PetscErrorCode TestSetup(DMLabel label, AppCtx *user)
{
PetscRandom r;
PetscInt n = (PetscInt) (user->fill*(user->pEnd - user->pStart)), i;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = PetscRandomCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(r);CHKERRQ(ierr);/* -random_type <> */
ierr = PetscRandomSetInterval(r, user->pStart, user->pEnd);CHKERRQ(ierr);
ierr = PetscRandomSetSeed(r, 123456789L);CHKERRQ(ierr);
ierr = PetscRandomSeed(r);CHKERRQ(ierr);
user->size = 0;
for(i = 0; i < n; ++i) {
PetscReal p;
PetscInt val;
ierr = PetscRandomGetValueReal(r, &p);CHKERRQ(ierr);
ierr = DMLabelGetValue(label, (PetscInt) p, &val);CHKERRQ(ierr);
if (val < 0) {
++user->size;
ierr = DMLabelSetValue(label, (PetscInt) p, i % user->numStrata);CHKERRQ(ierr);
}
}
ierr = PetscRandomDestroy(&r);CHKERRQ(ierr);
ierr = DMLabelCreateIndex(label, user->pStart, user->pEnd);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, "Created label with chart [%D, %D) and set %D values\n", user->pStart, user->pEnd, user->size);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
PetscInt i,n = 1000,*values;
PetscRandom rnd;
PetscScalar value,avg = 0.0;
PetscErrorCode ierr;
PetscMPIInt rank;
PetscInt view_rank=-1;
#if defined(PETSC_USE_LOG)
PetscLogEvent event;
#endif
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-view_randomvalues",&view_rank,NULL);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rnd);CHKERRQ(ierr);
/* force imaginary part of random number to always be zero; thus obtain reproducible results with real and complex numbers */
ierr = PetscRandomSetInterval(rnd,0.0,1.0);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rnd);CHKERRQ(ierr);
ierr = PetscMalloc1(n,&values);CHKERRQ(ierr);
for (i=0; i<n; i++) {
ierr = PetscRandomGetValue(rnd,&value);CHKERRQ(ierr);
avg += value;
if (view_rank == (PetscInt)rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] value[%D] = %6.4e\n",rank,i,(double)PetscRealPart(value));CHKERRQ(ierr);
}
values[i] = (PetscInt)(n*PetscRealPart(value) + 2.0);
}
avg = avg/((PetscReal)n);
if (view_rank == (PetscInt)rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] Average value %6.4e\n",rank,(double)PetscRealPart(avg));CHKERRQ(ierr);
}
ierr = PetscSortInt(n,values);CHKERRQ(ierr);
ierr = PetscLogEventRegister("Sort",0,&event);CHKERRQ(ierr);
ierr = PetscLogEventBegin(event,0,0,0,0);CHKERRQ(ierr);
ierr = PetscRandomSeed(rnd);CHKERRQ(ierr);
for (i=0; i<n; i++) {
ierr = PetscRandomGetValue(rnd,&value);CHKERRQ(ierr);
values[i] = (PetscInt)(n*PetscRealPart(value) + 2.0);
/* printf("value[%d] = %g\n",i,value); */
}
ierr = PetscSortInt(n,values);CHKERRQ(ierr);
ierr = PetscLogEventEnd(event,0,0,0,0);CHKERRQ(ierr);
for (i=1; i<n; i++) {
if (values[i] < values[i-1]) SETERRQ(PETSC_COMM_SELF,1,"Values not sorted");
}
ierr = PetscFree(values);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rnd);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
PetscErrorCode PCSetup_Noise(PC pc)
{
PetscErrorCode ierr;
PCNoise_Ctx *ctx;
PetscFunctionBeginUser;
ierr = PCShellGetContext(pc,(void**)&ctx);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&ctx->random);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(ctx->random,-1.0,1.0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@
PetscRandomSetFromOptions - Configures the random number generator from the options database.
Collective on PetscRandom
Input Parameter:
. rnd - The random number generator context
Options Database:
+ -random_seed <integer> - provide a seed to the random number generater
- -random_no_imaginary_part - makes the imaginary part of the random number zero, this is useful when you want the
same code to produce the same result when run with real numbers or complex numbers for regression testing purposes
Notes: To see all options, run your program with the -help option.
Must be called after PetscRandomCreate() but before the rnd is used.
Level: beginner
.keywords: PetscRandom, set, options, database
.seealso: PetscRandomCreate(), PetscRandomSetType()
@*/
PetscErrorCode PetscRandomSetFromOptions(PetscRandom rnd)
{
PetscErrorCode ierr;
PetscBool set,noimaginary = PETSC_FALSE;
PetscInt seed;
PetscFunctionBegin;
PetscValidHeaderSpecific(rnd,PETSC_RANDOM_CLASSID,1);
ierr = PetscObjectOptionsBegin((PetscObject)rnd);
CHKERRQ(ierr);
/* Handle PetscRandom type options */
ierr = PetscRandomSetTypeFromOptions_Private(PetscOptionsObject,rnd);
CHKERRQ(ierr);
/* Handle specific random generator's options */
if (rnd->ops->setfromoptions) {
ierr = (*rnd->ops->setfromoptions)(PetscOptionsObject,rnd);
CHKERRQ(ierr);
}
ierr = PetscOptionsInt("-random_seed","Seed to use to generate random numbers","PetscRandomSetSeed",0,&seed,&set);
CHKERRQ(ierr);
if (set) {
ierr = PetscRandomSetSeed(rnd,(unsigned long int)seed);
CHKERRQ(ierr);
ierr = PetscRandomSeed(rnd);
CHKERRQ(ierr);
}
ierr = PetscOptionsBool("-random_no_imaginary_part","The imaginary part of the random number will be zero","PetscRandomSetInterval",noimaginary,&noimaginary,&set);
CHKERRQ(ierr);
#if defined(PETSC_HAVE_COMPLEX)
if (set) {
if (noimaginary) {
PetscScalar low,high;
ierr = PetscRandomGetInterval(rnd,&low,&high);
CHKERRQ(ierr);
low = low - PetscImaginaryPart(low);
high = high - PetscImaginaryPart(high);
ierr = PetscRandomSetInterval(rnd,low,high);
CHKERRQ(ierr);
}
}
#endif
ierr = PetscOptionsEnd();
CHKERRQ(ierr);
ierr = PetscRandomViewFromOptions(rnd,NULL, "-random_view");
CHKERRQ(ierr);
PetscFunctionReturn(0);
}
void PetscVector::randomize( double alpha, double beta, double * /* ix */ )
{
int ierr;
PetscRandom rctx;
ierr = PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT,&rctx);
assert(ierr == 0);
ierr = PetscRandomSetInterval(rctx, alpha, beta );
assert(ierr == 0);
ierr = VecSetRandom(pv, rctx);
assert(ierr == 0);
ierr = PetscRandomDestroy(rctx);
assert(ierr == 0);
}
PetscErrorCode FormInitialState(Vec X, AppCtx* user)
{
PetscErrorCode ierr;
PetscRandom R;
PetscFunctionBegin;
ierr = PetscRandomCreate(PETSC_COMM_WORLD, &R);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(R);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(R, 0., 10.);CHKERRQ(ierr);
/*
* Initialize the state vector
*/
ierr = VecSetRandom(X, R);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&R);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FormTestMatrix(Mat A,PetscInt n,TestType type)
{
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(((PetscObject)A)->comm,1,"FormTestMatrix: These problems require complex numbers.");
#else
PetscScalar val[5];
PetscErrorCode ierr;
PetscInt i,j,Ii,J,col[5],Istart,Iend;
ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
if (type == TEST_1) {
val[0] = 1.0; val[1] = 4.0; val[2] = -2.0;
for (i=1; i<n-1; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);CHKERRQ(ierr);
