1######################################################################## 2## 3## Copyright (C) 2000-2021 The Octave Project Developers 4## 5## See the file COPYRIGHT.md in the top-level directory of this 6## distribution or <https://octave.org/copyright/>. 7## 8## This file is part of Octave. 9## 10## Octave is free software: you can redistribute it and/or modify it 11## under the terms of the GNU General Public License as published by 12## the Free Software Foundation, either version 3 of the License, or 13## (at your option) any later version. 14## 15## Octave is distributed in the hope that it will be useful, but 16## WITHOUT ANY WARRANTY; without even the implied warranty of 17## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18## GNU General Public License for more details. 19## 20## You should have received a copy of the GNU General Public License 21## along with Octave; see the file COPYING. If not, see 22## <https://www.gnu.org/licenses/>. 23## 24######################################################################## 25 26## -*- texinfo -*- 27## @deftypefn {} {@var{yi} =} interp1 (@var{x}, @var{y}, @var{xi}) 28## @deftypefnx {} {@var{yi} =} interp1 (@var{y}, @var{xi}) 29## @deftypefnx {} {@var{yi} =} interp1 (@dots{}, @var{method}) 30## @deftypefnx {} {@var{yi} =} interp1 (@dots{}, @var{extrap}) 31## @deftypefnx {} {@var{yi} =} interp1 (@dots{}, "left") 32## @deftypefnx {} {@var{yi} =} interp1 (@dots{}, "right") 33## @deftypefnx {} {@var{pp} =} interp1 (@dots{}, "pp") 34## 35## One-dimensional interpolation. 36## 37## Interpolate input data to determine the value of @var{yi} at the points 38## @var{xi}. If not specified, @var{x} is taken to be the indices of @var{y} 39## (@code{1:length (@var{y})}). If @var{y} is a matrix or an N-dimensional 40## array, the interpolation is performed on each column of @var{y}. 41## 42## The interpolation @var{method} is one of: 43## 44## @table @asis 45## @item @qcode{"nearest"} 46## Return the nearest neighbor. 47## 48## @item @qcode{"previous"} 49## Return the previous neighbor. 50## 51## @item @qcode{"next"} 52## Return the next neighbor. 53## 54## @item @qcode{"linear"} (default) 55## Linear interpolation from nearest neighbors. 56## 57## @item @qcode{"pchip"} 58## Piecewise cubic Hermite interpolating polynomial---shape-preserving 59## interpolation with smooth first derivative. 60## 61## @item @qcode{"cubic"} 62## Cubic interpolation (same as @qcode{"pchip"}). 63## 64## @item @qcode{"spline"} 65## Cubic spline interpolation---smooth first and second derivatives 66## throughout the curve. 67## @end table 68## 69## Adding '*' to the start of any method above forces @code{interp1} 70## to assume that @var{x} is uniformly spaced, and only @code{@var{x}(1)} 71## and @code{@var{x}(2)} are referenced. This is usually faster, 72## and is never slower. The default method is @qcode{"linear"}. 73## 74## If @var{extrap} is the string @qcode{"extrap"}, then extrapolate values 75## beyond the endpoints using the current @var{method}. If @var{extrap} is a 76## number, then replace values beyond the endpoints with that number. When 77## unspecified, @var{extrap} defaults to @code{NA}. 78## 79## If the string argument @qcode{"pp"} is specified, then @var{xi} should not 80## be supplied and @code{interp1} returns a piecewise polynomial object. This 81## object can later be used with @code{ppval} to evaluate the interpolation. 82## There is an equivalence, such that @code{ppval (interp1 (@var{x}, 83## @var{y}, @var{method}, @qcode{"pp"}), @var{xi}) == interp1 (@var{x}, 84## @var{y}, @var{xi}, @var{method}, @qcode{"extrap"})}. 85## 86## Duplicate points in @var{x} specify a discontinuous interpolant. There 87## may be at most 2 consecutive points with the same value. 