Index: /issm/trunk-jpl/src/m/contrib/gravity/Makefile
===================================================================
--- /issm/trunk-jpl/src/m/contrib/gravity/Makefile	(revision 18434)
+++ /issm/trunk-jpl/src/m/contrib/gravity/Makefile	(revision 18434)
@@ -0,0 +1,7 @@
+all:
+		g++ vfsa.cpp -o forward \
+			-I$(ISSM_DIR)/externalpackages/gsl/install/include \
+			-L$(ISSM_DIR)/externalpackages/gsl/install/lib -lgsl -lgslcblas
+
+clean:
+		rm -f forward
Index: /issm/trunk-jpl/src/m/contrib/gravity/vfsa.cpp
===================================================================
--- /issm/trunk-jpl/src/m/contrib/gravity/vfsa.cpp	(revision 18434)
+++ /issm/trunk-jpl/src/m/contrib/gravity/vfsa.cpp	(revision 18434)
@@ -0,0 +1,492 @@
+#include <iostream>
+#include <cmath>
+#include <fstream>
+#include <string>
+#include <cstdio>
+#include <cstdlib>
+#include <time.h>
+#include <cassert>
+#include <gsl/gsl_multifit.h>
+
+using namespace std;
+
+class Matrix{/*{{{*/
+	private:
+		int     M;        /*Number of lines   */
+		int     N;        /*Number if Columns */
+		double *values;
+	public:
+		Matrix(int m_in,int n_in){/*{{{*/
+			this->M = m_in;
+			this->N = n_in;
+			this->values = new double[M*N];
+		}/*}}}*/
+		~Matrix(){/*{{{*/
+			delete [] this->values;
+		}/*}}}*/
+		void Echo(void){/*{{{*/
+			for(int i=0;i<M;i++){
+				for(int j=0;j<N;j++){
+					cout << " " << this->values[i*N+j];
+				}
+				cout << endl;
+			}
+		}/*}}}*/
+		void SetValue(int i,int j,double value){/*{{{*/
+			this->values[i*N+j] = value;
+		}/*}}}*/
+		double GetValue(int i,int j){/*{{{*/
+			return this->values[i*N+j];
+		}/*}}}*/
+		void GetSize(int* pM,int* pN){/*{{{*/
+			*pM = this->M;
+			*pN = this->N;
+		}/*}}}*/
+		double* GetPointer(void){/*{{{*/
+			return this->values;
+		}/*}}}*/
+		void MatrixSum(Matrix* A,Matrix* B){/*{{{*/
+			/*Check that sizes are compatible*/
+			int M_B,N_B,M_A,N_A;
+			B->GetSize(&M_B,&N_B);
+			A->GetSize(&M_A,&N_A);
+			assert(this->M==M_B && this->N==N_B);
+			assert(this->M==M_A && this->N==N_A);
+			for(int i=0;i<this->M;i++){
+				for(int j=0;j<this->N;j++){
+					this->SetValue(i,j,A->GetValue(i,j) + B->GetValue(i,j));
+				}
+			}
+		}/*}}}*/
+		void MatrixDiff(Matrix* A,Matrix* B){/*{{{*/
+			/*Check that sizes are compatible*/
+			int M_B,N_B,M_A,N_A;
+			B->GetSize(&M_B,&N_B);
+			A->GetSize(&M_A,&N_A);
+			assert(this->M==M_B && this->N==N_B);
+			assert(this->M==M_A && this->N==N_A);
+			for(int i=0;i<this->M;i++){
+				for(int j=0;j<this->N;j++){
