V_INTERVAL Classify X values into a set of contiguous intervals with boundaries from Y [I,F]=(X,Y,M)
Usage: x=[1.6 2 3.8 0 6.5]; % test values (not necessarily monotonic)
y=[1 2 3 5 6]; % define boundaries of four unequal intervals (y must be increasing)
[i,f]=v_interval(x,y); % classify into intervals using default options 'eE'
% i=[1 2 3 1 4] and f=[0.6 0 0.4 -1 1.5]
Inputs: x(nx) Vector of test values
y(ny) Vector of monotonically increasing interval boundaries: interval i is [ y(i) , y(i+1) )
m(nx) string of mode options
if x(j)<y(1)
'e' extrapolate: set i(j)=1 and f(j)<0 [default]
'c' clip: set i(j)=1 and f(j)=0
'n' NaN: set i(j)=f(j)=NaN
'z' zero: set i(j)=0 and f(j)<0
if x(j)>=y(ny)
'E' set i(j)=ny-1 and f(j)>1 [default]
'C' set i(j)=ny-1 and f(j)=1
'N' set i(j)=f(j)=NaNj
'Z' set i(j)=ny and f(j)>1
Outputs: i(nx) Input x(j) lies in the interval [y(i(j)),y(i(j)+1)]
f(nx) f(j)=(x(j)-y(i(j)))/(y(i(j)+1))-y(i(j))) is the fractional position of x(j) within the interval.
Note that f(j) lies in the range [0,1) provided that y(1) <= x(j) < y(ny)0001 function [i,f]=v_interval(x,y,m) 0002 %V_INTERVAL Classify X values into a set of contiguous intervals with boundaries from Y [I,F]=(X,Y,M) 0003 % 0004 % Usage: x=[1.6 2 3.8 0 6.5]; % test values (not necessarily monotonic) 0005 % y=[1 2 3 5 6]; % define boundaries of four unequal intervals (y must be increasing) 0006 % [i,f]=v_interval(x,y); % classify into intervals using default options 'eE' 0007 % % i=[1 2 3 1 4] and f=[0.6 0 0.4 -1 1.5] 0008 % 0009 % Inputs: x(nx) Vector of test values 0010 % y(ny) Vector of monotonically increasing interval boundaries: interval i is [ y(i) , y(i+1) ) 0011 % m(nx) string of mode options 0012 % if x(j)<y(1) 0013 % 'e' extrapolate: set i(j)=1 and f(j)<0 [default] 0014 % 'c' clip: set i(j)=1 and f(j)=0 0015 % 'n' NaN: set i(j)=f(j)=NaN 0016 % 'z' zero: set i(j)=0 and f(j)<0 0017 % if x(j)>=y(ny) 0018 % 'E' set i(j)=ny-1 and f(j)>1 [default] 0019 % 'C' set i(j)=ny-1 and f(j)=1 0020 % 'N' set i(j)=f(j)=NaNj 0021 % 'Z' set i(j)=ny and f(j)>1 0022 % 0023 % Outputs: i(nx) Input x(j) lies in the interval [y(i(j)),y(i(j)+1)] 0024 % f(nx) f(j)=(x(j)-y(i(j)))/(y(i(j)+1))-y(i(j))) is the fractional position of x(j) within the interval. 0025 % Note that f(j) lies in the range [0,1) provided that y(1) <= x(j) < y(ny) 0026 % 0027 if nargin<3 0028 m=''; 0029 end 0030 [d,e,r]=v_sort([x(:)']); % find order of x values 0031 [d,e,j]=v_sort([y(:)' x(:)']); 0032 ny=numel(y); 0033 k=j(ny+1:end)-r; % next lower element of y for each x (in range [0,ny]) 0034 i=max(min(k,ny-1),1); % force to lie in range [1,ny-1] 0035 f=(x-y(i))./(y(i+1)-y(i)); % fractional position within the interval 0036 klo=k<1; 0037 if any(klo) 0038 if any(m=='c') 0039 f(klo)=0; 0040 elseif any(m=='n') 0041 i(klo)=NaN; 0042 f(klo)=NaN; 0043 elseif any(m=='z') 0044 i(klo)=0; 0045 end 0046 end 0047 khi=k>=ny; 0048 if any(khi) 0049 if any(m=='C') 0050 f(khi)=1; 0051 elseif any(m=='N') 0052 i(khi)=NaN; 0053 f(khi)=NaN; 0054 elseif any(m=='Z') 0055 i(khi)=ny; 0056 end 0057 end 0058 i=reshape(i,size(x)); % force shape to match x 0059 f=reshape(f,size(x)); % force shape to match x