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/* cspline
Cubic spline fitting and interpolation
Tim Behrens, FMRIB Image Analysis Group
Copyright (C) 1999-2000 University of Oxford */
/* CCOPYRIGHT */
#include <string>
#include <iostream>
#include <fstream>
#include "newmatap.h"
#include "newmatio.h"
#include "miscmaths.h"
#include "cspline.h"
#define WANT_STREAM
#define WANT_MATH
using namespace NEWMAT;
using namespace std;
///////////////////////////////////////////////////////
namespace MISCMATHS{
// void Cspline::Cspline(){}
void Cspline::set(ColumnVector& pnodes,ColumnVector& pvals){
nodes=pnodes;vals=pvals;
fitted=false;
n=vals.Nrows();
}
void Cspline::set(ColumnVector& pnodes, Matrix& pcoefs){
nodes=pnodes;coefs=pcoefs;
fitted=false;
n=vals.Nrows();
}
void Cspline::diff(const ColumnVector& x, ColumnVector& dx ){
// dx should be of length length(x)-1
dx.ReSize(x.Nrows()-1);
for(int i=2;i<=x.Nrows();i++){
dx(i-1)=x(i)-x(i-1);
}
}
void Cspline::fit(){
if(vals.Nrows()<4){
cerr<<"Cspline::fit - You have less than 4 data pts for spline fitting."<<endl;
exit(-1);
}
if(nodes.Nrows()!=vals.Nrows()){
cerr<<"Nodes and VALS must be the same length in your spline"<<endl;
exit(-1);
}
int n=vals.Nrows();
ColumnVector s(n);
ColumnVector dx,dy,dydx(n-1);
diff(nodes,dx);
diff(vals,dy);
for(int i=1;i<=n-1;i++){
dydx(i)=dy(i)/dx(i);
}
ColumnVector b(n);
b=0;
for(int i=2;i<=b.Nrows()-1;i++){
b(i)=3*(dx(i)*dydx(i-1)+dx(i-1)*dydx(i));
}
float x31=nodes(3)-nodes(1),xn=nodes(n)-nodes(n-2);
b(1)=((dx(1)+2*x31)*dx(2)*dydx(1)+dx(1)*dx(1)*dydx(2))/x31;
b(n)=(dx(n-1)*dx(n-1)*dydx(n-2)+(2*xn+dx(n-1))*dx(n-2)*dydx(n-1))/xn;
Matrix tridiag(n,n);
tridiag=0;
ColumnVector y3(n);
for(int j=2;j<=n-1;j++){
tridiag(j,j-1)=dx(j);
tridiag(j,j)=2*(dx(j)+dx(j-1));
tridiag(j,j+1)=dx(j-1);
}
tridiag(1,1)=dx(2);tridiag(1,2)=x31;
tridiag(n,n-1)=xn;tridiag(n,n)=dx(n-2);
s=tridiag.i()*b;
ColumnVector d(n-1),c(n-1);
for(int j=1;j<n;j++){
d(j)=(s(j)+s(j+1)-2*dydx(j))/dx(j);
c(j)=(dydx(j)-s(j))/dx(j)-d(j);
}
coefs.ReSize(n-1,4);
for(int j=1;j<n;j++){
coefs(j,1)=vals(j);
coefs(j,2)=s(j);
coefs(j,3)=c(j);
coefs(j,4)=d(j)/dx(j);
}
fitted=true;
}
float Cspline::interpolate(float xx) const{
// nodes must be monotonically increasing. I don't check this.
// On your head be it if you don't.
if(nodes.Nrows()!=vals.Nrows()){
cerr<<"Cspline:interpolate: Nodes and Vals should be the same length"<<endl;
exit(-1);
}
float ret;
if(!fitted){
cerr<<"Cspline::interpolate - Cspline has not been fitted"<<endl;
exit(-1);
}
else{
bool stop=false;
int ind=0;
if(xx<nodes(1)){
ind=1;
}
else if(xx>nodes(nodes.Nrows())){
ind=nodes.Nrows()-1;
}
else{
for(int i=1;i<nodes.Nrows();i++){
if(!stop){
if( (nodes(i)<=xx) && (nodes(i+1)>xx) ){
ind=i;
stop=true;
}
}
}
}
float a=coefs(ind,1);
float b=coefs(ind,2);
float c=coefs(ind,3);
float d=coefs(ind,4);
float t=xx-nodes(ind);
ret=a+b*t+c*t*t+d*t*t*t;
}
return ret;
}
float Cspline::interpolate(float xx, int ind) const{
float ret;
if(!fitted){
cerr<<"Cspline::interpolate - Cspline has not been fitted"<<endl;
exit(-1);
}
else{
if(ind>n-1){
cerr<<"Cspline::interpolate - segment index is greater than number of segments - exiting"<<endl;
exit(-1);
}
else if(ind<1){
cerr<<"Cspline::interpolate - segment index is less than 1 - exiting"<<endl;
exit(-1);
}
float a=coefs(ind,1);
float b=coefs(ind,2);
float c=coefs(ind,3);
float d=coefs(ind,4);
float t=xx-nodes(ind);
ret=a+b*t+c*t*t+d*t*t*t;
}
return ret;
}
ColumnVector Cspline::interpolate(const ColumnVector& x) const{
// nodes must be monotonically increasing. I don't check this.
// On your head be it if you don't.
if(nodes.Nrows()!=vals.Nrows()){
cerr<<"Cspline::interpolate - Nodes and Vals should be the same length"<<endl;
exit(-1);
}
ColumnVector ret(x.Nrows());
if(!fitted){
cerr<<"Cspline::interpolate - Cspline has not been fitted"<<endl;
exit(-1);
}
else{
for(int xnum=1;xnum<=x.Nrows();xnum++){
float xx=x(xnum);
bool stop=false;
int ind=0;
if(xx<nodes(1)){
ind=1;
}
else if(xx>=nodes(nodes.Nrows())){
ind=nodes.Nrows()-1;
}
else{
for(int i=1;i<nodes.Nrows();i++){
if(!stop){
if( (nodes(i)<=xx) && (nodes(i+1)>xx) ){
ind=i;
stop=true;
}
}
}
}
float a=coefs(ind,1);
float b=coefs(ind,2);
float c=coefs(ind,3);
float d=coefs(ind,4);
float t=xx-nodes(ind);
ret(xnum)=a+b*t+c*t*t+d*t*t*t;
}
}
return ret;
}
ColumnVector Cspline::interpolate(const ColumnVector& x,const ColumnVector& indvec) const{
// nodes must be monotonically increasing. I don't check this.
// On your head be it if you don't.
if(nodes.Nrows()!=vals.Nrows()){
cerr<<"Cspline::interpolate - Nodes and Vals should be the same length"<<endl;
exit(-1);
}
ColumnVector ret(x.Nrows());
if(!fitted){
cerr<<"Cspline::interpolate - Cspline has not been fitted"<<endl;
exit(-1);
}
else{
for(int xnum=1;xnum<=x.Nrows();xnum++){
float xx=x(xnum);
int ind=int(indvec(xnum));
float a=coefs(ind,1);
float b=coefs(ind,2);
float c=coefs(ind,3);
float d=coefs(ind,4);
float t=xx-nodes(ind);
ret(xnum)=a+b*t+c*t*t+d*t*t*t;
}
}
return ret;
}
}
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