Your data look like a two-dimensional parametric plot of (x,y) as a function of some underlying parameter t. As such, it may be possible to do a least-squares fit of x(t) and y(t) if you can come up with a reasonable model for them. Your data appear to describe a limacon.
I’m not sure if it’s the final solution, but it’s close: First thing your functions are all wrong. You need the value of the array, not of elements. Second, use matlab sign function. Finally, don’t forget to add the dot operator in front of theta. function main clc;clear; t=0:0.0001:(76*pi); x=((4619/60*sin(t+11/7)+109/8*sin(2*t+11/7)+9/7*sin(3*t+11/7)+89/15*sin(4*t+11/7)+5/11*sin(5*t+11/7)-9839/41).*theta(75*pi-t).*theta(t-71*pi)+(-179/8*sin(11/7-2*t)+2101/20*sin(t+11/7)+5/6*sin(3*t+23/5)+65/9*sin(4*t+33/7)+33/8*sin(5*t+8/5)-698/9).*theta(71*pi-t).*theta(t-67*pi)+(952/15*sin(t+11/7)+116/21*sin(2*t+19/12)+26/5*sin(3*t+11/7)+11/9*sin(4*t+11/7)+25/11*sin(5*t+11/7)+3071/10).*theta(67*pi-t).*theta(t-63*pi)+(-4/11*sin(17/11-4*t)+657/13*sin(t+33/7)+29/11*sin(2*t+47/10)+17/6*sin(3*t+14/9)+2/13*sin(5*t+22/13)+15/8*sin(6*t+33/7)+16/11*sin(7*t+47/10)+5/3*sin(8*t+47/10)+24/13*sin(9*t+33/7)+9/11*sin(10*t+47/10)+6/5*sin(11*t+47/10)+17/18*sin(12*t+47/10)+4/9*sin(13*t+75/16)+1163/3).*theta(63*pi-t).*theta(t-59*pi)+(-11/13*sin(11/7-6*t)-17/10*sin(11/7-4*t)+261/7*sin(t+11/7)+17/3*sin(2*t+33/7)+44/19*sin(3*t+11/7)+7/9*sin(5*t+14/9)+259/3).*theta(59*pi-t).*theta(t-55*pi)+(-9/11*sin(26/17-23*t)-287/9*sin(11/7-5*t)-271/9*sin(17/11-3*t)+1551/13*sin(t+17/11)+685/8*sin(2*t+17/11)+535/11*sin(4*t+14/9)+311/11*sin(6*t+14/9)+1141/60*sin(7*t+61/13)+19/9*sin(8*t+21/11)+55/8*sin(9*t+77/17)+239/12*sin(10*t+9/2)+7/9*sin(11*t+69/16)+59/6*sin(12*t+13/10)+73/24*sin(13*t+13/11)+17/12*sin(14*t+47/11)+11/16*sin(15*t+22/5)+17/6*sin(16*t+4/3)+7/11*sin(17*t+17/13)+17/9*sin(18*t+11/9)+7/4*sin(19*t+7/5)+5/4*sin(20*t+53/12)+50/13*sin(21*t+12/11)+103/13*sin(22*t+8/7)+13/5*sin(24*t+29/7)+1/2*sin(25*t+16/5)+31/16*sin(26*t+13/3)+8/7*sin(27*t+33/8)+17/14*sin(28*t+123/31)+22/9*sin(29*t+30/7)+2/3*sin(30*t+48/13)+19/12*sin(31*t+89/22)+18/11*sin(32*t+46/11)+417/8).*theta(55*pi-t).*theta(t-51*pi)+(-2/7*sin(14/9-10*t)-9/13*sin(14/9-8*t)-224/11*sin(11/7-3*t)+197/11*sin(t+11/7)+139/14*sin(2*t+11/7)+17/12*sin(4*t+47/10)+43/12*sin(5*t+33/7)+2/5*sin(6*t+47/10)+28/19*sin(7*t+47/10)+34/33*sin(9*t+47/10)+1/4*sin(11*t+14/3)+6/19*sin(12*t+19/12)-955/8).