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I am having some difficulty to replciate Matlab's regress function output using scipy linregress function.
Here is the data
pupVals = [3.40621246270059, 3.39361245626222, 3.37960434985898, 3.36422005129091, 3.34750704680340, 3.32952815194744,
3.31035997313977, 3.29009299139087, 3.26883227275573, 3.24668690892347, 3.22376158035874, 3.20015774115851,
3.17597533905954, 3.15130446393993, 3.12622016870185, 3.10078008972008, 3.07503065688319, 3.04901239477419,
3.02276360223545, 2.99632186567962, 2.96972062051014]
defVals = [ -0.676069340690958, -0.681299901070580, -0.687103823182625, -0.693490568594932, -0.700466450335011,
-0.708027898057120, -0.716167334731881, -0.724878961238070, -0.734138903033690, -0.743919748266449,
-0.754183596434113, -0.764899153546520, -0.776036371746185, -0.787551515041980, -0.799395767551789,
-0.811524533752894, -0.823893965641479, -0.836469554360099, -0.849231693452297, -0.862141390106238,
-0.875133488454364]
res = linregress(pupVals, defVals)
the matlab output looks like below
in matlab I make defvals as a 21x2 matrix with ones in first column as suggested in matlab regress help documentation
[SlopeFit,CIS] = regress(pupvals, defvals)
SlopeFit =
4.8830
2.1939
CIS =
4.8604 4.9056
2.1644 2.2234
and I use SlopeFit(2) and CIS(2,1), CIS(2,2)
Any suggestions on how to replicate the results?
thanks
Try the following:
res = linregress(pupVals, defVals)
SlopeFit = np.array([res.intercept, res.slope])
errs = np.array([res.stderr,intercept_stderr])
CIS = SlopeFit[:,None] + 1.96*errs[:,None]*np.array([[1,-1]])
I have the following code that I wish to estimate the parameters of a custom distribution using MATLAB's function mle(). For more details on the distribution.
The main code is:
x = [0 0 0 0 0.000649967501624919 0.00569971501424929 0.0251487425628719 0.0693465326733663 0.155342232888356 0.284835758212089 0.458277086145693 0.658567071646418 0.908404579771011 1.17284135793210 1.43977801109945 1.71951402429879 1.98925053747313 2.27553622318884 2.57147142642868 2.80390980450977 3.03829808509575 3.26583670816459 3.45642717864107 3.65106744662767 3.81950902454877 3.98275086245688 4.11259437028149 4.24683765811709 4.35043247837608 4.43832808359582 4.58427078646068 4.62286885655717 4.68361581920904 4.75686215689216 4.80245987700615 4.84005799710015 4.86280685965702 4.91675416229189 4.92725363731813 4.90890455477226 4.96570171491425 4.92315384230789 4.95355232238388 4.92790360481976 4.93135343232838 4.90310484475776 4.90885455727214 4.86765661716914 4.85490725463727 4.81940902954852 4.81450927453627 4.78621068946553 4.74206289685516 4.71791410429479 4.69961501924904 4.65706714664267 4.63611819409030 4.60176991150443 4.57512124393780 4.53507324633768 4.48252587370631 4.47062646867657 4.43127843607820 4.39963001849908 4.37598120093995 4.29548522573871 4.31033448327584 4.21708914554272 4.21913904304785 4.18669066546673 4.16719164041798 4.09774511274436 4.07989600519974 4.02869856507175 3.98485075746213 3.95785210739463 3.93945302734863 3.90240487975601 3.87025648717564 3.81185940702965 3.78461076946153 3.74091295435228 3.71666416679166 3.67276636168192 3.65846707664617 3.61361931903405 3.58712064396780 3.55452227388631 3.53082345882706 3.49197540122994 3.48582570871456 3.46512674366282 3.41227938603070 3.36278186090695 3.35528223588821 3.31238438078096 3.27213639318034 3.23863806809660 3.24173791310434 3.19339033048348 3.20118994050298 3.16489175541223 3.10739463026849 3.09484525773711 3.08094595270237 3.02129893505325 