/*
AppCtxInitialize - Sets initial values for the application context parameters
Input:
ptr - void user-defined application context
Output:
ptr - user-defined application context with the default or user-provided
parameters
*/
static int AppCtxInitialize(void *ptr) {
AppCtx *user = (AppCtx*)ptr;
PetscTruth flg;
int info;
/* Specify default parameters */
user->mx = user->my = 11;
user->b = -0.5;
user->t = 0.5;
user->l = -0.5;
user->r = 0.5;
user->fx=0.5;
user->fy=0.5;
user->bheight=0.0;
/* Check for command line arguments that override defaults */
info = PetscOptionsGetInt(TAO_NULL, "-mx", &user->mx, &flg); CHKERRQ(info);
info = PetscOptionsGetInt(TAO_NULL, "-my", &user->my, &flg); CHKERRQ(info);
info = PetscOptionsGetReal(TAO_NULL, "-bottom", &user->b, &flg); CHKERRQ(info);
info = PetscOptionsGetReal(TAO_NULL, "-top", &user->t, &flg); CHKERRQ(info);
info = PetscOptionsGetReal(TAO_NULL, "-left", &user->l, &flg); CHKERRQ(info);
info = PetscOptionsGetReal(TAO_NULL, "-right", &user->r, &flg); CHKERRQ(info);
info = PetscOptionsGetReal(PETSC_NULL,"-bmx",&user->fx,&flg); CHKERRQ(info);
info = PetscOptionsGetReal(PETSC_NULL,"-bmy",&user->fy,&flg); CHKERRQ(info);
info = PetscOptionsGetReal(PETSC_NULL,"-bheight",&user->bheight,&flg); CHKERRQ(info);
user->hx = (user->r - user->l) / (user->mx - 1);
user->hy = (user->t - user->b) / (user->my - 1);
user->area = 0.5 * user->hx * user->hy;
info = PetscLogFlops(8); CHKERRQ(info);
return 0;
} /* AppCtxInitialize */
static PetscErrorCode PCApply_PBJacobi_7(PC pc,Vec x,Vec y)
{
PC_PBJacobi *jac = (PC_PBJacobi*)pc->data;
PetscErrorCode ierr;
PetscInt i,m = jac->mbs;
const MatScalar *diag = jac->diag;
PetscScalar x0,x1,x2,x3,x4,x5,x6,*xx,*yy;
PetscFunctionBegin;
ierr = VecGetArray(x,&xx);CHKERRQ(ierr);
ierr = VecGetArray(y,&yy);CHKERRQ(ierr);
for (i=0; i<m; i++) {
x0 = xx[7*i]; x1 = xx[7*i+1]; x2 = xx[7*i+2]; x3 = xx[7*i+3]; x4 = xx[7*i+4]; x5 = xx[7*i+5]; x6 = xx[7*i+6];
yy[7*i] = diag[0]*x0 + diag[7]*x1 + diag[14]*x2 + diag[21]*x3 + diag[28]*x4 + diag[35]*x5 + diag[42]*x6;
yy[7*i+1] = diag[1]*x0 + diag[8]*x1 + diag[15]*x2 + diag[22]*x3 + diag[29]*x4 + diag[36]*x5 + diag[43]*x6;
yy[7*i+2] = diag[2]*x0 + diag[9]*x1 + diag[16]*x2 + diag[23]*x3 + diag[30]*x4 + diag[37]*x5 + diag[44]*x6;
yy[7*i+3] = diag[3]*x0 + diag[10]*x1 + diag[17]*x2 + diag[24]*x3 + diag[31]*x4 + diag[38]*x5 + diag[45]*x6;
yy[7*i+4] = diag[4]*x0 + diag[11]*x1 + diag[18]*x2 + diag[25]*x3 + diag[32]*x4 + diag[39]*x5 + diag[46]*x6;
yy[7*i+5] = diag[5]*x0 + diag[12]*x1 + diag[19]*x2 + diag[26]*x3 + diag[33]*x4 + diag[40]*x5 + diag[47]*x6;
yy[7*i+6] = diag[6]*x0 + diag[13]*x1 + diag[20]*x2 + diag[27]*x3 + diag[34]*x4 + diag[41]*x5 + diag[48]*x6;
diag += 49;
}
ierr = VecRestoreArray(x,&xx);CHKERRQ(ierr);
ierr = VecRestoreArray(y,&yy);CHKERRQ(ierr);
ierr = PetscLogFlops(80.0*m);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode MatSolve_SeqSBSTRM_5_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)
{
Mat_SeqSBAIJ *a =(Mat_SeqSBAIJ*)A->data;
PetscInt mbs=a->mbs,*ai=a->i,*aj=a->j,bs=A->rmap->bs,bs2 = a->bs2;
PetscScalar *x,*b;
PetscErrorCode ierr;
Mat_SeqSBSTRM *sbstrm = (Mat_SeqSBSTRM*)A->spptr;
MatScalar *as =sbstrm->as;
PetscFunctionBegin;
#if 0
#endif
ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
/* solve U^T * D * y = b by forward substitution */
ierr = PetscMemcpy(x,b,5*mbs*sizeof(PetscScalar));CHKERRQ(ierr); /* x <- b */
ierr = MatForwardSolve_SeqSBSTRM_5_NaturalOrdering(ai,aj,as,mbs,x);CHKERRQ(ierr);
/* solve U*x = y by back substitution */
ierr = MatBackwardSolve_SeqSBSTRM_5_NaturalOrdering(ai,aj,as,mbs,x);CHKERRQ(ierr);
ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
ierr = PetscLogFlops(4.0*bs2*a->nz - (bs+2.0*bs2)*mbs);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode PCApply_PBJacobi_5(PC pc,Vec x,Vec y)
{
PC_PBJacobi *jac = (PC_PBJacobi*)pc->data;
PetscErrorCode ierr;
PetscInt i,m = jac->mbs;
const MatScalar *diag = jac->diag;
PetscScalar x0,x1,x2,x3,x4,*xx,*yy;
PetscFunctionBegin;
ierr = VecGetArray(x,&xx);CHKERRQ(ierr);
ierr = VecGetArray(y,&yy);CHKERRQ(ierr);
for (i=0; i<m; i++) {
x0 = xx[5*i]; x1 = xx[5*i+1]; x2 = xx[5*i+2]; x3 = xx[5*i+3]; x4 = xx[5*i+4];
yy[5*i] = diag[0]*x0 + diag[5]*x1 + diag[10]*x2 + diag[15]*x3 + diag[20]*x4;
yy[5*i+1] = diag[1]*x0 + diag[6]*x1 + diag[11]*x2 + diag[16]*x3 + diag[21]*x4;
yy[5*i+2] = diag[2]*x0 + diag[7]*x1 + diag[12]*x2 + diag[17]*x3 + diag[22]*x4;
yy[5*i+3] = diag[3]*x0 + diag[8]*x1 + diag[13]*x2 + diag[18]*x3 + diag[23]*x4;
yy[5*i+4] = diag[4]*x0 + diag[9]*x1 + diag[14]*x2 + diag[19]*x3 + diag[24]*x4;
diag += 25;
}
ierr = VecRestoreArray(x,&xx);CHKERRQ(ierr);
ierr = VecRestoreArray(y,&yy);CHKERRQ(ierr);
ierr = PetscLogFlops(45.0*m);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
ComputeFunction - Evaluates nonlinear function, F(x).
