/*T
 *  Concepts: KSP^solving a system of linear equations
 *  Concepts: KSP^Laplacian, 2d
 *  Processors: n
 T **/

/*
 L *aplacian in 2D. Modeled by the partial differential equation
 
 div  grad u = f,  0 < x,y < 1,
 
 with forcing function
 
 f = e^{-(1 - x)^2/\nu} e^{-(1 - y)^2/\nu}
 
 with pure Neumann boundary conditions
 
 The functions are cell-centered
 
 This uses multigrid to solve the linear system
 
 Contributed by Andrei Draganescu <aidraga@sandia.gov>
 
 Note the nice multigrid convergence despite the fact it is only using
 peicewise constant interpolation/restriction. This is because cell-centered multigrid
 does not need the same rule:
 
 polynomial degree(interpolation) + polynomial degree(restriction) + 2 > degree of PDE
 
 that vertex based multigrid needs.
 */

static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n";

#include <petscdm.h>
#include <petscdmda.h>
#include <petscksp.h>

extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
extern PetscErrorCode ComputeGuess(KSP,Vec,void*);

typedef enum {DIRICHLET, NEUMANN} BCType;

typedef struct {
    PetscScalar nu;
    BCType      bcType;
} UserContext;

#undef __FUNCT__
#define __FUNCT__ "main"
int main(int argc,char **argv)
{
    KSP            ksp;
    DM             da;
    UserContext    user;
    const char     *bcTypes[2] = {"dirichlet","neumann"};
    PetscErrorCode ierr;
    PetscInt       bc;
    
    PetscInitialize(&argc,&argv,(char*)0,help);
    
    ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
    ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,12,12,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);CHKERRQ(ierr);
    ierr = DMDASetInterpolationType(da, DMDA_Q0);CHKERRQ(ierr);
    
    ierr = KSPSetDM(ksp,da);CHKERRQ(ierr);
    
    
    ierr        = PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DM");
    user.nu     = 0.1;
    ierr        = PetscOptionsScalar("-nu", "The width of the Gaussian source", "ex29.c", 0.1, &user.nu, NULL);CHKERRQ(ierr);
    bc          = (PetscInt)NEUMANN;
    ierr        = PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);CHKERRQ(ierr);
    user.bcType = (BCType)bc;
    ierr        = PetscOptionsEnd();
    
    ierr = KSPSetComputeRHS(ksp,ComputeRHS,&user);CHKERRQ(ierr);
    ierr = KSPSetComputeInitialGuess(ksp,ComputeGuess,&user);CHKERRQ(ierr);
    ierr = KSPSetComputeOperators(ksp,ComputeMatrix,&user);CHKERRQ(ierr);
    ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
    
    for(int i = 0; i < 9; ++i) {
        printf("KSPSolve\n");
//         KSPSetUp(ksp);
//         ierr = KSPSetComputeInitialGuess(ksp,ComputeGuess,&user);CHKERRQ(ierr);
        ierr = KSPSolve(ksp,NULL,NULL);CHKERRQ(ierr);
    }
    ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
    ierr = DMDestroy(&da);CHKERRQ(ierr);
    ierr = PetscFinalize();
    return 0;
}

#undef __FUNCT__
#define __FUNCT__ "ComputeGuess"
PetscErrorCode ComputeGuess(KSP ksp,Vec b,void *ctx)
{
    printf("ComputeGuess\n");
    
    VecSet(b, 1);
    PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "ComputeRHS"
PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
{
    printf("ComputeRHS\n");
    UserContext    *user = (UserContext*)ctx;
    PetscErrorCode ierr;
    PetscInt       i,j,mx,my,xm,ym,xs,ys;
    PetscScalar    Hx,Hy;
    PetscScalar    **array;
    DM             da;
    