3.02309884505775 2.99375031248438 2.95765211739413 2.93230338483076 2.89560521973901 2.87805609719514 2.85440727963602 2.82285885705715 2.80175991200440 2.79091045447728 2.73901304934753 2.72701364931753 2.73441327933603 2.71646417679116 2.68236588170592 2.65551722413879 2.63356832158392 2.60361981900905 2.58147092645368 2.57697115144243 2.54287285635718 2.53502324883756 2.47702614869257 2.50387480625969 2.46487675616219 2.45722713864307 2.42707864606770 2.41762911854407 2.39823008849558 2.38708064596770 2.34058297085146 2.35613219339033 2.32123393830309 2.30503474826259 2.27613619319034 2.27248637568122 2.25113744312784 2.24908754562272 2.22703864806760 2.20583970801460 2.17244137793110 2.15709214539273 2.16469176541173 2.12139393030348 2.12809359532023 2.11389430528474 2.09774511274436 2.07629618519074 2.07459627018649 2.05394730263487 2.04724763761812 2.01684915754212 2.01684915754212 2.00409979501025 1.98955052247388 1.96540172991350 1.95890205489726 1.93035348232588 1.92295385230738 1.90605469726514 1.89785510724464 1.87070646467677 1.88000599970002 1.86295685215739 1.84420778961052 1.82510874456277 1.80480975951202 1.80785960701965 1.80870956452177 1.77581120943953 1.76771161441928 1.77131143442828 1.76636168191590 1.75081245937703 1.73156342182891 1.69876506174691 1.70836458177091 1.70376481175941 1.67196640167992 1.68101594920254 1.66586670666467 1.66061696915154 1.64296785160742 1.63291835408230 1.62506874656267 1.62516874156292 1.60556972151392 1.59007049647518 1.59187040647968 1.57947102644868 1.57577121143943 1.54527273636318 1.57237138143093 1.54637268136593 1.54802259887006 1.50492475376231 1.52077396130193 1.50417479126044 1.50162491875406 1.50062496875156 1.48957552122394 1.47997600119994 1.47027648617569 1.44452777361132 1.45407729613519 1.44272786360682 1.43247837608120 1.41657917104145 1.40787960601970 1.39323033848308 1.40282985850707 1.39403029848508 1.38233088345583 1.37888105594720 1.37943102844858 1.36183190840458 1.34808259587021 1.34503274836258 1.33703314834258 1.33308334583271 1.32253387330633 1.32698365081746 1.29963501824909 1.30758462076896 1.29103544822759 1.29473526323684 1.27413629318534 1.26858657067147 1.27888605569722 1.26063696815159 1.27863606819659 1.25168741562922 1.23913804309785 1.24788760561972 1.22308884555772 1.24198790060497 1.22133893305335 1.20678966051697 1.20098995050247 1.20343982800860 1.18779061046948 1.19024048797560 1.17194140292985 1.17369131543423 1.16869156542173 1.15814209289536 1.15429228538573 1.15904204789761 1.12774361281936 1.15344232788361 1.13744312784361 1.12909354532273 1.12479376031198 1.11099445027749 1.11469426528674 1.11064446777661 1.10464476776161 1.10309484525774 1.10689465526724 1.07654617269137 1.07884605769712 1.07359632018399 1.06864656767162 1.07544622768862 1.06689665516724 1.04884755762212 1.06164691765412 1.04979751012449 1.04529773511324 1.02839858007100 1.03634818259087 1.01709914504275 1.02089895505225 1.01024948752562 1.01549922503875 1.01319934003300 1.01404929753512 1.00839958002100 0.995400229988501 0.989850507474626 0.978801059947003 0.977551122443878 0.980450977451127 0.975451227438628 0.969201539923004 0.964151792410380 0.964601769911504 0.958802059897005 0.955702214889256 0.948602569871506 0.960751962401880 0.941352932353382 0.928653567321634 0.949002549872506 0.937053147342633 0.913854307284636 0.916204189790510 0.915454227288636 0.902604869756512 0.909454527273636 0.895505224738763 0.898355082245888 0.894455277236138 0.902454877256137 0.883705814709265 0.888405579721014 