88## If @var{x} is increasing, the default discontinuous interpolant is 89## right-continuous. If @var{x} is decreasing, the default discontinuous 90## interpolant is left-continuous. 91## The continuity condition of the interpolant may be specified by using 92## the options @qcode{"left"} or @qcode{"right"} to select a left-continuous 93## or right-continuous interpolant, respectively. 94## Discontinuous interpolation is only allowed for @qcode{"nearest"} and 95## @qcode{"linear"} methods; in all other cases, the @var{x}-values must be 96## unique. 97## 98## An example of the use of @code{interp1} is 99## 100## @example 101## @group 102## xf = [0:0.05:10]; 103## yf = sin (2*pi*xf/5); 104## xp = [0:10]; 105## yp = sin (2*pi*xp/5); 106## lin = interp1 (xp, yp, xf); 107## near = interp1 (xp, yp, xf, "nearest"); 108## pch = interp1 (xp, yp, xf, "pchip"); 109## spl = interp1 (xp, yp, xf, "spline"); 110## plot (xf,yf,"r", xf,near,"g", xf,lin,"b", xf,pch,"c", xf,spl,"m", 111## xp,yp,"r*"); 112## legend ("original", "nearest", "linear", "pchip", "spline"); 113## @end group 114## @end example 115## 116## @seealso{pchip, spline, interpft, interp2, interp3, interpn} 117## @end deftypefn 118 119function yi = interp1 (x, y, varargin) 120 121 if (nargin < 2 || nargin > 6) 122 print_usage (); 123 endif 124 125 method = "linear"; 126 extrap = NA; 127 xi = []; 128 ispp = false; 129 have_xi = false; 130 rightcontinuous = NaN; 131 132 if (nargin > 2) 133 for i_arg = 1:length (varargin) 134 arg = varargin{i_arg}; 135 if (ischar (arg)) 136 arg = tolower (arg); 137 switch (arg) 138 case "extrap" 139 extrap = "extrap"; 140 case "pp" 141 ispp = true; 142 case {"right", "-right"} 143 rightcontinuous = true; 144 case {"left", "-left"} 145 rightcontinuous = false; 146 otherwise 147 method = arg; 148 endswitch 149 else 150 if (i_arg == 1) 151 xi = arg; 152 have_xi = true; 153 else 154 extrap = arg; 155 endif 156 endif 157 endfor 158 endif 159 160 if (! have_xi && ! ispp) 161 xi = y; 162 y = x; 163 if (isvector (y)) 164 x = 1:numel (y); 165 else 166 x = 1:rows (y); 167 endif 168 endif 169 170 ## reshape matrices for convenience 171 x = x(:); 172 nx = rows (x); 173 szx = size (xi); 174 if (isvector (y)) 175 y = y(:); 176 endif 177 178 szy = size (y); 179 y = y(:,:); 180 [ny, nc] = size (y); 181 xi = xi(:); 182 183 ## determine sizes 184 if (nx < 2 || ny < 2) 185 error ("interp1: minimum of 2 points required in each dimension"); 186 endif 187 188 ## check whether x is sorted; sort if not. 189 if (! issorted (x, "either")) 190 [x, p] = sort (x); 191 y = y(p,:); 192 endif 193 194 if (any (strcmp (method, {"previous", "*previous", "next", "*next"}))) 195 rightcontinuous = NaN; # needed for these methods to work 196 endif 197 198 if (isnan (rightcontinuous)) 199 ## If not specified, set the continuity condition 200 if (x(end) < x(1)) 201 rightcontinuous = false; 202 else 203 rightcontinuous = true; 204 endif 205 elseif ((rightcontinuous && (x(end) < x(1))) 206 || (! rightcontinuous && (x(end) > x(1)))) 207 ## Switch between left-continuous and right-continuous 208 x = flipud (x); 209 y = flipud (y); 210 endif 211 212 ## Because of the way mkpp works, it's easiest to implement "next" 213 ## by running "previous" with vectors flipped. 214 if (strcmp (method, "next")) 215 x = flipud (x); 216 y = flipud (y); 217 method = "previous"; 218 elseif (strcmp (method, "*next")) 219 x = flipud (x); 220 y = flipud (y); 221 method = "*previous"; 222 endif 223 224 starmethod = method(1) == "*"; 225 226 if (starmethod) 227 dx = x(2) - x(1); 228 else 229 jumps = x(1:end-1) == x(2:end); 230 have_jumps = any (jumps); 231 if (have_jumps) 232 if (strcmp (method, "linear") || strcmp (method, ("nearest"))) 233 if (any (jumps(1:nx-2) & jumps(2:nx-1))) 234 warning ("interp1: multiple discontinuities at the same X value"); 235 endif 236 else 237 error ("interp1: discontinuities not supported for METHOD '%s'", 238 method); 239 endif 240 endif 241 endif 242 243 ## Proceed with interpolating by all methods. 