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/*
* Copyright (c) 2010 Chuong Nguyen, Samit Basu
*
* This program 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 2 of the License, or
* (at your option) any later version.
*
* This program 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 this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
#include "Array.hpp"
#include "Interpreter.hpp"
#include "FunctionDef.hpp"
#include "Exception.hpp"
template <class T>
static void DoMultiInterpolation2DReal(const T* z, int zrows, int zcols,
const T* xi, const T* yi, int xicount,
T* zi, int method, double xtrapval) {
int ii, jj, nn, xifloor, yifloor;
register T dx, dy;
switch (method) {
default:
throw Exception("unhandled type in argument to DoMultiInterpolation2DReal");
case 0: //nearest
for (ii = 0; ii< xicount; ii++) {
if (xi[ii] < 1 || xi[ii] > zcols || yi[ii] < 1 || yi[ii] > zrows )
zi[ii] = xtrapval;
else {
dx = xi[ii];
dy = yi[ii];
xifloor = int(dx);
yifloor = int(dy);
dx = dx - xifloor;
dy = dy - yifloor;
if (dx >= 0.5)
xifloor++;
if (dy >= 0.5)
yifloor++;
nn = (xifloor-1)*zrows + yifloor-1;
zi[ii] = z[nn];
}
}
break;
case 1: //linear
for (ii = 0; ii< xicount; ii++) {
if (xi[ii] < 1 || xi[ii] > zcols || yi[ii] < 1 || yi[ii] > zrows )
zi[ii] = xtrapval;
else {
dx = xi[ii];
dy = yi[ii];
xifloor = int(dx);
yifloor = int(dy);
dx = dx - xifloor;
dy = dy - yifloor;
nn = (xifloor-1)*zrows + yifloor-1;
if (dx == 0)
zi[ii] = z[nn]*(1-dy) + z[nn+1]*dy;
else if (dy == 0)
zi[ii] = z[nn]*(1-dx) + z[nn+zrows]*dx;
else {
zi[ii] = (z[nn ]*(1-dy) + z[nn+1 ]*dy)*(1-dx) +
(z[nn+zrows]*(1-dy) + z[nn+1+zrows]*dy)*dx;
}
}
}
break;
case 2: //cubic
double xw0, xw1, xw2, xw3;
double yw0, yw1, yw2, yw3;
T const *pz;
register T *pzz;
//create a temporary array zz to hold z and extra boundary elements
int zzrows = zrows+2;
int zzcols = zcols+2;
T *zz = (T*) malloc(sizeof(T)*(zzrows)*(zzcols));
if (zz == NULL)
throw Exception("unable to locate memory in DoMultiInterpolation2DReal");
pz = z;
pzz = zz;
pzz+=zzrows; //skip the first column of zz
// copy z into the center of zz
for (ii = 0; ii< zcols; ii++) {
pzz++; //skip top element of zz
for (jj = 0; jj< zrows; jj++) {
*(pzz++) = *(pz++);
}
pzz++; //skip bottom element of zz
}
#define data(i,j) (zz[(i)*zzrows+(j)])
//filling extra elements on the boundary
for (ii = 0; ii< zzcols; ii++) {
//top and bottom elements
data(ii,0) = 3*data(ii, 1) - 3*data(ii, 2) + data(ii, 3);
data(ii,zzrows-1) = 3*data(ii,zzrows-2) - 3*data(ii,zzrows-3) + data(ii,zzrows-4);
}
for (jj = 0; jj< zzrows; jj++) {
//left and right elements
data(0,jj) = 3*data(1, jj) - 3*data(2, jj) + data(3, jj);
data(zzcols-1,jj) = 3*data(zzcols-2,jj) - 3*data(zzcols-3,jj) + data(zzcols-4,jj);
}
#undef data
//interpolate at given points
for (ii = 0; ii< xicount; ii++) {
if (xi[ii] < 1 || xi[ii] > zcols || yi[ii] < 1 || yi[ii] > zrows )
//assign to xtrapval for out of range elements
zi[ii] = xtrapval;
else {
dx = xi[ii];
dy = yi[ii];
xifloor = int(dx);
yifloor = int(dy);
dx = dx - xifloor;
dy = dy - yifloor;
//generate interpolation coefficients
if (dx != 0) {