0.876356182190891 0.881555922203890 0.878156092195390 0.868456577171141 0.870406479676016 0.863906804659767 0.862456877156142 0.858757062146893 0.851307434628269 0.851107444627769 0.833908304584771 0.843507824608770 0.831708414579271 0.836858157092145 0.829058547072646 0.828508574571272 0.822908854557272 0.820508974551273 0.815559222038898 0.819709014549273 0.809609519524024 0.813409329533523 0.800759962001900 0.806609669516524 0.806959652017399 0.792260386980651 0.787660616969152 0.783810809459527 0.794960251987401 0.771061446927654 0.788910554472276 0.789510524473776 0.763061846907655 0.776761161941903 0.767561621918904 0.773611319434028 0.750262486875656 0.765811709414529 0.765911704414779 0.748012599370032 0.741612919354032 0.757312134393280 0.752612369381531 0.741362931853407 0.742212889355532 0.741912904354782 0.743162841857907 0.732963351832408 0.732813359332033 0.733363331833408 0.721913904304785 0.716664166791661 0.726713664316784 0.709764511774411 0.700064996750163 0.710764461776911 0.717664116794160 0.707314634268287 0.707114644267787 0.705614719264037 0.709164541772911 0.696665166741663 0.680765961701915 0.686715664216789 0.694465276736163 0.683015849207540 0.681715914204290 0.694465276736163 0.688615569221539 0.680665966701665 0.672316384180791 0.672866356682166 0.656517174141293 0.665316734163292 0.671566421678916 0.666266686665667 0.652917354132293 0.663366831658417 0.651917404129794 0.663816809159542 0.661366931653417 0.647017649117544 0.655167241637918 0.647867606619669 0.636918154092295 0.645467726613669 0.633118344082796 0.640217989100545 0.634668266586671 0.618669066546673 0.635068246587671 0.632568371581421 0.623118844057797 0.623868806559672 0.623718814059297 0.621368931553422 0.623768811559422 0.608419579021049 0.616019199040048 0.609869506524674 0.606569671516424 0.614019299035048 0.610269486525674 0.596520173991300 0.595570221488926 0.593270336483176 0.596670166491675 0.598470076496175 0.597770111494425 0.593720313984301 0.592770361481926 0.585420728963552 0.580870956452177 0.584120793960302 0.580270986450677 0.577971101444928 0.579021048947553 0.572821358932053 0.585970701464927 0.572921353932303 0.567071646417679 0.569971501424929 0.571271436428179 0.568421578921054 0.567421628918554 0.569521523923804 0.563721813909305 0.558772061396930 0.562171891405430 0.557872106394680 0.549072546372681 0.558722063896805 0.536973151342433 0.561021948902555 0.544172791360432 0.552122393880306 0.553072346382681 0.546222688865557 0.551472426378681 0.540772961351932 0.541122943852807 0.542772861356932 0.530323483825809 0.526023698815059 0.529273536323184 0.524573771311435 0.525923703814809 0.524923753812309 0.516474176291185 0.527273636318184 0.527723613819309 0.518424078796060 0.517874106294685 0.516074196290186 0.517924103794810 0.523173841307935 0.514474276286186 0.513174341282936 0.498875056247188 0.518024098795060 0.507924603769812 0.505524723763812 0.507174641267937 0.502874856257187 0.502624868756562 0.500624968751562 0.510824458777061 0.490925453727314 0.492675366231688 0.489925503724814 0.478126093695315 0.485775711214439 0.491775411229439 0.489925503724814 0.491325433728314 0.487225638718064 0.485725713714314 0.485675716214189 0.477676116194190 0.483875806209690 0.478026098695065 0.470176491175441 0.471926403679816 0.483625818709065 0.469376531173441 0.474026298685066 0.467826608669567 0.462426878656067];
Censored = ones(1,size(x,2));%
custpdf = #eval_custpdf;
custcdf = #eval_custcdf;
phat = mle(x,'pdf', custpdf,'cdf', custcdf,'start',[1 0.1 0.3 0.1 0.01 -0.3],...
