n dimensional linear interpolation
vp = linear_interpn(xp1,xp2,..,xpn, x1, ..., xn, v [,out_mode])
:xp1, xp2, .., xpn real vectors (or matrices) of same size : :x1 ,x2, ..., xn strictly increasing row vectors (with at least 2
components) defining the n dimensional interpolation grid
: :vp vector or matrix of same size than xp1, ..., xpn :
Given a n dimensional grid defined by the n vectors x1 ,x2, ..., xn and the values v of a function (says f) at the grid points :
this function computes the linear interpolant of f from the grid (called s in the following) at the points which coordinates are defined by the vectors (or matrices) xp1, xp2, ..., xpn:
The out_mode parameter set the evaluation rule for extrapolation: if we note Pi=(xp1(i),xp2(i),...,xpn(i)) then out_mode defines the evaluation rule when:
The different choices are:
:”by_zero” an extrapolation by zero is done : :”by_nan” extrapolation by Nan : :”C0” the extrapolation is defined as follows:
s(P) = s(`proj`_(P)) `where`_ proj(P) is nearest point from P
located on the grid boundary.
: :”periodic” s is extended by periodicity. :
// example 1 : 1d linear interpolation
x = `linspace`_(0,2*%pi,11);
y = `sin`_(x);
xx = `linspace`_(-2*%pi,4*%pi,400)';
yy = linear_interpn(xx, x, y, "periodic");
`clf`_()
`plot2d`_(xx,yy,style=2)
`plot2d`_(x,y,style=-9, strf="000")
`xtitle`_("linear interpolation of sin(x) with 11 interpolation points")
// example 2 : bilinear interpolation
n = 8;
x = `linspace`_(0,2*%pi,n); y = x;
z = 2*`sin`_(x')*`sin`_(y);
xx = `linspace`_(0,2*%pi, 40);
[xp,yp] = `ndgrid`_(xx,xx);
zp = linear_interpn(xp,yp, x, y, z);
`clf`_()
`plot3d`_(xx, xx, zp, flag=[2 6 4])
[xg,yg] = `ndgrid`_(x,x);
`param3d1`_(xg,yg, `list`_(z,-9*`ones`_(1,n)), flag=[0 0])
`xtitle`_("Bilinear interpolation of 2sin(x)sin(y)")
`legends`_("interpolation points",-9,1)
`show_window`_()
// example 3 : bilinear interpolation and experimentation
// with all the outmode features
nx = 20; ny = 30;
x = `linspace`_(0,1,nx);
y = `linspace`_(0,2, ny);
[X,Y] = `ndgrid`_(x,y);
z = 0.4*`cos`_(2*%pi*X).*`cos`_(%pi*Y);
nxp = 60 ; nyp = 120;
xp = `linspace`_(-0.5,1.5, nxp);
yp = `linspace`_(-0.5,2.5, nyp);
[XP,YP] = `ndgrid`_(xp,yp);
zp1 = linear_interpn(XP, YP, x, y, z, "natural");
zp2 = linear_interpn(XP, YP, x, y, z, "periodic");
zp3 = linear_interpn(XP, YP, x, y, z, "C0");
zp4 = linear_interpn(XP, YP, x, y, z, "by_zero");
zp5 = linear_interpn(XP, YP, x, y, z, "by_nan");
`clf`_()
`subplot`_(2,3,1)
`plot3d`_(x, y, z, leg="x@y@z", flag = [2 4 4])
`xtitle`_("initial function 0.4 cos(2 pi x) cos(pi y)")
`subplot`_(2,3,2)
`plot3d`_(xp, yp, zp1, leg="x@y@z", flag = [2 4 4])
`xtitle`_("Natural")
`subplot`_(2,3,3)
`plot3d`_(xp, yp, zp2, leg="x@y@z", flag = [2 4 4])
`xtitle`_("Periodic")
`subplot`_(2,3,4)
`plot3d`_(xp, yp, zp3, leg="x@y@z", flag = [2 4 4])
`xtitle`_("C0")
`subplot`_(2,3,5)
`plot3d`_(xp, yp, zp4, leg="x@y@z", flag = [2 4 4])
`xtitle`_("by_zero")
`subplot`_(2,3,6)
`plot3d`_(xp, yp, zp5, leg="x@y@z", flag = [2 4 4])
`xtitle`_("by_nan")
`show_window`_()
// example 4 : trilinear interpolation (see splin3d help
// page which have the same example with
// tricubic spline interpolation)
`exec`_("SCI/modules/interpolation/demos/interp_demo.sci")
func = "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
`deff`_("v=f(x,y,z)",func);
n = 5;
x = `linspace`_(0,1,n); y=x; z=x;
[X,Y,Z] = `ndgrid`_(x,y,z);
V = f(X,Y,Z);
// compute (and display) the linear interpolant on some slices
m = 41;
`dir`_ = ["z=" "z=" "z=" "x=" "y="];
val = [ 0.1 0.5 0.9 0.5 0.5];
ebox = [0 1 0 1 0 1];
XF=[]; YF=[]; ZF=[]; VF=[];
for i = 1:`length`_(val)
[Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(`dir`_(i), val(i), ebox, m, m, m);
Vm = linear_interpn(Xm,Ym,Zm, x, y, z, V);
[xf,yf,zf,vf] = nf3dq(Xm,Ym,Zm,Vm,1);
XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
Vp = linear_interpn(Xp,Yp,Zp, x, y, z, V);
[xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1);
XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
end
nb_col = 128;
vmin = `min`_(VF); vmax = `max`_(VF);
`color`_ = dsearch(VF,`linspace`_(vmin,vmax,nb_col+1));
`xset`_("colormap",`jetcolormap`_(nb_col));
`clf`_()
`xset`_("hidden3d",`xget`_("background"))
`colorbar`_(vmin,vmax)
`plot3d`_(XF, YF, `list`_(ZF,`color`_), flag=[-1 6 4])
`xtitle`_("tri-linear interpolation of "+func)
`show_window`_()
Version Description 5.4.0 previously, imaginary part of input arguments were implicitly ignored. .. _splin: splin.html .. _splin3d: splin3d.html .. _interpln: interpln.html .. _splin2d: splin2d.html