I want to fit data with my custom function to calculate parameters of the model. Data of x and y are attached at the end. The custom function is:
y=a+(-((4/3)*3.14*((60e-10)^3-((60e-10)-x).^3).*b*(c-1096)/c+4*3.14*(60e-10)^2.*(d.*((60e-10)-x).^2/(60e-10)^2+e+(f-e-d.*((60e-10)-x).^2/(60e-10)^2).*exp(-x./g)))/(1e3*1.38e-23*1090))
and parameters have constraints and initials:
-inf<a<inf, a=2e4
1e11<b<1e12, b=7.8e11
1120<c<1300, c=1200
70<d<130, d=127
300<e<700, e=680
400<f<900, f=850
1e-10<g<3e-10, g=2.5e-10
However, I both tried matlab and rigin to fit data with the model, but they all failed to find a good fit. I am appreciate if you can provide any suggestions. In fact, I understand there are too many parameters, and I also tried to fix parameter b, d, e and g while free others, but still no good results.
x=[3.70400000000000e-10
3.80400000000000e-10
3.90400000000000e-10
4.00400000000000e-10
4.10400000000000e-10
4.20400000000000e-10
4.30400000000000e-10
4.40400000000000e-10
4.50400000000000e-10
4.60400000000000e-10
4.70400000000000e-10
4.80400000000000e-10
4.90400000000000e-10
5.00400000000000e-10
5.10400000000000e-10
5.20400000000000e-10
5.30400000000000e-10
5.40400000000000e-10
5.50400000000000e-10
5.60400000000000e-10
5.70400000000000e-10
5.80400000000000e-10
5.90400000000000e-10
6.00400000000000e-10
6.10400000000000e-10
6.20400000000000e-10
6.30400000000000e-10
6.40400000000000e-10
6.50400000000000e-10
6.60400000000000e-10
6.70400000000000e-10
6.80400000000000e-10
6.90400000000000e-10
7.00400000000000e-10
7.10400000000000e-10
7.20400000000000e-10
7.30400000000000e-10
7.40400000000000e-10
7.50400000000000e-10
7.60400000000000e-10
7.70400000000000e-10
7.80400000000000e-10
7.90400000000000e-10
8.00400000000000e-10
8.10400000000000e-10
8.20400000000000e-10
8.30400000000000e-10
8.40400000000000e-10
8.50400000000000e-10
8.60400000000000e-10
8.70400000000000e-10
8.80400000000000e-10
8.90400000000000e-10
9.00400000000000e-10
9.10400000000000e-10
9.20400000000000e-10
9.30400000000000e-10
9.40400000000000e-10
9.50400000000000e-10
9.60400000000000e-10
9.70400000000000e-10
9.80400000000000e-10
9.90400000000000e-10
1.00040000000000e-09
1.01040000000000e-09
1.02040000000000e-09
1.03040000000000e-09
1.04040000000000e-09
1.05040000000000e-09
1.06040000000000e-09
1.07040000000000e-09
1.08040000000000e-09
1.09040000000000e-09
1.10040000000000e-09
1.11040000000000e-09
1.12040000000000e-09
1.13040000000000e-09
1.14040000000000e-09
1.15040000000000e-09
1.16040000000000e-09
1.17040000000000e-09
1.18040000000000e-09
1.19040000000000e-09
1.20040000000000e-09
1.21040000000000e-09
1.22040000000000e-09
1.23040000000000e-09
1.24040000000000e-09
1.25040000000000e-09
1.26040000000000e-09
1.27040000000000e-09
1.28040000000000e-09
1.29040000000000e-09
1.30040000000000e-09
1.31040000000000e-09
1.32040000000000e-09
1.33040000000000e-09
1.34040000000000e-09
1.35040000000000e-09
1.36040000000000e-09
1.37040000000000e-09
1.38040000000000e-09
1.39040000000000e-09
1.40040000000000e-09
1.41040000000000e-09
1.42040000000000e-09
1.43040000000000e-09
1.44040000000000e-09
1.45040000000000e-09
1.46040000000000e-09
1.47040000000000e-09
1.48040000000000e-09
1.49040000000000e-09
1.50040000000000e-09
1.51040000000000e-09
1.52040000000000e-09
1.53040000000000e-09
1.54040000000000e-09
1.55040000000000e-09
1.56040000000000e-09
1.57040000000000e-09
1.58040000000000e-09
1.59040000000000e-09
1.60040000000000e-09
1.61040000000000e-09
1.62040000000000e-09