*theta(51*pi-t).*theta(t-47*pi)+(-149/28*sin(11/7-5*t)-65/6*sin(11/7-3*t)-641/12*sin(11/7-t)+265/9*sin(2*t+11/7)+37/5*sin(4*t+11/7)+7931/15).*theta(47*pi-t).*theta(t-43*pi)+(1810/9*sin(t+11/7)+1904/5*sin(2*t+11/7)+481/24*sin(3*t+61/13)+181/30*sin(4*t+11/7)+277/10*sin(5*t+19/12)+292/11*sin(6*t+19/12)+25/7*sin(7*t+47/10)+38/5*sin(8*t+8/5)+74/11*sin(9*t+8/5)+75/13*sin(10*t+8/5)+18/11*sin(11*t+19/12)+3109/13).*theta(43*pi-t).*theta(t-39*pi)+(-19/9*sin(11/7-12*t)-21/8*sin(11/7-10*t)-1/11*sin(17/11-8*t)-32/19*sin(14/9-6*t)+4137/22*sin(t+11/7)+177/14*sin(2*t+33/7)+173/14*sin(3*t+11/7)+3/2*sin(4*t+19/12)+5/8*sin(5*t+14/9)+21/8*sin(7*t+11/7)+19/10*sin(9*t+11/7)+41/15*sin(11*t+11/7)+2104/3).*theta(39*pi-t).*theta(t-35*pi)+(-5/6*sin(17/12-11*t)-7/15*sin(5/12-10*t)-32/13*sin(7/13-3*t)-139/7*sin(2/7-2*t)+2224/15*sin(t+9/10)+103/10*sin(4*t+23/5)+45/44*sin(5*t+7/3)+35/9*sin(6*t+23/8)+21/10*sin(7*t+25/11)+10/11*sin(8*t+4/5)+23/15*sin(9*t+5/7)+4/5*sin(12*t+9/2)+1339/11).*theta(35*pi-t).*theta(t-31*pi)+(1069/6*sin(t+18/13)+643/28*sin(2*t+11/7)+255/16*sin(3*t+11/15)+247/29*sin(4*t+45/13)+53/6*sin(5*t+9/11)+14/29*sin(6*t+31/7)+21/5*sin(7*t+19/7)+53/20*sin(8*t+3/14)+24/13*sin(9*t+24/11)+sin(10*t+27/14)+7/8*sin(11*t+11/9)+1/3*sin(12*t+7/4)+4512/25).*theta(31*pi-t).*theta(t-27*pi)+(-73/8*sin(1/9-11*t)-101/7*sin(7/8-3*t)+3221/13*sin(t+4/5)+389/8*sin(2*t+36/11)+368/11*sin(4*t+80/27)+107/4*sin(5*t+1/4)+29/2*sin(6*t+13/4)+237/19*sin(7*t+1/6)+263/17*sin(8*t+10/3)+79/9*sin(9*t+5/14)+68/9*sin(10*t+67/22)+43/5*sin(12*t+29/9)-3139/7).*theta(27*pi-t).*theta(t-23*pi)+(-7/9*sin(9/10-17*t)-22/13*sin(86/85-11*t)-43/10*sin(1/33-7*t)-64/7*sin(2/9-5*t)-19/10*sin(7/10-4*t)+2327/9*sin(t+19/5)+46*sin(2*t+7/4)+52/7*sin(3*t+31/9)+44/13*sin(6*t+17/11)+35/13*sin(8*t+23/8)+45/17*sin(9*t+9/2)+35/17*sin(10*t+34/9)+17/10*sin(12*t+17/8)+3/5*sin(13*t+41/10)+15/13*sin(14*t+41/14)+10/19*sin(15*t+139/35)+7/9*sin(16*t+24/11)+7/8*sin(18*t+3/5)+9/8*sin(19*t+6/7)+7/9*sin(20*t+25/14)+17/18*sin(21*t+7/11)+9/8*sin(22*t+22/15)+3/7*sin(23*t+11/4)+7/12*sin(24*t+26/9)+3/14*sin(25*t+26/7)+12/25*sin(26*t+62/25)+7/11*sin(27*t+64/15)+1/4*sin(28*t+95/24)+7/20*sin(29*t+3)+4/9*sin(30*t+14/5)+1/9*sin(31*t+4)+1/11*sin(32*t+9/11)+3/13*sin(33*t+8/5)+1/8*sin(34*t+20/11)+2/5*sin(35*t+2/7)-16257/22).