+					this->SetValue(i,j,A->GetValue(i,j) - B->GetValue(i,j));
+				}
+			}
+		}/*}}}*/
+		void MatrixAbs(Matrix* A){/*{{{*/
+			for(int i=0;i<this->M;i++){
+				for(int j=0;j<this->N;j++){
+					this->SetValue(i,j,fabs(A->GetValue(i,j)));
+				}
+			}
+		}/*}}}*/
+		void MatrixEqual(Matrix* A){/*{{{*/
+			for(int i=0;i<this->M;i++){
+				for(int j=0;j<this->N;j++){
+					this->SetValue(i,j,A->GetValue(i,j));
+				}
+			}
+		}/*}}}*/
+		double MatrixInternSum(){/*{{{*/
+			double sum=0;
+			for(int i=0;i<this->M;i++){
+				for(int j=0;j<this->N;j++){
+					sum+=this->GetValue(i,j);
+				}
+			}
+			return sum;
+		}/*}}}*/
+		void ExtractLine(Matrix* A,int i){/*{{{*/
+			/* Check that the size of A is compatible */
+			int M_A,N_A;
+			A->GetSize(&M_A,&N_A);
+			assert(M_A==1 && this->N==N_A);
+			for(int j=0;j<this->N;j++){
+				A->SetValue(0,j,this->GetValue(i,j));
+			}
+		}/*}}}*/
+		void ExtractColumn(Matrix* A,int j){/*{{{*/
+			/* Check that the size of A is compatible */
+			int M_A,N_A;
+			A->GetSize(&M_A,&N_A);
+			assert(N_A==1 && this->M==M_A);
+			for(int i=0;i<this->M;i++){
+				A->SetValue(i,0,this->GetValue(i,j));
+			}
+		}/*}}}*/
+		void AddNumber(double a){/*{{{*/
+			for(int i=0;i<this->M;i++){
+				for(int j=0;j<this->N;j++){
+					this->SetValue(i,j,this->GetValue(i,j) + a);
+				}
+			}
+		}/*}}}*/
+};/*}}}*/
+
+/*Local prototypes{{{*/
+void makep(Matrix *Pobs,int nx,int ny, int dx, int dy);
+void vec2grid(Matrix *V,Matrix *V1,Matrix *V2,int nx, int ny);
+void msplit( Matrix *m, Matrix *m1,Matrix *m2,double dlevel);
+void plouff(Matrix *g,Matrix *Pobs,Matrix *Pp,Matrix * mesh,Matrix *rho,int dx,int dy, int dn,int m,int n,int l);
+void vec2gridsimple(Matrix *V,Matrix *V1,int nx, int ny);
+void reshape(Matrix* V,Matrix* V1,int nx,int ny);
+double misfit(Matrix* m0,Matrix* evalid,Matrix* gobs,int dlevel,Matrix* Pobs,Matrix* xobs,Matrix* yobs,Matrix* Pp,Matrix* rho1, Matrix* rho2,int dx,int dy,int dn,int nx,int ny, int mx,int my);
+void GSLsquarefit(Matrix** pX,Matrix* A,Matrix* B);
+/*}}}*/
+
+int main(){/*{{{*/
+
+	/* Seed the random number generator {{{*/
+	srand (time(NULL));               /*}}}*/
+	/* Define the variables {{{*/
+
+	int    dx     = 500;   /* prism dimension in x-direction                           */
+	int    dy     = 500;   /* prism dimension in y-direction                           */
+	int    mx     = 39;    /* number of prisms in x-direction                          */
+	int    my     = 60;    /* number of prisms in y-direction                          */