}
i = n-1; col[0] = n-2; col[1] = n-1;
ierr = MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);CHKERRQ(ierr);
i = 0; col[0] = 0; col[1] = 1; val[0] = 4.0; val[1] = -2.0;
ierr = MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);CHKERRQ(ierr);
}
else if (type == TEST_2) {
val[0] = 1.0; val[1] = 0.0; val[2] = 2.0; val[3] = 1.0;
for (i=2; i<n-1; i++) {
col[0] = i-2; col[1] = i-1; col[2] = i; col[3] = i+1;
ierr = MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);CHKERRQ(ierr);
}
i = n-1; col[0] = n-3; col[1] = n-2; col[2] = n-1;
ierr = MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);CHKERRQ(ierr);
i = 1; col[0] = 0; col[1] = 1; col[2] = 2;
ierr = MatSetValues(A,1,&i,3,col,&val[1],INSERT_VALUES);CHKERRQ(ierr);
i = 0;
ierr = MatSetValues(A,1,&i,2,col,&val[2],INSERT_VALUES);CHKERRQ(ierr);
}
else if (type == TEST_3) {
val[0] = PETSC_i * 2.0;
val[1] = 4.0; val[2] = 0.0; val[3] = 1.0; val[4] = 0.7;
for (i=1; i<n-3; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1; col[3] = i+2; col[4] = i+3;
ierr = MatSetValues(A,1,&i,5,col,val,INSERT_VALUES);CHKERRQ(ierr);
}
i = n-3; col[0] = n-4; col[1] = n-3; col[2] = n-2; col[3] = n-1;
ierr = MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);CHKERRQ(ierr);
i = n-2; col[0] = n-3; col[1] = n-2; col[2] = n-1;
ierr = MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);CHKERRQ(ierr);
i = n-1; col[0] = n-2; col[1] = n-1;
ierr = MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);CHKERRQ(ierr);
i = 0; col[0] = 0; col[1] = 1; col[2] = 2; col[3] = 3;
ierr = MatSetValues(A,1,&i,4,col,&val[1],INSERT_VALUES);CHKERRQ(ierr);
}
else if (type == HELMHOLTZ_1) {
/* Problem domain: unit square: (0,1) x (0,1)
Solve Helmholtz equation:
-delta u - sigma1*u + i*sigma2*u = f,
where delta = Laplace operator
Dirichlet b.c.'s on all sides
*/
PetscRandom rctx;
PetscReal h2,sigma1 = 5.0;
PetscScalar sigma2;
ierr = PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
h2 = 1.0/((n+1)*(n+1));
for (Ii=Istart; Ii<Iend; Ii++) {
*val = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr);
*val = 4.0 - sigma1*h2 + sigma2*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);CHKERRQ(ierr);
}
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
}
else if (type == HELMHOLTZ_2) {
/* Problem domain: unit square: (0,1) x (0,1)
Solve Helmholtz equation:
-delta u - sigma1*u = f,
where delta = Laplace operator
Dirichlet b.c.'s on 3 sides
du/dn = i*alpha*u on (1,y), 0<y<1
*/
PetscReal h2,sigma1 = 200.0;
PetscScalar alpha_h;
ierr = PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);CHKERRQ(ierr);
h2 = 1.0/((n+1)*(n+1));
alpha_h = (PETSC_i * 10.0) / (PetscReal)(n+1); /* alpha_h = alpha * h */
for (Ii=Istart; Ii<Iend; Ii++) {
*val = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);CHKERRQ(ierr);}
*val = 4.0 - sigma1*h2;
if (!((Ii+1)%n)) *val += alpha_h;
ierr = MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);CHKERRQ(ierr);
}
}
else SETERRQ(((PetscObject)A)->comm,1,"FormTestMatrix: unknown test matrix type");
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
#endif
return 0;
}
int main(int argc,char **args)
{
Vec x,b,u; /* approx solution, RHS, exact solution */
Mat A; /* linear system matrix */
KSP ksp; /* linear solver context */
PetscReal norm; /* norm of solution error */
PetscInt dim,i,j,Ii,J,Istart,Iend,n = 6,its,use_random;
PetscErrorCode ierr;
PetscScalar v,none = -1.0,sigma2,pfive = 0.5,*xa;
PetscRandom rctx;
PetscReal h2,sigma1 = 100.0;
PetscBool flg = PETSC_FALSE;
PetscScalar a = 1.0+PETSC_i;
PetscInitialize(&argc,&args,(char*)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,1,"This example requires complex numbers");
#endif
a=1.0+PETSC_i;
printf("%g+%gi\n",(double)PetscRealPart(a),(double)PetscImaginaryPart(a));
ierr = PetscOptionsGetReal(NULL,"-sigma1",&sigma1,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
dim = n*n;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrix and right-hand-side vector that define
the linear system, Ax = b.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create parallel matrix, specifying only its global dimensions.
When using MatCreate(), the matrix format can be specified at
runtime. Also, the parallel partitioning of the matrix is
determined by PETSc at runtime.
*/
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
/*
Currently, all PETSc parallel matrix formats are partitioned by
contiguous chunks of rows across the processors. Determine which
rows of the matrix are locally owned.
*/
ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
/*
Set matrix elements in parallel.
- Each processor needs to insert only elements that it owns
locally (but any non-local elements will be sent to the
appropriate processor during matrix assembly).
- Always specify global rows and columns of matrix entries.
*/
ierr = PetscOptionsGetBool(NULL,"-norandom",&flg,NULL);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
for (Ii=Istart; Ii<Iend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (use_random) {ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2 + sigma2*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd()
Computations can be done while messages are in transition
by placing code between these two statements.
*/
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/*
Create parallel vectors.
- When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
we specify only the vector's global
dimension; the parallel partitioning is determined at runtime.
- Note: We form 1 vector from scratch and then duplicate as needed.
*/
ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
ierr = VecSetSizes(u,PETSC_DECIDE,dim);CHKERRQ(ierr);
ierr = VecSetFromOptions(u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecDuplicate(b,&x);CHKERRQ(ierr);
/*
Set exact solution; then compute right-hand-side vector.
*/
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecSetRandom(u,rctx);CHKERRQ(ierr);
} else {
ierr = VecSet(u,pfive);CHKERRQ(ierr);
}
ierr = MatMult(A,u,b);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the linear solver and set various options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create linear solver context
*/
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
/*
Set operators. Here the matrix that defines the linear system
also serves as the preconditioning matrix.
*/
ierr = KSPSetOperators(ksp,A,A);CHKERRQ(ierr);
/*
Set runtime options, e.g.,
-ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
*/
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the linear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Check solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Print the first 3 entries of x; this demonstrates extraction of the
real and imaginary components of the complex vector, x.