244 switch (method) 245 246 case "nearest" 247 pp = mkpp ([x(1); (x(1:nx-1)+x(2:nx))/2; x(nx)], 248 shiftdim (y, 1), szy(2:end)); 249 pp.orient = "first"; 250 251 if (ispp) 252 yi = pp; 253 else 254 yi = ppval (pp, reshape (xi, szx)); 255 endif 256 257 case "*nearest" 258 pp = mkpp ([x(1), x(1)+[0.5:(nx-1)]*dx, x(nx)], 259 shiftdim (y, 1), szy(2:end)); 260 pp.orient = "first"; 261 262 if (ispp) 263 yi = pp; 264 else 265 yi = ppval (pp, reshape (xi, szx)); 266 endif 267 268 case "previous" 269 pp = mkpp ([x(1:nx); 2*x(nx)-x(nx-1)], 270 shiftdim (y, 1), szy(2:end)); 271 pp.orient = "first"; 272 273 if (ispp) 274 yi = pp; 275 else 276 yi = ppval (pp, reshape (xi, szx)); 277 endif 278 279 case "*previous" 280 pp = mkpp (x(1)+[0:nx]*dx, 281 shiftdim (y, 1), szy(2:end)); 282 pp.orient = "first"; 283 284 if (ispp) 285 yi = pp; 286 else 287 yi = ppval (pp, reshape (xi, szx)); 288 endif 289 290 case "linear" 291 292 xx = x; 293 nxx = nx; 294 yy = y; 295 dy = diff (yy); 296 if (have_jumps) 297 ## Omit zero-size intervals. 298 xx(jumps) = []; 299 nxx = rows (xx); 300 yy(jumps, :) = []; 301 dy(jumps, :) = []; 302 endif 303 304 dx = diff (xx); 305 dx = repmat (dx, [1 size(dy)(2:end)]); 306 307 coefs = [(dy./dx).', yy(1:nxx-1, :).']; 308 309 pp = mkpp (xx, coefs, szy(2:end)); 310 pp.orient = "first"; 311 312 if (ispp) 313 yi = pp; 314 else 315 yi = ppval (pp, reshape (xi, szx)); 316 endif 317 318 case "*linear" 319 dy = diff (y); 320 coefs = [(dy/dx).'(:), y(1:nx-1, :).'(:)]; 321 pp = mkpp (x, coefs, szy(2:end)); 322 pp.orient = "first"; 323 324 if (ispp) 325 yi = pp; 326 else 327 yi = ppval (pp, reshape (xi, szx)); 328 endif 329 330 case {"pchip", "*pchip", "cubic", "*cubic"} 331 if (nx == 2 || starmethod) 332 x = linspace (x(1), x(nx), ny); 333 endif 334 335 if (ispp) 336 y = shiftdim (reshape (y, szy), 1); 337 yi = pchip (x, y); 338 yi.orient = "first"; 339 else 340 y = shiftdim (y, 1); 341 yi = pchip (x, y, reshape (xi, szx)); 342 if (! isvector (y)) 343 yi = shiftdim (yi, 1); 344 endif 345 endif 346 347 case {"spline", "*spline"} 348 if (nx == 2 || starmethod) 349 x = linspace (x(1), x(nx), ny); 350 endif 351 352 if (ispp) 353 y = shiftdim (reshape (y, szy), 1); 354 yi = spline (x, y); 355 yi.orient = "first"; 356 else 357 y = shiftdim (y, 1); 358 yi = spline (x, y, reshape (xi, szx)); 359 if (! isvector (y)) 360 yi = shiftdim (yi, 1); 361 endif 362 endif 363 364 otherwise 365 error ("interp1: invalid METHOD '%s'", method); 366 367 endswitch 368 369 if (! ispp && isnumeric (extrap)) 370 ## determine which values are out of range and set them to extrap, 371 ## unless extrap == "extrap". 372 minx = min (x(1), x(nx)); 373 maxx = max (x(1), x(nx)); 374 375 xi = reshape (xi, szx); 376 outliers = (xi < minx) | ! (xi <= maxx); # this even catches NaNs 377 if (size_equal (outliers, yi)) 378 yi(outliers) = extrap; 379 yi = reshape (yi, szx); 380 elseif (! isscalar (yi)) 381 yi(outliers, :) = extrap; 382 else 383 warning ("interp1: Unreachable state. Please submit data that produced this warning to bugs.octave.org"); 384 yi(outliers.') = extrap; 385 endif 386 387 endif 388 389endfunction 390 391 392%!demo 393%! clf; 394%! xf = 0:0.05:10; yf = sin (2*pi*xf/5); 395%! xp = 0:10; yp = sin (2*pi*xp/5); 396%! lin = interp1 (xp,yp,xf, 'linear'); 397%! spl = interp1 (xp,yp,xf, 'spline'); 398%! pch = interp1 (xp,yp,xf, 'pchip'); 399%! near= interp1 (xp,yp,xf, 'nearest'); 400%! plot (xf,yf,'r',xf,near,'g',xf,lin,'b',xf,pch,'c',xf,spl,'m',xp,yp,'r*'); 401%! legend ('original', 'nearest', 'linear', 'pchip', 'spline'); 402%! title ('Interpolation of continuous function sin (x) w/various methods'); 403%! %-------------------------------------------------------- 