'lowerbound',[0 0 0 0 0 -inf],'upperbound',[inf inf inf inf inf inf],'Censoring',Censored);
% Cheking how close the estimated PDF and CDF match with those from the data x
t = 0.001:0.001:0.5;
figure();
plot(t,x);hold on
plot(t,custpdf(t, phat(1), phat(2), phat(3), phat(4), phat(5), phat(6)))
figure();
plot(t,cumsum(x)./sum(x));hold on
plot(t,custcdf(t, phat(1), phat(2), phat(3), phat(4), phat(5), phat(6)))
The functions are:
function out = eval_custpdf(x,myalpha,mybeta,mytheta,a,b,c)
first_integral = integral(#(x) eval_K(x,a,b,c),0,1).^-1;
theta_t_ratio = (mytheta./x);
incomplete_gamma = igamma(myalpha,theta_t_ratio.^mybeta);
n_gamma = gamma(myalpha);
exponent_term = exp(-theta_t_ratio.^mybeta-(c.*(incomplete_gamma./n_gamma)));
numerator = first_integral.* mybeta.*incomplete_gamma.^(a-1).*...
theta_t_ratio.^(myalpha*mybeta+1).*exponent_term;
denominator = mytheta.* n_gamma.^(a+b-1).* (n_gamma-incomplete_gamma.^mybeta).^(1-b);
out = numerator./denominator;
end
function out = eval_custcdf(x,myalpha,mybeta,mytheta,a,b,c)
first_integral = integral(#(x) eval_K(x,a,b,c),0,1).^-1;
theta_t_ratio = (mytheta./x);
incomplete_gamma = igamma(myalpha,theta_t_ratio.^mybeta);
n_gamma = gamma(myalpha);
second_integral = integral(#(x) eval_K(x,a,b,c),0, incomplete_gamma.^mybeta./n_gamma);
% |<----- PROBLEMATIC LINE ----->|
out = first_integral*second_integral;
end
function out = eval_K(x,a,b,c)
out = x.^(a-1).*(1-x).^(b-1).*exp(-c.*x);
end
The integral that is causing the problem is the second intergral in the function eval_custcdf() as its upper limit is an array (denoted by PROBLEMATIC LINE).
Is there a way to take a single value from the array x such that the upper limit remains a scalar? And then calculate the cdf such that the output of the cdf is an array? Using a forloop, maybe? But I cannot seem to figure how to implement that?
How can I work around this problem?
Any help would be appreciated.
Thanks in advance.
eval_custcdf is a function expected to return 1D array of length n for
a given n data input.
I use a for loop to compute the output for a given input, then
return the whole array as output of eval_custcdf
I passed the input array elements one at a time
This is how eval_custcdf may look like
function out = eval_custcdf(x,myalpha,mybeta,mytheta,a,b,c)
out = zeros(size(x));
for i = 1: length(x)
first_integral = integral(#(w) eval_K(w,a,b,c),0,1).^-1;
theta_t_ratio = (mytheta./x(i));
incomplete_gamma = igamma(myalpha,theta_t_ratio.^mybeta);
n_gamma = gamma(myalpha);
second_integral = integral(#(w) eval_K(w,a,b,c),0, incomplete_gamma.^mybeta./n_gamma);
out(i) = first_integral*second_integral;
end
end
I have a code that computes the max value. this code consists of four variables www is the function of a,b, and c labaled xx, yy, and zz respectively, so my question is how can i plot www against xx,yy, and zz? Thanks for helping
objfun file
function f=W4qubit(x,a,b,c,d)
c1=-cos(x(1))*(cos(x(5))*(cos(x(9))*(cos(x(13))-cos(x(15)))-cos(x(11))*(cos(x(13))+cos(x(15))))+...
cos(x(7))*(cos(x(11))*(cos(x(15))-cos(x(13)))-cos(x(9))*(cos(x(13))+cos(x(15)))))-...
cos(x(3))*(cos(x(5))*(cos(x(11))*(cos(x(15))-cos(x(13)))-cos(x(9))*(cos(x(13))+cos(x(15))))-...
cos(x(7))*(cos(x(9))*(cos(x(13))-cos(x(15)))-cos(x(11))*(cos(x(13))+cos(x(15)))));
c2=cos(x(1))*(cos(x(5))*(sin(x(9))*(sin(x(13))*cos(x(10)-x(14))-sin(x(15))*cos(x(10)-x(16)))-...
sin(x(11))*(sin(x(13))*cos(x(12)-x(14))+sin(x(15))*cos(x(12)-x(16))))+...