Input Parameters:
. X - input vector
. user - user-defined application context
Output Parameter:
. F - function vector
*/
PetscErrorCode ComputeFunction(AppCtx *user,Vec X,Vec F)
{
PetscErrorCode ierr;
PetscInt i,j,row,mx,my,xs,ys,xm,ym,gxs,gys,gxm,gym;
PetscReal two = 2.0,one = 1.0,lambda,hx,hy,hxdhy,hydhx,sc;
PetscScalar u,uxx,uyy,*x,*f;
Vec localX = user->localX;
mx = user->mx; my = user->my; lambda = user->param;
hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
/*
Scatter ghost points to local vector, using the 2-step process
DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
By placing code between these two statements, computations can be
done while messages are in transition.
*/
ierr = DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
/*
Get pointers to vector data
*/
ierr = VecGetArray(localX,&x);CHKERRQ(ierr);
ierr = VecGetArray(F,&f);CHKERRQ(ierr);
/*
Get local grid boundaries
*/
ierr = DMDAGetCorners(user->da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
ierr = DMDAGetGhostCorners(user->da,&gxs,&gys,NULL,&gxm,&gym,NULL);CHKERRQ(ierr);
/*
Compute function over the locally owned part of the grid
*/
for (j=ys; j<ys+ym; j++) {
row = (j - gys)*gxm + xs - gxs - 1;
for (i=xs; i<xs+xm; i++) {
row++;
if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
f[row] = x[row];
continue;
}
u = x[row];
uxx = (two*u - x[row-1] - x[row+1])*hydhx;
uyy = (two*u - x[row-gxm] - x[row+gxm])*hxdhy;
f[row] = uxx + uyy - sc*PetscExpScalar(u);
}
}
/*
Restore vectors
*/
ierr = VecRestoreArray(localX,&x);CHKERRQ(ierr);
ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
ierr = PetscLogFlops(11.0*ym*xm);CHKERRQ(ierr);
return 0;
}
PetscErrorCode MatMultTranspose_SeqBSTRM_5(Mat A,Vec xx,Vec zz)
{
Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
Mat_SeqBSTRM *sbstrm = (Mat_SeqBSTRM*)A->spptr;
PetscScalar zero = 0.0;
PetscScalar *z = 0;
PetscScalar *x,*xb;
const MatScalar *v1, *v2, *v3, *v4, *v5;
PetscScalar x1, x2, x3, x4, x5;
PetscErrorCode ierr;
PetscInt mbs =a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j;
PetscInt nonzerorow=0;
PetscInt slen;
PetscFunctionBegin;
ierr = VecSet(zz,zero);CHKERRQ(ierr);
ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
slen = 5*(ai[mbs]-ai[0]);
v1 = sbstrm->as;
v2 = v1 + slen;
v3 = v2 + slen;
v4 = v3 + slen;
v5 = v4 + slen;
xb = x;
for (i=0; i<mbs; i++) {
n = ai[i+1] - ai[i];
nonzerorow += (n>0);
x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5 = xb[4]; xb += 5;
ib = aj + ai[i];
PetscPrefetchBlock(ib+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
PetscPrefetchBlock(v1+5*n,5*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
PetscPrefetchBlock(v2+5*n,5*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
PetscPrefetchBlock(v3+5*n,5*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
PetscPrefetchBlock(v4+5*n,5*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
PetscPrefetchBlock(v5+5*n,5*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
for (j=0; j<n; j++) {
cval = ib[j]*5;
z[cval] += v1[0]*x1 + v2[0]*x2 + v3[0]*x3 + v4[0]*x4 + v5[0]*x5;
z[cval+1] += v1[1]*x1 + v2[1]*x2 + v3[1]*x3 + v4[1]*x4 + v5[1]*x5;
z[cval+2] += v1[2]*x1 + v2[2]*x2 + v3[2]*x3 + v4[2]*x4 + v5[2]*x5;
z[cval+3] += v1[3]*x1 + v2[3]*x2 + v3[3]*x3 + v4[3]*x4 + v5[3]*x5;
z[cval+4] += v1[4]*x1 + v2[4]*x2 + v3[4]*x3 + v4[4]*x4 + v5[4]*x5;
v1 += 5; v2 += 5; v3 += 5; v4 += 5; v5 += 5;
}
}
ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
ierr = PetscLogFlops(50.0*a->nz - 5.0*nonzerorow);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
FormFunction - Evaluates the function, f(X).
Input Parameters:
. tao - the Tao context
. X - the input vector
. ptr - optional user-defined context, as set by TaoSetFunction()
Output Parameters:
. f - the newly evaluated function
*/
PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
{
AppCtx *user = (AppCtx *) ptr;
PetscReal hx = user->hx, hy = user->hy, area, three = 3.0, p5 = 0.5;
PetscReal zero = 0.0, vb, vl, vr, vt, dvdx, dvdy, flin = 0.0, fquad = 0.0;
PetscReal v, cdiv3 = user->param/three;
PetscReal *x;
PetscErrorCode ierr;
PetscInt nx = user->mx, ny = user->my, i, j, k;
/* Get pointer to vector data */
ierr = VecGetArray(X,&x);CHKERRQ(ierr);
/* Compute function contributions over the lower triangular elements */
for (j=-1; j<ny; j++) {
for (i=-1; i<nx; i++) {
k = nx*j + i;
v = zero;
vr = zero;
vt = zero;
if (i >= 0 && j >= 0) v = x[k];
if (i < nx-1 && j > -1) vr = x[k+1];
if (i > -1 && j < ny-1) vt = x[k+nx];
dvdx = (vr-v)/hx;
dvdy = (vt-v)/hy;
fquad += dvdx*dvdx + dvdy*dvdy;
flin -= cdiv3*(v+vr+vt);
}
}
/* Compute function contributions over the upper triangular elements */
for (j=0; j<=ny; j++) {
for (i=0; i<=nx; i++) {
k = nx*j + i;
vb = zero;
vl = zero;
v = zero;
if (i < nx && j > 0) vb = x[k-nx];
if (i > 0 && j < ny) vl = x[k-1];
if (i < nx && j < ny) v = x[k];
dvdx = (v-vl)/hx;
dvdy = (v-vb)/hy;
fquad = fquad + dvdx*dvdx + dvdy*dvdy;