404%! % confirm that interpolated function matches the original 405 406%!demo 407%! clf; 408%! xf = 0:0.05:10; yf = sin (2*pi*xf/5); 409%! xp = 0:10; yp = sin (2*pi*xp/5); 410%! lin = interp1 (xp,yp,xf, '*linear'); 411%! spl = interp1 (xp,yp,xf, '*spline'); 412%! pch = interp1 (xp,yp,xf, '*pchip'); 413%! near= interp1 (xp,yp,xf, '*nearest'); 414%! plot (xf,yf,'r',xf,near,'g',xf,lin,'b',xf,pch,'c',xf,spl,'m',xp,yp,'r*'); 415%! legend ('*original', '*nearest', '*linear', '*pchip', '*spline'); 416%! title ('Interpolation of continuous function sin (x) w/various *methods'); 417%! %-------------------------------------------------------- 418%! % confirm that interpolated function matches the original 419 420%!demo 421%! clf; 422%! fstep = @(x) x > 1; 423%! xf = 0:0.05:2; yf = fstep (xf); 424%! xp = linspace (0,2,10); yp = fstep (xp); 425%! pch = interp1 (xp,yp,xf, 'pchip'); 426%! spl = interp1 (xp,yp,xf, 'spline'); 427%! plot (xf,yf,'r',xf,pch,'b',xf,spl,'m',xp,yp,'r*'); 428%! title ({'Interpolation of step function with discontinuity at x==1', ... 429%! 'Note: "pchip" is shape-preserving, "spline" (continuous 1st, 2nd derivatives) is not'}); 430%! legend ('original', 'pchip', 'spline'); 431 432%!demo 433%! clf; 434%! t = 0 : 0.3 : pi; dt = t(2)-t(1); 435%! n = length (t); k = 100; dti = dt*n/k; 436%! ti = t(1) + [0 : k-1]*dti; 437%! y = sin (4*t + 0.3) .* cos (3*t - 0.1); 438%! ddys = diff (diff (interp1 (t,y,ti, 'spline'))./dti)./dti; 439%! ddyp = diff (diff (interp1 (t,y,ti, 'pchip')) ./dti)./dti; 440%! ddyc = diff (diff (interp1 (t,y,ti, 'cubic')) ./dti)./dti; 441%! plot (ti(2:end-1),ddys,'b*', ti(2:end-1),ddyp,'c^', ti(2:end-1),ddyc,'g+'); 442%! title ({'Second derivative of interpolated "sin (4*t + 0.3) .* cos (3*t - 0.1)"', ... 443%! 'Note: "spline" has continuous 2nd derivative, others do not'}); 444%! legend ('spline', 'pchip', 'cubic'); 445 446%!demo 447%! clf; 448%! xf = 0:0.05:10; yf = sin (2*pi*xf/5) - (xf >= 5); 449%! xp = [0:.5:4.5,4.99,5:.5:10]; yp = sin (2*pi*xp/5) - (xp >= 5); 450%! lin = interp1 (xp,yp,xf, 'linear'); 451%! near= interp1 (xp,yp,xf, 'nearest'); 452%! plot (xf,yf,'r', xf,near,'g', xf,lin,'b', xp,yp,'r*'); 453%! legend ('original', 'nearest', 'linear'); 454%! %-------------------------------------------------------- 455%! % confirm that interpolated function matches the original 456 457%!demo 458%! clf; 459%! x = 0:0.5:3; 460%! x1 = [3 2 2 1]; 461%! x2 = [1 2 2 3]; 462%! y1 = [1 1 0 0]; 463%! y2 = [0 0 1 1]; 464%! h = plot (x, interp1 (x1, y1, x), 'b', x1, y1, 'sb'); 465%! hold on 466%! g = plot (x, interp1 (x2, y2, x), 'r', x2, y2, '*r'); 467%! axis ([0.5 3.5 -0.5 1.5]); 468%! legend ([h(1), g(1)], {'left-continuous', 'right-continuous'}, ... 469%! 'location', 'northwest') 470%! legend boxoff 471%! %-------------------------------------------------------- 472%! % red curve is left-continuous and blue is right-continuous at x = 2 473 474##FIXME: add test for N-d arguments here 475 476## For each type of interpolated test, confirm that the interpolated 477## value at the knots match the values at the knots. Points away 478## from the knots are requested, but only "nearest" and "linear" 479## confirm they are the correct values. 480 481%!shared xp, yp, xi, style 482%! xp = 0:2:10; 483%! yp = sin (2*pi*xp/5); 484%! xi = [-1, 0, 2.2, 4, 6.6, 10, 11]; 485 486## The following BLOCK/ENDBLOCK section is repeated for each style 487## nearest, previous, next, linear, cubic, spline, pchip 488## The test for ppval of cubic has looser tolerance, but otherwise 489## the tests are identical. 490## Note that the block checks style and *style; if you add more tests 491## be sure to add them to both sections of each block. One test, 492## style vs. *style, occurs only in the first section. 