cos(x(7))*(sin(x(11))*(sin(x(15))*cos(x(12)-x(16))-sin(x(13))*cos(x(12)-x(14)))-...
sin(x(9))*(sin(x(13))*cos(x(10)-x(14))+sin(x(15))*cos(x(10)-x(16)))))+...
cos(x(3))*(cos(x(5))*(sin(x(11))*(sin(x(15))*cos(x(12)-x(16))-sin(x(13))*cos(x(12)-x(14)))-...
sin(x(9))*(sin(x(13))*cos(x(10)-x(14))+sin(x(15))*cos(x(10)-x(16))))-...
cos(x(7))*(sin(x(9))*(sin(x(13))*cos(x(10)-x(14))-sin(x(15))*cos(x(10)-x(16)))-...
sin(x(11))*(sin(x(13))*cos(x(12)-x(14))+sin(x(15))*cos(x(12)-x(16)))));
c3=cos(x(1))*(sin(x(5))*(cos(x(9))*(sin(x(13))*cos(x(6)-x(14))-sin(x(15))*cos(x(6)-x(16)))-...
cos(x(11))*(sin(x(13))*cos(x(6)-x(14))+sin(x(15))*cos(x(6)-x(16))))+...
sin(x(7))*(cos(x(11))*(sin(x(15))*cos(x(8)-x(16))-sin(x(13))*cos(x(8)-x(14)))-...
cos(x(9))*(sin(x(13))*cos(x(8)-x(14))+sin(x(15))*cos(x(8)-x(16)))))+...
cos(x(3))*(sin(x(5))*(cos(x(11))*(sin(x(15))*cos(x(6)-x(16))-sin(x(13))*cos(x(6)-x(14)))-...
cos(x(9))*(sin(x(13))*cos(x(6)-x(14))+sin(x(15))*cos(x(6)-x(16))))-...
sin(x(7))*(cos(x(9))*(sin(x(13))*cos(x(8)-x(14))-sin(x(15))*cos(x(8)-x(16)))-...
cos(x(11))*(sin(x(13))*cos(x(8)-x(14))+sin(x(15))*cos(x(8)-x(16)))));
c4=cos(x(1))*(sin(x(5))*(sin(x(9))*cos(x(6)-x(10))*(cos(x(13))-cos(x(15)))-sin(x(11))*cos(x(6)-x(12))*(cos(x(13))+cos(x(15))))+...
sin(x(7))*(sin(x(11))*cos(x(8)-x(12))*(cos(x(15))-cos(x(13)))-sin(x(9))*cos(x(8)-x(10))*(cos(x(13))+cos(x(15)))))+...
cos(x(3))*(sin(x(5))*(sin(x(11))*cos(x(6)-x(12))*(cos(x(15))-cos(x(13)))-sin(x(9))*cos(x(6)-x(10))*(cos(x(13))+cos(x(15))))-...
sin(x(7))*(sin(x(9))*cos(x(8)-x(10))*(cos(x(13))-cos(x(15)))-sin(x(11))*cos(x(8)-x(12))*(cos(x(13))+cos(x(15)))));
c5=sin(x(1))*(cos(x(5))*(cos(x(9))*(sin(x(13))*cos(x(2)-x(14))-sin(x(15))*cos(x(2)-x(16)))-...
cos(x(11))*(sin(x(13))*cos(x(2)-x(14))+sin(x(15))*cos(x(2)-x(16))))+...
cos(x(7))*(cos(x(11))*(sin(x(15))*cos(x(2)-x(16))-sin(x(13))*cos(x(2)-x(14)))-...
cos(x(9))*(sin(x(13))*cos(x(2)-x(14))+sin(x(15))*cos(x(2)-x(16)))))+...
sin(x(3))*(cos(x(5))*(cos(x(11))*(sin(x(15))*cos(x(4)-x(16))-sin(x(13))*cos(x(4)-x(14)))-...
cos(x(9))*(sin(x(13))*cos(x(4)-x(14))+sin(x(15))*cos(x(4)-x(16))))-...
cos(x(7))*(cos(x(9))*(sin(x(13))*cos(x(4)-x(14))-sin(x(15))*cos(x(4)-x(16)))-...