flin = flin - cdiv3*(vb+vl+v);
}
}
/* Restore vector */
ierr = VecRestoreArray(X,&x);CHKERRQ(ierr);
/* Scale the function */
area = p5*hx*hy;
*f = area*(p5*fquad+flin);
ierr = PetscLogFlops(nx*ny*24);CHKERRQ(ierr);
return 0;
}
/*
Shared by both sequential and parallel versions of CRL matrix: MATMPIAIJCRL and MATSEQAIJCRL
- the scatter is used only in the parallel version
*/
PetscErrorCode MatMult_AIJCRL(Mat A,Vec xx,Vec yy)
{
Mat_AIJCRL *aijcrl = (Mat_AIJCRL*) A->spptr;
PetscInt m = aijcrl->m; /* Number of rows in the matrix. */
PetscInt rmax = aijcrl->rmax,*icols = aijcrl->icols;
PetscScalar *acols = aijcrl->acols;
PetscErrorCode ierr;
PetscScalar *x,*y;
#if !defined(PETSC_USE_FORTRAN_KERNEL_MULTCRL)
PetscInt i,j,ii;
#endif
#if defined(PETSC_HAVE_PRAGMA_DISJOINT)
#pragma disjoint(*x,*y,*aa)
#endif
PetscFunctionBegin;
if (aijcrl->xscat) {
ierr = VecCopy(xx,aijcrl->xwork);CHKERRQ(ierr);
/* get remote values needed for local part of multiply */
ierr = VecScatterBegin(aijcrl->xscat,xx,aijcrl->fwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(aijcrl->xscat,xx,aijcrl->fwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
xx = aijcrl->xwork;
}
ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
#if defined(PETSC_USE_FORTRAN_KERNEL_MULTCRL)
fortranmultcrl_(&m,&rmax,x,y,icols,acols);
#else
/* first column */
for (j=0; j<m; j++) y[j] = acols[j]*x[icols[j]];
/* other columns */
#if defined(PETSC_HAVE_CRAY_VECTOR)
#pragma _CRI preferstream
#endif
for (i=1; i<rmax; i++) {
ii = i*m;
#if defined(PETSC_HAVE_CRAY_VECTOR)
#pragma _CRI prefervector
#endif
for (j=0; j<m; j++) y[j] = y[j] + acols[ii+j]*x[icols[ii+j]];
}
#if defined(PETSC_HAVE_CRAY_VECTOR)
#pragma _CRI ivdep
#endif
#endif
ierr = PetscLogFlops(2.0*aijcrl->nz - m);CHKERRQ(ierr);
ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode VecNorm_MPI(Vec xin,NormType type,PetscReal *z)
{
Vec_MPI *x = (Vec_MPI*)xin->data;
PetscReal sum,work = 0.0;
PetscScalar *xx = x->array;
PetscErrorCode ierr;
PetscInt n = xin->map->n;
PetscFunctionBegin;
if (type == NORM_2 || type == NORM_FROBENIUS) {
#if defined(PETSC_HAVE_SLOW_BLAS_NORM2)
#if defined(PETSC_USE_FORTRAN_KERNEL_NORM)
fortrannormsqr_(xx,&n,&work);
#elif defined(PETSC_USE_UNROLLED_NORM)
switch (n & 0x3) {
case 3: work += PetscRealPart(xx[0]*PetscConj(xx[0])); xx++;
case 2: work += PetscRealPart(xx[0]*PetscConj(xx[0])); xx++;
case 1: work += PetscRealPart(xx[0]*PetscConj(xx[0])); xx++; n -= 4;
}
while (n>0) {
work += PetscRealPart(xx[0]*PetscConj(xx[0])+xx[1]*PetscConj(xx[1])+
xx[2]*PetscConj(xx[2])+xx[3]*PetscConj(xx[3]));
xx += 4; n -= 4;
}
#else
{PetscInt i; for (i=0; i<n; i++) work += PetscRealPart((xx[i])*(PetscConj(xx[i])));}
#endif
#else
{PetscBLASInt one = 1,bn = PetscBLASIntCast(n);
work = BLASnrm2_(&bn,xx,&one);
work *= work;
}
#endif
ierr = MPI_Allreduce(&work,&sum,1,MPIU_REAL,MPI_SUM,((PetscObject)xin)->comm);CHKERRQ(ierr);
*z = sqrt(sum);
ierr = PetscLogFlops(2.0*xin->map->n);CHKERRQ(ierr);
} else if (type == NORM_1) {
/* Find the local part */
ierr = VecNorm_Seq(xin,NORM_1,&work);CHKERRQ(ierr);
/* Find the global max */
ierr = MPI_Allreduce(&work,z,1,MPIU_REAL,MPI_SUM,((PetscObject)xin)->comm);CHKERRQ(ierr);
} else if (type == NORM_INFINITY) {
/* Find the local max */
ierr = VecNorm_Seq(xin,NORM_INFINITY,&work);CHKERRQ(ierr);
/* Find the global max */
ierr = MPI_Allreduce(&work,z,1,MPIU_REAL,MPI_MAX,((PetscObject)xin)->comm);CHKERRQ(ierr);
} else if (type == NORM_1_AND_2) {
PetscReal temp[2];
ierr = VecNorm_Seq(xin,NORM_1,temp);CHKERRQ(ierr);
ierr = VecNorm_Seq(xin,NORM_2,temp+1);CHKERRQ(ierr);
temp[1] = temp[1]*temp[1];
ierr = MPI_Allreduce(temp,z,2,MPIU_REAL,MPI_SUM,((PetscObject)xin)->comm);CHKERRQ(ierr);
z[1] = sqrt(z[1]);
}
PetscFunctionReturn(0);
}
PetscErrorCode VecAYPX_Seq(Vec yin,PetscScalar alpha,Vec xin)
{
PetscErrorCode ierr;
PetscInt n = yin->map->n;
PetscScalar *yy;
const PetscScalar *xx;
PetscFunctionBegin;
if (alpha == (PetscScalar)0.0) {
ierr = VecCopy(xin,yin);CHKERRQ(ierr);
} else if (alpha == (PetscScalar)1.0) {
ierr = VecAXPY_Seq(yin,alpha,xin);CHKERRQ(ierr);
} else if (alpha == (PetscScalar)-1.0) {
PetscInt i;
ierr = VecGetArrayRead(xin,&xx);CHKERRQ(ierr);
ierr = VecGetArray(yin,&yy);CHKERRQ(ierr);
for (i=0; i<n; i++) {
yy[i] = xx[i] - yy[i];
}
ierr = VecRestoreArrayRead(xin,&xx);CHKERRQ(ierr);
ierr = VecRestoreArray(yin,&yy);CHKERRQ(ierr);
ierr = PetscLogFlops(1.0*n);CHKERRQ(ierr);
} else {
ierr = VecGetArrayRead(xin,&xx);CHKERRQ(ierr);
ierr = VecGetArray(yin,&yy);CHKERRQ(ierr);
#if defined(PETSC_USE_FORTRAN_KERNEL_AYPX)
{
PetscScalar oalpha = alpha;
fortranaypx_(&n,&oalpha,xx,yy);
}
#else
{
PetscInt i;
for (i=0; i<n; i++) {
yy[i] = xx[i] + alpha*yy[i];
}
}
#endif
ierr = VecRestoreArrayRead(xin,&xx);CHKERRQ(ierr);
ierr = VecRestoreArray(yin,&yy);CHKERRQ(ierr);
ierr = PetscLogFlops(2.0*n);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
/*
RHSFunction - Evaluates nonlinear function, F(u).