493## There is an ENDBLOCKTEST after the final block 494 495%!test style = "nearest"; 496## BLOCK 497%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 498%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 499%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 500%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 501%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 502%!assert (isempty (interp1 (xp',yp',[],style))) 503%!assert (isempty (interp1 (xp,yp,[],style))) 504%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 505%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 506%!assert (interp1 (xp,yp,xi,style),... 507%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 508%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 509%! interp1 (xp,yp,xi,style,"extrap"),10*eps) 510%!error interp1 (1,1,1, style) 511%!assert (interp1 (xp,[yp',yp'],xi,style), 512%! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) 513%!test style = ["*",style]; 514%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 515%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 516%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 517%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 518%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 519%!assert (isempty (interp1 (xp',yp',[],style))) 520%!assert (isempty (interp1 (xp,yp,[],style))) 521%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 522%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 523%!assert (interp1 (xp,yp,xi,style),... 524%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 525%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 526%! interp1 (xp,yp,xi,style,"extrap"),10*eps) 527%!assert (interp1 (yp, xi, style, 0), ... 528%! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) 529%!error interp1 (1,1,1, style) 530## ENDBLOCK 531 532%!test style = "previous"; 533## BLOCK 534%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 535%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 536%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 537%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 538%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 539%!assert (isempty (interp1 (xp',yp',[],style))) 540%!assert (isempty (interp1 (xp,yp,[],style))) 541%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 542%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 543## This test is expected to fail, so commented out. 544## "previous" and "next" options are not symmetric w.r.t to flipping xp,yp 545#%!assert (interp1 (xp,yp,xi,style),... 546#%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 547%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 548%! interp1 (xp,yp,xi,style,"extrap"),10*eps) 549%!error interp1 (1,1,1, style) 550%!assert (interp1 (xp,[yp',yp'],xi,style), 551%! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) 552%!test style = ["*",style]; 553%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 554%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 555%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 556%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 557%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 558%!assert (isempty (interp1 (xp',yp',[],style))) 559%!assert (isempty (interp1 (xp,yp,[],style))) 560%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 561%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 562#%!assert (interp1 (xp,yp,xi,style),... 563#%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 564%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 565%! interp1 (xp,yp,xi,style,"extrap"),10*eps) 566%!assert (interp1 (yp, xi, style, 0), ... 567%! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) 568%!error interp1 (1,1,1, style) 569## ENDBLOCK 570 571%!test style = "next"; 572## BLOCK 573%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 574%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 575%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 576%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 577%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 578%!assert (isempty (interp1 (xp',yp',[],style))) 579%!assert (isempty (interp1 (xp,yp,[],style))) 580%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 581%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 582#%!assert (interp1 (xp,yp,xi,style),... 583#%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 584%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 585%! interp1 (xp,yp,xi,style,"extrap"),10*eps) 586%!error interp1 (1,1,1, style) 587%!assert (interp1 (xp,[yp',yp'],xi,style), 588%! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) 589%!test style = ["*",style]; 590%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 591%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 592%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 593%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 594%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 595%!assert (isempty (interp1 (xp',yp',[],style))) 596%!assert (isempty (interp1 (xp,yp,[],style))) 597%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 598%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 599#%!assert (interp1 (xp,yp,xi,style),... 600#%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 601%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 602%! interp1 (xp,yp,xi,style,"extrap"),10*eps) 603%!assert (interp1 (yp, xi, style, 0), ... 604%! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) 605%!error interp1 (1,1,1, style) 606## ENDBLOCK 607 608%!test style = "linear"; 609## BLOCK 610%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 611%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 612%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 613%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 614%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 615%!assert (isempty (interp1 (xp',yp',[],style))) 616%!assert (isempty (interp1 (xp,yp,[],style))) 617%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 618%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 619%!assert (interp1 (xp,yp,xi,style),... 620%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 621%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 622%! interp1 (xp,yp,xi,style,"extrap"),10*eps) 623%!error interp1 (1,1,1, style) 624%!assert (interp1 (xp,[yp',yp'],xi,style), 625%! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) 626%!test style = ['*',style]; 627%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 628%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 629%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 630%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 631%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 632%!assert (isempty (interp1 (xp',yp',[],style))) 633%!assert (isempty (interp1 (xp,yp,[],style))) 634%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 635%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 636%!assert (interp1 (xp,yp,xi,style),... 637%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 638%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 639%! interp1 (xp,yp,xi,style,"extrap"),10*eps) 640%!assert (interp1 (yp, xi, style, 0), ... 641%! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) 642%!assert (interp1 ([1 2 2 3], [1 2 3 4], 2), 3) 643%!assert (interp1 ([3 2 2 1], [4 3 2 1], 2), 2) 644%!error interp1 (1,1,1, style) 645## ENDBLOCK 646 647%!test style = "cubic"; 648## BLOCK 649%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 650%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 651%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 652%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 653%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 654%!assert (isempty (interp1 (xp',yp',[],style))) 655%!assert (isempty (interp1 (xp,yp,[],style))) 656%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 657%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 658%!assert (interp1 (xp,yp,xi,style),... 