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view scripts/general/interp1.m @ 27918:b442ec6dda5c
use centralized file for copyright info for individual contributors
* COPYRIGHT.md: New file.
* In most other files, use "Copyright (C) YYYY-YYYY The Octave Project
Developers" instead of tracking individual names in separate source
files. The motivation is to reduce the effort required to update the
notices each year.
Until now, the Octave source files contained copyright notices that
list individual contributors. I adopted these file-scope copyright
notices because that is what everyone was doing 30 years ago in the
days before distributed version control systems. But now, with many
contributors and modern version control systems, having these
file-scope copyright notices causes trouble when we update copyright
years or refactor code.
Over time, the file-scope copyright notices may become outdated as new
contributions are made or code is moved from one file to
another. Sometimes people contribute significant patches but do not
add a line claiming copyright. Other times, people add a copyright
notice for their contribution but then a later refactoring moves part
or all of their contribution to another file and the notice is not
moved with the code. As a practical matter, moving such notices is
difficult -- determining what parts are due to a particular
contributor requires a time-consuming search through the project
history. Even managing the yearly update of copyright years is
problematic. We have some contributors who are no longer
living. Should we update the copyright dates for their contributions
when we release new versions? Probably not, but we do still want to
claim copyright for the project as a whole.
To minimize the difficulty of maintaining the copyright notices, I
would like to change Octave's sources to use what is described here:
https://softwarefreedom.org/resources/2012/ManagingCopyrightInformation.html
in the section "Maintaining centralized copyright notices":
The centralized notice approach consolidates all copyright
notices in a single location, usually a top-level file.
This file should contain all of the copyright notices
provided project contributors, unless the contribution was
clearly insignificant. It may also credit -- without a copyright
notice -- anyone who helped with the project but did not
contribute code or other copyrighted material.
This approach captures less information about contributions
within individual files, recognizing that the DVCS is better
equipped to record those details. As we mentioned before, it
does have one disadvantage as compared to the file-scope
approach: if a single file is separated from the distribution,
the recipient won't see the contributors' copyright notices.
But this can be easily remedied by including a single
copyright notice in each file's header, pointing to the
top-level file:
Copyright YYYY-YYYY The Octave Project Developers
See the COPYRIGHT file at the top-level directory
of this distribution or at https://octave.org/COPYRIGHT.html.
followed by the usual GPL copyright statement.
For more background, see the discussion here:
https://lists.gnu.org/archive/html/octave-maintainers/2020-01/msg00009.html
Most files in the following directories have been skipped intentinally
in this changeset:
doc
libgui/qterminal
liboctave/external
m4
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Mon, 06 Jan 2020 15:38:17 -0500 |
parents | 00f796120a6d |
children | 1891570abac8 |
line wrap: on
line source
## Copyright (C) 2000-2019 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this distribution ## or <https://octave.org/COPYRIGHT.html/>. ## ## ## 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 ## Author: Paul Kienzle ## Date: 2000-03-25 ## added 'nearest' as suggested by Kai Habel ## 2000-07-17 Paul Kienzle ## added '*' methods and matrix y ## check for proper table lengths ## 2002-01-23 Paul Kienzle ## fixed extrapolation function yi = interp1 (x, y, varargin) if (nargin < 2 || nargin > 6) print_usage (); endif method = "linear"; extrap = NA; xi = []; ispp = false; firstnumeric = true; rightcontinuous = NaN; if (nargin > 2) for i = 1:length (varargin) arg = varargin{i}; 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 (firstnumeric) xi = arg; firstnumeric = false; else extrap = arg; endif endif endfor endif if (isempty (xi) && firstnumeric && ! ispp) xi = y; y = x; if (isvector (y)) x = 1:numel (y); else x = 1:rows (y); 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 continous 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 (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 (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) ## 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)]) ## 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 (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) ## 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 (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 (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) ## 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 (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 (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 ([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 (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 (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) ## 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 (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 (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) ## 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 (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 (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) ## 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 interp1 () %!error 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")