    PetscFunctionBeginUser;
    ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
    ierr = DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
    Hx   = 1.0 / (PetscReal)(mx);
    Hy   = 1.0 / (PetscReal)(my);
    ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
    ierr = DMDAVecGetArray(da, b, &array);CHKERRQ(ierr);
    for (j=ys; j<ys+ym; j++) {
        for (i=xs; i<xs+xm; i++) {
            array[j][i] = PetscExpScalar(-(((PetscReal)i+0.5)*Hx)*(((PetscReal)i+0.5)*Hx)/user->nu)*PetscExpScalar(-(((PetscReal)j+0.5)*Hy)*(((PetscReal)j+0.5)*Hy)/user->nu)*Hx*Hy;
        }
    }
    ierr = DMDAVecRestoreArray(da, b, &array);CHKERRQ(ierr);
    ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
    ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
    
    /* force right hand side to be consistent for singular matrix */
    /* note this is really a hack, normally the model would provide you with a consistent right handside */
    if (user->bcType == NEUMANN) {
        MatNullSpace nullspace;
        
        ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr);
        ierr = MatNullSpaceRemove(nullspace,b);CHKERRQ(ierr);
        ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr);
    }
    PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "ComputeMatrix"
PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac, void *ctx)
{
    printf("ComputeMatrix\n");
    UserContext    *user = (UserContext*)ctx;
    PetscErrorCode ierr;
    PetscInt       i,j,mx,my,xm,ym,xs,ys,num, numi, numj;
    PetscScalar    v[5],Hx,Hy,HydHx,HxdHy;
    MatStencil     row, col[5];
    DM             da;
    
    PetscFunctionBeginUser;
    ierr  = KSPGetDM(ksp,&da);CHKERRQ(ierr);
    ierr  = DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
    Hx    = 1.0 / (PetscReal)(mx);
    Hy    = 1.0 / (PetscReal)(my);
    HxdHy = Hx/Hy;
    HydHx = Hy/Hx;
    ierr  = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
    for (j=ys; j<ys+ym; j++) {
        for (i=xs; i<xs+xm; i++) {
            row.i = i; row.j = j;
            if (i==0 || j==0 || i==mx-1 || j==my-1) {
                if (user->bcType == DIRICHLET) {
                    v[0] = 2.0*(HxdHy + HydHx);
                    ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
                    SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Dirichlet boundary conditions not supported !\n");
                } else if (user->bcType == NEUMANN) {
                    num = 0; numi=0; numj=0;
                    if (j!=0) {
                        v[num] = -HxdHy;
                        col[num].i = i;
                        col[num].j = j-1;
                        num++; numj++;
                    }
                    if (i!=0) {
                        v[num]     = -HydHx;
                        col[num].i = i-1;
                        col[num].j = j;
                        num++; numi++;
                    }
                    if (i!=mx-1) {
                        v[num]     = -HydHx;
                        col[num].i = i+1;
                        col[num].j = j;
                        num++; numi++;
                    }
                    if (j!=my-1) {
                        v[num]     = -HxdHy;
                        col[num].i = i;
                        col[num].j = j+1;
                        num++; numj++;
                    }
                    v[num] = (PetscReal)(numj)*HxdHy + (PetscReal)(numi)*HydHx; col[num].i = i;   col[num].j = j;
                    num++;
                    ierr = MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);CHKERRQ(ierr);
                }
            } else {
                v[0] = -HxdHy;              col[0].i = i;   col[0].j = j-1;
                v[1] = -HydHx;              col[1].i = i-1; col[1].j = j;
                v[2] = 2.0*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
                v[3] = -HydHx;              col[3].i = i+1; col[3].j = j;
                v[4] = -HxdHy;              col[4].i = i;   col[4].j = j+1;
                ierr = MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
            }
        }
    }
    ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    if (user->bcType == NEUMANN) {
        MatNullSpace nullspace;
        
        ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr);
        ierr = MatSetNullSpace(jac,nullspace);CHKERRQ(ierr);
        ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr);
    }
    PetscFunctionReturn(0);
}