659%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 660%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 661%! interp1 (xp,yp,xi,style,"extrap"),100*eps) 662%!error interp1 (1,1,1, style) 663%!assert (interp1 (xp,[yp',yp'],xi,style), 664%! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) 665%!test style = ["*",style]; 666%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 667%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 668%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 669%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 670%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 671%!assert (isempty (interp1 (xp',yp',[],style))) 672%!assert (isempty (interp1 (xp,yp,[],style))) 673%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 674%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 675%!assert (interp1 (xp,yp,xi,style),... 676%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 677%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 678%! interp1 (xp,yp,xi,style,"extrap"),100*eps) 679%!assert (interp1 (yp, xi, style, 0), ... 680%! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) 681%!error interp1 (1,1,1, style) 682## ENDBLOCK 683 684%!test style = "pchip"; 685## BLOCK 686%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 687%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 688%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 689%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 690%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 691%!assert (isempty (interp1 (xp',yp',[],style))) 692%!assert (isempty (interp1 (xp,yp,[],style))) 693%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 694%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 695%!assert (interp1 (xp,yp,xi,style),... 696%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 697%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 698%! interp1 (xp,yp,xi,style,"extrap"),10*eps) 699%!error interp1 (1,1,1, style) 700%!assert (interp1 (xp,[yp',yp'],xi,style), 701%! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) 702%!test style = ["*",style]; 703%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 704%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 705%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 706%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 707%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 708%!assert (isempty (interp1 (xp',yp',[],style))) 709%!assert (isempty (interp1 (xp,yp,[],style))) 710%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 711%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 712%!assert (interp1 (xp,yp,xi,style),... 713%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 714%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 715%! interp1 (xp,yp,xi,style,"extrap"),10*eps) 716%!assert (interp1 (yp, xi, style, 0), ... 717%! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) 718%!error interp1 (1,1,1, style) 719## ENDBLOCK 720 721%!test style = "spline"; 722## BLOCK 723%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 724%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 725%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 726%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 727%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 728%!assert (isempty (interp1 (xp',yp',[],style))) 729%!assert (isempty (interp1 (xp,yp,[],style))) 730%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 731%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 732%!assert (interp1 (xp,yp,xi,style),... 