cos(x(11))*(sin(x(13))*cos(x(4)-x(14))+sin(x(15))*cos(x(4)-x(16)))));
c6=sin(x(1))*(cos(x(5))*(sin(x(9))*cos(x(2)-x(10))*(cos(x(13))-cos(x(15)))-sin(x(11))*cos(x(2)-x(12))*(cos(x(13))+cos(x(15))))+...
cos(x(7))*(sin(x(11))*cos(x(2)-x(12))*(cos(x(15))-cos(x(13)))-sin(x(9))*cos(x(2)-x(10))*(cos(x(13))+cos(x(15)))))+...
sin(x(3))*(cos(x(5))*(sin(x(11))*cos(x(4)-x(12))*(cos(x(15))-cos(x(13)))-sin(x(9))*cos(x(4)-x(10))*(cos(x(13))+cos(x(15))))-...
cos(x(7))*(sin(x(9))*cos(x(4)-x(10))*(cos(x(13))-cos(x(15)))-sin(x(11))*cos(x(4)-x(12))*(cos(x(13))+cos(x(15)))));
c7=sin(x(1))*(sin(x(5))*cos(x(2)-x(6))*(cos(x(9))*(cos(x(13))-cos(x(15)))-cos(x(11))*(cos(x(13))+cos(x(15))))-...
sin(x(7))*cos(x(2)-x(8))*(cos(x(11))*(cos(x(15))-cos(x(13)))-cos(x(9))*(cos(x(13))+cos(x(15)))))+...
sin(x(3))*(sin(x(5))*cos(x(4)-x(6))*(cos(x(11))*(cos(x(15))-cos(x(13)))-cos(x(9))*(cos(x(13))+cos(x(15))))-...
sin(x(7))*cos(x(4)-x(8))*(cos(x(9))*(cos(x(13))-cos(x(15)))-cos(x(11))*(cos(x(13))+cos(x(15)))));
A2=2*a*b;
A3=2*a*c;
A4=2*b*c;
A5=2*a*d;
A6=2*b*d;
A7=2*c*d;
f1=c1+A2*c2+A3*c3+A4*c4+A5*c5+A6*c6+A7*c7;
f=-(f1^2);
my main file of the code
clear
close
clc
%x=[x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9),x(10),x(11),x(12),x(13),x(14),x(15),x(16)]; % angles;
lb=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
ub=[pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi];
options = optimoptions(#fmincon,'TolX',10^-12,'MaxIter',1500,'MaxFunEvals',10^8,'Algorithm','sqp','TolFun',10^-8);
a=0:0.1:1;
b=0:0.1:1;
c=0:0.1:1;
w=NaN(length(a),length(b),length(c));
ww=NaN(length(a),length(b),length(c));
www=NaN(length(a),length(c));
for k=1:100
x0=rand([1,16]).*ub*.9986;%7976
for i=1:length(a)
for j=1:length(b)
for l=1:length(c)
dhelp=1-(a(i)^2)-(b(j)^2)-(c(l)^2);
if (dhelp>0 || dhelp==0)
d=sqrt(dhelp);
[~,fval]=fmincon(#(x)W4qubit(x,a(i),b(j),c(l),d),x0,[],[],[],[],lb,ub,[],options);
w(i,j,l)=sqrt(-fval);
else
w(i,j,l)=nan;
end
ww=max(w,ww);
end
end
end
end
www=max(ww,[],3);
yy=b.^2;xx=a.^2;zz=c.^2;
meshc(xx,yy,www)
grid on
zlabel('\fontname{Times New Roman} M_{max}')
xlabel('\fontname{Times New Roman}\alpha^2')
ylabel('\fontname{Times New Roman}\gamma^2')
%title('fontname{Times New Roman} Maximum of the Svetlichny operator. Method 1 (alpha|0001>+beta|0010>+gamma|1000>)')
Not sure, but doesn't
plot(www,[xx;yy;zz]);
do the job for you? I do not have the optimization toolbox, so I can't test your script. But in principle, this should work.