Input Parameters:
. ts - the TS context
. U - input vector
. ptr - optional user-defined context, as set by TSSetFunction()
Output Parameter:
. F - function vector
*/
PetscErrorCode RHSFunction(TS ts,PetscReal ftime,Vec U,Vec F,void *ptr)
{
/* PETSC_UNUSED AppCtx *user=(AppCtx*)ptr; */
DM da;
PetscErrorCode ierr;
PetscInt i,j,Mx,My,xs,ys,xm,ym;
PetscReal two = 2.0,hx,hy,sx,sy;
PetscScalar u,uxx,uyy,**uarray,**f;
Vec localU;
PetscFunctionBeginUser;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localU);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
/*
Scatter ghost points to local vector,using the 2-step process
DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
By placing code between these two statements, computations can be
done while messages are in transition.
*/
ierr = DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
/* Get pointers to vector data */
ierr = DMDAVecGetArray(da,localU,&uarray);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/* Get local grid boundaries */
ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
/* Compute function over the locally owned part of the grid */
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
f[j][i] = uarray[j][i];
continue;
}
u = uarray[j][i];
uxx = (-two*u + uarray[j][i-1] + uarray[j][i+1])*sx;
uyy = (-two*u + uarray[j-1][i] + uarray[j+1][i])*sy;
f[j][i] = uxx + uyy;
}
}
/* Restore vectors */
ierr = DMDAVecRestoreArray(da,localU,&uarray);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localU);CHKERRQ(ierr);
ierr = PetscLogFlops(11.0*ym*xm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode MatMult_SeqBSTRM_4(Mat A,Vec xx,Vec zz)
{
Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
Mat_SeqBSTRM *bstrm = (Mat_SeqBSTRM*)A->spptr;
PetscScalar *z = 0,sum1,sum2,sum3,sum4,x1,x2,x3,x4,*zarray;
const PetscScalar *x,*xb;
const MatScalar *v1, *v2, *v3, *v4;
PetscErrorCode ierr;
PetscInt mbs,i,*idx,*ii,j,n,*ridx=NULL,nonzerorow=0;
PetscBool usecprow=a->compressedrow.use;
PetscInt slen;
PetscFunctionBegin;
ierr = VecGetArray(xx,(PetscScalar**)&x);CHKERRQ(ierr);
ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
idx = a->j;
if (usecprow) {
mbs = a->compressedrow.nrows;
ii = a->compressedrow.i;
ridx = a->compressedrow.rindex;
} else {
mbs = a->mbs;
ii = a->i;
z = zarray;
}
slen = 4*(ii[mbs]-ii[0]);
v1 = bstrm->as;
v2 = v1 + slen;
v3 = v2 + slen;
v4 = v3 + slen;
for (i=0; i<mbs; i++) {
n = ii[1] - ii[0]; ii++;
sum1 = 0.0; sum2 = 0.0; sum3 = 0.0; sum4 = 0.0;
nonzerorow += (n>0);
for (j=0; j<n; j++) {
xb = x + 4*(*idx++);
x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3];
sum1 += v1[0]*x1 + v1[1]*x2 + v1[2]*x3 + v1[3]*x4;
sum2 += v2[0]*x1 + v2[1]*x2 + v2[2]*x3 + v2[3]*x4;
sum3 += v3[0]*x1 + v3[1]*x2 + v3[2]*x3 + v3[3]*x4;
sum4 += v4[0]*x1 + v4[1]*x2 + v4[2]*x3 + v4[3]*x4;
v1 += 4; v2 += 4; v3 += 4; v4 += 4;
}
if (usecprow) z = zarray + 4*ridx[i];
z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4;
if (!usecprow) z += 4;
}
ierr = VecRestoreArray(xx,(PetscScalar**)&x);CHKERRQ(ierr);
ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
ierr = PetscLogFlops(32*a->nz - 4*nonzerorow);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
Evaluates FU = Gradiant(L(w,u,lambda))
This local function acts on the ghosted version of U (accessed via DMCompositeGetLocalVectors() and
DMCompositeScatter()) BUT the global, nonghosted version of FU (via DMCompositeGetAccess()).
*/
PetscErrorCode ComputeFunction(SNES snes,Vec U,Vec FU,void *ctx)
{
PetscErrorCode ierr;
PetscInt xs,xm,i,N;
ULambda *u_lambda,*fu_lambda;
PetscScalar d,h,*w,*fw;
Vec vw,vfw,vu_lambda,vfu_lambda;
DM packer,red,da;
PetscFunctionBeginUser;
ierr = VecGetDM(U, &packer);CHKERRQ(ierr);
ierr = DMCompositeGetEntries(packer,&red,&da);CHKERRQ(ierr);
ierr = DMCompositeGetLocalVectors(packer,&vw,&vu_lambda);CHKERRQ(ierr);
ierr = DMCompositeScatter(packer,U,vw,vu_lambda);CHKERRQ(ierr);
ierr = DMCompositeGetAccess(packer,FU,&vfw,&vfu_lambda);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
ierr = VecGetArray(vw,&w);CHKERRQ(ierr);
ierr = VecGetArray(vfw,&fw);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,vu_lambda,&u_lambda);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,vfu_lambda,&fu_lambda);CHKERRQ(ierr);
d = N-1.0;
h = 1.0/d;
/* derivative of L() w.r.t. w */
if (xs == 0) { /* only first processor computes this */
fw[0] = -2.0*d*u_lambda[0].lambda;
}
/* derivative of L() w.r.t. u */
for (i=xs; i<xs+xm; i++) {
if (i == 0) fu_lambda[0].lambda = h*u_lambda[0].u + 2.*d*u_lambda[0].lambda - d*u_lambda[1].lambda;
else if (i == 1) fu_lambda[1].lambda = 2.*h*u_lambda[1].u + 2.*d*u_lambda[1].lambda - d*u_lambda[2].lambda;
else if (i == N-1) fu_lambda[N-1].lambda = h*u_lambda[N-1].u + 2.*d*u_lambda[N-1].lambda - d*u_lambda[N-2].lambda;
else if (i == N-2) fu_lambda[N-2].lambda = 2.*h*u_lambda[N-2].u + 2.*d*u_lambda[N-2].lambda - d*u_lambda[N-3].lambda;
else fu_lambda[i].lambda = 2.*h*u_lambda[i].u - d*(u_lambda[i+1].lambda - 2.0*u_lambda[i].lambda + u_lambda[i-1].lambda);
}
/* derivative of L() w.r.t. lambda */
for (i=xs; i<xs+xm; i++) {
if (i == 0) fu_lambda[0].u = 2.0*d*(u_lambda[0].u - w[0]);
else if (i == N-1) fu_lambda[N-1].u = 2.0*d*u_lambda[N-1].u;
else fu_lambda[i].u = -(d*(u_lambda[i+1].u - 2.0*u_lambda[i].u + u_lambda[i-1].u) - 2.0*h);
}
ierr = VecRestoreArray(vw,&w);CHKERRQ(ierr);
ierr = VecRestoreArray(vfw,&fw);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,vu_lambda,&u_lambda);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,vfu_lambda,&fu_lambda);CHKERRQ(ierr);
ierr = DMCompositeRestoreLocalVectors(packer,&vw,&vu_lambda);CHKERRQ(ierr);
ierr = DMCompositeRestoreAccess(packer,FU,&vfw,&vfu_lambda);CHKERRQ(ierr);
ierr = PetscLogFlops(13.0*N);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
MSA_InitialPoint - Calculates the initial guess in one of three ways.