1.63040000000000e-09
1.64040000000000e-09
1.65040000000000e-09
1.66040000000000e-09
1.67040000000000e-09
1.68040000000000e-09
1.69040000000000e-09
1.70040000000000e-09
1.71040000000000e-09
1.72040000000000e-09
1.73040000000000e-09
1.74040000000000e-09
1.75040000000000e-09
1.76040000000000e-09
1.77040000000000e-09
1.78040000000000e-09
1.79040000000000e-09
1.80040000000000e-09
1.81040000000000e-09
1.82040000000000e-09
1.83040000000000e-09
1.84040000000000e-09
1.85040000000000e-09
1.86040000000000e-09
1.87040000000000e-09
1.88040000000000e-09
1.89040000000000e-09]
y=[-22.8405306447565
-22.2450287793417
-21.6577585104770
-21.0787198381626
-20.5079127623984
-19.9453372831843
-19.3909934005205
-18.8448811144068
-18.3070004248434
-17.7773513318301
-17.2559338353671
-16.7427479354542
-16.2377936320915
-15.7410709252790
-15.2525798150167
-14.7723203013046
-14.3002923841427
-13.8364960635310
-13.3809313394694
-12.9335982119581
-12.4944966809970
-12.0636267465860
-11.6409884087253
-11.2265816674147
-10.8204065226543
-10.4224629744442
-10.0327510227842
-9.65127066767441
-9.27802190911481
-8.91300474710541
-8.55621918164621
-8.20766521273719
-7.86734284037838
-7.53525206456975
-7.21139288531131
-6.89576530260307
-6.58836931644503
-6.28920492683717
-5.99827213377951
-5.71557093727205
-5.44110133731477
-5.17486333390769
-4.91685692705081
-4.66708211674411
-4.42553890298761
-4.19222728578130
-3.96714726512519
-3.75029884101927
-3.54168201346354
-3.34129678245801
-3.14914314800267
-2.96522111009752
-2.78953066874256
-2.62207182393780
-2.46284457568323
-2.31184892397886
-2.16908486882468
-2.03455241022069
-1.90825154816689
-1.79018228266329
-1.68034461370989
-1.57873854130667
-1.48536406545365
-1.40022118615082
-1.32330990339818
-1.25463021719574
-1.19418212754349
-1.14196563444144
-1.09798073788958
-1.06222743788791
-1.03470573443643
-1.01541562753515
-1.00435711718406
-1.00153020338316
-1.00693488613246
-1.02057116543195
-1.04243904128163
-1.07253851368151
-1.11086958263158
-1.15743224813184
-1.21222651018230
-1.27525236878295
-1.34650982393380
-1.42599887563483
-1.51371952388606
-1.60967176868748
-1.71385561003910
-1.82627104794091
-1.94691808239291
-2.07579671339511
-2.21290694094750
-2.35824876505008
-2.51182218570286
-2.67362720290583
-2.84366381665899
-3.02193202696235
-3.20843183381589
-3.40316323721964
-3.60612623717357
-3.81732083367770
-4.03674702673202
-4.26440481633653
-4.50029420249125
-4.74441518519615
-4.99676776445124
-5.25735194025653
-5.52616771261201
-5.80321508151769
-6.08849404697355
-6.38200460897961
-6.68374676753587
-6.99372052264231
-7.31192587429896
-7.63836282250579
-7.97303136726282
-8.31593150857004
-8.66706324642746
-9.02642658083506
-9.39402151179286
-9.76984803930086
-10.1539061633590
-10.5461958839674
-10.9467172011260
-11.3554701148348
-11.7724546250937
-12.1976707319029
-12.6311184352622
-13.0727977351718
-13.5227086316315
-13.9808511246414
-14.4472252142016
-14.9218309003119
-15.4046681829724
-15.8957370621831
-16.3950375379440
-16.9025696102550
-17.4183332791163
-17.9423285445278
-18.4745554064895
-19.0150138650013
-19.5637039200634
-20.1206255716756
-20.6857788198381
-21.2591636645507
-21.8407801058135
-22.4306281436265
-23.0287077779897
-23.6350190089032
-24.2495618363668
-24.8723362603805
-25.5033422809445
-26.1425798980587
-26.7900491117231]
Related
I am working on a signal. The problem I am facing is that when I apply FFT at a higher resolution, the results are distorted or inaccurate.