*/
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-print_x3",&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = VecGetArray(x,&xa);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"The first three entries of x are:\n");CHKERRQ(ierr);
for (i=0; i<3; i++) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"x[%D] = %g + %g i\n",i,(double)PetscRealPart(xa[i]),(double)PetscImaginaryPart(xa[i]));CHKERRQ(ierr);
}
ierr = VecRestoreArray(x,&xa);CHKERRQ(ierr);
}
/*
Check the error
*/
ierr = VecAXPY(x,none,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);CHKERRQ(ierr);
/*
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
*/
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
ierr = VecDestroy(&u);CHKERRQ(ierr); ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr); ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc, char** args){
PetscErrorCode err;
PetscViewer fd = NULL;
Mat invL1 = NULL, invU1 = NULL, invL2 = NULL, invU2 = NULL, H12 = NULL, H21 = NULL;
Vec order = NULL, r = NULL; //, or = NULL; //dimension: n: n1 + n2
Vec seeds = NULL;
// Vec r1 = NULL, q1 = NULL, t1_1 = NULL, t1_2 = NULL, t1_3 = NULL, t1_4 = NULL, t1_5 = NULL; // dimension: n1
// Vec r2 = NULL, q2 = NULL, q_tilda = NULL, t2_1 = NULL, t2_2 = NULL, t2_3 = NULL; // dimension: n2
PetscRandom rand;
PetscLogDouble tic, toc, total_time, time;
PetscInt n, i;
PetscMPIInt rank, size;
PetscInt seed;
PetscScalar c, val;
PetscInt QN = 100;
// Initialize PETSC and MPI
err = PetscInitialize(&argc, &args, (char*) 0, help); CHKERRQ(err);
err = MPI_Comm_size(PETSC_COMM_WORLD, &size); CHKERRQ(err);
err = MPI_Comm_rank(PETSC_COMM_WORLD, &rank); CHKERRQ(err);
err = PetscPrintf(PETSC_COMM_WORLD, "mpi size: %d\n", size); CHKERRQ(err);
// Read matrices and an ordering vector
err = PetscPrintf(PETSC_COMM_WORLD, "Read inputs (invL1, invU1, invL2, invU2, H12, H21, order)\n"); CHKERRQ(err);
err = loadMat("./data/invL1.dat", &invL1, PETSC_COMM_WORLD, MATMPIAIJ, &fd); CHKERRQ(err);
err = checkMat("invL1", invL1); CHKERRQ(err);
err = loadMat("./data/invU1.dat", &invU1, PETSC_COMM_WORLD, MATMPIAIJ, &fd); CHKERRQ(err);
err = checkMat("invU1", invU1); CHKERRQ(err);
err = loadMat("./data/invL2.dat", &invL2, PETSC_COMM_WORLD, MATMPIAIJ, &fd); CHKERRQ(err);
err = checkMat("invL2", invL2); CHKERRQ(err);
err = loadMat("./data/invU2.dat", &invU2, PETSC_COMM_WORLD, MATMPIAIJ, &fd); CHKERRQ(err);
err = checkMat("invU2", invU2); CHKERRQ(err);
err = loadMat("./data/H12.dat", &H12, PETSC_COMM_WORLD, MATMPIAIJ, &fd); CHKERRQ(err);
err = checkMat("H12", H12); CHKERRQ(err);
err = loadMat("./data/H21.dat", &H21, PETSC_COMM_WORLD, MATMPIAIJ, &fd); CHKERRQ(err);
err = checkMat("H21", H21); CHKERRQ(err);
err = loadVec("./data/order.dat", &order, PETSC_COMM_SELF, &fd); CHKERRQ(err); //all processes must have this vector for ordering the result vector.
err = checkVec("order", order); CHKERRQ(err);
// shift -1 for zero-based index
err = VecShift(order, -1); CHKERRQ(err);
err = VecGetSize(order, &n); CHKERRQ(err);
seed = 5;
c = 0.05;
err = PetscTime(&tic); CHKERRQ(err);
//err = BearQueryMat(seed, c, invL1, invU1, invL2, invU2, H12, H21, order); CHKERRQ(err);
//err = PetscTime(&toc); CHKERRQ(err);
//time = toc - tic;
//err = PetscPrintf(PETSC_COMM_WORLD, "running time: %f sec\n", time); CHKERRQ(err);
///* 100 times querying
err = VecCreateSeq(PETSC_COMM_SELF, QN, &seeds); CHKERRQ(err);
err = VecSetFromOptions(seeds); CHKERRQ(err);
err = PetscRandomCreate(PETSC_COMM_WORLD, &rand); CHKERRQ(err);
err = PetscRandomSetSeed(rand, 100); CHKERRQ(err);
err = PetscRandomSetInterval(rand, (PetscScalar) 0, (PetscScalar) n); CHKERRQ(err);
err = PetscRandomSetFromOptions(rand); CHKERRQ(err);
err = VecSetRandom(seeds, rand); CHKERRQ(err);
err = PetscRandomDestroy(&rand); CHKERRQ(err);
seed = 5; //seed is give by user on one-based index
c = 0.05;
i = 0;
err = VecDuplicate(order, &r); CHKERRQ(err);
for(i = 0; i < QN; i++){
err = VecGetValues(seeds, 1, &i, &val);
seed = (PetscInt) val;
//err = PetscPrintf(PETSC_COMM_SELF, "rank: %d, seed: %d\n", rank, seed);
err = PetscTime(&tic); CHKERRQ(err);
err = BearQuery(seed, c, invL1, invU1, invL2, invU2, H12, H21, order, r); CHKERRQ(err);
err = PetscTime(&toc); CHKERRQ(err);
time = toc - tic;
err = PetscPrintf(PETSC_COMM_WORLD, "running time: %f sec\n", time); CHKERRQ(err);
total_time += time;
}
err = PetscPrintf(PETSC_COMM_WORLD, "average running time: %f sec\n", total_time/QN); CHKERRQ(err);
err = VecDestroy(&r);
/* err = MatGetSize(H12, &n1, &n2); CHKERRQ(err);
n = n1 + n2;
err = PetscPrintf(PETSC_COMM_WORLD, "n1: %d, n2: %d\n", n1, n2); CHKERRQ(err);
err = VecCreateMPI(PETSC_COMM_WORLD, PETSC_DECIDE, n, &r); CHKERRQ(err);
err = VecCreateMPI(PETSC_COMM_WORLD, PETSC_DECIDE, n1, &q1); CHKERRQ(err);
err = VecCreateMPI(PETSC_COMM_WORLD, PETSC_DECIDE, n2, &q2); CHKERRQ(err);
err = VecSet(q1, 0); CHKERRQ(err);
err = VecSet(q2, 0); CHKERRQ(err);
seed = seed - 1; // shift -1 for zero-based index
err = VecGetValues(order, 1, &seed, &val); CHKERRQ(err);
oseed = (PetscInt) val;
err = PetscPrintf(PETSC_COMM_WORLD, "Given seed: %d, Reorered seed: %d (0 ~ n-1)\n", seed, oseed); CHKERRQ(err);
if(oseed < n1){
err = VecSetValues(q1, 1, &oseed, &one, INSERT_VALUES); CHKERRQ(err);
}else{
oseed = oseed - n1;
err = VecSetValues(q2, 1, &oseed, &one, INSERT_VALUES); CHKERRQ(err);
//err = printVecSum(q2);
}
err = VecAssemblyBegin(q1); CHKERRQ(err);
err = VecAssemblyBegin(q2); CHKERRQ(err);
err = VecAssemblyEnd(q1); CHKERRQ(err);
err = VecAssemblyEnd(q2); CHKERRQ(err);
err = VecDuplicate(q1, &r1); CHKERRQ(err);
err = VecDuplicate(q1, &t1_1); CHKERRQ(err);
err = VecDuplicate(q1, &t1_2); CHKERRQ(err);
err = VecDuplicate(q1, &t1_3); CHKERRQ(err);
err = VecDuplicate(q1, &t1_4); CHKERRQ(err);
err = VecDuplicate(q1, &t1_5); CHKERRQ(err);
err = VecDuplicate(q2, &r2); CHKERRQ(err);
err = VecDuplicate(q2, &q_tilda); CHKERRQ(err);
err = VecDuplicate(q2, &t2_1); CHKERRQ(err);
err = VecDuplicate(q2, &t2_2); CHKERRQ(err);
err = VecDuplicate(q2, &t2_3); CHKERRQ(err);
// Start matrix-vec multiplications
err = MatMult(invL1, q1, t1_1); CHKERRQ(err);
err = MatMult(invU1, t1_1, t1_2); CHKERRQ(err);
err = MatMult(H21, t1_2, t2_1); CHKERRQ(err);
err = VecAXPBYPCZ(q_tilda, 1.0, -1.0, 0.0, q2, t2_1); CHKERRQ(err);
err = MatMult(invL2, q_tilda, t2_2); CHKERRQ(err);
err = MatMult(invU2, t2_2, r2); CHKERRQ(err);
err = MatMult(H12, r2, t1_3); CHKERRQ(err);
err = VecAXPBYPCZ(t1_4, 1.0, -1.0, 0.0, q1, t1_3); CHKERRQ(err);
err = MatMult(invL1, t1_4, t1_5); CHKERRQ(err);