I wrote the following function:
function [output_signal] = AddDirectivityError (bat_loc_index, butter_deg_vector, sound_matrix)
global chirp_initial_freq ;
global chirp_end_freq;
global sampling_rate;
global num_of_mics;
global sound_signal_length;
for (i=1 : num_of_mics)
normalized_co_freq = (chirp_initial_freq + chirp_end_freq)/ (1.6* sampling_rate);
A=sound_matrix ( i, : ) ;
peak_signal=max(A);
B=find(abs(A)>peak_signal/100);
if (butter_deg_vector(i)==0)
butter_deg_vector(i)=2;
end
[num, den] = butter(butter_deg_vector(i), normalized_co_freq, 'low');// HERE!!!
filtered_signal=filter(num,den, A );
output_signal(i, :)=filtered_signal;
end
This functions runs many-many times without any error. However, when I reach the line: [num, den] = butter ( butter_deg_vector(i), normalized_co_freq, 'low');
And the local variables are: i=3, butter_deg_vector(i)=1, normalized_co_freq=5.625000e-001
MATLAB prompts an error says:
??? Error using ==> buttap Expected N to be integer-valued.
"Error in ==> buttap at 15 validateattributes(n,{'numeric'},{'scalar','integer','positive'},'buttap','N');
Error in ==> butter at 70 [z,p,k] = buttap(n);"
I don't understand why this problem occurs especially in this iteration. Why does this function prompt an error especially in this case?
Try to change the code line for:
[num, den] = butter (round(butter_deg_vector(i)), normalized_co_freq, 'low');
Suppose that we have following array:
0.196238259763928
0.0886250228175519
0.417543614272817
0.182403230538167
0.136500793051860
0.389922187581014
0.0344012946153299
0.381603315802419
0.0997542838649466
0.274807632628596
0.601652859233616
0.209431489000677
0.396925294300794
0.0351587496999554
0.177321874549738
0.369200511917405
0.287108838007101
0.477076452316346
0.127558716868438
0.792431584110476
0.0459982776925879
0.612598437936600
0.228340227044324
0.190267907472804
0.564751537228850
0.00269368929400299
0.940538666131177
0.101588565140294
0.426175626669060
0.600215481734847
0.127859067121782
0.985881201195063
0.0945679498528667
0.950077461673118
0.415212985598547
0.467423473845033
1.24336273213410
0.0848695928658021
1.84522775800633
0.289288949281834
1.38792131632743
1.73186592736729
0.554254947026916
3.46075557122590
0.0872957577705428
4.93259798197976
2.03544238985229
3.71059303259615
8.47095716918618
0.422940369071662
25.2287636895831
4.14535369056670
63.7312173032838
152.080907190007
1422.19492782494
832.134744027851
0.0220089962114756
60.8238733887811
7.71053463387430
10.4151913932115
11.3141744831953
0.988978595613829
8.65598040591953
0.219820300144944
3.92785491164888
2.28370963778411
1.60232807621444
2.51086405960291
0.0181622519984990
2.27469230188760
0.487809730727909
0.961063613990814
1.90435488292485
0.515640996120482
1.25933693517960
0.0953200831348589
1.52851575480462
0.582109930768162
0.933543409438383
0.717947488528521
0.0445235241119612
1.21157308704582
0.0942421028083462
0.536069075206508
0.821400666720535
0.308956823975938
1.28706199713640
0.0339217632187507
1.19575886464231
0.0853733920496230
0.736744959694641
0.635218502184121
0.262305581223588
0.986899895695809
0.0398800891449550
0.758792061180657
0.134279188964854
0.442531129290843
0.542782326712391
0.377221037448628
0.704787750202814
0.224180325609783
0.998785634315287
0.408055416702400
0.329684702125840
0.522384453408780
0.154542718256493
0.602294251721841
0.240357912028348
0.359040779285709
0.525224294805813
0.427539247203335
0.624034405807298
0.298184846094056
0.498659616687732
0.0962076792277457
0.430092706132805
0.656212420735658
0.278310520474744
0.866037361133916
0.184971060800812
0.481149730712771
0.624405636807668
0.382388147099945
0.435350646037440
0.216499523971397
1.22960953802959
0.330841706900755
0.891793067878849
0.628241046456751
0.278687691121678
1.06358076764171
0.365652714373067
1.34921178081181
0.652888708375276
0.861138633227739
1.02878577330537