% This is the Signal
ppg=[112.876329616814
112.658408873981
112.621201482138
112.229109437548
111.965434300402
111.819245235084
111.841263181141
112.034975558851
112.229725672171
112.401002397509
112.483441565446
112.537095785523
112.542167639986
112.517623071764
112.530208400404
112.494331187315
112.458340941558
112.491893571651
112.446357268045
112.437848223891
112.468898497367
112.492229975598
112.513807423899
112.558165404527
112.585333504471
112.632528318017
112.602232391053
112.667122234561
112.702144016400
112.742078840809
112.770641027009
112.705587358155
112.725453248592
112.610860932793
112.505600920437
112.487277414681
112.411549384328
112.371246006390
112.360145209525
112.353754972283
112.326490619891
112.334771225799
112.308532889401
112.351352504480
112.374822910342
112.400805703872
112.377898361460
112.427400530787
112.441468011030
112.487825137776
112.439115590095
112.466759319904
112.452625972089
112.406563665424
112.280788492275
112.293628779368
112.168353755994
112.159275439531
112.124102673341
112.135144200310
112.114654566371
112.100083083019
112.080270978462
112.120150827635
112.134439453760
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112.287027263325
112.333599889113
112.355033113993
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112.204188788361
112.260325725976
112.317032864848
112.257972343352
112.363700230453
112.436783319341
112.457697907478
112.438722450783
112.430362124392
112.355503599989
112.242165740932
112.166705570292
112.163616654977
112.085798076462
112.184362698808
112.153380937729
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112.224531961545
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112.339695911893
112.378147248247
112.473536985823
112.514993681027
112.529122799596
112.528742074844
112.605329735200
112.526943835385
112.462135267330
112.385319738140
112.441471501166
112.448451454950
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112.551141668789
112.513411425176
112.628942486085
112.571133412043
112.408067990111
112.379208267462
112.387577797402
112.394219329184
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112.405313640608
112.384305237246
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112.801068716104
112.895339954163
112.905992700110
112.922162804516
112.960653154463
113.001264968797
112.995510620634
112.925014237129
112.945664727579
112.950660002563
112.977230979538
113.027126318937
113.051945832799
113.176574533880
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% plotting frequency domain
plot(abs(fft(ppg,1024)));
the result i get for 1024 point resolution is,
% plotting frequency domain
plot(abs(fft(ppg,2048)));
the result I get for 2048 point resolution is,
In my knowledge, increasing resolution does not distort the fft result. If someone knows why is this happening please let me know.
Note: I am using property editor from figure window to zoom out my results.
fft(ppg,2048) pads ppg with zeros to make it 2048 elements long, then applies the FFT. Padding your signal with zeros is bad because it introduces a big jump, your signal is all close to 112. This jump will influence the output of the FFT much more than the actual data.
If you want to increase the resolution of the frequency domain that you compute, you will have to sample your signal for longer. There are no shortcuts.
I found "unk" token in the glove vector file glove.6B.50d.txt downloaded from https://nlp.stanford.edu/projects/glove/. Its value is as follows:
unk -0.79149 0.86617 0.11998 0.00092287 0.2776 -0.49185 0.50195 0.00060792 -0.25845 0.17865 0.2535 0.76572 0.50664 0.4025 -0.0021388 -0.28397 -0.50324 0.30449 0.51779 0.01509 -0.35031 -1.1278 0.33253 -0.3525 0.041326 1.0863 0.03391 0.33564 0.49745 -0.070131 -1.2192 -0.48512 -0.038512 -0.13554 -0.1638 0.52321 -0.31318 -0.1655 0.11909 -0.15115 -0.15621 -0.62655 -0.62336 -0.4215 0.41873 -0.92472 1.1049 -0.29996 -0.0063003 0.3954
Is it a token to be used for unknown words or is it some kind of abbreviation?
The unk token in the pretrained GloVe files is not an unknown token!
See this google groups thread where Jeffrey Pennington (GloVe author) writes:
The pre-trained vectors do not have an unknown token, and currently the code just ignores out-of-vocabulary words when producing the co-occurrence counts.
It's an embedding learned like any other on occurrences of "unk" in the corpus (which appears to happen occasionally!)
