_values=-1.0j2.0pi*0.01
	global varr_L
	L=400
	c=2.99792458
	delta_f= 0.001953125 #---delta_w = 4THz/2048 = 1953125000
	constant=fix_values(delta_fL/c)
	z=complex(0.0,1.0)
	n1=complex(1.0,0.0)
	n3=complex(1.0,0.0)
	global Pwl_omega

	##==============================================================================##

	##-----------ALL DEFINITIONS-----------##

	def twopower(x):
	y=int(math.log(x,2))
	return 2**y

	#===========================================
	#======T formulated=========================
	#===========================================

	def Tformulated(n,k,w):
	v3=w*constant
	n2=complex(n,-k)
	v1=1.0/(1.0-(((n2-n1)(n2-n3)exp(2v3n2))/((n2+n1)*(n2+n3))))
	FP=v1
	v2=((2.0n2(n1+n3))/((n2+n1)(n2+n3)))((exp((n2-n1)v3)))FP
	Tform=v2
	return(Tform)

	#===================================
	#======CONFIG FILE READ=====================
	#===========================================
	fp=open("YOUR PATH\configfile.txt",'r')
	for line in fp:
	var_type,func_type,freq_sel_a,freq_sel_b=map(str,line.split())
	freq_sel_a=int(freq_sel_a)
	freq_sel_b=int(freq_sel_b)
	fp.close()
	#===========================================
	##==============================================================================##

	##-----------MAIN ALGORITHM-----------##

	#============= Generating T(w) for given n2,k2 and range of w ==================
	freq=[]
	Tw_read_cmplx=[]
	Tw_read_real=[]
	Tw_read_imag=[]
	Tw_read_abs=[]
	Tw_read_phi=[]
	Tw_abs_log10=[]
	Tw_wrapphi=[]

	if var_type == "fix":
	Tw_read=open("YOUR PATH\Tw_fix.txt",'rt')
	elif var_type == "linear":
	Tw_read = open("YOUR PATH\Tw_lin.txt",'rt')
	elif var_type=="pdf":
	Tw_read=open("YOUR PATH\Tw_norm.txt",'rt')
	else :
	disp("INVALID TYPE OF VARIATION")
	exit()

	for line in Tw_read:
	a,b,c,d,e=map(float,line.split())
	freq.append(a)
	Tw_read_real.append(b)
	Tw_read_imag.append(c)
	Tw_read_abs.append(d)
	Tw_read_phi.append(e)

	n2=4 #the parameters to
	k2=3 #generate Tmeas()
	Tw_abs=Tw_read_abs #Tmeas() is the generation function
	Tw_abs_log10=[log10(i) for i in Tw_abs]
	Tw_phi=Tw_read_phi

	for i in range(len(Tw_read_imag)):
	Tw_wrapphi.append(atan2(Tw_read_imag[i],Tw_read_real[i]))

	pyplot.figure()
	p1,=pyplot.plot(range(len(Tw_abs_log10)),Tw_abs_log10)
	p2,=pyplot.plot(range(len(Tw_phi)),Tw_phi)
	p3,=pyplot.plot(range(len(Tw_wrapphi)),Tw_wrapphi)
	p4,=pyplot.plot(range(len(Tw_abs)),Tw_abs)
	pyplot.title("Formula Generated T(w)")
	pyplot.legend([p1,p2,p3,p4],["Tw_abs_10","Tw_phi","Tw_wrapphi","T_abs"])
	pyplot.show()

	#===========ERROR FUNCTIONS=====================================================

	error=lambda x,w: (log(abs(Tformulated(x[0],x[1],w))) - log(Tw_abs[w]))2 + (atan2(Tformulated(x[0],x[1],w).imag,Tformulated(x[0],x[1],w).real) - Tw_wrapphi[w])2

	#========================initial guess vector===================================

	v0_nm=[1,1]
	omega=[500]
	snm_n2=[]
	snm_k2=[]


	#===========================Scipy POWELL========================================

	a=freq_sel_a;b=freq_sel_b
	err_arr=[]
	for w in range(a,b):
	omega[0]=w
	retval2 = optimize.minimize(error,v0_nm,args=(omega),method='Nelder-Mead',options={'gtol':1e-9})
	print w
	#print "minimize Nelder-Mead : ",retval2.x
	#print "VALUE of COUTAZ at (%f,%f) = %s"%(retval2.x[0],retval2.x[1],error([retval2.x[0],retval2.x[1]],omega[0]))
	snm_n2.append(retval2.x[0])
	snm_k2.append(retval2.x[1])
	v0_nm=[retval2.x[0],retval2.x[1]]
	err_arr.append(error(v0_nm,w))

	n=[]
	k=[]

	if var_type == "fix":
	for i in range(a,b):
	n.append(3)
	k.append(1)
	elif var_type == "linear":
	for i in range(a,b):
	n.append(3.5 + 0.2*i/1000)
	k.append(0.1 + 0.1*i/1000)
	elif var_type == "pdf":
	global n2_arr
	global k2_arr
	spread_n2=linspace(1,4,2048)
	spread_k2=linspace(0.01,0.9,2048)
	n2_arr = 1.0+4.0*norm.pdf(spread_n2,2.5,0.5)
	k2_arr= 0.25*norm.pdf(spread_k2,0.5,0.1)
	for i in range(a,b):
	n.append(n2_arr[i])
	k.append(k2_arr[i])

	n_err = [(snm_n2[i] - n[i]) for i in range(len(snm_n2))]
	k_err = [(snm_k2[i] - k[i]) for i in range(len(snm_k2))]


	p4,=pyplot.plot(range(a,b),snm_k2)
	p6,=pyplot.plot(range(len(k)),k,'g+')
	pyplot.legend([p4,p6], ["mini Nelder Mead","k2"])
	pyplot.title("K2")
	pyplot.show()

	p4,=pyplot.plot(range(a,b),snm_n2)
	p6,=pyplot.plot(range(len(n)),n,'g+')
	pyplot.legend([p4,p6], ["mini Nelder Mead_n2","n2"])
	pyplot.title("N2")
	pyplot.show()

	p1,=pyplot.plot(range(len(snm_n2)),n_err)
	p2,=pyplot.plot(range(len(snm_k2)),k_err)
	p3,=pyplot.plot(range(len(err_arr)),err_arr)
	pyplot.legend([p1,p2,p3],["n_err","k_err","err_arr"])
	pyplot.title("error in n and k and total error")
	pyplot.show()