+	int    nx     = 39;    /* number of data points in x-direction                     */
+	int    ny     = 60;    /* number of data points in y-direction                     */
+	int    dn     = 15000; /* distance for neighbouting prisms for gravity calculation */
+	double ptval  = 100.;  /* max. amount to perturb model                             */
+	double ptval2 = 100.;
+
+	Matrix *Pobs=new Matrix(nx*ny,2); /* data positions */
+	makep(Pobs,nx,ny,dx,dy);
+// Pobs->Echo();
+
+
+	Matrix *Pp=new Matrix(mx*my,2); /* data positions */
+	makep(Pp,mx,my,dx,dy);
+// Pp->Echo();
+
+	double  rhoi = 890;           /* ice density     */
+	double  rhow = 1030;          /* water density   */
+// double  rhos = 2013;		      /* sediment density */
+	double  rhoc = 2670;          /* bedrock density */
+	
+	Matrix *Rho  = new Matrix(1,2);
+	Rho->SetValue(0,0,rhoi);
+	Rho->SetValue(0,1,rhow);
+	Matrix *rho1  = new Matrix(1,3);
+	rho1->SetValue(0,0,rhoi);
+	rho1->SetValue(0,1,rhow);
+	rho1->SetValue(0,2,rhoc);
+	Matrix *rho2  = new Matrix(1,2);
+	rho2->SetValue(0,0,rhoi-rhoc);
+	rho2->SetValue(0,1,rhow-rhoc);
+	
+	double ctr=1;            /* parameter for filtering */
+	double sd=0.1;
+
+	Matrix *xobs= new Matrix(ny,nx);
+	Matrix *yobs= new Matrix(ny,nx);
+
+	vec2grid(Pobs,xobs,yobs,nx,ny);
+//	xobs->Echo();
+//	yobs->Echo();
+
+	double dlevel= 860;                /* mean level of data acquisition */
+
+	double mmax  = 1000;               /* max value for layer interfaces */
+	double mmax2 = 1000;
+	double mmax3 = 1000;
+
+	/* control parameter for temperature schedule  */
+
+	double ca=0.9;                    /* for acceptance */
+	double cm=0.5;                    /* for model perturbation */
+	                     /*}}}*/     
+	/* load the data {{{*/
+
+	/* Observed gravity anomaly */
+
+	ifstream file1("store_fa500_36s.txt");
+	Matrix * gobs= new Matrix(nx*ny,1);
+	double inputnumber;
+	for(int i=0;i<ny*nx; i++){ 
+		file1 >> inputnumber;
+		gobs->SetValue(i,0, inputnumber*1e-5);
+	}
+	file1.close();
+//	gobs->Echo();
+	
+	/* load data about the ice thickness */
+
+	ifstream file2("store_flag_icethick500.txt");
+	Matrix * icethick= new Matrix(mx*my,1);
+	for(int s=0;s<mx*my; s++){ 
+		file2 >> inputnumber;
+		icethick->SetValue(s,0,inputnumber);
+	}
+	file2.close();
+//	icethick->Echo();
+
+	/* load the batimethry data */
+
+	ifstream file3("store_flag_bathy500.txt");
+	Matrix * bathy= new Matrix(mx*my,1);
+	for(int s=0;s<mx*my; s++){ 
+		file3 >> inputnumber;
+		bathy->SetValue(s,0,inputnumber);
+	}
