interp2d bicubic spline (2d) evaluation function [zp[, dzpdx, dzpdy[, d2zpdxx, d2zpdxy, d2zpdyy]]]=interp2d(xp, yp, x, y, C [,out_mode]) xp a mx-by-my matrix of doubles, the x coordinates of the points where the spline is to be evaluated. yp a mx-by-my matrix of doubles, the y coordinates of the points where the spline is to be evaluated. x a 1-by-nx matrix of doubles, the x coordinate of the interpolation points. We must have x(i)<x(i+1), for i=1,2,...,nx-1. y a 1-by-ny matrix of doubles, the y coordinate of the interpolation points. We must have y(i)<y(i+1), for i=1,2,...,ny-1. C The coefficients of the bicubic spline. The input argument of the interp2d function is the output argument of the splin2d function. out_mode a 1-by-1 matrix of strings, the evaluation of s outside the range [x(1),x(nx)] by [y(1),y(ny)]. zp a mx-by-my matrix of doubles, the evaluation of the z coordinate of the spline, i.e. zp(i,j)=s(xp(i,j),yp(i,j)), for i=1,2,...,mx and j = 1,2,...,my. dzpdx a mx-by-my matrix of doubles, the first derivative of the spline with respect to x. dzpdy a mx-by-my matrix of doubles, the first derivative of the spline with respect to y. d2zpdxx a mx-by-my matrix of doubles, the second derivative of the spline with respect to x. d2zpdxy a mx-by-my matrix of doubles, the second derivative of the spline with respect to x and y. d2zpdyy a mx-by-my matrix of doubles, the second derivative of the spline with respect to y. 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)) : 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)] : "by_zero" an extrapolation by zero is done "by_nan" extrapolation by Nan "C0" the extrapolation is defined as follows : "natural" the extrapolation is done by using the nearest bicubic-patch from (x,y). "periodic" s is extended by periodicity. 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; // discretization 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"); plot3d(xx, yy, zz1, flag=[2 6 4]) xtitle("extrapolation with the C0 outmode") 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; // discretization parameter of the evaluation grid xx = linspace(-0.5*%pi,2.5*%pi,m); yy = xx; [XX,YY] = ndgrid(xx,yy); zz2 = interp2d(XX,YY, x, y, C, "by_zero"); plot3d(xx, yy, zz2, flag=[2 6 4]) xtitle("extrapolation with the by_zero outmode") 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; // discretization parameter of the evaluation grid xx = linspace(-0.5*%pi,2.5*%pi,m); yy = xx; [XX,YY] = ndgrid(xx,yy); zz3 = interp2d(XX,YY, x, y, C, "periodic"); plot3d(xx, yy, zz3, flag=[2 6 4]) xtitle("extrapolation with the periodic outmode") 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; // discretization parameter of the evaluation grid xx = linspace(-0.5*%pi,2.5*%pi,m); yy = xx; [XX,YY] = ndgrid(xx,yy); zz4 = interp2d(XX,YY, x, y, C, "natural"); plot3d(xx, yy, zz4, flag=[2 6 4]) xtitle("extrapolation with the natural outmode") splin2d 5.4.0 Previously, imaginary part of input arguments were implicitly ignored.