err = MatMult(invU1, t1_5, r1); CHKERRQ(err);
//err = printVecSum(r1);
//err = VecView(r2, PETSC_VIEWER_STDOUT_WORLD);
// Concatenate r1 and r2
err = VecMerge(r1, r2, r); CHKERRQ(err);
err = VecScale(r, c); CHKERRQ(err);
//err = VecView(r, PETSC_VIEWER_STDOUT_WORLD);
err = VecDuplicate(r, &or); CHKERRQ(err);
err = VecReorder(r, order, or); CHKERRQ(err);
//err = VecView(or, PETSC_VIEWER_STDOUT_WORLD);*/
// Destory matrices and vectors
err = MatDestroy(&invL1); CHKERRQ(err);
err = MatDestroy(&invU1); CHKERRQ(err);
err = MatDestroy(&invL2); CHKERRQ(err);
err = MatDestroy(&invU2); CHKERRQ(err);
err = MatDestroy(&H12); CHKERRQ(err);
err = MatDestroy(&H21); CHKERRQ(err);
err = VecDestroy(&order); CHKERRQ(err);
err = VecDestroy(&r); CHKERRQ(err);
err = VecDestroy(&seeds); CHKERRQ(err);
//err = VecDestroy(&or); CHKERRQ(err);
/* err = VecDestroy(&r1); CHKERRQ(err);
err = VecDestroy(&q1); CHKERRQ(err);
err = VecDestroy(&t1_1); CHKERRQ(err);
err = VecDestroy(&t1_2); CHKERRQ(err);
err = VecDestroy(&t1_3); CHKERRQ(err);
err = VecDestroy(&t1_4); CHKERRQ(err);
err = VecDestroy(&t1_5); CHKERRQ(err);
err = VecDestroy(&r2); CHKERRQ(err);
err = VecDestroy(&q2); CHKERRQ(err);
err = VecDestroy(&q_tilda); CHKERRQ(err);
err = VecDestroy(&t2_1); CHKERRQ(err);
err = VecDestroy(&t2_2); CHKERRQ(err);
err = VecDestroy(&t2_3); CHKERRQ(err);*/
// Finalize
err = PetscFinalize(); CHKERRQ(err);
return 0;
}
PetscInt main(PetscInt argc,char **args)
{
Mat A,As;
Vec x,y,ys;
PetscTruth flg,disp_mat=PETSC_FALSE,disp_vec=PETSC_FALSE;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscInt m,i,j;
PetscScalar v,sigma2;
PetscRandom rctx;
PetscReal h2,sigma1=100.0,norm;
PetscInt dim,Ii,J,n = 3,use_random,rstart,rend;
PetscInitialize(&argc,&args,(char *)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(1,"This example requires complex numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-display_mat", &disp_mat);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-display_vec", &disp_vec);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
dim = n*n;
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetType(A,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL,"-norandom",&flg);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr); /* RealPart(sigma2) == 0.0 */
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
for (Ii=rstart; Ii<rend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is symmetric */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_symmetric", &flg);CHKERRQ(ierr);
if (flg) {
Mat Trans;
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
ierr = MatEqual(A, Trans, &flg);
if (!flg) SETERRQ(PETSC_ERR_USER,"A is not symmetric");
ierr = MatDestroy(Trans);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
/* make A complex Hermitian */
Ii = 0; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
Ii = dim-2; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is Hermitian */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_Hermitian", &flg);CHKERRQ(ierr);
if (flg) {
Mat Hermit;
if (disp_mat){
if (!rank) printf(" A:\n");
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatHermitianTranspose(A,MAT_INITIAL_MATRIX, &Hermit);
if (disp_mat){
if (!rank) printf(" A_Hermitian:\n");
ierr = MatView(Hermit,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatEqual(A, Hermit, &flg);
if (!flg) SETERRQ(PETSC_ERR_USER,"A is not Hermitian");
ierr = MatDestroy(Hermit);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
/* Create a Hermitian matrix As in sbaij format */
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&As);CHKERRQ(ierr);
if (disp_mat){
if (!rank) {ierr = PetscPrintf(PETSC_COMM_SELF," As:\n");CHKERRQ(ierr);}
ierr = MatView(As,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,n,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
if (use_random){
ierr = VecSetRandom(x,rctx);CHKERRQ(ierr);
} else {
ierr = VecSet(x,1.0);CHKERRQ(ierr);
}
/* Create vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&y);CHKERRQ(ierr);
ierr = VecSetSizes(y,m,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(y);CHKERRQ(ierr);
ierr = VecDuplicate(y,&ys);CHKERRQ(ierr);
/* Test MatMult */
ierr = MatMult(A,x,y);CHKERRQ(ierr);
ierr = MatMult(As,x,ys);CHKERRQ(ierr);
if (disp_vec){
printf("y = A*x:\n");
ierr = VecView(y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"ys = As*x:\n");
ierr = VecView(ys,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = VecAXPY(y,-1.0,ys);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_INFINITY,&norm);CHKERRQ(ierr);
if (norm > 1.e-12 || disp_vec){
printf("|| A*x - As*x || = %G\n",norm);
}
/* Free spaces */
if (use_random) {ierr = PetscRandomDestroy(rctx);CHKERRQ(ierr);}
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = MatDestroy(As);CHKERRQ(ierr);
ierr = VecDestroy(x);CHKERRQ(ierr);
ierr = VecDestroy(y);CHKERRQ(ierr);
ierr = VecDestroy(ys);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
PetscErrorCode TestTriangle(MPI_Comm comm, PetscBool interpolate, PetscBool transform)
{
DM dm;
PetscRandom r, ang, ang2;
PetscInt dim, t;
PetscErrorCode ierr;
PetscFunctionBegin;
/* Create reference triangle */
dim = 2;
ierr = DMCreate(comm, &dm);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) dm, "triangle");CHKERRQ(ierr);
ierr = DMSetType(dm, DMPLEX);CHKERRQ(ierr);
ierr = DMPlexSetDimension(dm, dim);CHKERRQ(ierr);
{
PetscInt numPoints[2] = {3, 1};
PetscInt coneSize[4] = {3, 0, 0, 0};
PetscInt cones[3] = {1, 2, 3};
PetscInt coneOrientations[3] = {0, 0, 0};
PetscScalar vertexCoords[6] = {-1.0, -1.0, 1.0, -1.0, -1.0, 1.0};
ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
if (interpolate) {
DM idm;
ierr = DMPlexInterpolate(dm, &idm);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) idm, "triangle");CHKERRQ(ierr);
ierr = DMPlexCopyCoordinates(dm, idm);CHKERRQ(ierr);
ierr = DMDestroy(&dm);CHKERRQ(ierr);
dm = idm;
}
ierr = DMSetFromOptions(dm);CHKERRQ(ierr);
}
/* Check reference geometry: determinant is scaled by reference volume (2.0) */
{
PetscReal v0Ex[2] = {-1.0, -1.0};
PetscReal JEx[4] = {1.0, 0.0, 0.0, 1.0};
PetscReal invJEx[4] = {1.0, 0.0, 0.0, 1.0};
PetscReal detJEx = 1.0;
PetscReal centroidEx[2] = {-0.333333333333, -0.333333333333};
PetscReal normalEx[2] = {0.0, 0.0};
PetscReal volEx = 2.0;
ierr = CheckFEMGeometry(dm, 0, dim, v0Ex, JEx, invJEx, detJEx);CHKERRQ(ierr);
if (interpolate) {ierr = CheckFVMGeometry(dm, 0, dim, centroidEx, normalEx, volEx);CHKERRQ(ierr);}
}
/* Check random triangles: rotate, scale, then translate */
if (transform) {