+	file3.close();
+//	bathy->Echo();
+	
+	/* id of grid to evaluate misfit */
+
+
+	ifstream file4("store_flag_eval500.txt");
+	Matrix * evalid= new Matrix(mx*my,1);
+	for(int s=0;s<mx*my; s++){ 
+		file4 >> inputnumber;
+		evalid->SetValue(s,0,inputnumber);
+	}
+	file4.close();
+//	evalid->Echo();
+	
+	/* initial guess of the model */
+
+	ifstream file5("m0_140114b.txt");
+	Matrix * mesh_ini= new Matrix(mx*my,3);
+	for(int s=0;s<mx*my; s++){ 
+		for(int j=0;j<3;j++){
+		file5 >> inputnumber;
+		mesh_ini->SetValue(s,j,inputnumber);
+	}
+	}
+	file5.close();
+//	mesh_ini->Echo();
+                           /*}}}*/
+	double q=0;
+ q=misfit(mesh_ini,evalid,gobs,dlevel,Pobs,xobs,yobs,Pp,rho1,rho2,dx,dy,dn,nx,ny,mx,my);
+     cout<< q;
+/*	Matrix* G=new Matrix(4,3);
+	Matrix* df=new Matrix(4,1);
+	Matrix* o=new Matrix(4,1);
+	for(int i= 0;i<4;i++){
+		for(int j=0;j<3;j++){
+			if(j==2){G->SetValue(i,j,1);}
+			else{G->SetValue(i,j,i+j);}
+		}
+		df->SetValue(i,0,i*1e-3);
+	}
+		G->SetValue(0,0,1);
+		G->SetValue(0,1,2);
+
+	Matrix* M = NULL;
+	GSLsquarefit(&M,G,df);
+	for(int i= 0;i<4;i++){
+		o->SetValue(i,0,G->GetValue(i,0)*M->GetValue(0,0)+G->GetValue(i,1)*M->GetValue(1,0)+G->GetValue(i,2)*M->GetValue(2,0));}
+
+	G->Echo();
+	df->Echo();
+	M->Echo();
+	o->Echo();*/
+
+	return 0;
+}/*}}}*/
+
+void GSLsquarefit(Matrix** pX,Matrix* A,Matrix* B){/*{{{*/
+
+	/*GSL Matrices and vectors: */
+	int    M,N;
+	double chisq;
+
+	/*Get system size*/
+	A->GetSize(&M,&N);
+
+	/*Initialize gsl matrices and vectors: */
+	gsl_matrix* a = gsl_matrix_alloc(M,N);
+	for(int i=0;i<M;i++){
+		for(int j=0;j<N;j++){
+			gsl_matrix_set (a,i,j,A->GetValue(i,j));
+		}
+	}
+	gsl_vector* b = gsl_vector_alloc(M);
+	for(int i=0;i<M;i++){
+		gsl_vector_set(b,i,B->GetValue(i,0));
+	}
+
+	gsl_vector* x = gsl_vector_alloc(N);
+	gsl_matrix* cov = gsl_matrix_alloc(N,N);
+
+	/*Least square fit: */
+	gsl_multifit_linear_workspace* work = gsl_multifit_linear_alloc(M,N);
+	gsl_multifit_linear (a, b, x, cov, &chisq, work);
+	gsl_multifit_linear_free (work);
+
+	/*Clean up and assign output pointer*/
+	Matrix* X = new Matrix(N,1);
+	for(int j=0;j<N;j++){
+		X->SetValue(j,0,gsl_vector_get(x,j));
+	}
+	*pX = X;
+
+	gsl_matrix_free(a);
+	gsl_vector_free(b);
+	gsl_matrix_free(cov);
+
+}/*}}}*/
+void makep(Matrix *Pobs,int nx,int ny, int dx, int dy){/*{{{*/
+	for(int i=0;i<ny;i++){
+		for(int j=0;j<nx;j++){
+			Pobs->SetValue(j+nx*i,0,j*dx);
+			Pobs->SetValue(j+nx*i,1,i*dy);
+		}
+	}
+}/*}}}*/
+void vec2grid(Matrix *V,Matrix *V1,Matrix *V2,int nx, int ny){/*{{{*/