0.591174450919664
1.93594290806582
0.497631035062465
1.14486512201656
0.978067581547298
0.948931658572253
2.01004088022982
0.917415940349743
2.24124811810385
1.42691656876436
2.15636037453584
1.92812357585099
1.12786835077183
4.81721425534142
1.70055431306602
4.87939454466131
3.90293284926105
5.16542230018432
10.5783535493504
1.74023535081791
27.0572221453758
7.78813114379733
69.2528169436690
167.769806437531
1490.03057130613
869.247150795648
3.27543244752518
62.3527480644562
9.74192115073051
13.6074209231800
10.5686495478844
7.70239986387120
9.62850426896699
9.85304975304259
7.09026325332085
12.8782040428502
16.3163128995995
7.00070066635845
74.1532966917877
4.80506505312457
1042.52337489620
1510.37374385290
118.514435606795
80.7915675273571
2.96352221859211
27.7825124315786
1.55102367292252
8.66382951478539
5.02910503820560
1.25219344189599
7.72195587189507
0.356973215117373
6.06702456628919
1.01953617014621
2.76489896186652
3.35353608882459
0.793376336025486
4.90341095941571
0.00742857354167949
5.07665716731356
1.16863474789604
4.47635486149688
4.33050121578669
2.42974020115261
9.79494608790444
0.0568839453395247
22.9153086380666
4.48791386399205
59.6962194708933
97.8636220152072
1119.97978883924
806.144299041605
7.33252581243942
57.0699524267842
0.900104994068117
15.2791339483160
3.31266162202546
3.20809490583211
5.36617545130941
0.648122925703121
3.90480316969632
0.0338850542128927
2.58828964019220
0.543604662856673
1.16385064506181
1.01835324272839
0.172915006573539
1.55998411282069
0.00221570175453666
1.14803074836796
0.0769335878967426
0.421762398811163
0.468260146832541
0.203765185125597
0.467641715366303
0.00142988680149041
0.698088976126660
0.0413316717103625
0.190548157914037
0.504713663418641
0.325697764871308
0.375910057283262
0.123307135682793
0.331115262928959
0.00263961045860704
0.204555648718379
0.139008751575803
0.182936666944843
0.154943314848474
0.0840483576044629
0.293075999812128
0.00306911699543199
0.272993318570981
0.0864711337990886
0.280495615619829
0.0910123210559269
0.148399626645134
0.141945002415500
0.0512001531781583
0.0295283557338525
In MATLAB it is very easy to find peaks using findpeaks, like so:
[pxx_peaks,location] = findpeaks(Pxx);
If we plot pxx_peaks, we get
plot(pxx_peaks)
Of course, besides these peaks, there are smaller peaks which are not shown on the picture, but my goal is to find all peaks which are 95-96% above all other peaks.
I have tried like this:
>> average = mean(pxx_peaks);
>> stand = std(pxx_peaks);
>> final_peaks = pxx_peaks( pxx_peaks > average + 3*stand );
The result of this is
>> final_peaks
final_peaks =
1.0e+03 *
1.4222
1.4900
1.5104
1.1200
but how to return their corresponding locations? I want to write it as one m-file, so please help me
EDIT
also please help me in this question: can I parameterize the confidence interval? For instance instead of 95%, I want to find peaks that are 60% above then other peaks, is it possible?
Note that 3σ ≈ 99.73%
As for your first question, it's easy, you just have to keep track of the locations in the same way as you do for the peaks:
inds = pxx_peaks > mean(pxx_peaks) + 3*std(pxx_peaks);
final_peaks = pxx_peaks(inds);
final_locations = location(inds);
plot(Pxx), hold on
plot(final_locations, final_peaks, 'r.')
As for your second question, that's a little more complicated. If you want to formulate it like you say, you'll have to convert a desired percentage to the correct number of σ. That involves an integration of the standard normal, and a root finding:
%// Convert confidence interval percentage to number-of-sigmas
F = #(P) fzero(#(sig) quadgk(#(x) exp(-x.^2/2),-sig,+sig)/sqrt(2*pi) - P/100, 1);
% // Repeat with the desired percentage
inds = pxx_peaks > mean(pxx_peaks) + F(63)*std(pxx_peaks); %// 63%
final_peaks = pxx_peaks(inds);
final_locations = location(inds);
plot(final_locations, final_peaks, 'r.')