Input Parameters:
. user - user-defined application context
. X - vector for initial guess
Output Parameters:
. X - newly computed initial guess
*/
static int MSA_InitialPoint(AppCtx * user, Vec X)
{
int info;
PetscInt start2=-1,i,j;
PetscReal start1=0;
PetscTruth flg1,flg2;
info = PetscOptionsGetReal(PETSC_NULL,"-start",&start1,&flg1); CHKERRQ(info);
info = PetscOptionsGetInt(PETSC_NULL,"-random",&start2,&flg2); CHKERRQ(info);
if (flg1){ /* The zero vector is reasonable */
info = VecSet(X, start1); CHKERRQ(info);
} else if (flg2 && start2>0){ /* Try a random start between -0.5 and 0.5 */
PetscRandom rctx; PetscScalar np5=-0.5;
info = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
CHKERRQ(info);
for (i=0; i<start2; i++){
info = VecSetRandom(X, rctx); CHKERRQ(info);
}
info = PetscRandomDestroy(rctx); CHKERRQ(info);
info = VecShift(X, np5); CHKERRQ(info);
} else { /* Take an average of the boundary conditions */
PetscInt xs,xm,ys,ym;
PetscInt mx=user->mx,my=user->my;
PetscScalar **x;
/* Get local mesh boundaries */
info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
/* Get pointers to vector data */
info = DAVecGetArray(user->da,X,(void**)&x);
/* Perform local computations */
for (j=ys; j<ys+ym; j++){
for (i=xs; i< xs+xm; i++){
x[j][i] = ( ((j+1)*user->bottom[i-xs+1]+(my-j+1)*user->top[i-xs+1])/(my+2)+
((i+1)*user->left[j-ys+1]+(mx-i+1)*user->right[j-ys+1])/(mx+2))/2.0;
}
}
/* Restore vectors */
info = DAVecRestoreArray(user->da,X,(void**)&x); CHKERRQ(info);
info = PetscLogFlops(9*xm*ym); CHKERRQ(info);
}
return 0;
}
PetscErrorCode VecPointwiseMax_Seq(Vec win,Vec xin,Vec yin)
{
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = PetscThreadCommRunKernel3(PetscObjectComm((PetscObject)win),(PetscThreadKernel)VecPointwiseMax_kernel,win,xin,yin);
CHKERRQ(ierr);
ierr = PetscLogFlops(win->map->n);
CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
Special case where the matrix was ILU(0) factored in the natural
ordering. This eliminates the need for the column and row permutation.
*/
PetscErrorCode MatSolve_SeqBAIJ_1_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)
{
Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
const PetscInt n = a->mbs,*vi,*ai=a->i,*aj=a->j,*diag=a->diag;
PetscErrorCode ierr;
const MatScalar *aa=a->a,*v;
PetscScalar *x;
const PetscScalar *b;
PetscScalar s1,x1;
PetscInt jdx,idt,idx,nz,i;
PetscFunctionBegin;
ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
/* forward solve the lower triangular */
idx = 0;
x[0] = b[0];
for (i=1; i<n; i++) {
v = aa + ai[i];
vi = aj + ai[i];
nz = diag[i] - ai[i];
idx += 1;
s1 = b[idx];
while (nz--) {
jdx = *vi++;
x1 = x[jdx];
s1 -= v[0]*x1;
v += 1;
}
x[idx] = s1;
}
/* backward solve the upper triangular */
for (i=n-1; i>=0; i--) {
v = aa + diag[i] + 1;
vi = aj + diag[i] + 1;
nz = ai[i+1] - diag[i] - 1;
idt = i;
s1 = x[idt];
while (nz--) {
idx = *vi++;
x1 = x[idx];
s1 -= v[0]*x1;
v += 1;
}
v = aa + diag[i];
x[idt] = v[0]*s1;
}
ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
ierr = PetscLogFlops(2.0*(a->nz) - A->cmap->n);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode EvaluateFunction(Tao tao, Vec X, Vec F, void *ptr)
{
AppCtx *user = (AppCtx *)ptr;
PetscInt i;
PetscReal *x,*f;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = VecGetArray(X,&x);CHKERRQ(ierr);
ierr = VecGetArray(F,&f);CHKERRQ(ierr);
if (user->size == 1) {
/* Single processor */
for (i=0;i<NOBSERVATIONS;i++) {
ierr = RunSimulation(x,i,&f[i],user);CHKERRQ(ierr);
}
} else {
/* Multiprocessor master */
PetscMPIInt tag;
PetscInt finishedtasks,next_task,checkedin;
PetscReal f_i;
MPI_Status status;
next_task=0;
finishedtasks=0;
checkedin=0;
while(finishedtasks < NOBSERVATIONS || checkedin < user->size-1) {
ierr = MPI_Recv(&f_i,1,MPIU_REAL,MPI_ANY_SOURCE,MPI_ANY_TAG,PETSC_COMM_WORLD,&status);CHKERRQ(ierr);
if (status.MPI_TAG == IDLE_TAG) {
checkedin++;
} else {
tag = status.MPI_TAG;
f[tag] = (PetscReal)f_i;
finishedtasks++;
}
if (next_task<NOBSERVATIONS) {
ierr = MPI_Send(x,NPARAMETERS,MPIU_REAL,status.MPI_SOURCE,next_task,PETSC_COMM_WORLD);CHKERRQ(ierr);
next_task++;
} else {
/* Send idle message */
ierr = MPI_Send(x,NPARAMETERS,MPIU_REAL,status.MPI_SOURCE,IDLE_TAG,PETSC_COMM_WORLD);CHKERRQ(ierr);
}
}
}
ierr = VecRestoreArray(X,&x);CHKERRQ(ierr);
ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
PetscLogFlops(6*NOBSERVATIONS);
PetscFunctionReturn(0);
}
PetscErrorCode MatScale_MPIDense(Mat inA,PetscScalar alpha)
{
Mat_MPIDense *A = (Mat_MPIDense*)inA->data;
Mat_SeqDense *a = (Mat_SeqDense*)A->A->data;
PetscScalar oalpha = alpha;
PetscErrorCode ierr;
PetscBLASInt one = 1,nz = PetscBLASIntCast(inA->rmap->n*inA->cmap->N);
PetscFunctionBegin;
BLASscal_(&nz,&oalpha,a->v,&one);
ierr = PetscLogFlops(nz);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static int MatMult_SeqAIJ_DXML(Mat A,Vec x,Vec y)
{
Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
PetscScalar *xx,*yy;
int ierr,zero = 0;
PetscFunctionBegin;
ierr = VecGetArray(x,&xx);CHKERRQ(ierr);
ierr = VecGetArray(y,&yy);CHKERRQ(ierr);
dmatvec_genr_(&zero,a->a,a->i,a->j,&a->nz,0,xx,yy,&A->rmap->n);
