function v = interp1(varargin)
%INTERP1 1-D interpolation (table lookup).
%   YI = INTERP1(X,Y,XI) interpolates to find YI, the values of
%   the underlying function Y at the points in the vector XI.
%   The vector X specifies the points at which the data Y is
%   given. If Y is a matrix, then the interpolation is performed
%   for each column of Y and YI will be length(XI)-by-size(Y,2).
%
%   YI = INTERP1(Y,XI) assumes X = 1:N, where N is the length(Y)
%   for vector Y or SIZE(Y,1) for matrix Y.
%
%   Interpolation is the same operation as "table lookup".  Described in
%   "table lookup" terms, the "table" is [X,Y] and INTERP1 "looks-up"
%   the elements of XI in X, and, based upon their location, returns
%   values YI interpolated within the elements of Y.
%
%   YI = INTERP1(X,Y,XI,'method') specifies alternate methods.
%   The default is linear interpolation.  Available methods are:
%
%     'nearest'  - nearest neighbor interpolation
%     'linear'   - linear interpolation
%     'spline'   - piecewise cubic spline interpolation (SPLINE)
%     'pchip'    - piecewise cubic Hermite interpolation (PCHIP)
%     'cubic'    - same as 'pchip'
%     'v5cubic'  - the cubic interpolation from MATLAB 5, which does not
%                  extrapolate and uses 'spline' if X is not equally spaced.
%
%   YI = INTERP1(X,Y,XI,'method','extrap') uses the specified method for
%   extrapolation for any elements of XI outside the interval spanned by X.
%   Alternatively, YI = INTERP1(X,Y,XI,'method',EXTRAPVAL) replaces
%   these values with EXTRAPVAL.  NaN and 0 are often used for EXTRAPVAL.
%   The default extrapolation behavior with four input arguments is 'extrap'
%   for 'spline' and 'pchip' and EXTRAPVAL = NaN for the other methods.
%
%   For example, generate a coarse sine curve and interpolate over a
%   finer abscissa:
%       x = 0:10; y = sin(x); xi = 0:.25:10;
%       yi = interp1(x,y,xi); plot(x,y,'o',xi,yi)
%
%   See also INTERP1Q, INTERPFT, SPLINE, INTERP2, INTERP3, INTERPN.

%   Copyright 1984-2000 The MathWorks, Inc.
%   $Revision: 5.36 $  $Date: 2000/09/27 01:04:12 $

% Determine input arguments.

ix = 1; % Is x given as the first argument?
if (nargin==2) | (nargin==3 & isstr(varargin{3})) | ...
      (nargin==4 & ~isstr(varargin{4}));
   ix = 0;
end

if nargin >= 3+ix & ~isempty(varargin{3+ix})
   method = varargin{3+ix};
else
   method = 'linear';
end
% Ignore '*' in v5 option, '*method'.
if method(1) == '*'
   method(1) = [];
end

if nargin >= 4+ix
   extrapval = varargin{4+ix};
else
   switch method(1)
      case {'s','p','c'}
         extrapval = 'extrap';
      otherwise
         extrapval = NaN;
   end
end

u = varargin{2+ix}; 
y = varargin{1+ix}; 
if ix, x = varargin{ix}; else, x = 1:length(y); end


% Check dimensions.  Work with column vectors.
      
if size(y,1) == 1, y = y.'; end
[m,n] = size(y);
if length(x) ~= m
   error('Y must have length(X) rows.')
end
if (m < 2)
   if isempty(u)
      v = [];
      return
   else
      error('There should be at least two data points.')
   end
end
if ~isreal(x)
   error('The data abscissae should be real.')
end
if ~isreal(u)
   error('The interpolation points should be real.')
end
x = x(:);
h = diff(x);
if any(h < 0)
   [x,p] = sort(x);
   y = y(p,:);
   h = diff(x);
end
if any(h == 0)
   error('The data abscissae should be distinct.');
end
siz = size(u);
u = u(:);
p = [];
      
% Interpolate

switch method(1)

   case 's'  % 'spline'
  
      v = spline(x,y.',u.').';

   case {'c','p'}  % 'cubic' or 'pchip'
  
      v = pchip(x,y.',u.').';

   otherwise

      v = zeros(size(u,1),n*size(u,2));
      q = length(u);
      if any(diff(u) < 0)
         [u,p] = sort(u);
      else
         p = 1:q;
      end

      % Find indices of subintervals, x(k) <= u < x(k+1), 
      % or u < x(1) or u >= x(m-1).

      if isempty(u)
         k = u;
      else
         [ignore,k] = histc(u,x);
         k(u<x(1) | ~isfinite(u)) = 1;
         k(u>=x(m)) = m-1;
      end

      switch method(1)

         case 'n'  % 'nearest'
      
            i = find(u >= (x(k)+x(k+1))/2);
            k(i) = k(i)+1;
            v(p,:) = y(k,:);
      
         case 'l'  % 'linear'
      
            s = u - x(k);
            for j = 1:n
               del = diff(y(:,j))./h;
               v(p,j) = y(k,j) + s.*del(k);
            end

         case 'v'  % 'v5cubic'

            extrapval = NaN;
            if norm(diff(h),Inf) <= eps*norm(x,Inf)
               % Equally spaced
               s = (u - x(k))./h(k);
               s2 = s.*s;
               s3 = s.*s2;
               % Add extra points for first and last interval
               y = [3*y(1,:)-3*y(2,:)+y(3,:); y;
                    3*y(m,:)-3*y(m-1,:)+y(m-2,:)];
               for j = 1:n
                  v(p,j) = (y(k,j).*(-s3+2*s2-s) + y(k+1,j).*(3*s3-5*s2+2) ...
                          + y(k+2,j).*(-3*s3+4*s2+s) + y(k+3,j).*(s3-s2))/2;
               end
            else
               % Not equally spaced
               v = spline(x,y.',u(:).').';
            end

         otherwise
 
            error('Invalid method.')

      end
end

% Override extrapolation?

if ~isequal(extrapval,'extrap')
   if isempty(p)
      p = 1:length(u);
   end
   k = find(u<min(x) | u>max(x));
   v(p(k),:) = extrapval;
end

% Reshape result.

if min(size(v))==1 & prod(siz)>1
   v = reshape(v,siz);
end