+	for(int i=0;i<ny;i++){
+		for (int j=0;j<nx;j++){
+			V1->SetValue(i,j, V->GetValue(j+nx*i,0));
+			V2->SetValue(i,j, V->GetValue(j+nx*i,1));
+		}
+	}
+}/*}}}*/
+void msplit( Matrix *m, Matrix *m1,Matrix *m2,double dlevel){/*{{{*/
+	int sizem1,sizem2;
+	m->GetSize(&sizem1,&sizem2);
+	for(int i=0;i<sizem1;i++){
+		for(int j=0;j<sizem2+1;j++){
+			if(j<sizem2){
+				m1->SetValue(i,j,1e-10*(sizem2+1-j));
+				m2->SetValue(i,j,m->GetValue(i,j));
+				if(m->GetValue(i,j)<0){
+					m1->SetValue(i,j,m->GetValue(i,j));
+					m2->SetValue(i,j,i*1e-10);
+				}
+			}
+			else{
+				m1->SetValue(i,j,1e-10);
+			}
+		}
+	}
+	m1->AddNumber(dlevel);
+	m2->AddNumber(dlevel);
+}/*}}}*/
+void plouff(Matrix *g,Matrix *Pobs,Matrix *Pp,Matrix * mesh,Matrix *rho,int dx,int dy, int dn,int m,int n,int l){/*{{{*/
+		double gg=6.673e-11;
+		int si,sj,id,s;
+		double R,Q,P;
+		Matrix *xp= new Matrix(1,2);
+		Matrix *yp= new Matrix(1,2);
+		Matrix *xpp= new Matrix(1,2);
+		Matrix *ypp= new Matrix(1,2);
+		Matrix *U= new Matrix(l,4);
+		Matrix *U1=new Matrix(1,4);
+		Matrix *U2=new Matrix(1,4);
+		Matrix *gl= new Matrix(1,l-1);
+		bool test=true;
+		for(int c=0;c<n;c++){
+			g->SetValue(c,0,0);
+			for(int a=0;a<m;a++){
+				test=true;
+				xp->SetValue(0,0,Pp->GetValue(a,0)-Pobs->GetValue(c,0));
+				xp->SetValue(0,1,Pp->GetValue(a,0)-Pobs->GetValue(c,0)+dx);
+				if(xp->GetValue(0,0)<0 && xp->GetValue(0,0)<xp->GetValue(0,1) && xp->GetValue(0,0)*xp->GetValue(0,1)>=0){
+					xpp->SetValue(0,0,xp->GetValue(0,1));
+					xpp->SetValue(0,1,xp->GetValue(0,0));
+					xp->MatrixAbs(xpp);
+				}
+				yp->SetValue(0,0,Pp->GetValue(a,1)-Pobs->GetValue(c,1));
+				yp->SetValue(0,1,Pp->GetValue(a,1)-Pobs->GetValue(c,1)+dy);
+				if(yp->GetValue(0,0)<0 && yp->GetValue(0,0)<yp->GetValue(0,1) && yp->GetValue(0,0)*yp->GetValue(0,1)>=0){
+					ypp->SetValue(0,0,yp->GetValue(0,1));
+					ypp->SetValue(0,1,yp->GetValue(0,0));
+					yp->MatrixAbs(ypp);
+				}
+				P=sqrt(xp->GetValue(0,0)*xp->GetValue(0,0)+yp->GetValue(0,0)*yp->GetValue(0,0));
+				if(P>dn){
+					test=false;
+					for(int i=0;i<l-1;i++){
+						gl->SetValue(0,i,0);
+					}
+				}
+				if(test==true){
+					si=1;
+					sj=1;
+					id=0;
+					for(int i=0;i<2;i++){
+						si*=-1;
+						for(int j=0;j<2;j++){
+							si*=-1;
+							s=si*sj;
+							for(int k=0;k<l;k++){
+								R=sqrt(xp->GetValue(0,i)*xp->GetValue(0,i)+yp->GetValue(0,j)*yp->GetValue(0,j)+mesh->GetValue(a,k)*mesh->GetValue(a,k));
+								Q=atan(xp->GetValue(0,i)*yp->GetValue(0,j)/(mesh->GetValue(a,k)*R));