733%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 734%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 735%! interp1 (xp,yp,xi,style,"extrap"),10*eps) 736%!error interp1 (1,1,1, style) 737%!assert (interp1 (xp,[yp',yp'],xi,style), 738%! interp1 (xp,[yp',yp'],xi,["*",style]),100*eps) 739%!test style = ["*",style]; 740%!assert (interp1 (xp, yp, [min(xp)-1, max(xp)+1],style), [NA, NA]) 741%!assert (interp1 (xp,yp,xp,style), yp, 100*eps) 742%!assert (interp1 (xp,yp,xp',style), yp', 100*eps) 743%!assert (interp1 (xp',yp',xp',style), yp', 100*eps) 744%!assert (interp1 (xp',yp',xp,style), yp, 100*eps) 745%!assert (isempty (interp1 (xp',yp',[],style))) 746%!assert (isempty (interp1 (xp,yp,[],style))) 747%!assert (interp1 (xp,[yp',yp'],xi(:),style),... 748%! [interp1(xp,yp,xi(:),style),interp1(xp,yp,xi(:),style)]) 749%!assert (interp1 (xp,yp,xi,style),... 750%! interp1 (fliplr (xp),fliplr (yp),xi,style),100*eps) 751%!assert (ppval (interp1 (xp,yp,style,"pp"),xi), 752%! interp1 (xp,yp,xi,style,"extrap"),10*eps) 753%!assert (interp1 (yp, xi, style, 0), ... 754%! interp1 (1:numel (yp), yp, xi, style, 0), 10*eps) 755%!error interp1 (1,1,1, style) 756## ENDBLOCK 757## ENDBLOCKTEST 758 759## test extrapolation 760%!assert (interp1 ([1:5],[3:2:11],[0,6],"linear","extrap"), [1, 13], eps) 761%!assert (interp1 ([1:5],[3:2:11],[0,6],"nearest","extrap"), [3, 11], eps) 762%!assert (interp1 ([1:5],[3:2:11],[0,6],"previous","extrap"), [3, 11], eps) 763%!assert (interp1 ([1:5],[3:2:11],[0,6],"next","extrap"), [3, 11], eps) 764%!assert (interp1 (xp, yp, [-1, max(xp)+1],"linear",5), [5, 5]) 765%!assert (interp1 ([0,1],[1,0],[0.1,0.9;0.2,1.1]), [0.9 0.1; 0.8 NA], eps) 766%!assert (interp1 ([0,1],[1,0],[0.1,0.9;0.2,1]), [0.9 0.1; 0.8 0], eps) 767 768## Basic sanity checks 769%!assert (interp1 (1:2,1:2,1.4,"nearest"), 1) 770%!assert (interp1 (1:2,1:2,1.6,"previous"), 1) 771%!assert (interp1 (1:2,1:2,1.4,"next"), 2) 772%!assert (interp1 (1:2,1:2,1.4,"linear"), 1.4) 773%!assert (interp1 (1:4,1:4,1.4,"cubic"), 1.4) 774%!assert (interp1 (1:2,1:2,1.1,"spline"), 1.1) 775%!assert (interp1 (1:3,1:3,1.4,"spline"), 1.4) 776 777%!assert (interp1 (1:2:4,1:2:4,1.4,"*nearest"), 1) 778%!assert (interp1 (1:2:4,1:2:4,2.2,"*previous"), 1) 779%!assert (interp1 (1:2:4,1:2:4,1.4,"*next"), 3) 780%!assert (interp1 (1:2:4,1:2:4,[0,1,1.4,3,4],"*linear"), [NA,1,1.4,3,NA]) 781%!assert (interp1 (1:2:8,1:2:8,1.4,"*cubic"), 1.4) 782%!assert (interp1 (1:2,1:2,1.3, "*spline"), 1.3) 783%!assert (interp1 (1:2:6,1:2:6,1.4,"*spline"), 1.4) 784 785%!assert (interp1 ([3,2,1],[3,2,2],2.5), 2.5) 786 787%!assert (interp1 ([4,4,3,2,0],[0,1,4,2,1],[1.5,4,4.5], "linear"), [1.75,1,NA]) 788%!assert (interp1 (0:4, 2.5), 1.5) 789 790## Left and Right discontinuities 791%!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]) 792%!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]) 793 794## Test input validation 795%!error interp1 () 796%!error interp1 (1,2,3,4,5,6,7) 797%!error <minimum of 2 points required> interp1 (1,1,1, "linear") 798%!error <minimum of 2 points required> interp1 (1,1,1, "*nearest") 799%!error <minimum of 2 points required> interp1 (1,1,1, "*linear") 800%!error <minimum of 2 points required> interp1 (1,1,1, "previous") 801%!error <minimum of 2 points required> interp1 (1,1,1, "*previous") 802%!warning <multiple discontinuities> interp1 ([1 1 1 2], [1 2 3 4], 1); 803%!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "next") 804%!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "pchip") 805%!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "cubic") 806%!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "spline") 807%!error <invalid METHOD 'invalid'> interp1 (1:2,1:2,1, "invalid") 808