ierr = PetscLogFlops(2.0*a->nz - A->rmap->n);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FormIFunctionLocal(DMDALocalInfo *info,PetscScalar ptime,PetscScalar **x,PetscScalar **xt,PetscScalar **f,void *ctx)
{
PetscErrorCode ierr;
PetscInt i,j;
PetscReal hx,hy,hxdhy,hydhx,scale;
PetscScalar u,uxx,uyy;
Vec C;
PetscScalar **c;
PetscFunctionBeginUser;
ierr = DMGetNamedGlobalVector(info->da,"coefficient",&C);CHKERRQ(ierr);
ierr = DMDAVecGetArray(info->da,C,&c);CHKERRQ(ierr);
hx = 10.0/((PetscReal)(info->mx-1));
hy = 10.0/((PetscReal)(info->my-1));
/*
dhx = 1. / hx;
dhy = 1. / hy;
*/
hxdhy = hx/hy;
hydhx = hy/hx;
scale = hx*hy;
for (j=info->ys; j<info->ys+info->ym; j++) {
for (i=info->xs; i<info->xs+info->xm; i++) {
f[j][i] = xt[j][i]*scale;
if (i == 0) {
/* f[j][i] += (x[j][i] - x[j][i+1])*dhx; */
} else if (i == info->mx-1) {
/* f[j][i] += (x[j][i] - x[j][i-1])*dhx; */
} else if (j == 0) {
/* f[j][i] += (x[j][i] - x[j+1][i])*dhy; */
} else if (j == info->my-1) {
/* f[j][i] += (x[j][i] - x[j-1][i])*dhy; */
} else {
u = x[j][i];
uyy = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy;
uxx = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx;
f[j][i] += c[j][i]*(uxx + uyy);
}
}
}
ierr = PetscLogFlops(11.*info->ym*info->xm);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(info->da,C,&c);CHKERRQ(ierr);
ierr = DMRestoreNamedGlobalVector(info->da,"coefficient",&C);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* FormFunctionLocalMMS2 - Evaluates nonlinear function, F(x) on local process patch */
PetscErrorCode FormFunctionLocalMMS2(DMDALocalInfo *info,PetscScalar **vx,PetscScalar **f,AppCtx *user)
{
PetscErrorCode ierr;
PetscInt i,j;
PetscReal lambda,hx,hy,hxdhy,hydhx;
PetscScalar u,ue,uw,un,us,uxx,uyy;
PetscReal x,y;
DM coordDA;
Vec coordinates;
DMDACoor2d **coords;
PetscFunctionBeginUser;
lambda = user->param;
hx = 1.0/(PetscReal)(info->mx-1);
hy = 1.0/(PetscReal)(info->my-1);
hxdhy = hx/hy;
hydhx = hy/hx;
/* Extract coordinates */
ierr = DMGetCoordinateDM(info->da, &coordDA);CHKERRQ(ierr);
ierr = DMGetCoordinates(info->da, &coordinates);CHKERRQ(ierr);
ierr = DMDAVecGetArray(coordDA, coordinates, &coords);CHKERRQ(ierr);
/* Compute function over the locally owned part of the grid */
for (j=info->ys; j<info->ys+info->ym; j++) {
for (i=info->xs; i<info->xs+info->xm; i++) {
if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
f[j][i] = 2.0*(hydhx+hxdhy)*vx[j][i];
} else {
x = PetscRealPart(coords[j][i].x);
y = PetscRealPart(coords[j][i].y);
u = vx[j][i];
uw = vx[j][i-1];
ue = vx[j][i+1];
un = vx[j-1][i];
us = vx[j+1][i];
if (i-1 == 0) uw = 0.;
if (i+1 == info->mx-1) ue = 0.;
if (j-1 == 0) un = 0.;
if (j+1 == info->my-1) us = 0.;
uxx = (2.0*u - uw - ue)*hydhx;
uyy = (2.0*u - un - us)*hxdhy;
f[j][i] = uxx + uyy - hx*hy*(lambda*PetscExpScalar(u) + 2*PetscSqr(PETSC_PI)*PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y) - lambda*exp(PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y)));
}
}
}
ierr = DMDAVecRestoreArray(coordDA, coordinates, &coords);CHKERRQ(ierr);
ierr = PetscLogFlops(11.0*info->ym*info->xm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FormFunction1(SNES snes,Vec X,Vec F,void *ptr)
{
AppCtx *user = (AppCtx*)ptr;
PetscErrorCode ierr;
PetscInt i,j,k,loc,mx,my,mz,xs,ys,zs,xm,ym,zm,Xs,Ys,Zs,Xm,Ym,Zm,base1,base2;
PetscReal two = 2.0,one = 1.0,lambda,Hx,Hy,Hz,HxHzdHy,HyHzdHx,HxHydHz;
PetscScalar u,uxx,uyy,sc,*x,*f,uzz;
Vec localX = user->localX,localF = user->localF;
mx = user->mx; my = user->my; mz = user->mz; lambda = user->param;
Hx = one / (PetscReal)(mx-1);
Hy = one / (PetscReal)(my-1);
Hz = one / (PetscReal)(mz-1);
sc = Hx*Hy*Hz*lambda; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
HxHydHz = Hx*Hy/Hz;
ierr = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
ierr = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
ierr = VecGetArray(localX,&x);CHKERRQ(ierr);
ierr = VecGetArray(localF,&f);CHKERRQ(ierr);
ierr = DAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);CHKERRQ(ierr);
ierr = DAGetGhostCorners(user->da,&Xs,&Ys,&Zs,&Xm,&Ym,&Zm);CHKERRQ(ierr);
for (k=zs; k<zs+zm; k++) {
base1 = (Xm*Ym)*(k-Zs);
for (j=ys; j<ys+ym; j++) {
base2 = base1 + (j-Ys)*Xm;
for (i=xs; i<xs+xm; i++) {
loc = base2 + (i-Xs);
if (i == 0 || j == 0 || k== 0 || i == mx-1 || j == my-1 || k == mz-1) {
f[loc] = x[loc];
}
else {
u = x[loc];
uxx = (two*u - x[loc-1] - x[loc+1])*HyHzdHx;
uyy = (two*u - x[loc-Xm] - x[loc+Xm])*HxHzdHy;
uzz = (two*u - x[loc-Xm*Ym] - x[loc+Xm*Ym])*HxHydHz;
f[loc] = uxx + uyy + uzz - sc*PetscExpScalar(u);
}
}
}
}
ierr = VecRestoreArray(localX,&x);CHKERRQ(ierr);
ierr = VecRestoreArray(localF,&f);CHKERRQ(ierr);
/* stick values into global vector */
ierr = DALocalToGlobal(user->da,localF,INSERT_VALUES,F);CHKERRQ(ierr);
ierr = PetscLogFlops(11.0*ym*xm*zm);CHKERRQ(ierr);
return 0;
}
PetscErrorCode MatSolveTranspose_SeqBAIJ_1_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
PetscErrorCode ierr;
const PetscInt *adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
PetscInt i,n = a->mbs,j;
PetscInt nz;
PetscScalar *x,*tmp,s1;
const MatScalar *aa = a->a,*v;