*theta(23*pi-t).*theta(t-19*pi)+(-3/8*sin(2/7-5*t)-51/19*sin(1/28-3*t)-34/7*sin(3/8-2*t)+20/9*sin(t+155/52)+16/17*sin(4*t+25/7)+4/9*sin(6*t+24/7)+3/10*sin(7*t+3/7)+3/11*sin(8*t+41/11)+2/11*sin(9*t+9/19)+1/8*sin(10*t+389/97)+1/6*sin(11*t+2/7)+1/6*sin(12*t+47/16)+5910/19).*theta(19*pi-t).*theta(t-15*pi)+(-4/15*sin(12/23-7*t)+24/7*sin(t+21/8)+15/4*sin(2*t+3/2)+31/9*sin(3*t+7/5)+8/5*sin(4*t+25/7)+13/17*sin(5*t+1/4)+2/3*sin(6*t+46/15)+5/13*sin(8*t+3)+3/7*sin(9*t+2/5)+3/10*sin(10*t+53/15)+2/7*sin(11*t+2/5)+1/3*sin(12*t+25/7)+109/2).*theta(15*pi-t).*theta(t-11*pi)+(-53/14*sin(18/13-4*t)+592/7*sin(t+21/10)+107/27*sin(2*t+17/4)+29/13*sin(3*t+41/11)+859/12).*theta(11*pi-t).*theta(t-7*pi)+(287/3*sin(t+19/9)+16/5*sin(2*t+43/13)+57/10*sin(3*t+21/8)+33/17*sin(4*t+31/7)+1877/6).*theta(7*pi-t).*theta(t-3*pi)+(-5/8*sin(2/3-15*t)-17/8*sin(11/10-12*t)-11/6*sin(9/13-9*t)-507/10*sin(2/9-3*t)-69/13*sin(41/27-2*t)+1813/5*sin(t+11/3)+63/13*sin(4*t+25/8)+63/4*sin(5*t+23/5)+122/11*sin(6*t+49/16)+32/7*sin(7*t+19/9)+37/8*sin(8*t+12/7)+20/9*sin(10*t+17/8)+43/17*sin(11*t+1/69)+31/14*sin(13*t+21/5)+5/3*sin(14*t+32/11)+66/65*sin(16*t+53/14)+760/3).*theta(3*pi-t).*theta(t+pi)).*theta(sqrt(sign(sin(t/2)))); y=((-13/5*sin(11/7-5*t)-51/8*sin(11/7-3*t)-28*sin(11/7-t)+97/6*sin(2*t+11/7)+124/25*sin(4*t+11/7)-7811/8).*theta(75*pi-t).*theta(t-71*pi)+(-76/7*sin(13/9-4*t)-69/4*sin(43/29-3*t)-50*sin(17/11-2*t)+229/12*sin(t+17/11)+13/8*sin(5*t+4/5)-2538/7).*theta(71*pi-t).*theta(t-67*pi)+(-17/4*sin(11/7-3*t)-217/11*sin(11/7-t)+79/7*sin(2*t+11/7)+11/6*sin(4*t+11/7)+15/14*sin(5*t+33/7)-79/6).*theta(67*pi-t).*theta(t-63*pi)+(-164/9*sin(11/7-2*t)+845/12*sin(t+11/7)+7/8*sin(3*t+18/11)+89/10*sin(4*t+33/7)+34/23*sin(5*t+47/10)+105/26*sin(6*t+33/7)+8/11*sin(7*t+14/9)+1/8*sin(8*t+17/11)+25/12*sin(9*t+11/7)+13/9*sin(10*t+11/7)+33/16*sin(11*t+14/9)+13/27*sin(12*t+14/9)+2/3*sin(13*t+14/9)+2671/13).*theta(63*pi-t).*theta(t-59*pi)+(-64/65*sin(14/9-6*t)-25/9*sin(14/9-5*t)-34/9*sin(14/9-4*t)-57/14*sin(14/9-3*t)-19/14*sin(11/7-2*t)+21/2*sin(t+11/7)+3133/11).*theta(59*pi-t).