ierr = PetscRandomCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(r);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(r, 0.0, 10.0);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_SELF, &ang);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(ang);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(ang, 0.0, 2*PETSC_PI);CHKERRQ(ierr);
for (t = 0; t < 100; ++t) {
PetscScalar vertexCoords[6] = {-1.0, -1.0, 1.0, -1.0, -1.0, 1.0}, trans[2];
PetscReal v0Ex[2] = {-1.0, -1.0};
PetscReal JEx[4] = {1.0, 0.0, 0.0, 1.0}, R[4], rot[2], rotM[4];
PetscReal invJEx[4] = {1.0, 0.0, 0.0, 1.0};
PetscReal detJEx = 1.0, scale, phi;
PetscReal centroidEx[2] = {-0.333333333333, -0.333333333333};
PetscReal normalEx[2] = {0.0, 0.0};
PetscReal volEx = 2.0;
PetscInt d, e, f, p;
ierr = PetscRandomGetValueReal(r, &scale);CHKERRQ(ierr);
ierr = PetscRandomGetValueReal(ang, &phi);CHKERRQ(ierr);
R[0] = cos(phi); R[1] = -sin(phi);
R[2] = sin(phi); R[3] = cos(phi);
for (p = 0; p < 3; ++p) {
for (d = 0; d < dim; ++d) {
for (e = 0, rot[d] = 0.0; e < dim; ++e) {
rot[d] += R[d*dim+e] * vertexCoords[p*dim+e];
}
}
for (d = 0; d < dim; ++d) vertexCoords[p*dim+d] = rot[d];
}
for (d = 0; d < dim; ++d) {
for (e = 0, rot[d] = 0.0; e < dim; ++e) {
rot[d] += R[d*dim+e] * centroidEx[e];
}
}
for (d = 0; d < dim; ++d) centroidEx[d] = rot[d];
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
for (f = 0, rotM[d*dim+e] = 0.0; f < dim; ++f) {
rotM[d*dim+e] += R[d*dim+f] * JEx[f*dim+e];
}
}
}
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
JEx[d*dim+e] = rotM[d*dim+e];
}
}
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
for (f = 0, rotM[d*dim+e] = 0.0; f < dim; ++f) {
rotM[d*dim+e] += invJEx[d*dim+f] * R[e*dim+f];
}
}
}
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
invJEx[d*dim+e] = rotM[d*dim+e];
}
}
for (d = 0; d < dim; ++d) {
ierr = PetscRandomGetValueReal(r, &trans[d]);CHKERRQ(ierr);
for (p = 0; p < 3; ++p) {
vertexCoords[p*dim+d] *= scale;
vertexCoords[p*dim+d] += trans[d];
}
v0Ex[d] = vertexCoords[d];
for (e = 0; e < dim; ++e) {
JEx[d*dim+e] *= scale;
invJEx[d*dim+e] /= scale;
}
detJEx *= scale;
centroidEx[d] *= scale;
centroidEx[d] += trans[d];
volEx *= scale;
}
ierr = ChangeCoordinates(dm, dim, vertexCoords);CHKERRQ(ierr);
ierr = CheckFEMGeometry(dm, 0, dim, v0Ex, JEx, invJEx, detJEx);CHKERRQ(ierr);
if (interpolate) {ierr = CheckFVMGeometry(dm, 0, dim, centroidEx, normalEx, volEx);CHKERRQ(ierr);}
}
ierr = PetscRandomDestroy(&r);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&ang);CHKERRQ(ierr);
}
/* Move to 3D: Check reference geometry: determinant is scaled by reference volume (2.0) */
dim = 3;
{
PetscScalar vertexCoords[9] = {-1.0, -1.0, 0.0, 1.0, -1.0, 0.0, -1.0, 1.0, 0.0};
PetscReal v0Ex[3] = {-1.0, -1.0, 0.0};
PetscReal JEx[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
PetscReal invJEx[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
PetscReal detJEx = 1.0;
PetscReal centroidEx[3] = {-0.333333333333, -0.333333333333, 0.0};
PetscReal normalEx[3] = {0.0, 0.0, 1.0};
PetscReal volEx = 2.0;
ierr = ChangeCoordinates(dm, dim, vertexCoords);CHKERRQ(ierr);
ierr = CheckFEMGeometry(dm, 0, dim, v0Ex, JEx, invJEx, detJEx);CHKERRQ(ierr);
if (interpolate) {ierr = CheckFVMGeometry(dm, 0, dim, centroidEx, normalEx, volEx);CHKERRQ(ierr);}
}
/* Rotated reference element */
{
PetscScalar vertexCoords[9] = {0.0, -1.0, -1.0, 0.0, 1.0, -1.0, 0.0, -1.0, 1.0};
PetscReal v0Ex[3] = {0.0, -1.0, -1.0};
PetscReal JEx[9] = {0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0};
PetscReal invJEx[9] = {0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0};
PetscReal detJEx = 1.0;
PetscReal centroidEx[3] = {0.0, -0.333333333333, -0.333333333333};
PetscReal normalEx[3] = {1.0, 0.0, 0.0};
PetscReal volEx = 2.0;
ierr = ChangeCoordinates(dm, dim, vertexCoords);CHKERRQ(ierr);
ierr = CheckFEMGeometry(dm, 0, dim, v0Ex, JEx, invJEx, detJEx);CHKERRQ(ierr);
if (interpolate) {ierr = CheckFVMGeometry(dm, 0, dim, centroidEx, normalEx, volEx);CHKERRQ(ierr);}
}
/* Check random triangles: scale, translate, then rotate */
if (transform) {
ierr = PetscRandomCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(r);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(r, 0.0, 10.0);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_SELF, &ang);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(ang);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(ang, 0.0, 2*PETSC_PI);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_SELF, &ang2);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(ang2);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(ang2, 0.0, PETSC_PI);CHKERRQ(ierr);
for (t = 0; t < 100; ++t) {
PetscScalar vertexCoords[9] = {-1.0, -1.0, 0.0, 1.0, -1.0, 0.0, -1.0, 1.0, 0.0}, trans[3];
PetscReal v0Ex[3] = {-1.0, -1.0, 0.0};
PetscReal JEx[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0}, R[9], rot[3], rotM[9];
PetscReal invJEx[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
PetscReal detJEx = 1.0, scale, phi, theta, psi = 0.0;
PetscReal centroidEx[3] = {-0.333333333333, -0.333333333333, 0.0};
PetscReal normalEx[3] = {0.0, 0.0, 1.0};
PetscReal volEx = 2.0;
PetscInt d, e, f, p;
ierr = PetscRandomGetValueReal(r, &scale);CHKERRQ(ierr);
ierr = PetscRandomGetValueReal(ang, &phi);CHKERRQ(ierr);
ierr = PetscRandomGetValueReal(ang2, &theta);CHKERRQ(ierr);
for (d = 0; d < dim; ++d) {
ierr = PetscRandomGetValueReal(r, &trans[d]);CHKERRQ(ierr);
for (p = 0; p < 3; ++p) {
vertexCoords[p*dim+d] *= scale;
vertexCoords[p*dim+d] += trans[d];
}
centroidEx[d] *= scale;
centroidEx[d] += trans[d];
for (e = 0; e < dim-1; ++e) {
JEx[d*dim+e] *= scale;
invJEx[d*dim+e] /= scale;
}
if (d < dim-1) {
detJEx *= scale;
volEx *= scale;
}
}
R[0] = cos(theta)*cos(psi); R[1] = sin(phi)*sin(theta)*cos(psi) - cos(phi)*sin(psi); R[2] = sin(phi)*sin(psi) + cos(phi)*sin(theta)*cos(psi);
R[3] = cos(theta)*sin(psi); R[4] = cos(phi)*cos(psi) + sin(phi)*sin(theta)*sin(psi); R[5] = cos(phi)*sin(theta)*sin(psi) - sin(phi)*cos(psi);
R[6] = -sin(theta); R[7] = sin(phi)*cos(theta); R[8] = cos(phi)*cos(theta);
for (p = 0; p < 3; ++p) {
for (d = 0; d < dim; ++d) {
for (e = 0, rot[d] = 0.0; e < dim; ++e) {
rot[d] += R[d*dim+e] * vertexCoords[p*dim+e];
}
}
for (d = 0; d < dim; ++d) vertexCoords[p*dim+d] = rot[d];
}
for (d = 0; d < dim; ++d) {
for (e = 0, rot[d] = 0.0; e < dim; ++e) {
rot[d] += R[d*dim+e] * centroidEx[e];
}
}
for (d = 0; d < dim; ++d) centroidEx[d] = rot[d];
for (d = 0; d < dim; ++d) {
for (e = 0, rot[d] = 0.0; e < dim; ++e) {
rot[d] += R[d*dim+e] * normalEx[e];