Instead, Pennington suggests (in the same post):
...I've found that just taking an average of all or a subset of the word vectors produces a good unknown vector.
You can do that with the following code (should work with any pretrained GloVe file):
import numpy as np
GLOVE_FILE = 'glove.6B.50d.txt'
# Get number of vectors and hidden dim
with open(GLOVE_FILE, 'r') as f:
for i, line in enumerate(f):
pass
n_vec = i + 1
hidden_dim = len(line.split(' ')) - 1
vecs = np.zeros((n_vec, hidden_dim), dtype=np.float32)
with open(GLOVE_FILE, 'r') as f:
for i, line in enumerate(f):
vecs[i] = np.array([float(n) for n in line.split(' ')[1:]], dtype=np.float32)
average_vec = np.mean(vecs, axis=0)
print(average_vec)
For glove.6B.50d.txt this gives:
[-0.12920076 -0.28866628 -0.01224866 -0.05676644 -0.20210965 -0.08389011
0.33359843 0.16045167 0.03867431 0.17833012 0.04696583 -0.00285802
0.29099807 0.04613704 -0.20923874 -0.06613114 -0.06822549 0.07665912
0.3134014 0.17848536 -0.1225775 -0.09916984 -0.07495987 0.06413227
0.14441176 0.60894334 0.17463093 0.05335403 -0.01273871 0.03474107
-0.8123879 -0.04688699 0.20193407 0.2031118 -0.03935686 0.06967544
-0.01553638 -0.03405238 -0.06528071 0.12250231 0.13991883 -0.17446303
-0.08011883 0.0849521 -0.01041659 -0.13705009 0.20127155 0.10069408
0.00653003 0.01685157]
And because it is fairly compute intensive to do this with the larger glove files, I went ahead and computed the vector for glove.840B.300d.txt for you:
0.22418134 -0.28881392 0.13854356 0.00365387 -0.12870757 0.10243822 0.061626635 0.07318011 -0.061350107 -1.3477012 0.42037755 -0.063593924 -0.09683349 0.18086134 0.23704372 0.014126852 0.170096 -1.1491593 0.31497982 0.06622181 0.024687296 0.076693475 0.13851812 0.021302193 -0.06640582 -0.010336159 0.13523154 -0.042144544 -0.11938788 0.006948221 0.13333307 -0.18276379 0.052385733 0.008943111 -0.23957317 0.08500333 -0.006894406 0.0015864656 0.063391194 0.19177166 -0.13113557 -0.11295479 -0.14276934 0.03413971 -0.034278486 -0.051366422 0.18891625 -0.16673574 -0.057783455 0.036823478 0.08078679 0.022949161 0.033298038 0.011784158 0.05643189 -0.042776518 0.011959623 0.011552498 -0.0007971594 0.11300405 -0.031369694 -0.0061559738 -0.009043574 -0.415336 -0.18870236 0.13708843 0.005911723 -0.113035575 -0.030096142 -0.23908928 -0.05354085 -0.044904727 -0.20228513 0.0065645403 -0.09578946 -0.07391877 -0.06487607 0.111740574 -0.048649278 -0.16565254 -0.052037314 -0.078968436 0.13684988 0.0757494 -0.006275573 0.28693774 0.52017444 -0.0877165 -0.33010918 -0.1359622 0.114895485 -0.09744406 0.06269521 0.12118575 -0.08026362 0.35256687 -0.060017522 -0.04889904 -0.06828978 0.088740796 0.003964443 -0.0766291 0.1263925 0.07809314 -0.023164088 -0.5680669 -0.037892066 -0.1350967 -0.11351585 -0.111434504 -0.0905027 0.25174105 -0.14841858 0.034635577 -0.07334565 0.06320108 -0.038343467 -0.05413284 0.042197507 -0.090380974 -0.070528865 -0.009174437 0.009069661 0.1405178 0.02958134 -0.036431845 -0.08625681 0.042951006 0.08230793 0.0903314 -0.12279937 -0.013899368 0.048119213 0.08678239 -0.14450377 -0.04424887 0.018319942 0.015026873 -0.100526 0.06021201 0.74059093 -0.0016333034 -0.24960588 -0.023739101 0.016396184 0.11928964 0.13950661 -0.031624354 -0.01645025 0.14079992 -0.0002824564 -0.08052984 -0.0021310581 -0.025350995 0.086938225 0.14308536 0.17146006 -0.13943303 0.048792403 0.09274929 -0.053167373 0.031103406 0.012354865 0.21057427 0.32618305 0.18015954 -0.15881181 0.15322933 -0.22558987 -0.04200665 0.0084689725 