*theta(t-55*pi)+(-25/24*sin(23/15-27*t)-5/14*sin(14/11-25*t)-2/3*sin(16/11-17*t)-55/9*sin(40/27-8*t)-352/13*sin(14/9-5*t)-1519/38*sin(14/9-3*t)+3329/32*sin(t+47/10)+297/4*sin(2*t+14/9)+1939/38*sin(4*t+14/9)+239/9*sin(6*t+32/21)+34/9*sin(7*t+19/15)+107/6*sin(9*t+10/7)+271/10*sin(10*t+40/9)+693/13*sin(11*t+86/19)+160/7*sin(12*t+13/9)+289/16*sin(13*t+7/6)+385/48*sin(14*t+9/7)+44/9*sin(15*t+5/4)+41/11*sin(16*t+13/10)+12/13*sin(18*t+12/5)+46/9*sin(19*t+40/9)+10/9*sin(20*t+38/25)+46/31*sin(21*t+75/16)+37/16*sin(22*t+41/10)+35/11*sin(23*t+43/10)+10/13*sin(24*t+63/16)+2/3*sin(26*t+47/13)+19/7*sin(28*t+6/5)+13/10*sin(29*t+59/13)+3/2*sin(30*t+4/3)+11/10*sin(31*t+5/7)+17/13*sin(32*t+15/4)-11101/75).*theta(55*pi-t).*theta(t-51*pi)+(-3/10*sin(14/9-12*t)-29/12*sin(11/7-6*t)-38/9*sin(11/7-4*t)-59/8*sin(11/7-t)+183/7*sin(2*t+11/7)+125/13*sin(3*t+11/7)+31/16*sin(5*t+19/12)+4/9*sin(7*t+11/7)+3/13*sin(8*t+47/10)+64/63*sin(9*t+14/9)+3/13*sin(10*t+33/7)+1/2*sin(11*t+19/12)-11360/13).*theta(51*pi-t).*theta(t-47*pi)+(-60/11*sin(11/7-4*t)-528/31*sin(11/7-3*t)-661/55*sin(11/7-2*t)-623/3*sin(11/7-t)+39/8*sin(5*t+33/7)-5871/8).*theta(47*pi-t).*theta(t-43*pi)+(-43/13*sin(14/9-11*t)-45/8*sin(11/7-9*t)-41/15*sin(14/9-8*t)-57/11*sin(14/9-7*t)-157/6*sin(11/7-5*t)-1813/6*sin(11/7-t)+1997/15*sin(2*t+11/7)+89/6*sin(3*t+47/10)+19/6*sin(4*t+23/15)+191/8*sin(6*t+11/7)+191/17*sin(10*t+19/12)-7307/9).*theta(43*pi-t).*theta(t-39*pi)+(-15/8*sin(11/7-12*t)-72/73*sin(14/9-11*t)-19/9*sin(11/7-10*t)-35/11*sin(11/7-9*t)-7/11*sin(14/9-8*t)-60/11*sin(11/7-7*t)-191/13*sin(11/7-5*t)-184/5*sin(11/7-3*t)-109/10*sin(11/7-2*t)-609/2*sin(11/7-t)+1/6*sin(4*t+5/4)+11/5*sin(6*t+47/10)-6582/11).*theta(39*pi-t).*theta(t-35*pi)+(-11/15*sin(6/7-9*t)-47/13*sin(26/25-5*t)-67/27*sin(13/12-4*t)-633/8*sin(3/10-t)+251/7*sin(2*t+9/8)+123/8*sin(3*t+64/15)+23/8*sin(6*t+22/13)+26/9*sin(7*t+23/6)+14/9*sin(8*t+3/5)+19/12*sin(10*t+9/7)+25/19*sin(11*t+13/3)+11/17*sin(12*t+7/12)-5757/11).*theta(35*pi-t).*theta(t-31*pi)+(-50/3*sin(3/4-3*t)+263/10*sin(t+83/28)+669/13*sin(2*t+11/5)+17*sin(4*t+13/7)+67/11*sin(5*t+19/8)+11/3*sin(6*t+1/12)+38/17*sin(7*t+9/5)+51/14*sin(8*t+5/3)+49/25*sin(9*t+41/10)+17/12*sin(10*t+7/12)+53/54*sin(11*t+24/7)+5/7*sin(12*t+7/4)-10661/26).*theta(31*pi-t).*theta(t-27*pi)+(-127/10*sin(16/17-7*t)-119/9*sin(11/9-5*t)-1191/4*sin(1/3-t)+735/11*sin(2*t+2/9)+287/8*sin(3*t+61/16)+504/19*sin(4*t+17/9)+73/9*sin(6*t+9/5)+62/7*sin(8*t+14/5)+32/5*sin(9*t+1/6)+7/2*sin(10*t+19/7)+19/7*sin(11*t+1/44)+167/56*sin(12*t+51/14)-12878/17).