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view scripts/general/interp1.m @ 31253:a40c0b7aa376
maint: changes to follow Octave coding conventions.
* NEWS.8.md: Wrap lines to 72 chars.
* LSODE-opts.in: Use two spaces after sentence ending period.
* LSODE.cc: Use minimum of two spaces between code and start of comment.
* MemoizedFunction.m: Change copyright date to 2022 since this is the year it
was accepted into core. Don't wrap error() lines to 80 chars. Use newlines
to improve readability of switch statements. Use minimum of two spaces between
code and start of comment.
* del2.m, integral.m, interp1.m, interp2.m, griddata.m, inpolygon.m, waitbar.m,
cubehelix.m, ind2x.m, importdata.m, textread.m, logm.m, lighting.m, shading.m,
xticklabels.m, yticklabels.m, zticklabels.m, colorbar.m, meshc.m, print.m,
__gnuplot_draw_axes__.m, struct2hdl.m, ppval.m, ismember.m, iqr.m: Use a space
between comment character '#' and start of comment. Use hyphen for adjectives
describing dimensions such as "1-D".
* vectorize.m, ode23s.m: Use is_function_handle() instead of "isa (x, "function_handle")"
for clarity and performance.
* clearAllMemoizedCaches.m: Change copyright date to 2022 since this is the
year it was accepted into core. Remove input validation which is done by
interpreter. Use two newlines between end of code and start of BIST tests.
* memoize.m: Change copyright date to 2022 since this is the year it was
accepted into core. Re-wrap documentation to 80 chars. Use
is_function_handle() instead of "isa (x, "function_handle")" for clarity and
performance. Use two newlines between end of code and start of BIST tests.
Use semicolon for assert statements within %!test block. Re-write BIST tests
for input validation.
* __memoize__.m: Change copyright date to 2022 since this is the year it was
accepted into core. Use spaces in for statements to improve readability.
* unique.m: Add FIXME note to commented BIST test
* dec2bin.m: Remove stray newline at end of file.
* triplequad.m: Reduce doubly-commented BIST syntax using "#%!#" to "#%!".
* delaunayn.m: Use input variable names in error() statements. Use minimum of
two spaces between code and start of comment. Use hyphen for describing
dimensions. Use two newlines between end of code and start of BIST tests.
Update BIST tests to pass.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 03 Oct 2022 18:06:55 -0700 |
parents | 79d6280fb00a |
children | 5d6b058a22dc |
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######################################################################## ## ## Copyright (C) 2000-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{yi} =} interp1 (@var{x}, @var{y}, @var{xi}) ## @deftypefnx {} {@var{yi} =} interp1 (@var{y}, @var{xi}) ## @deftypefnx {} {@var{yi} =} interp1 (@dots{}, @var{method}) ## @deftypefnx {} {@var{yi} =} interp1 (@dots{}, @var{extrap}) ## @deftypefnx {} {@var{yi} =} interp1 (@dots{}, "left") ## @deftypefnx {} {@var{yi} =} interp1 (@dots{}, "right") ## @deftypefnx {} {@var{pp} =} interp1 (@dots{}, "pp") ## ## One-dimensional interpolation. ## ## Interpolate input data to determine the value of @var{yi} at the points ## @var{xi}. If not specified, @var{x} is taken to be the indices of @var{y} ## (@code{1:length (@var{y})}). If @var{y} is a matrix or an N-dimensional ## array, the interpolation is performed on each column of @var{y}. ## ## The interpolation @var{method} is one of: ## ## @table @asis ## @item @qcode{"nearest"} ## Return the nearest neighbor. ## ## @item @qcode{"previous"} ## Return the previous neighbor. ## ## @item @qcode{"next"} ## Return the next neighbor. ## ## @item @qcode{"linear"} (default) ## Linear interpolation from