0.038156632 0.15188617 0.13274793 0.113756925 -0.095273495 -0.049490947 -0.10265804 -0.27064866 -0.034567792 -0.018810693 -0.0010360252 0.10340131 0.13883452 0.21131058 -0.01981019 0.1833468 -0.10751636 -0.03128868 0.02518242 0.23232952 0.042052146 0.11731903 -0.15506615 0.0063580726 -0.15429358 0.1511722 0.12745973 0.2576985 -0.25486213 -0.0709463 0.17983761 0.054027 -0.09884228 -0.24595179 -0.093028545 -0.028203879 0.094398156 0.09233813 0.029291354 0.13110267 0.15682974 -0.016919162 0.23927948 -0.1343307 -0.22422817 0.14634751 -0.064993896 0.4703685 -0.027190214 0.06224946 -0.091360025 0.21490277 -0.19562101 -0.10032754 -0.09056772 -0.06203493 -0.18876675 -0.10963594 -0.27734384 0.12616494 -0.02217992 -0.16058226 -0.080475815 0.026953284 0.110732645 0.014894041 0.09416802 0.14299914 -0.1594008 -0.066080004 -0.007995227 -0.11668856 -0.13081996 -0.09237365 0.14741232 0.09180138 0.081735 0.3211204 -0.0036552632 -0.047030564 -0.02311798 0.048961394 0.08669574 -0.06766279 -0.50028914 -0.048515294 0.14144728 -0.032994404 -0.11954345 -0.14929578 -0.2388355 -0.019883996 -0.15917352 -0.052084364 0.2801028 -0.0029121689 -0.054581646 -0.47385484 0.17112483 -0.12066923 -0.042173345 0.1395337 0.26115036 0.012869649 0.009291686 -0.0026459037 -0.075331464 0.017840583 -0.26869613 -0.21820338 -0.17084768 -0.1022808 -0.055290595 0.13513643 0.12362477 -0.10980586 0.13980341 -0.20233242 0.08813751 0.3849736 -0.10653763 -0.06199595 0.028849555 0.03230154 0.023856193 0.069950655 0.19310954 -0.077677034 -0.144811
Since I can't comment, writing another answer.
If anyone's having trouble using the above vector given by #jayelm because copy pasting won't work. I am writing 2 lines of code that will give you the vector ready to be used in python.
vec_string = '0.22418134 -0.28881392 0.13854356 0.00365387 -0.12870757 0.10243822 0.061626635 0.07318011 -0.061350107 -1.3477012 0.42037755 -0.063593924 -0.09683349 0.18086134 0.23704372 0.014126852 0.170096 -1.1491593 0.31497982 0.06622181 0.024687296 0.076693475 0.13851812 0.021302193 -0.06640582 -0.010336159 0.13523154 -0.042144544 -0.11938788 0.006948221 0.13333307 -0.18276379 0.052385733 0.008943111 -0.23957317 0.08500333 -0.006894406 0.0015864656 0.063391194 0.19177166 -0.13113557 -0.11295479 -0.14276934 0.03413971 -0.034278486 -0.051366422 0.18891625 -0.16673574 -0.057783455 0.036823478 0.08078679 0.022949161 0.033298038 0.011784158 0.05643189 -0.042776518 0.011959623 0.011552498 -0.0007971594 0.11300405 -0.031369694 -0.0061559738 -0.009043574 -0.415336 -0.18870236 0.13708843 0.005911723 -0.113035575 -0.030096142 -0.23908928 -0.05354085 -0.044904727 -0.20228513 0.0065645403 -0.09578946 -0.07391877 -0.06487607 0.111740574 -0.048649278 -0.16565254 -0.052037314 -0.078968436 0.13684988 0.0757494 -0.006275573 0.28693774 0.52017444 -0.0877165 -0.33010918 -0.1359622 0.114895485 -0.09744406 0.06269521 0.12118575 -0.08026362 0.35256687 -0.060017522 -0.04889904 -0.06828978 0.088740796 0.003964443 -0.0766291 0.1263925 0.07809314 -0.023164088 -0.5680669 -0.037892066 -0.1350967 -0.11351585 -0.111434504 -0.0905027 0.25174105 -0.14841858 0.034635577 -0.07334565 0.06320108 -0.038343467 -0.05413284 0.042197507 -0.090380974 -0.070528865 -0.009174437 0.009069661 0.1405178 0.02958134 -0.036431845 -0.08625681 0.042951006 0.08230793 0.0903314 -0.12279937 -0.013899368 0.048119213 0.08678239 -0.14450377 -0.04424887 0.018319942 0.015026873 -0.100526 0.06021201 0.74059093 -0.0016333034 -0.24960588 -0.023739101 0.016396184 0.11928964 