*theta(27*pi-t).*theta(t-23*pi)+(-5/12*sin(14/15-32*t)-1/18*sin(17/13-31*t)-23/11*sin(1/6-19*t)-11/9*sin(38/25-18*t)-243/61*sin(25/17-8*t)-35/9*sin(11/21-7*t)-87/7*sin(4/5-6*t)-2249/15*sin(1/10-2*t)+1997/10*sin(t+23/12)+725/13*sin(3*t+1)+67/8*sin(4*t+9/4)+216/11*sin(5*t+23/5)+18/11*sin(9*t+32/31)+48/13*sin(10*t+19/8)+211/35*sin(11*t+16/5)+36/13*sin(12*t+64/15)+30/29*sin(13*t+8/13)+20/11*sin(14*t+28/13)+11/17*sin(15*t+37/16)+5/8*sin(16*t+23/14)+4/7*sin(17*t+14/9)+91/45*sin(20*t+14/27)+47/31*sin(21*t+8/5)+6/7*sin(22*t+29/15)+8/9*sin(23*t+53/20)+13/10*sin(24*t+89/30)+8/9*sin(25*t+39/10)+7/20*sin(26*t+97/24)+4/9*sin(27*t+18/13)+7/8*sin(28*t+45/14)+2/7*sin(29*t+42/13)+3/11*sin(30*t+22/5)+8/17*sin(33*t+4/11)+5/9*sin(34*t+18/13)+3/14*sin(35*t+12/5)-3384/11).*theta(23*pi-t).*theta(t-19*pi)+(-1/38*sin(2/11-7*t)-35/11*sin(9/14-t)+341/85*sin(2*t+25/14)+34/11*sin(3*t+22/21)+42/43*sin(4*t+223/56)+14/15*sin(5*t+3/4)+12/23*sin(6*t+7/2)+1/7*sin(8*t+4)+2/11*sin(9*t+9/8)+2/11*sin(10*t+73/29)+1/7*sin(11*t+1/4)+2/11*sin(12*t+74/25)+2961/20).*theta(19*pi-t).*theta(t-15*pi)+(-3/11*sin(13/25-12*t)-1/3*sin(15/29-10*t)-1/9*sin(4/3-8*t)-16/9*sin(12/13-4*t)+35/18*sin(t+89/19)+33/8*sin(2*t+49/16)+43/14*sin(3*t+33/13)+3/10*sin(5*t+26/11)+3/10*sin(6*t+4/11)+9/17*sin(7*t+94/27)+1/5*sin(9*t+35/11)+1/4*sin(11*t+20/7)+2917/15).*theta(15*pi-t).*theta(t-11*pi)+(949/15*sin(t+11/3)+63/11*sin(2*t+19/9)+26/7*sin(3*t+22/5)+7/8*sin(4*t+28/13)+3715/23).*theta(11*pi-t).*theta(t-7*pi)+(658/9*sin(t+107/27)+57/10*sin(2*t+9/5)+56/13*sin(3*t+38/9)+7/6*sin(4*t+10/11)+1681/16).*theta(7*pi-t).*theta(t-3*pi)+(-9/11*sin(13/10-16*t)-14/15*sin(2/7-15*t)-12/7*sin(3/8-12*t)-29/6*sin(5/11-8*t)-80/9*sin(5/14-4*t)+3076/7*sin(t+12/5)+343/18*sin(2*t+13/3)+230/17*sin(3*t+31/8)+21/4*sin(5*t+53/21)+23/10*sin(6*t+1/5)+27/7*sin(7*t+5/12)+60/17*sin(9*t+38/9)+11/8*sin(10*t+49/16)+10/7*sin(11*t+2/3)+4/7*sin(13*t+18/5)+17/12*sin(14*t+9/7)+598/9).*theta(3*pi-t).*theta(t+pi)).*theta(sqrt(sign(sin(t/2)))); plot(x,y,’.’); end % function … Read more
A square bracket creates a vector or matrix, whereas curly brackets creates a cell array. When working with numbers, I’d say that 99% of the time, you will use square brackets. Cell arrays allow you to store different types of data at each location, e.g. a 10×5 matrix at (1,1), a string array at (1,2), … Read more
