#include "Python.h"
#include "Numeric/arrayobject.h"
#include "math.h"
#include <stdio.h>
const double pi = 3.14159265358979;


// Shared code snippets
#include "util_ext.h"


/* double max(double a, double b) { */
/* 	double z; */
/* 	z=(a>b)?a:b; */
/* 	return z;} */
	
/* double min(double a, double b) { */
/* 	double z; */
/* 	z=(a<b)?a:b; */
/* 	return z;} */
	

//Innermost flux function (using w=z+h)
int _flux_function(double *q_left, double *q_right,
        double z_left, double z_right,
		double normals, double g, double epsilon,
		double *edgeflux, double *max_speed) {
		
		int i;
		double ql[2], qr[2], flux_left[2], flux_right[2];
		double z, w_left, h_left, uh_left, soundspeed_left, u_left;
		double w_right, h_right, uh_right, soundspeed_right, u_right;
		double s_max, s_min, denom;
		
		
		ql[0] = q_left[0];
		ql[1] = q_left[1];
		ql[1] = ql[1]*normals;
	
		qr[0] = q_right[0];
		qr[1] = q_right[1];
		qr[1] = qr[1]*normals;
	  
		z = (z_left+z_right)/2.0;		   
				   
		w_left = ql[0];
		h_left = w_left-z;
		uh_left = ql[1];
		


		// Compute speeds in x-direction
		w_left = ql[0];          
		h_left = w_left-z;
		uh_left = ql[1];
		if (h_left < epsilon) {
			u_left = 0.0; h_left = 0.0;
		}
		else {
			u_left = uh_left/h_left;
		}
	
		w_right = qr[0];
		h_right = w_right-z;
		uh_right = qr[1];
		if (h_right < epsilon) {
			u_right = 0.0; h_right = 0.0; 
		}
		else {
			u_right = uh_right/h_right;
		}
  
		soundspeed_left = sqrt(g*h_left);
		soundspeed_right = sqrt(g*h_right);
		
		s_max = max(u_left+soundspeed_left, u_right+soundspeed_right);
		if (s_max < 0.0) s_max = 0.0;
	
		s_min = min(u_left-soundspeed_left, u_right-soundspeed_right);
		if (s_min > 0.0) s_min = 0.0;
		
		
		// Flux formulas
		flux_left[0] = u_left*h_left;
		flux_left[1] = u_left*uh_left + 0.5*g*h_left*h_left;

		flux_right[0] = u_right*h_right;
		flux_right[1] = u_right*uh_right + 0.5*g*h_right*h_right;

		// Flux computation
		denom = s_max-s_min;
		if (denom < epsilon) {
			for (i=0; i<2; i++) edgeflux[i] = 0.0;
			*max_speed = 0.0;
		} else {
			edgeflux[0] = s_max*flux_left[0] - s_min*flux_right[0];
			edgeflux[0] += s_max*s_min*(qr[0]-ql[0]);
			edgeflux[0] /= denom;
			edgeflux[1] = s_max*flux_left[1] - s_min*flux_right[1];
			edgeflux[1] += s_max*s_min*(qr[1]-ql[1]);
			edgeflux[1] /= denom;
			edgeflux[1] *= normals;
    
		// Maximal wavespeed
        *max_speed = max(fabs(s_max), fabs(s_min));
		}  
    return 0;		
	}
		
		
	