0.13950661 -0.031624354 -0.01645025 0.14079992 -0.0002824564 -0.08052984 -0.0021310581 -0.025350995 0.086938225 0.14308536 0.17146006 -0.13943303 0.048792403 0.09274929 -0.053167373 0.031103406 0.012354865 0.21057427 0.32618305 0.18015954 -0.15881181 0.15322933 -0.22558987 -0.04200665 0.0084689725 0.038156632 0.15188617 0.13274793 0.113756925 -0.095273495 -0.049490947 -0.10265804 -0.27064866 -0.034567792 -0.018810693 -0.0010360252 0.10340131 0.13883452 0.21131058 -0.01981019 0.1833468 -0.10751636 -0.03128868 0.02518242 0.23232952 0.042052146 0.11731903 -0.15506615 0.0063580726 -0.15429358 0.1511722 0.12745973 0.2576985 -0.25486213 -0.0709463 0.17983761 0.054027 -0.09884228 -0.24595179 -0.093028545 -0.028203879 0.094398156 0.09233813 0.029291354 0.13110267 0.15682974 -0.016919162 0.23927948 -0.1343307 -0.22422817 0.14634751 -0.064993896 0.4703685 -0.027190214 0.06224946 -0.091360025 0.21490277 -0.19562101 -0.10032754 -0.09056772 -0.06203493 -0.18876675 -0.10963594 -0.27734384 0.12616494 -0.02217992 -0.16058226 -0.080475815 0.026953284 0.110732645 0.014894041 0.09416802 0.14299914 -0.1594008 -0.066080004 -0.007995227 -0.11668856 -0.13081996 -0.09237365 0.14741232 0.09180138 0.081735 0.3211204 -0.0036552632 -0.047030564 -0.02311798 0.048961394 0.08669574 -0.06766279 -0.50028914 -0.048515294 0.14144728 -0.032994404 -0.11954345 -0.14929578 -0.2388355 -0.019883996 -0.15917352 -0.052084364 0.2801028 -0.0029121689 -0.054581646 -0.47385484 0.17112483 -0.12066923 -0.042173345 0.1395337 0.26115036 0.012869649 0.009291686 -0.0026459037 -0.075331464 0.017840583 -0.26869613 -0.21820338 -0.17084768 -0.1022808 -0.055290595 0.13513643 0.12362477 -0.10980586 0.13980341 -0.20233242 0.08813751 0.3849736 -0.10653763 -0.06199595 0.028849555 0.03230154 0.023856193 0.069950655 0.19310954 -0.077677034 -0.144811'
import numpy as np
average_glove_vector = np.array(vec_string.split(" "))
print(average_glove_vector)
I'm using MATLAB to plot a colormap of the following data matrix:
1010.89914200000 1006.07847500000 1013.91775300000 1016.37012500000 1012.64447500000 1005.15384200000 998.323644400000 1007.09643600000 1010.39007800000 1010.71070000000 1007.75920300000 1003.43986900000 1001.77407500000 1000.93290600000 1009.19935000000 1010.79651100000 1006.15733600000 1001.08001400000 1006.62765600000 1008.98760600000 1012.59690300000 1014.13669400000 1012.41850000000 1002.83265600000
1010.20939200000 1006.22354400000 1014.13985000000 1016.01628600000 1012.16700600000 1004.47184200000 1000.64279200000 1006.93063300000 1009.98950000000 1010.53409400000 1007.46695300000 1003.07056100000 1001.31949400000 1001.61572800000 1009.12864700000 1010.45935000000 1006.24603900000 1001.40907500000 1006.31782500000 1009.00493300000 1012.13883300000 1013.93106700000 1011.88797800000 1003.01553600000
1009.70062500000 1006.35064700000 1014.37573900000 1015.70891100000 1011.51357800000 1003.79413100000 1001.69951400000 1006.79389200000 1009.72253100000 1010.41560600000 1007.01026100000 1002.91738300000 1000.86708100000 1002.11736400000 1009.09675300000 1009.98591400000 1005.46058600000 1000.94756700000 1006.18716400000 1008.73213100000 1012.14396700000 1013.51734400000 1010.97627200000 1003.29271400000
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using:
imagesc(data)
Now I need to normalize each column separately in the following way: finding the maximum value of each column and set it's color, and finding the lowest value of each column and set it's color as well.