nearest neighbors. ## ## @item @qcode{"pchip"} ## Piecewise cubic Hermite interpolating polynomial---shape-preserving ## interpolation with smooth first derivative. ## ## @item @qcode{"cubic"} ## Cubic interpolation (same as @qcode{"pchip"}). ## ## @item @qcode{"spline"} ## Cubic spline interpolation---smooth first and second derivatives ## throughout the curve. ## @end table ## ## Adding '*' to the start of any method above forces @code{interp1} ## to assume that @var{x} is uniformly spaced, and only @code{@var{x}(1)} ## and @code{@var{x}(2)} are referenced. This is usually faster, ## and is never slower. The default method is @qcode{"linear"}. ## ## If @var{extrap} is the string @qcode{"extrap"}, then extrapolate values ## beyond the endpoints using the current @var{method}. If @var{extrap} is a ## number, then replace values beyond the endpoints with that number. When ## unspecified, @var{extrap} defaults to @code{NA}. ## ## If the string argument @qcode{"pp"} is specified, then @var{xi} should not ## be supplied and @code{interp1} returns a piecewise polynomial object. This ## object can later be used with @code{ppval} to evaluate the interpolation. ## There is an equivalence, such that @code{ppval (interp1 (@var{x}, ## @var{y}, @var{method}, @qcode{"pp"}), @var{xi}) == interp1 (@var{x}, ## @var{y}, @var{xi}, @var{method}, @qcode{"extrap"})}. ## ## Duplicate points in @var{x} specify a discontinuous interpolant. There ## may be at most 2 consecutive points with the same value. ## If @var{x} is increasing, the default discontinuous interpolant is ## right-continuous. If @var{x} is decreasing, the default discontinuous ## interpolant is left-continuous. ## The continuity condition of the interpolant may be specified by using ## the options @qcode{"left"} or @qcode{"right"} to select a left-continuous ## or right-continuous interpolant, respectively. ## Discontinuous interpolation is only allowed for @qcode{"nearest"} and ## @qcode{"linear"} methods; in all other cases, the @var{x}-values must be ## unique. ## ## An example of the use of @code{interp1} is ## ## @example ## @group ## xf = [0:0.05:10]; ## yf = sin (2*pi*xf/5); ## xp = [0:10]; ## yp = sin (2*pi*xp/5); ## lin = interp1 (xp, yp, xf); ## near = interp1 (xp, yp, xf, "nearest"); ## pch = interp1 (xp, yp, xf, "pchip"); ## spl = interp1 (xp, yp, xf, "spline"); ## plot (xf,yf,"r", xf,near,"g", xf,lin,"b", xf,pch,"c", xf,spl,"m", ## xp,yp,"r*"); ## legend ("original", "nearest", "linear", "pchip", "spline"); ## @end group ## @end example ## ## @seealso{pchip, spline, interpft, interp2, interp3, interpn} ## @end deftypefn function yi = interp1 (x, y, varargin) if (nargin < 2 || nargin > 6) print_usage (); endif method = "linear"; extrap = []; xi = []; ispp = false; have_xi = false; rightcontinuous = NaN; if (nargin > 2) for i_arg = 1:length (varargin) arg = varargin{i_arg}; if (ischar (arg)) arg = tolower (arg); switch (arg) case "extrap" extrap = "extrap"; case "pp" ispp = true; case {"right", "-right"} rightcontinuous = true; case {"left", "-left"} rightcontinuous = false; otherwise method = arg; endswitch else if (i_arg == 1) xi = arg; have_xi = true; else extrap = arg; endif endif endfor endif if (! have_xi && ! ispp) xi = y; y = x; if (isvector (y)) x = 1:numel (y); else x = 1:rows (y); endif endif if (isempty (extrap)) if (iscomplex (y)) extrap = NA + 1i*NA; else extrap = NA; endif endif ## reshape matrices for convenience x = x(:); nx = rows (x); szx = size (xi); if (isvector (y)) y = y(:); endif szy = size (y); y = y(:,:); [ny, nc] = size (y); xi = xi(:); ## determine sizes if (nx < 2 || ny < 2) error ("interp1: minimum of 2 points required in each dimension"); endif ## check whether x is sorted; sort if not. if (! issorted (x, "either")) [x, p] = sort (x); y = y(p,:); endif if (any (strcmp (method, {"previous", "*previous", "next", "*next"}))) rightcontinuous = NaN; # needed for these methods to work endif if (isnan (rightcontinuous)) ## If not specified, set the continuity condition if (x(end) < x(1)) rightcontinuous = false; else rightcontinuous = true; endif elseif ((rightcontinuous && (x(end) < x(1))) || (! rightcontinuous && (x(end) > x(1)))) ## Switch between left-continuous and right-continuous x = flipud (x); y = flipud (y); endif ## Because of the way mkpp works, it's easiest to implement "next" ## by running "previous" with vectors flipped. if (strcmp (method, "next")) x = flipud (x); y = flipud (y); method = "previous"; elseif (strcmp (method, "*next")) x = flipud (x); y = flipud (y); method = "*previous"; endif starmethod = method(1) == "*"; if (starmethod) dx = x(2) - x(1); else jumps = x(1:end-1) == x(2:end); have_jumps = any (jumps); if (have_jumps) if (strcmp (method, "linear") || strcmp (method, ("nearest"))) if (any (jumps(1:nx-2) & jumps(2:nx-1))) warning ("interp1: multiple discontinuities at the same X value"); endif else error ("interp1: discontinuities not supported for METHOD '%s'", method); endif endif endif ## Proceed with interpolating by all methods. switch (method) case "nearest" pp = mkpp ([x(1); (x(1:nx-1)+x(2:nx))/2; x(nx)], shiftdim (y, 1), szy(2:end)); pp.orient = "first"; if (ispp) yi = pp; else yi = ppval (pp, reshape (xi, szx)); endif case "*nearest" pp = mkpp ([x(1), x(1)+[0.5:(nx-1)]*dx, x(nx)], shiftdim (y, 1), szy(2:end)); pp.orient = "first"; if (ispp) yi = pp; else yi = ppval (pp, reshape (xi, szx)); endif case "previous" pp = mkpp ([x(1:nx); 2*x(nx)-x(nx-1)], shiftdim (y, 1), szy(2:end)); pp.orient = "first"; if (ispp) yi = pp; else yi = ppval (pp, reshape (xi, szx)); endif case "*previous" pp = mkpp (x(1)+[0:nx]*dx, shiftdim (y, 1), szy(2:end)); pp.orient = "first"; if (ispp) yi = pp; else yi = ppval (pp, reshape (xi, szx)); endif case "linear" xx = x; nxx = nx; yy = y; dy = diff (yy); if (have_jumps) ## Omit zero-size intervals. xx(jumps) = []; nxx = rows (xx); yy(jumps, :) = []; dy(jumps, :) = []; endif dx = diff (xx); dx = repmat (dx, [1 size(dy)(2:end)]); coefs = [(dy./dx).', yy(1:nxx-1, :).']; pp = mkpp (xx, coefs, szy(2:end)); pp.orient = "first"; if (ispp) yi = pp; else yi = ppval (pp, reshape (xi, szx)); endif case "*linear" dy = diff (y); coefs = [(dy/dx).'(:), y(1:nx-1, :).'(:)]; pp = mkpp (x, coefs, szy(2:end)); pp.orient = "first"; if (ispp) yi = pp; else yi = ppval (pp, reshape (xi, szx)); endif case {"pchip", "*pchip", "cubic", "*cubic"} if (nx == 2 || starmethod) x = linspace (x(1), x(nx), ny); endif if (ispp) y = shiftdim (reshape (y, szy), 1); yi = pchip (x, y); yi.orient = "first"; else y = shiftdim (y, 1); yi = pchip (x, y, reshape (xi, szx)); if (! isvector (y)) yi = shiftdim (yi, 1); endif endif case {"spline", "*spline"} if (nx == 2 || starmethod) x = linspace (x(1), x(nx), ny); endif if (ispp) y = shiftdim (reshape (y, szy), 1); yi = spline (x, y); yi.orient = "first"; else y = shiftdim (y, 1); yi = spline (x, y, reshape (xi, szx)); if (! isvector (y)) yi = shiftdim (yi, 1); endif endif otherwise error ("interp1: invalid METHOD '%s'", method); endswitch if (! ispp && isnumeric (extrap)) ## determine which values are out of range and set them to extrap, ## unless extrap == "extrap". minx = min (x(1), x(nx)); maxx = max (x(1), x(nx)); xi = reshape (xi, szx); outliers = (xi < minx) | ! (xi <= maxx); # this even catches NaNs if (size_equal (outliers, yi)) yi(outliers) = extrap; yi = reshape (yi, szx); elseif (! isscalar (yi)) yi(outliers, :) = extrap; else warning ("interp1: Unreachable state. Please submit data that produced this warning to bugs.octave.org"); yi(outliers.') = extrap; endif endif endfunction %!demo %! clf; %! xf = 0:0.05:10; yf = sin (2*pi*xf/5); %! xp = 0:10; yp = sin (2*pi*xp/5); %! lin = interp1 (xp,yp,xf, 'linear'); %! spl = interp1 (xp,yp,xf, 'spline'); %! pch = interp1 (xp,yp,xf, 'pchip'); %! near= interp1 (xp,yp,xf, 'nearest'); %! plot (xf,yf,'r',xf,near,'g',xf,lin,'b',xf,pch,'c',xf,spl,'m',xp,yp,'r*'); %! legend ('original', 'nearest', 'linear', 'pchip', 'spline'); %! title ('Interpolation of continuous function sin (x) w/various methods'); %! %-------------------------------------------------------- %! % confirm that interpolated function matches the original %!demo %! clf; %! xf = 0:0.05:10; yf = sin (2*pi*xf/5); %! xp = 0:10; yp = sin (2*pi*xp/5); %! lin = interp1 (xp,yp,xf, '*linear'); %! spl = interp1 (xp,yp,xf, '*spline'); %! pch = interp1 (xp,yp,xf, '*pchip'); %! near= interp1 (xp,yp,xf, '*nearest'); %! plot (xf,yf,'r',xf,near,'g',xf,lin,'b',xf,pch,'c',xf,spl,'m',xp,yp,'r*'); %! legend ('*original', '*nearest', '*linear', '*pchip', '*spline'); %! title ('Interpolation of continuous function sin (x) w/various *methods'); %! %-------------------------------------------------------- %! % confirm that interpolated function matches the original %!demo %! clf; %! fstep = @(x) x > 1; %! xf = 0:0.05:2; yf = fstep (xf); %! xp = linspace (0,2,10); yp = fstep (xp); %! pch = interp1 (xp,yp,xf, 'pchip'); %! spl = interp1 (xp,yp,xf, 'spline'); %! plot (xf,yf,'r',xf,pch,'b',xf,spl,'m',xp,yp,'r*'); %! title ({'Interpolation of step function with discontinuity at x==1', ... %! 'Note: "pchip" is shape-preserving, "spline" (continuous 1st, 2nd derivatives) is not'}); %! legend ('original', 'pchip', 'spline'); %!demo %! clf; %! t = 0 : 0.3 : pi; dt = t(2)-t(1); %! n = length (t); k = 100; dti = dt*n/k; %! ti = t(1) + [0 : k-1]*dti; %! y = sin (4*t + 0.3) .* cos (3*t - 0.1); %! ddys = diff (diff (interp1 (t,y,ti, 'spline'))./dti)./dti; %! ddyp = diff (diff (interp1 (t,y,ti, 'pchip')) ./dti)./dti; %! ddyc = diff (diff (interp1 (t,y,ti, 'cubic')) ./dti)./dti; %! plot (ti(2:end-1),ddys,'b*', ti(2:end-1),ddyp,'c^', ti(2:end-1),ddyc,'g+'); %! title ({'Second derivative of interpolated "sin (4*t + 0.3) .* cos (3*t - 0.1)"', ... %! 'Note: "spline" has continuous 2nd derivative, others do not'}); %! legend ('spline', 'pchip', 'cubic'); %!demo %! clf; %! xf = 0:0.05:10; yf = sin (2*pi*xf/5) - (xf >= 5); %! xp = [0:.5:4.5,4.99,5:.5:10]; yp = sin (2*pi*xp/5) - (xp >= 5); %! lin = interp1 (xp,yp,xf, 'linear'); %! near= interp1 (xp,yp,xf, 'nearest'); %! plot (xf,yf,'r', xf,near,'g', xf,lin,'b', xp,yp,'r*'); %! legend ('original', 'nearest', 'linear'); %! %-------------------------------------------------------- %! % confirm that interpolated function matches the original %!demo %! clf; %! x = 0:0.5:3; %! x1 = [3 2 2 1]; %! x2 = [1 2 2 3]; %! y1 = [1 1 0 0]; %! y2 = [0 0 1 1]; %! h = plot (x, interp1 (x1, y1, x), 'b', x1, y1, 'sb'); %! hold on %! g = plot (x, interp1 (x2, y2, x), 'r', x2, y2, '*r'); %! axis ([0.5 3.5 -0.5 1.5]); %! legend ([h(1), g(1)], {'left-continuous', 'right-continuous'}, ... %! 