interp2d - bicubic spline (2d) evaluation function
Given three vectors (x,y,C) defining a bicubic spline or sub-spline function (see splin2d ) this function evaluates s (and ds/dx, ds/dy, d2s/dxx, d2s/dxy, d2s/dyy if needed) at (xp(i),yp(i)) :
zp(i) = s(xp(i),yp(i)) dzpdx(i) = ds/dx(xp(i),yp(i)) dzpdy(i) = ds/dy(xp(i),yp(i)) d2zpdxx(i) = d2s/dx2(xp(i),yp(i)) d2zpdxy(i) = d2s/dxdy(xp(i),yp(i)) d2zpdyy(i) = d2s/dy2(xp(i),yp(i))
The out_mode parameter defines the evaluation rule for extrapolation, i.e. for (xp(i),yp(i)) not in [x(1),x(nx)]x[y(1),y(ny)]:
s(x,y) = s(proj(x,y)) where proj(x,y) is nearest point of [x(1),x(nx)]x[y(1),y(ny)] from (x,y)
// see the examples of splin2d // this example shows some different extrapolation features // interpolation of cos(x)cos(y) n = 7; // a n x n interpolation grid x = linspace(0,2*%pi,n); y = x; z = cos(x')*cos(y); C = splin2d(x, y, z, "periodic"); // now evaluate on a bigger domain than [0,2pi]x [0,2pi] m = 80; // discretisation parameter of the evaluation grid xx = linspace(-0.5*%pi,2.5*%pi,m); yy = xx; [XX,YY] = ndgrid(xx,yy); zz1 = interp2d(XX,YY, x, y, C, "C0"); zz2 = interp2d(XX,YY, x, y, C, "by_zero"); zz3 = interp2d(XX,YY, x, y, C, "periodic"); zz4 = interp2d(XX,YY, x, y, C, "natural"); xbasc() subplot(2,2,1) plot3d(xx, yy, zz1, flag=[2 6 4]) xtitle("extrapolation with the C0 outmode") subplot(2,2,2) plot3d(xx, yy, zz2, flag=[2 6 4]) xtitle("extrapolation with the by_zero outmode") subplot(2,2,3) plot3d(xx, yy, zz3, flag=[2 6 4]) xtitle("extrapolation with the periodic outmode") subplot(2,2,4) plot3d(xx, yy, zz4, flag=[2 6 4]) xtitle("extrapolation with the natural outmode") xselect()
splin2d ,
B. Pincon