const PetscScalar *b;
PetscFunctionBegin;
ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
tmp = a->solve_work;
/* copy the b into temp work space according to permutation */
for (i=0; i<n; i++) tmp[i] = b[i];
/* forward solve the U^T */
for (i=0; i<n; i++) {
v = aa + adiag[i+1] + 1;
vi = aj + adiag[i+1] + 1;
nz = adiag[i] - adiag[i+1] - 1;
s1 = tmp[i];
s1 *= v[nz]; /* multiply by inverse of diagonal entry */
for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
tmp[i] = s1;
}
/* backward solve the L^T */
for (i=n-1; i>=0; i--) {
v = aa + ai[i];
vi = aj + ai[i];
nz = ai[i+1] - ai[i];
s1 = tmp[i];
for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
}
/* copy tmp into x according to permutation */
for (i=0; i<n; i++) x[i] = tmp[i];
ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* FormObjectiveLocal - Evaluates nonlinear function, F(x) on local process patch */
PetscErrorCode FormObjectiveLocal(DMDALocalInfo *info,PetscScalar **x,PetscReal *obj,AppCtx *user)
{
PetscErrorCode ierr;
PetscInt i,j;
PetscReal lambda,hx,hy,hxdhy,hydhx,sc,lobj=0;
PetscScalar u,ue,uw,un,us,uxux,uyuy;
MPI_Comm comm;
PetscFunctionBeginUser;
*obj = 0;
ierr = PetscObjectGetComm((PetscObject)info,&comm);CHKERRQ(ierr);
lambda = user->param;
hx = 1.0/(PetscReal)(info->mx-1);
hy = 1.0/(PetscReal)(info->my-1);
sc = hx*hy*lambda;
hxdhy = hx/hy;
hydhx = hy/hx;
/*
Compute function over the locally owned part of the grid
*/
for (j=info->ys; j<info->ys+info->ym; j++) {
for (i=info->xs; i<info->xs+info->xm; i++) {
if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
lobj += PetscRealPart((hydhx + hxdhy)*x[j][i]*x[j][i]);
} else {
u = x[j][i];
uw = x[j][i-1];
ue = x[j][i+1];
un = x[j-1][i];
us = x[j+1][i];
if (i-1 == 0) uw = 0.;
if (i+1 == info->mx-1) ue = 0.;
if (j-1 == 0) un = 0.;
if (j+1 == info->my-1) us = 0.;
/* F[u] = 1/2\int_{\omega}\nabla^2u(x)*u(x)*dx */
uxux = u*(2.*u - ue - uw)*hydhx;
uyuy = u*(2.*u - un - us)*hxdhy;
lobj += PetscRealPart(0.5*(uxux + uyuy) - sc*PetscExpScalar(u));
}
}
}
ierr = PetscLogFlops(12.0*info->ym*info->xm);CHKERRQ(ierr);
ierr = MPI_Allreduce(&lobj,obj,1,MPIU_REAL,MPIU_SUM,comm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
FormHessian - Evaluates Hessian matrix.
Input Parameters:
. tao - the Tao context
. x - input vector
. ptr - optional user-defined context, as set by TaoSetHessian()
Output Parameters:
. H - Hessian matrix
Note: Providing the Hessian may not be necessary. Only some solvers
require this matrix.
*/
PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
{
AppCtx *user = (AppCtx*)ptr;
PetscErrorCode ierr;
PetscInt i, ind[2];
PetscReal alpha=user->alpha;
PetscReal v[2][2];
const PetscScalar *x;
PetscBool assembled;
PetscFunctionBeginUser;
/* Zero existing matrix entries */
ierr = MatAssembled(H,&assembled);CHKERRQ(ierr);
if (assembled){ierr = MatZeroEntries(H); CHKERRQ(ierr);}
/* Get a pointer to vector data */
ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
/* Compute H(X) entries */
if (user->chained) {
ierr = MatZeroEntries(H);CHKERRQ(ierr);
for (i=0; i<user->n-1; i++) {
PetscScalar t1 = x[i+1] - x[i]*x[i];
v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
v[0][1] = 2*alpha*(-2*x[i]);
v[1][0] = 2*alpha*(-2*x[i]);
v[1][1] = 2*alpha*t1;
ind[0] = i; ind[1] = i+1;
ierr = MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);CHKERRQ(ierr);
}
} else {
for (i=0; i<user->n/2; i++){
v[1][1] = 2*alpha;
v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
ind[0]=2*i; ind[1]=2*i+1;
ierr = MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
/* Assemble matrix */
ierr = MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscLogFlops(9.0*user->n/2.0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ptr)
{
AppCtx *user = (AppCtx *) ptr;
PetscInt i, j, row, mx, my, xs, ys, xm, ym, Xs, Ys, Xm, Ym;
PetscErrorCode ierr;
double two = 2.0, one = 1.0, lambda,hx, hy, hxdhy, hydhx,sc;
PetscScalar u, uxx, uyy, *x,*f;
Vec localX = user->fine.localX, localF = user->fine.localF;
mx = user->fine.mx; my = user->fine.my; lambda = user->param;
hx = one/(double)(mx-1); hy = one/(double)(my-1);
sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
/* Get ghost points */
ierr = DMGlobalToLocalBegin(user->fine.da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(user->fine.da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMDAGetCorners(user->fine.da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
ierr = DMDAGetGhostCorners(user->fine.da,&Xs,&Ys,0,&Xm,&Ym,0);CHKERRQ(ierr);
ierr = VecGetArray(localX,&x);CHKERRQ(ierr);
ierr = VecGetArray(localF,&f);CHKERRQ(ierr);
/* Evaluate function */
for (j=ys; j<ys+ym; j++) {
row = (j - Ys)*Xm + xs - Xs - 1;
for (i=xs; i<xs+xm; i++) {
row++;
if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
u = x[row];
uxx = (two*u - x[row-1] - x[row+1])*hydhx;
uyy = (two*u - x[row-Xm] - x[row+Xm])*hxdhy;
f[row] = uxx + uyy - sc*exp(u);
} else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)){
f[row] = .5*two*(hydhx + hxdhy)*x[row];
} else {
f[row] = .25*two*(hydhx + hxdhy)*x[row];
}
}
}
ierr = VecRestoreArray(localX,&x);CHKERRQ(ierr);