	
// Computational function for flux computation
double _compute_fluxes_ext(double timestep,
		double epsilon,
		double g,
		long* neighbours,
		long* neighbour_vertices,
		double* normals,
		double* areas,
		double* stage_edge_values,
		double* xmom_edge_values,
		double* bed_edge_values,
		double* stage_boundary_values,
		double* xmom_boundary_values,
		double* stage_explicit_update,
		double* xmom_explicit_update,
		int number_of_elements,
		double* max_speed_array) {
		
		double flux[2], ql[2], qr[2], edgeflux[2];
		double zl, zr, max_speed, normal;
		int k, i, ki, n, m, nm=0;
		
		for (k=0; k<number_of_elements; k++) {
			flux[0] = 0.0;
			flux[1] = 0.0;
			
			for (i=0; i<2; i++) {
				ki = k*2+i;
				
				ql[0] = stage_edge_values[ki];
				ql[1] = xmom_edge_values[ki];
				zl = bed_edge_values[ki];
				
				n = neighbours[ki];
				if (n<0) {
					m = -n-1;
					qr[0] = stage_boundary_values[m];
					qr[1] = xmom_boundary_values[m];
					zr = zl;
				} else {
					m = neighbour_vertices[ki];
					nm = n*2+m;
					qr[0] = stage_edge_values[nm];
					qr[1] = xmom_edge_values[nm];
					zr = bed_edge_values[nm];				
				}
				
				normal = normals[ki];
				_flux_function(ql, qr, zl, zr, normal, g, epsilon, edgeflux, &max_speed);
				flux[0] -= edgeflux[0];
				flux[1] -= edgeflux[1];
				
				// Update timestep based on edge i and possibly neighbour n
				if (max_speed > epsilon) {
	                // Original CFL calculation
					
					timestep = min(timestep, 0.5*areas[k]/max_speed); //Here, CFL=1.0 is assumed. ?????????????????????????????????????????????
					if (n>=0) {
						timestep = min(timestep, 0.5*areas[n]/max_speed); //Here, CFL=1.0 is assumed. ?????????????????????????????????????????????
					}
				}
            } // End edge i (and neighbour n)
			flux[0] /= areas[k];
			stage_explicit_update[k] = flux[0];
			flux[1] /= areas[k];
			xmom_explicit_update[k] = flux[1];
			
			//Keep track of maximal speeds
			max_speed_array[k]=max_speed;
		}
		return timestep;	}
	
	
	
	
	



//=========================================================================
// Python Glue
//=========================================================================
PyObject *compute_fluxes_ext(PyObject *self, PyObject *args) {
  
    PyArrayObject 
	*neighbours, 
	*neighbour_vertices,
	*normals, 
	*areas,
	*stage_edge_values,
	*xmom_edge_values,
	*bed_edge_values,
	*stage_boundary_values,
	*xmom_boundary_values,
	*stage_explicit_update,
	*xmom_explicit_update,
	*max_speed_array;
    
  double timestep, epsilon, g;
  int number_of_elements;
    
  // Convert Python arguments to C
  if (!PyArg_ParseTuple(args, "dddOOOOOOOOOOOiO",
			&timestep,
			&epsilon,
			&g,
			&neighbours,
			&neighbour_vertices,
			&normals,
			&areas,
			&stage_edge_values,
			&xmom_edge_values,
			&bed_edge_values,
			&stage_boundary_values,
			&xmom_boundary_values,
			&stage_explicit_update,
			&xmom_explicit_update,
			&number_of_elements,
			&max_speed_array)) {
    PyErr_SetString(PyExc_RuntimeError, "comp_flux_ext.c: compute_fluxes_ext could not parse input");
    return NULL;
  }

 
  // Call underlying flux computation routine and update 
  // the explicit update arrays 
  timestep = _compute_fluxes_ext(timestep,
				 epsilon,
				 g,
				 (long*) neighbours -> data,
				 (long*) neighbour_vertices -> data,
				 (double*) normals -> data,
				 (double*) areas -> data,
				 (double*) stage_edge_values -> data,
				 (double*) xmom_edge_values -> data,
				 (double*) bed_edge_values -> data,
				 (double*) stage_boundary_values -> data,
				 (double*) xmom_boundary_values -> data,
				 (double*) stage_explicit_update -> data,
				 (double*) xmom_explicit_update -> data,
				 number_of_elements,
				 (double*) max_speed_array -> data);