}
}
for (d = 0; d < dim; ++d) normalEx[d] = rot[d];
for (d = 0; d < dim; ++d) {
v0Ex[d] = vertexCoords[d];
for (e = 0; e < dim; ++e) {
for (f = 0, rotM[d*dim+e] = 0.0; f < dim; ++f) {
rotM[d*dim+e] += R[d*dim+f] * JEx[f*dim+e];
}
}
}
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
JEx[d*dim+e] = rotM[d*dim+e];
}
}
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
for (f = 0, rotM[d*dim+e] = 0.0; f < dim; ++f) {
rotM[d*dim+e] += invJEx[d*dim+f] * R[e*dim+f];
}
}
}
for (d = 0; d < dim; ++d) {
for (e = 0; e < dim; ++e) {
invJEx[d*dim+e] = rotM[d*dim+e];
}
}
ierr = ChangeCoordinates(dm, dim, vertexCoords);CHKERRQ(ierr);
ierr = CheckFEMGeometry(dm, 0, dim, v0Ex, JEx, invJEx, detJEx);CHKERRQ(ierr);
if (interpolate) {ierr = CheckFVMGeometry(dm, 0, dim, centroidEx, normalEx, volEx);CHKERRQ(ierr);}
}
ierr = PetscRandomDestroy(&r);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&ang);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&ang2);CHKERRQ(ierr);
}
/* Cleanup */
ierr = DMDestroy(&dm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode ComputeMatrix(DM da,Mat B)
{
PetscErrorCode ierr;
PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,dof,k1,k2,k3;
PetscScalar *v,*v_neighbor,Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy,r1,r2;
MatStencil row,col;
PetscRandom rand;
PetscFunctionBegin;
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetType(rand,PETSCRAND);CHKERRQ(ierr);
ierr = PetscRandomSetSeed(rand,1);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rand,-.001,.001);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
/* For simplicity, this example only works on mx=my=mz */
if ( mx != my || mx != mz) SETERRQ3(PETSC_COMM_SELF,1,"This example only works with mx %d = my %d = mz %d\n",mx,my,mz);
Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
ierr = PetscMalloc((2*dof*dof+1)*sizeof(PetscScalar),&v);CHKERRQ(ierr);
v_neighbor = v + dof*dof;
ierr = PetscMemzero(v,(2*dof*dof+1)*sizeof(PetscScalar));CHKERRQ(ierr);
k3 = 0;
for (k1=0; k1<dof; k1++){
for (k2=0; k2<dof; k2++){
if (k1 == k2){
v[k3] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
v_neighbor[k3] = -HxHydHz;
} else {
ierr = PetscRandomGetValue(rand,&r1);CHKERRQ(ierr);
ierr = PetscRandomGetValue(rand,&r2);CHKERRQ(ierr);
v[k3] = r1;
v_neighbor[k3] = r2;
}
k3++;
}
}
ierr = DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);CHKERRQ(ierr);
for (k=zs; k<zs+zm; k++){
for (j=ys; j<ys+ym; j++){
for (i=xs; i<xs+xm; i++){
row.i = i; row.j = j; row.k = k;
if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1){ /* boudary points */
ierr = MatSetValuesBlockedStencil(B,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
} else { /* interior points */
/* center */
col.i = i; col.j = j; col.k = k;
ierr = MatSetValuesBlockedStencil(B,1,&row,1,&col,v,INSERT_VALUES);CHKERRQ(ierr);
/* x neighbors */
col.i = i-1; col.j = j; col.k = k;
ierr = MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);CHKERRQ(ierr);
col.i = i+1; col.j = j; col.k = k;
ierr = MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);CHKERRQ(ierr);
/* y neighbors */
col.i = i; col.j = j-1; col.k = k;
ierr = MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);CHKERRQ(ierr);
col.i = i; col.j = j+1; col.k = k;
ierr = MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);CHKERRQ(ierr);
/* z neighbors */
col.i = i; col.j = j; col.k = k-1;
ierr = MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);CHKERRQ(ierr);
col.i = i; col.j = j; col.k = k+1;
ierr = MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
}
ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscFree(v);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscInt main(PetscInt argc,char **args)
{
Mat A,As;
PetscBool flg,disp_mat=PETSC_FALSE;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscInt i,j;
PetscScalar v,sigma2;
PetscRandom rctx;
PetscReal h2,sigma1=100.0;
PetscInt dim,Ii,J,n = 3,use_random,rstart,rend;
KSP ksp;
PC pc;
Mat F;
PetscInt nneg, nzero, npos;
PetscInitialize(&argc,&args,(char *)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,1,"This example requires complex numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-display_mat", &disp_mat);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
dim = n*n;
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetType(A,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL,"-norandom",&flg);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr); /* RealPart(sigma2) == 0.0 */
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
for (Ii=rstart; Ii<rend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is symmetric */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_symmetric", &flg);CHKERRQ(ierr);
if (flg) {
Mat Trans;
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
ierr = MatEqual(A, Trans, &flg);
if (!flg) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"A is not symmetric");
ierr = MatDestroy(&Trans);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
/* make A complex Hermitian */
Ii = 0; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
Ii = dim-2; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is Hermitian */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_Hermitian", &flg);CHKERRQ(ierr);
if (flg) {
Mat Hermit;
if (disp_mat){
if (!rank) printf(" A:\n");
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatHermitianTranspose(A,MAT_INITIAL_MATRIX, &Hermit);
if (disp_mat){
if (!rank) printf(" A_Hermitian:\n");
ierr = MatView(Hermit,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatEqual(A, Hermit, &flg);
if (!flg) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"A is not Hermitian");
ierr = MatDestroy(&Hermit);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
/* Create a Hermitian matrix As in sbaij format */
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&As);CHKERRQ(ierr);
if (disp_mat){
if (!rank) {ierr = PetscPrintf(PETSC_COMM_SELF," As:\n");CHKERRQ(ierr);}
ierr = MatView(As,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Test MatGetInertia() */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetType(ksp,KSPPREONLY);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,As,As,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCCHOLESKY);CHKERRQ(ierr);
ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
ierr = PCSetUp(pc);CHKERRQ(ierr);
ierr = PCFactorGetMatrix(pc,&F);CHKERRQ(ierr);
ierr = MatGetInertia(F,&nneg,&nzero,&npos);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
if (!rank){