ierr = VecRestoreArray(localF,&f);CHKERRQ(ierr);
/* Insert values into global vector */
ierr = DMLocalToGlobalBegin(user->fine.da,localF,INSERT_VALUES,F);CHKERRQ(ierr);
ierr = DMLocalToGlobalEnd(user->fine.da,localF,INSERT_VALUES,F);CHKERRQ(ierr);
ierr = PetscLogFlops(11.0*ym*xm);CHKERRQ(ierr);
return 0;
}
PetscErrorCode MatMultTranspose_SeqBSTRM_4(Mat A,Vec xx,Vec zz)
{
Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
Mat_SeqBSTRM *sbstrm = (Mat_SeqBSTRM*)A->spptr;
PetscScalar zero = 0.0;
PetscScalar x1,x2,x3,x4;
PetscScalar *x, *xb, *z;
MatScalar *v1, *v2, *v3, *v4;
PetscErrorCode ierr;
PetscInt mbs =a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j;
PetscInt nonzerorow=0;
PetscInt slen;
PetscFunctionBegin;
ierr = VecSet(zz,zero);CHKERRQ(ierr);
ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
slen = 4*(ai[mbs]-ai[0]);
v1 = sbstrm->as;
v2 = v1 + slen;
v3 = v2 + slen;
v4 = v3 + slen;
xb = x;
for (i=0; i<mbs; i++) {
n = ai[i+1] - ai[i];
x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; xb += 4;
nonzerorow += (n>0);
ib = aj + ai[i];
for (j=0; j<n; j++) {
cval = ib[j]*4;
z[cval] += v1[0]*x1 + v2[0]*x2 + v3[0]*x3 + v4[0]*x4;
z[cval+1] += v1[1]*x1 + v2[1]*x2 + v3[1]*x3 + v4[1]*x4;
z[cval+2] += v1[2]*x1 + v2[2]*x2 + v3[2]*x3 + v4[2]*x4;
z[cval+3] += v1[3]*x1 + v2[3]*x2 + v3[3]*x3 + v4[3]*x4;
v1 += 4; v2 += 4; v3 += 4; v4 += 4;
}
}
ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
ierr = PetscLogFlops(32*a->nz - 4*nonzerorow);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* FormJacobianLocal - Evaluates Jacobian matrix on local process patch */
PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat A,Mat jac, MatStructure *str,ObsCtx *user)
{
PetscErrorCode ierr;
PetscInt i,j;
MatStencil col[5],row;
PetscReal v[5],dx,dy,oxx,oyy;
PetscFunctionBeginUser;
dx = 4.0 / (PetscReal)(info->mx-1);
dy = 4.0 / (PetscReal)(info->my-1);
oxx = 1.0 / (dx * dx);
oyy = 1.0 / (dy * dy);
for (j=info->ys; j<info->ys+info->ym; j++) {
for (i=info->xs; i<info->xs+info->xm; i++) {
row.j = j; row.i = i;
if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) { /* boundary */
v[0] = 1.0;
ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
} else { /* interior grid points */
v[0] = -oyy; col[0].j = j - 1; col[0].i = i;
v[1] = -oxx; col[1].j = j; col[1].i = i - 1;
v[2] = 2.0 * (oxx + oyy); col[2].j = j; col[2].i = i;
v[3] = -oxx; col[3].j = j; col[3].i = i + 1;
v[4] = -oyy; col[4].j = j + 1; col[4].i = i;
ierr = MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
/* Assemble matrix, using the 2-step process: */
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (A != jac) {
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
*str = SAME_NONZERO_PATTERN;
/* Tell the matrix we will never add a new nonzero location to the
matrix. If we do, it will generate an error. */
ierr = MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
ierr = PetscLogFlops(2.0*info->ym*info->xm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FluidFieldDivergence_3D( DALocalInfo info,
Coor d, Vec US, Vec VS, Vec WS, Vec DIV )
{
int i,j,k;
PetscReal xe, xs, ye, ys, ze, zs;
PetscReal ***u, ***v, ***w, ***div;
PetscErrorCode ierr;
PetscFunctionBegin;
xs = info.xs;
xs = xs == 0 ? 2 : xs;
xe = info.xs+info.xm;
xe = xe == info.mx ? info.mx-3 : xe;
ys = info.ys;
ys = ys == 0 ? 2 : ys;
ye = info.ys+info.ym;
ye = ye == info.my ? info.my-3 : ye;
zs = info.zs;
zs = zs == 0 ? 2 : zs;
ze = info.zs+info.zm;
ze = ze == info.mz ? info.mz-3 : ze;
ierr = DAVecGetArray(info.da,US,&u); CHKERRQ(ierr);
ierr = DAVecGetArray(info.da,VS,&v); CHKERRQ(ierr);
ierr = DAVecGetArray(info.da,WS,&w); CHKERRQ(ierr);
ierr = DAVecGetArray(info.da,DIV,&div); CHKERRQ(ierr);
for( k = zs; k < ze; ++k)
{
for (j = ys; j < ye; ++j)
{
for (i = xs; i < xe; ++i)
{
div[k][j][i] = (u[k][j][i+1] - u[k][j][i]) / d.x +
(v[k][j+1][i] - v[k][j][i]) / d.y +
(w[k+1][j][i] - w[k][j][i]) / d.z;
}
}
}
ierr = DAVecRestoreArray(info.da,US,&u); CHKERRQ(ierr);
ierr = DAVecRestoreArray(info.da,VS,&v); CHKERRQ(ierr);
ierr = DAVecRestoreArray(info.da,WS,&w); CHKERRQ(ierr);
ierr = DAVecRestoreArray(info.da,DIV,&div); CHKERRQ(ierr);
PetscLogFlops(8*(xe-xs)*(ye-ys)*(ze-zs));
PetscFunctionReturn(0);
}
PetscErrorCode MatSolve_SeqBAIJ_1_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
PetscErrorCode ierr;
const PetscInt n = a->mbs,*ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
PetscScalar *x,sum;
const PetscScalar *b;
const MatScalar *aa = a->a,*v;
PetscInt i,nz;
PetscFunctionBegin;
if (!n) PetscFunctionReturn(0);
ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
/* forward solve the lower triangular */
x[0] = b[0];
v = aa;
vi = aj;
for (i=1; i<n; i++) {
nz = ai[i+1] - ai[i];
sum = b[i];
PetscSparseDenseMinusDot(sum,x,v,vi,nz);
v += nz;
vi += nz;
x[i] = sum;
}
/* backward solve the upper triangular */
for (i=n-1; i>=0; i--) {
v = aa + adiag[i+1] + 1;
vi = aj + adiag[i+1] + 1;
nz = adiag[i] - adiag[i+1]-1;
sum = x[i];
PetscSparseDenseMinusDot(sum,x,v,vi,nz);
x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
}
ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
PetscFunctionReturn(0);
}