xw0 = ((2.0-dx)*dx-1.0)*dx;
xw1 = (3.0*dx-5.0)*dx*dx+2.0;
xw2 = ((4.0-3.0*dx)*dx+1.0)*dx;
xw3 = (dx-1.0)*dx*dx;
}
if (dy != 0) {
yw0 = ((2.0-dy)*dy-1.0)*dy;
yw1 = (3.0*dy-5.0)*dy*dy+2.0;
yw2 = ((4.0-3.0*dy)*dy+1.0)*dy;
yw3 = (dy-1.0)*dy*dy;
}
//obtain interpolated value
pzz = zz + xifloor*zzrows + yifloor;
# define data(i,j) (pzz[(i)*zzrows+(j)])
if (dx == 0)
if (dy == 0)
zi[ii] = data(0,0);
else
zi[ii] = (yw0*data(0,-1) + yw1*data(0,0) + yw2*data(0,1) + yw3*data(0,2))*0.5;
else if (dy == 0)
zi[ii] = (xw0*data(-1,0) + xw1*data(0,0) + xw2*data(1,0) + xw3*data(2,0))*0.5;
else
zi[ii] = (( xw0*data(-1,-1) + xw1*data(0,-1) + xw2*data(1,-1) + xw3*data(2,-1) )*yw0 +
( xw0*data(-1, 0) + xw1*data(0, 0) + xw2*data(1, 0) + xw3*data(2, 0) )*yw1 +
( xw0*data(-1, 1) + xw1*data(0, 1) + xw2*data(1, 1) + xw3*data(2, 1) )*yw2 +
( xw0*data(-1, 2) + xw1*data(0, 2) + xw2*data(1, 2) + xw3*data(2, 2) )*yw3)*0.25;
#undef data
}
}
//free temporary array
if (zz != NULL){
free(zz);
zz = NULL;
}
pzz = NULL;
break;
}//end of switch
}//end of DoMultiInterpolation2DReal
template <typename T>
static BasicArray<T> Minterp2(const BasicArray<T> &z, const BasicArray<T> &xi, const BasicArray<T> &yi, int method, double xtrapflag) {
BasicArray<T> zi(xi.dimensions());
DoMultiInterpolation2DReal(z.constData(),int(z.rows()),int(z.cols()),
xi.constData(),yi.constData(),int(xi.length()),
zi.data(), method, xtrapflag);
return zi;
}
//@@Signature
//function interp2 Interp2Function jitsafe
//inputs z xi yi method extrapflag
//outputs zi
//DOCBLOCK curvefit_interp2
ArrayVector Interp2Function(int nargout, const ArrayVector& arg) {
if (arg.size() < 3)
throw Exception("interp2 requires at least three arguments (z,xi,yi)");
Array z(arg[0].toClass(Double));
Array xi(arg[1].toClass(Double));
Array yi(arg[2].toClass(Double));
z = z.asDenseArray();
xi = xi.asDenseArray();
yi = yi.asDenseArray();
if (xi.isComplex() || yi.isComplex())
throw Exception("xi and yi cannot be complex in interp2");
// Make sure xi and yi are the same size
if (xi.cols() != yi.cols() || xi.rows() != yi.rows())
throw Exception("vectors xi and yi must be the same size");
// Check for extrapolation flag
int method = 1; //default linear
if (arg.size() >= 4) {
if (!arg[3].isString())
throw Exception("method must be a string");
QString method_c = arg[3].asString();
if (method_c=="nearest")
method = 0;
else if (method_c=="linear")
method = 1;
else if (method_c=="cubic")
method = 2;
else
throw Exception("unrecognized method to routine interp2");
}
// Check for extrapolation value
double xtrap = NaN();
if (arg.size() >= 5) {
if (!arg[4].isScalar())
throw Exception("extrapolation value must be a number");
xtrap = arg[4].asDouble();
}
if (z.allReal()) {
return ArrayVector(Array(Minterp2(z.constReal<double>(),xi.constReal<double>(),yi.constReal<double>(),method,xtrap)));
}
else {
return ArrayVector(Array(Minterp2(z.constReal<double>(),xi.constReal<double>(),yi.constReal<double>(),method,xtrap),
Minterp2(z.constImag<double>(),xi.constReal<double>(),yi.constReal<double>(),method,xtrap)));
}
}
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