Evaluating a function with three variables

Dear all, Since I am new in MatLab, I want to evaluate the following equation y=(1./((x.^2)+1))-(p./((x+w).^2+1))-(p./((x-w).^2+1)); I want to sweep the variables x,p and w as follows x from -5 to 5 with 100 steps ,p from 0 to 1 with 100 steps ,w from 0 to 3 with 100 steps and then I want to normalized the functiony and then I want to extract the specific values of x (lets name new variable r) which give me specific value of y (lets say y=0.5) for each combination of variables x,w,p. After that I want to make a surface graph of ( r,w and p)

thanks

[Walter Roberson]

Please do not close questions that have an answer.

Answer 1

[KSSV]

    N = 100 ;
    x = linspace(-5,5,N) ;
    p = linspace(0,1,N) ;
    w = linspace(0,3,N) ;
    [x,p,w] = meshgrid(x,p,w) ;

    y=(1./((x.^2)+1))-(p./((x+w).^2+1))-(p./((x-w).^2+1));

    figure
    hold on
    for i = 1:N
        surf(x(:,:,i),p(:,:,i),w(:,:,i),y(:,:,i))
    end
    % GEt manually y = 0.5 
    idx = abs(y-0.5)<=10^-3 ;
    xr = x(idx) ; 
    pr = p(idx) ; 
    wr = w(idx) ; 

    figure
    scatter3(xr,pr,wr,10,wr)

    % use isosurface 
    p = patch(isosurface(x,p,w,y,0.5));
    p.FaceColor = 'red';
    p.EdgeColor = 'none';
    daspect([1 1 1])
    view(3); 
    axis tight
    camlight 
    lighting gouraud

[Alin Brad]

thank you for answer.

now, I to want to extract values of x which give me certain values of y. lets say r= value of x which gives me the certainvalues of y for each combination, I define for example this required value of y as follows yabs=abs(min(y)); Ycertain=(max(y)-yabs)/2; and make a surface graph (r,w,p)

thanks

[KSSV]

I have edited the answer...

[Alin Brad]

kindly. I want now to not get the value of y as 0.5, but I want it as Ycertain=(max abs(y)-min(abs(y))/2 and then extract the value of corresponding x thanks

[KSSV]

You find the value and and place the value inplace of 0.5....it is simple.

val = max(y(:)-abs(y(:)/2)) ;

[Alin Brad]

I have made the modification and change the value of y to idx = (max(y(:))-(abs(min((y(:)))))/2) however, I got one value of idx and now values of xr and got the following message #Array indices must be positive integers or logical values#.

[Walter Roberson]

You would not use val as idx. You would use

idx = abs(y-val)<=10^-3 ;

Answer 2

[Alin Brad]

I have made this modification to make surface and make xr as Z dimension , but it doesnot work properly

 N = 100 ;
    x = linspace(-5,5,N) ;
    p = linspace(0,1,N) ;
    w = linspace(0,3,N) ;
    [x,p,w] = meshgrid(x,p,w) ;
    y=(1./((x.^2)+1))-(p./((x+w).^2+1))-(p./((x-w).^2+1));
    figure
    hold on
    for i = 1:N
        surf(x(:,:,i),p(:,:,i),w(:,:,i),y(:,:,i))
    end
    % GEt manually y 
    val=(max(y(:))-(abs(min((y(:)))))/2)
    idx = abs(y-val)>=10^-3 ;
    xr = x(idx) ; 
    pr = p(idx) ; 
    wr = w(idx) ; 
    figure
    scatter3(xr,pr,wr,10,wr)
    % use isosurface 
    p = patch(isosurface(xr,pr,wr,y,val));
    p.FaceColor = 'red';
    p.EdgeColor = 'none';
    daspect([1 1 1])
    view(3); 
    axis tight
    camlight 
    lighting gouraud

[KSSV]

 p = patch(isosurface(x,p,w,y,val));

[Walter Roberson]

You cannot use isosurface() for scattered points.

    idx = abs(y-val)>=10^-3 ;

is creating a logical mask that talks about individual points inside the grid y . When you take x(idx) and so on you are extracting only those points -- scattered points.

Consider

yt = y;
yt(~idx) = nan;
p = patch(isosurface(x, y, w, yt, val));

You will probably want to do that in a different plot, or erase what you have drawn first: the values form a thin irregular sheet that is effectively hidden by the heavy point density of the scatter3()

[Alin Brad]

Thank you The bellow program returns a message The size of X must match the size of V or the number of columns of V. and show a plot of p as z axis which should be xr as z axis

 N = 100 ;
    x = linspace(-5,5,N) ;
    p = linspace(0,1,N) ;
    w = linspace(0,3,N) ;
    [x,p,w] = meshgrid(x,p,w) ;
    y=(1./((x.^2)+1))-(p./((x+w).^2+1))-(p./((x-w).^2+1));
    figure
    hold on
    for i = 1:N
        surf(x(:,:,i),p(:,:,i),w(:,:,i),y(:,:,i))
    end
    % GEt y 
    val=(max(y(:))-(abs(min((y(:)))))/2)
    idx = abs(y-val)>=10^-3 ;
   yt = y;
yt(~idx) = nan;
    xr = x(idx) ; 
    pr = p(idx) ; 
    wr = w(idx) ; 
    figure
    scatter3(xr,pr,wr,10,wr)
    % use isosurface 
p= patch(isosurface(xr, pr, wr, yt, val));
    p.FaceColor = 'red';
    p.EdgeColor = 'none';
    daspect([1 1 1])
    view(3); 
    axis tight
    camlight 
    lighting gouraud

[Walter Roberson]

Notice in my call I did not select subsets of x and so on for the isosurface call: I left them the original size but assigned nan to locations in the grid that were not of interest.