'location', 'northwest') %! legend boxoff %! %-------------------------------------------------------- %! % red curve is left-continuous and blue is right-continuous at x = 2 ## FIXME: add test for N-d arguments here ## For each type of interpolated test, confirm that the interpolated ## value at the knots match the values at the knots. Points away ## from the knots are requested, but only "nearest" and "linear" ## confirm they are the correct values. %!shared xp, yp, xi, style %! xp = 0:2:10; %! yp = sin (2*pi*xp/5); %! xi = [-1, 0, 2.2, 4, 6.6, 10, 11]; ## The following BLOCK/ENDBLOCK section is repeated for each style ## nearest, previous, next, linear, cubic, spline, pchip ## The test for ppval of cubic has looser tolerance, but otherwise ## the tests are identical. ## Note that the block checks style and *style; if you add more tests ## be sure to add them to both sections of each block. One test, ## style vs. *style, occurs only in the first section. ## There is an ENDBLOCKTEST after the final block %!test style = "nearest"; ## BLOCK %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) %!assert (interp1 (xp,[yp',yp'],xi,style), %! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) %!test style = ["*",style]; %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!assert (interp1 (yp, xi, style, 0), ... %! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) %!error interp1 (1,1,1, style) ## ENDBLOCK %!test style = "previous"; ## BLOCK %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) ## This test is expected to fail, so commented out. ## "previous" and "next" options are not symmetric w.r.t to flipping xp,yp #%!assert (interp1 (xp,yp,xi,style),... #%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) %!assert (interp1 (xp,[yp',yp'],xi,style), %! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) %!test style = ["*",style]; %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) #%!assert (interp1 (xp,yp,xi,style),... #%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!assert (interp1 (yp, xi, style, 0), ... %! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) %!error interp1 (1,1,1, style) ## ENDBLOCK %!test style = "next"; ## BLOCK %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) #%!assert (interp1 (xp,yp,xi,style),... #%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) %!assert (interp1 (xp,[yp',yp'],xi,style), %! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) %!test style = ["*",style]; %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) #%!assert (interp1 (xp,yp,xi,style),... #%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!assert (interp1 (yp, xi, style, 0), ... %! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) %!error interp1 (1,1,1, style) ## ENDBLOCK %!test style = "linear"; ## BLOCK %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) %!assert (interp1 (xp,[yp',yp'],xi,style), %! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) %!test style = ['*',style]; %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!assert (interp1 (yp, xi, style, 0), ... %! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) %!assert (interp1 ([1 2 2 3], [1 2 3 4], 2), 3) %!assert (interp1 ([3 2 2 1], [4 3 2 1], 2), 2) %!error interp1 (1,1,1, style) ## ENDBLOCK %!test style = "cubic"; ## BLOCK %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),100*eps) %!error interp1 (1,1,1, style) %!assert (interp1 (xp,[yp',yp'],xi,style), %! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) %!test style = ["*",style]; %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),100*eps) %!assert (interp1 (yp, xi, style, 0), ... %! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) %!error interp1 (1,1,1, style) ## ENDBLOCK %!test style = "pchip"; ## BLOCK %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) %!assert (interp1 (xp,[yp',yp'],xi,style), %! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) %!test style = ["*",style]; %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!assert (interp1 (yp, xi, style, 0), ... %! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) %!error interp1 (1,1,1, style) ## ENDBLOCK %!test style = "spline"; ## BLOCK %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!error interp1 (1,1,1, style) %!assert (interp1 (xp,[yp',yp'],xi,style), %! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) %!test style = ["*",style]; %!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) %!assert (interp1 (xp,yp,xp,style), yp, 100*eps) %!assert (interp1 (xp,yp,xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp',style), yp', 100*eps) %!assert (interp1 (xp',yp',xp,style), yp, 100*eps) %!assert (isempty (interp1 (xp',yp',[],style))) %!assert (isempty (interp1 (xp,yp,[],style))) %!assert (interp1 (xp,[yp',yp'],xi(:),style),... %! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) %!assert <*61903> ... %! (interp1 (xp, yp + 1i * yp.^2, xi, style),... %! interp1 (xp,yp,xi,style) + 1i * interp1 (xp,yp.^2,xi,style)) %!assert (interp1 (xp,yp,xi,style),... %! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) %!assert (ppval (interp1 (xp,yp,style,"pp"),xi), %! interp1 (xp,yp,xi,style,"extrap"),10*eps) %!assert (interp1 (yp, xi, style, 0), ... %! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) %!error interp1 (1,1,1, style) ## ENDBLOCK ## ENDBLOCKTEST ## test extrapolation %!assert (interp1 ([1:5],[3:2:11],[0,6],"linear","extrap"), [1, 13], eps) %!assert (interp1 ([1:5],[3:2:11],[0,6],"nearest","extrap"), [3, 11], eps) %!assert (interp1 ([1:5],[3:2:11],[0,6],"previous","extrap"), [3, 11], eps) %!assert (interp1 ([1:5],[3:2:11],[0,6],"next","extrap"), [3, 11], eps) %!assert (interp1 (xp, yp, [-1, max(xp)+1],"linear",5), [5, 5]) %!assert (interp1 ([0,1],[1,0],[0.1,0.9;0.2,1.1]), [0.9 0.1; 0.8 NA], eps) %!assert (interp1 ([0,1],[1,0],[0.1,0.9;0.2,1]), [0.9 0.1; 0.8 0], eps) ## Basic sanity checks %!assert (interp1 (1:2,1:2,1.4,"nearest"), 1) %!assert (interp1 (1:2,1:2,1.6,"previous"), 1) %!assert (interp1 (1:2,1:2,1.4,"next"), 2) %!assert (interp1 (1:2,1:2,1.4,"linear"), 1.4) %!assert (interp1 (1:4,1:4,1.4,"cubic"), 1.4) %!assert (interp1 (1:2,1:2,1.1,"spline"), 1.1) %!assert (interp1 (1:3,1:3,1.4,"spline"), 1.4) %!assert (interp1 (1:2:4,1:2:4,1.4,"*nearest"), 1) %!assert (interp1 (1:2:4,1:2:4,2.2,"*previous"), 1) %!assert (interp1 (1:2:4,1:2:4,1.4,"*next"), 3) %!assert (interp1 (1:2:4,1:2:4,[0,1,1.4,3,4],"*linear"), [NA,1,1.4,3,NA]) %!assert (interp1 (1:2:8,1:2:8,1.4,"*cubic"), 1.4) %!assert (interp1 (1:2,1:2,1.3, "*spline"), 1.3) %!assert (interp1 (1:2:6,1:2:6,1.4,"*spline"), 1.4) %!assert (interp1 ([3,2,1],[3,2,2],2.5), 2.5) %!assert (interp1 ([4,4,3,2,0],[0,1,4,2,1],[1.5,4,4.5], "linear"), [1.75,1,NA]) %!assert (interp1 (0:4, 2.5), 1.5) ## Left and Right discontinuities %!assert (interp1 ([1,2,2,3,4],[0,1,4,2,1],[-1,1.5,2,2.5,3.5], "linear", "extrap", "right"), [-2,0.5,4,3,1.5]) %!assert (interp1 ([1,2,2,3,4],[0,1,4,2,1],[-1,1.5,2,2.5,3.5], "linear", "extrap", "left"), [-2,0.5,1,3,1.5]) ## Test input validation %!error <Invalid call> interp1 () %!error <Invalid call> interp1 (1) %!error <Invalid call> interp1 (1,2,3,4,5,6,7) %!error <minimum of 2 points required> interp1 (1,1,1, "linear") %!error <minimum of 2 points required> interp1 (1,1,1, "*nearest") %!error <minimum of 2 points required> interp1 (1,1,1, "*linear") %!error <minimum of 2 points required> interp1 (1,1,1, "previous") %!error <minimum of 2 points required> interp1 (1,1,1, "*previous") %!warning <multiple discontinuities> interp1 ([1 1 1 2], [1 2 3 4], 1); %!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "next") %!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "pchip") %!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "cubic") %!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "spline") %!error <invalid METHOD 'invalid'> interp1 (1:2,1:2,1, "invalid")