  // Return updated flux timestep
  return Py_BuildValue("d", timestep);
}


PyObject *compute_fluxes_ext_short(PyObject *self, PyObject *args) {
  
   PyObject 
	*domain,
	*stage, 
	*xmom, 
	*bed;

    PyArrayObject 
	*neighbours, 
	*neighbour_vertices,
	*normals, 
	*areas,
	*stage_vertex_values,
	*xmom_vertex_values,
	*bed_vertex_values,
	*stage_boundary_values,
	*xmom_boundary_values,
	*stage_explicit_update,
	*xmom_explicit_update,
	*max_speed_array;
    
  double timestep, epsilon, g;
  int number_of_elements;

    
  // Convert Python arguments to C
  if (!PyArg_ParseTuple(args, "dOOOO",
			&timestep,
			&domain,
			&stage,
			&xmom,
			&bed)) {
      PyErr_SetString(PyExc_RuntimeError, "comp_flux_ext.c: compute_fluxes_ext_short could not parse input");
      return NULL;
  }


    epsilon           = get_python_double(domain,"epsilon");
    g                 = get_python_double(domain,"g");
 
    
    neighbours        = get_consecutive_array(domain, "neighbours");
    neighbour_vertices= get_consecutive_array(domain, "neighbour_vertices"); 
    normals           = get_consecutive_array(domain, "normals");
    areas             = get_consecutive_array(domain, "areas");    
    max_speed_array   = get_consecutive_array(domain, "max_speed_array");
    
    stage_vertex_values = get_consecutive_array(stage, "vertex_values");    
    xmom_vertex_values  = get_consecutive_array(xmom, "vertex_values");    
    bed_vertex_values   = get_consecutive_array(bed, "vertex_values");    

    stage_boundary_values = get_consecutive_array(stage, "boundary_values");    
    xmom_boundary_values  = get_consecutive_array(xmom, "boundary_values");    


    stage_explicit_update = get_consecutive_array(stage, "explicit_update");    
    xmom_explicit_update  = get_consecutive_array(xmom, "explicit_update");    



    number_of_elements = stage_vertex_values -> dimensions[0];


 
    // Call underlying flux computation routine and update 
    // the explicit update arrays 
    timestep = _compute_fluxes_ext(timestep,
				 epsilon,
				 g,
				 (long*) neighbours -> data,
				 (long*) neighbour_vertices -> data,
				 (double*) normals -> data,
				 (double*) areas -> data,
				 (double*) stage_vertex_values -> data,
				 (double*) xmom_vertex_values -> data,
				 (double*) bed_vertex_values -> data,
				 (double*) stage_boundary_values -> data,
				 (double*) xmom_boundary_values -> data,
				 (double*) stage_explicit_update -> data,
				 (double*) xmom_explicit_update -> data,
				 number_of_elements,
				 (double*) max_speed_array -> data);


  Py_DECREF(neighbours);
  Py_DECREF(neighbour_vertices);
  Py_DECREF(normals);
  Py_DECREF(areas);
  Py_DECREF(stage_vertex_values);
  Py_DECREF(xmom_vertex_values);
  Py_DECREF(bed_vertex_values);
  Py_DECREF(stage_boundary_values);
  Py_DECREF(xmom_boundary_values);
  Py_DECREF(stage_explicit_update);
  Py_DECREF(xmom_explicit_update);
  Py_DECREF(max_speed_array);




  // Return updated flux timestep
  return Py_BuildValue("d", timestep);
}

 


//-------------------------------
// Method table for python module
//-------------------------------

static struct PyMethodDef MethodTable[] = {
  {"compute_fluxes_ext", compute_fluxes_ext, METH_VARARGS, "Print out"},
  {"compute_fluxes_ext_short", compute_fluxes_ext_short, METH_VARARGS, "Print out"},
  {NULL, NULL}
};

// Module initialisation
void initcomp_flux_ext(void){
  Py_InitModule("comp_flux_ext", MethodTable);
  import_array();
}