ierr = PetscPrintf(PETSC_COMM_SELF," MatInertia: nneg: %D, nzero: %D, npos: %D\n",nneg,nzero,npos);CHKERRQ(ierr);
}
/* Free spaces */
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&As);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscInt main(PetscInt argc,char **args)
{
Mat A,A_dense,B;
Vec *evecs;
PetscBool flg,TestZHEEV=PETSC_TRUE,TestZHEEVX=PETSC_FALSE,TestZHEGV=PETSC_FALSE,TestZHEGVX=PETSC_FALSE;
PetscErrorCode ierr;
PetscBool isSymmetric;
PetscScalar sigma,*arrayA,*arrayB,*evecs_array=NULL,*work;
PetscReal *evals,*rwork;
PetscMPIInt size;
PetscInt m,i,j,nevs,il,iu,cklvl=2;
PetscReal vl,vu,abstol=1.e-8;
PetscBLASInt *iwork,*ifail,lwork,lierr,bn;
PetscReal tols[2];
PetscInt nzeros[2],nz;
PetscReal ratio;
PetscScalar v,none = -1.0,sigma2,pfive = 0.5,*xa;
PetscRandom rctx;
PetscReal h2,sigma1 = 100.0;
PetscInt dim,Ii,J,Istart,Iend,n = 6,its,use_random,one=1;
PetscInitialize(&argc,&args,(char*)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,1,"This example requires complex numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
ierr = PetscOptionsHasName(NULL, "-test_zheevx", &flg);CHKERRQ(ierr);
if (flg) {
TestZHEEV = PETSC_FALSE;
TestZHEEVX = PETSC_TRUE;
}
ierr = PetscOptionsHasName(NULL, "-test_zhegv", &flg);CHKERRQ(ierr);
if (flg) {
TestZHEEV = PETSC_FALSE;
TestZHEGV = PETSC_TRUE;
}
ierr = PetscOptionsHasName(NULL, "-test_zhegvx", &flg);CHKERRQ(ierr);
if (flg) {
TestZHEEV = PETSC_FALSE;
TestZHEGVX = PETSC_TRUE;
}
ierr = PetscOptionsGetReal(NULL,"-sigma1",&sigma1,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
dim = n*n;
ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,"-norandom",&flg);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
for (Ii=0; Ii<dim; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (use_random) {ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
/* make A complex Hermitian */
v = sigma2*h2;
Ii = 0; J = 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
m = n = dim;
/* Check whether A is symmetric */
ierr = PetscOptionsHasName(NULL, "-check_symmetry", &flg);CHKERRQ(ierr);
if (flg) {
Mat Trans;
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
ierr = MatEqual(A, Trans, &isSymmetric);
if (!isSymmetric) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"A must be symmetric");
ierr = MatDestroy(&Trans);CHKERRQ(ierr);
}
/* Convert aij matrix to MatSeqDense for LAPACK */
ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQDENSE,&flg);CHKERRQ(ierr);
if (flg) {
ierr = MatDuplicate(A,MAT_COPY_VALUES,&A_dense);CHKERRQ(ierr);
} else {
ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&A_dense);CHKERRQ(ierr);
}
ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
ierr = MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetType(B,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(B);CHKERRQ(ierr);
v = 1.0;
for (Ii=0; Ii<dim; Ii++) {
ierr = MatSetValues(B,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
/* Solve standard eigenvalue problem: A*x = lambda*x */
/*===================================================*/
ierr = PetscBLASIntCast(2*n,&lwork);CHKERRQ(ierr);
ierr = PetscBLASIntCast(n,&bn);CHKERRQ(ierr);
ierr = PetscMalloc(n*sizeof(PetscReal),&evals);CHKERRQ(ierr);
ierr = PetscMalloc(lwork*sizeof(PetscScalar),&work);CHKERRQ(ierr);
ierr = MatDenseGetArray(A_dense,&arrayA);CHKERRQ(ierr);
if (TestZHEEV) { /* test zheev() */
printf(" LAPACKsyev: compute all %d eigensolutions...\n",m);
ierr = PetscMalloc((3*n-2)*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
LAPACKsyev_("V","U",&bn,arrayA,&bn,evals,work,&lwork,rwork,&lierr);
ierr = PetscFree(rwork);CHKERRQ(ierr);
evecs_array = arrayA;
nevs = m;
il =1; iu=m;
}
if (TestZHEEVX) {
il = 1;
ierr = PetscBLASIntCast((0.2*m),&iu);CHKERRQ(ierr);
printf(" LAPACKsyevx: compute %d to %d-th eigensolutions...\n",il,iu);
ierr = PetscMalloc((m*n+1)*sizeof(PetscScalar),&evecs_array);CHKERRQ(ierr);
ierr = PetscMalloc((7*n+1)*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
ierr = PetscMalloc((5*n+1)*sizeof(PetscBLASInt),&iwork);CHKERRQ(ierr);
ierr = PetscMalloc((n+1)*sizeof(PetscBLASInt),&ifail);CHKERRQ(ierr);
/* in the case "I", vl and vu are not referenced */
vl = 0.0; vu = 8.0;
LAPACKsyevx_("V","I","U",&bn,arrayA,&bn,&vl,&vu,&il,&iu,&abstol,&nevs,evals,evecs_array,&n,work,&lwork,rwork,iwork,ifail,&lierr);
ierr = PetscFree(iwork);CHKERRQ(ierr);
ierr = PetscFree(ifail);CHKERRQ(ierr);
ierr = PetscFree(rwork);CHKERRQ(ierr);
}
if (TestZHEGV) {
printf(" LAPACKsygv: compute all %d eigensolutions...\n",m);
ierr = PetscMalloc((3*n+1)*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
ierr = MatDenseGetArray(B,&arrayB);CHKERRQ(ierr);
LAPACKsygv_(&one,"V","U",&bn,arrayA,&bn,arrayB,&bn,evals,work,&lwork,rwork,&lierr);
evecs_array = arrayA;
nevs = m;
il = 1; iu=m;
ierr = MatDenseRestoreArray(B,&arrayB);CHKERRQ(ierr);
ierr = PetscFree(rwork);CHKERRQ(ierr);
}
if (TestZHEGVX) {
il = 1;
ierr = PetscBLASIntCast((0.2*m),&iu);CHKERRQ(ierr);
printf(" LAPACKsygv: compute %d to %d-th eigensolutions...\n",il,iu);
ierr = PetscMalloc((m*n+1)*sizeof(PetscScalar),&evecs_array);CHKERRQ(ierr);
ierr = PetscMalloc((6*n+1)*sizeof(PetscBLASInt),&iwork);CHKERRQ(ierr);
ifail = iwork + 5*n;
ierr = PetscMalloc((7*n+1)*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
ierr = MatDenseGetArray(B,&arrayB);CHKERRQ(ierr);
vl = 0.0; vu = 8.0;
LAPACKsygvx_(&one,"V","I","U",&bn,arrayA,&bn,arrayB,&bn,&vl,&vu,&il,&iu,&abstol,&nevs,evals,evecs_array,&n,work,&lwork,rwork,iwork,ifail,&lierr);
ierr = MatDenseRestoreArray(B,&arrayB);CHKERRQ(ierr);
ierr = PetscFree(iwork);CHKERRQ(ierr);
ierr = PetscFree(rwork);CHKERRQ(ierr);
}
ierr = MatDenseRestoreArray(A_dense,&arrayA);CHKERRQ(ierr);
if (nevs <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED, "nev=%d, no eigensolution has found", nevs);
/* View evals */
ierr = PetscOptionsHasName(NULL, "-eig_view", &flg);CHKERRQ(ierr);
if (flg) {
printf(" %d evals: \n",nevs);
for (i=0; i<nevs; i++) printf("%d %G\n",i+il,evals[i]);
}
/* Check residuals and orthogonality */
ierr = PetscMalloc((nevs+1)*sizeof(Vec),&evecs);CHKERRQ(ierr);
for (i=0; i<nevs; i++) {
ierr = VecCreate(PETSC_COMM_SELF,&evecs[i]);CHKERRQ(ierr);
ierr = VecSetSizes(evecs[i],PETSC_DECIDE,n);CHKERRQ(ierr);
ierr = VecSetFromOptions(evecs[i]);CHKERRQ(ierr);
ierr = VecPlaceArray(evecs[i],evecs_array+i*n);CHKERRQ(ierr);
}
tols[0] = 1.e-8; tols[1] = 1.e-8;
ierr = CkEigenSolutions(cklvl,A,il-1,iu-1,evals,evecs,tols);CHKERRQ(ierr);
for (i=0; i<nevs; i++) { ierr = VecDestroy(&evecs[i]);CHKERRQ(ierr);}
ierr = PetscFree(evecs);CHKERRQ(ierr);
/* Free work space. */