+								U->SetValue(k,id,s*(mesh->GetValue(a,k)*Q-xp->GetValue(0,i)*log(R+yp->GetValue(0,j))-yp->GetValue(0,j)*log(R+xp->GetValue(0,i))));
+							}
+							id++;
+						}
+					}
+					for(int b=0;b<l-1;b++){
+						U->ExtractLine(U1,b);
+						U->ExtractLine(U2,b+1);
+						gl->SetValue(0,b,rho->GetValue(0,b)*(U1->MatrixInternSum()*(-1)+U2->MatrixInternSum()));
+					}
+				}
+				g->SetValue(c,0,g->GetValue(c,0)+gg*gl->MatrixInternSum());
+			}
+		}
+		delete xp;
+		delete yp;
+		delete xpp;
+		delete ypp;
+		delete gl;
+		delete U;
+		delete U1;
+		delete U2;
+	}/*}}}*/
+void vec2gridsimple(Matrix *V,Matrix *V1,int nx, int ny){/*{{{*/
+	for(int i=0;i<ny;i++){
+		for (int j=0;j<nx;j++){
+			V1->SetValue(i,j, V->GetValue(j+nx*i,0));
+		}
+	}
+}/*}}}*/
+void reshape(Matrix* V,Matrix* V1,int nx,int ny){/*{{{*/
+	for (int i=0;i<ny;i++){
+		for(int j=0;j<nx;j++){
+			V1->SetValue(j+nx*i,0,V->GetValue(i,j));
+		}
+	}
+}/*}}}*/
+double misfit(Matrix* m0,Matrix* evalid,Matrix* gobs,int dlevel,Matrix* Pobs,Matrix* xobs,Matrix* yobs,Matrix* Pp,Matrix* rho1, Matrix* rho2,int dx,int dy,int dn,int nx,int ny, int mx,int my){/*{{{*/
+	Matrix* m1=new Matrix(mx*my,4);
+	Matrix* m2=new Matrix(mx*my,3);
+	Matrix* g1=new Matrix(nx*ny,1);
+	Matrix* g2=new Matrix(nx*ny,1);
+	Matrix* g=new Matrix(nx*ny,1);
+	Matrix* gcalgr=new Matrix(ny,nx);
+	Matrix* gcalvec=new Matrix(mx*my,1);
+	Matrix* df=new Matrix(mx*my,1);
+	Matrix* G=new Matrix(mx*my,3);
+	double a=0;
+	double b=0;
+	double e=0;
+	msplit(m0,m1,m2,dlevel);
+   plouff(g1,Pobs,Pp,m1,rho1,dx,dy,dn,mx*my,nx*ny,4);
+   plouff(g2,Pobs,Pp,m2,rho2,dx,dy,dn,mx*my,nx*ny,3);
+	g->MatrixSum(g1,g2);
+	vec2gridsimple(g,gcalgr,nx,ny);
+	reshape(gcalgr,gcalvec,mx,my);
+	for (int i=0;i<mx*my;i++){
+		df->SetValue(i,0,evalid->GetValue(i,0)*(gobs->GetValue(i,0)-gcalvec->GetValue(i,0)));
+		G->SetValue(i,0,evalid->GetValue(i,0)*Pobs->GetValue(i,0));
+		G->SetValue(i,1,evalid->GetValue(i,0)*Pobs->GetValue(i,1));
+		G->SetValue(i,2,evalid->GetValue(i,0));
+	}
+	Matrix* M = NULL;
+	GSLsquarefit(&M,G,df);
+
+	for (int i=0;i<my;i++){
+		for(int j=0;j<mx;j++){
+			gcalgr->SetValue(i,j,gcalgr->GetValue(i,j)+xobs->GetValue(i,j)*M->GetValue(0,0)+yobs->GetValue(i,j)*M->GetValue(1,0)+M->GetValue(2,0));
+		}
+	}
+	reshape(gcalgr,g,mx,my);
+	for (int i=0;i<mx*my;i++){
+		a=a+fabs(evalid->GetValue(i,0)*(gobs->GetValue(i,0)-g->GetValue(i,0)));
+		b=b+fabs(evalid->GetValue(i,0)*(gobs->GetValue(i,0)+g->GetValue(i,0)));
+	}
+	e=2*a/(a+b);
+	return e;
+}/*}}}*/