So in the end I need a colormap which have the same color for every local maximum and minimum of a column.
I'm quite new to plotting, so I tried looking for normalized colormaps here and on the web, but didn't find anything that can help me.
You're not going to be able to do this strictly with a colormap because the colormap is applied globally to the image and the color used for the local max in one column would be applied to all elements with that value regardless of whether they were the local max of their respective column.
Instead, you can normalize each column of your data and then display that.
%// Subtract off the minimum of each column
D = bsxfun(#minus, data, min(data, [], 1));
%// Divide by the maximum
D = bsxfun(#rdivide, D, max(D, [], 1));
%// Display the result
imagesc(D);
I have a vector of 810 doubles, which have a very good reason (not relevant, so reason left out here) to roughly follow a Gaussian distribution. I now wish to verify this.
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Since the vector is not ordered, directly plotting them in current order gives a messy plot like this.
What is a smart way of easily reordering the data so that I can verify whether they roughly follow a normal distribution or not?
To see if your data follow a Gaussian distribution you can use normplot. It draws the empirical distribution function of the data on a scale such that a Gaussian corresponds to a straight line. The more straight the line is, the more similar to a Gaussian.
If often happens that the curve is straight in the central part, and deviates on its ends. That's the case with your data; see figure below.
The explanation is that the Gaussian distribution usually arises from a sum of random variables, by virtue of the Central Limit Theorem. The distribution of the sum is Gaussian in the limit as the number of summands tends to infinity. For a finite number of terms the distribution is only approximately Gaussian; and the approximation is better at the center than on the tails (in fact, that's why the theorem is called central).
If you have the Statistics Toolbox, you could also run one of the hypothesis tests, like the Jarque-Bera Test, which will tell you (within a confidence limit) how likely it is that your points were drawn from a normal distribution.
[h, p] = jbtest(X, 0.05);
if h
disp(sprintf('There is less than %.3f%% chance that your data is abnormal', 100 * p));
else
disp(sprintf('Your data is not normal within your confidence limit'));
end
This doesn't give you a pretty plot, but it will give you a less biased answer than just eyeballing it.
In this case, there is better than 99.9% chance that your data set was drawn from a normal distribution.
Simply use the histogram function:
histogram(X)
To view the PDF you can use:
if exist('histogram','func')
histogram(data)
else
hist(data)
end
This looks pretty normal to me. You can always try modeling it with a gaussian.
I'd like to make one period representative signal.
There are several signals in different periods.
I don't want to cut one period signal from several signals.
How can I solve this problem in matlab?
Below is the signal data values.
Thank you.
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If by "one period representative signal" you mean "get the average signal over all the periods", this is how.
This is what your data looks like:
If you know in advance how many cycles are in your signal (9 for your data above), then just reshape your signal into a 9x178 matrix (==numel(signal)/9) and find column means (ie a 1x178 matrix with the average signal).
nwaves = 9;
sig2 = reshape(sig,[numel(sig)/nwaves nwaves])';
avgSig = mean(sig2,1);
plot(avgSig);
If you don't know how many cycles in your signal...you could try doing the fourier transform, but it's not guaranteed...and if the number of data points isn't an exact multiple of the period length, then you'll have to modify the code to deal with that.
% get fourier transform
a = fft(sig);
% get period with max amplitude (but not period=0)
[val ix] = max(abs(a(2:end))) % don't include period=0
nwaves = ix + 1 % add 1 because of the offset above
% then calculate avg & plot as before with this `nwaves`.
(If you plot each 'cycle' though you'll notice that splitting into every 178 elements doesn't quite section your wave into parts from minimum to minimum - you might need to find a smarter way of doing that).