There are several differences between a cell array and a matrix in MATLAB: A cell array may contain any arbitrary type of element in each cell; while a matrix requires the types of its elements to be homogeneous i.e. of the same type. As far as memory layout goes, all elements of a matrix are … Read more
If you notice, there is a distinct pattern to the adjacency matrices you are creating. Specifically, they are symmetric and banded. You can take advantage of this fact to easily create your matrices using the diag function (or the spdiags function if you want to make a sparse matrix). Here is how you can create … Read more
Short answer, if you’re only interested in solving a prediction task: use Naive Bayes. A Bayesian network (has a good wikipedia page) models relationships between features in a very general way. If you know what these relationships are, or have enough data to derive them, then it may be appropriate to use a Bayesian network. … Read more
You first create the filter with fspecial and then convolve the image with the filter using imfilter (which works on multidimensional images as in the example). You specify sigma and hsize in fspecial. Code: %%# Read an image I = imread(‘peppers.png’); %# Create the gaussian filter with hsize = [5 5] and sigma = 2 … Read more
So how does one identify if a matrix is truly singular? (In MATLAB, without using paper and pencil or symbolic computations, or hand written row operations?) The textbooks sometimes tell students to use the determinant, so I’ll start there. In theory, one can simply test if the determinant of your matrix is zero. Thus M … Read more
Using a Value (Vanilla) Class When using a value class you need to tell Matlab to store a modified copy of the object to save the changes in the property value. So, >> a=testprop >> a.Request(5); % will NOT change the value of a.numRequests. 5 >> a.Request(5) 5 >> a.numRequests ans = 0 >> a=a.Request; … Read more
Actually, Mikhail’s answer is not quite right. In the case that someFunction is a function that returns a value even if none is requested, which is how a function indicates that the value should be assigned to ans, Mikhail’s wrapper will fail. For example, if someFunction were replaced with sin and you compared running wrapper … Read more