if (TestZHEEVX || TestZHEGVX) {
ierr = PetscFree(evecs_array);CHKERRQ(ierr);
}
ierr = PetscFree(evals);CHKERRQ(ierr);
ierr = PetscFree(work);CHKERRQ(ierr);
ierr = MatDestroy(&A_dense);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscErrorCode random_network(PetscInt nvertex,PetscInt *pnbranch,Node **pnode,Branch **pbranch,PetscInt **pedgelist,PetscInt seed)
{
PetscErrorCode ierr;
PetscInt i, j, nedges = 0;
PetscInt *edgelist;
PetscInt nbat, ncurr, fr, to;
PetscReal *x, *y, value, xmax = 10.0; /* generate points in square */
PetscReal maxdist = 0.0, dist, alpha, beta, prob;
PetscRandom rnd;
Branch *branch;
Node *node;
Edge *head = NULL, *nnew= NULL, *aux= NULL;
PetscFunctionBeginUser;
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rnd);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rnd);CHKERRQ(ierr);
ierr = PetscRandomSetSeed(rnd, seed);CHKERRQ(ierr);
ierr = PetscRandomSeed(rnd);CHKERRQ(ierr);
/* These parameters might be modified for experimentation */
nbat = (PetscInt)(0.1*nvertex);
ncurr = (PetscInt)(0.1*nvertex);
alpha = 0.6;
beta = 0.2;
ierr = PetscMalloc2(nvertex,&x,nvertex,&y);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rnd,0.0,xmax);CHKERRQ(ierr);
for (i=0; i<nvertex; i++) {
ierr = PetscRandomGetValueReal(rnd,&x[i]);CHKERRQ(ierr);
ierr = PetscRandomGetValueReal(rnd,&y[i]);CHKERRQ(ierr);
}
/* find maximum distance */
for (i=0; i<nvertex; i++) {
for (j=0; j<nvertex; j++) {
dist = findDistance(x[i],x[j],y[i],y[j]);
if (dist >= maxdist) maxdist = dist;
}
}
ierr = PetscRandomSetInterval(rnd,0.0,1.0);CHKERRQ(ierr);
for (i=0; i<nvertex; i++) {
for (j=0; j<nvertex; j++) {
if (j != i) {
dist = findDistance(x[i],x[j],y[i],y[j]);
prob = beta*PetscExpScalar(-dist/(maxdist*alpha));
ierr = PetscRandomGetValueReal(rnd,&value);CHKERRQ(ierr);
if (value <= prob) {
ierr = PetscMalloc1(1,&nnew);CHKERRQ(ierr);
if (head == NULL) {
head = nnew;
head->next = NULL;
head->n = nedges;
head->i = i;
head->j = j;
} else {
aux = head;
head = nnew;
head->n = nedges;
head->next = aux;
head->i = i;
head->j = j;
}
nedges += 1;
}
}
}
}
ierr = PetscMalloc1(2*nedges,&edgelist);CHKERRQ(ierr);
for (aux = head; aux; aux = aux->next) {
edgelist[(aux->n)*2] = aux->i;
edgelist[(aux->n)*2 + 1] = aux->j;
}
aux = head;
while (aux != NULL) {
nnew = aux;
aux = aux->next;
ierr = PetscFree(nnew);CHKERRQ(ierr);
}
ierr = PetscCalloc2(nvertex,&node,nedges,&branch);CHKERRQ(ierr);
for (i = 0; i < nvertex; i++) {
node[i].id = i;
node[i].inj = 0;
node[i].gr = PETSC_FALSE;
}
for (i = 0; i < nedges; i++) {
branch[i].id = i;
branch[i].r = 1.0;
branch[i].bat = 0;
}
/* Chose random node as ground voltage */
ierr = PetscRandomSetInterval(rnd,0.0,nvertex);CHKERRQ(ierr);
ierr = PetscRandomGetValueReal(rnd,&value);CHKERRQ(ierr);
node[(int)value].gr = PETSC_TRUE;
/* Create random current and battery injectionsa */
for (i=0; i<ncurr; i++) {
ierr = PetscRandomSetInterval(rnd,0.0,nvertex);CHKERRQ(ierr);
ierr = PetscRandomGetValueReal(rnd,&value);CHKERRQ(ierr);
fr = edgelist[(int)value*2];
to = edgelist[(int)value*2 + 1];
node[fr].inj += 1.0;
node[to].inj -= 1.0;
}
for (i=0; i<nbat; i++) {
ierr = PetscRandomSetInterval(rnd,0.0,nedges);CHKERRQ(ierr);
ierr = PetscRandomGetValueReal(rnd,&value);CHKERRQ(ierr);
branch[(int)value].bat += 1.0;
}
ierr = PetscFree2(x,y);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rnd);CHKERRQ(ierr);
/* assign pointers */
*pnbranch = nedges;
*pedgelist = edgelist;
*pbranch = branch;
*pnode = node;
PetscFunctionReturn(ierr);
}
int main(int argc,char **argv)
{
Mat A1,A2; /* problem matrices */
EPS eps; /* eigenproblem solver context */
PetscScalar value[3];
PetscReal tol=1000*PETSC_MACHINE_EPSILON,v;
Vec d;
PetscInt n=30,i,Istart,Iend,col[3];
PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
PetscRandom myrand;
PetscErrorCode ierr;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nTridiagonal with random diagonal, n=%D\n\n",n);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create matrix tridiag([-1 0 -1])
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A1);CHKERRQ(ierr);
ierr = MatSetSizes(A1,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(A1);CHKERRQ(ierr);
ierr = MatSetUp(A1);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A1,&Istart,&Iend);CHKERRQ(ierr);
if (Istart==0) FirstBlock=PETSC_TRUE;
if (Iend==n) LastBlock=PETSC_TRUE;
value[0]=-1.0; value[1]=0.0; value[2]=-1.0;
for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
col[0]=i-1; col[1]=i; col[2]=i+1;
ierr = MatSetValues(A1,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
if (LastBlock) {
i=n-1; col[0]=n-2; col[1]=n-1;
ierr = MatSetValues(A1,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
if (FirstBlock) {
i=0; col[0]=0; col[1]=1; value[0]=0.0; value[1]=-1.0;
ierr = MatSetValues(A1,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A1,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A1,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create two matrices by filling the diagonal with rand values
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDuplicate(A1,MAT_COPY_VALUES,&A2);CHKERRQ(ierr);
ierr = MatGetVecs(A1,NULL,&d);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&myrand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(myrand);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(myrand,0.0,1.0);CHKERRQ(ierr);
for (i=0; i<n; i++) {
ierr = PetscRandomGetValueReal(myrand,&v);CHKERRQ(ierr);
ierr = VecSetValue(d,i,v,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(d);CHKERRQ(ierr);
ierr = VecAssemblyEnd(d);CHKERRQ(ierr);
ierr = MatDiagonalSet(A1,d,INSERT_VALUES);CHKERRQ(ierr);
for (i=0; i<n; i++) {
ierr = PetscRandomGetValueReal(myrand,&v);CHKERRQ(ierr);
ierr = VecSetValue(d,i,v,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(d);CHKERRQ(ierr);
ierr = VecAssemblyEnd(d);CHKERRQ(ierr);
ierr = MatDiagonalSet(A2,d,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecDestroy(&d);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&myrand);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the eigensolver
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr);
ierr = EPSSetProblemType(eps,EPS_HEP);CHKERRQ(ierr);
ierr = EPSSetTolerances(eps,tol,PETSC_DEFAULT);CHKERRQ(ierr);
ierr = EPSSetOperators(eps,A1,NULL);CHKERRQ(ierr);
ierr = EPSSetFromOptions(eps);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve first eigenproblem
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = EPSSolve(eps);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," - - - First matrix - - -\n");CHKERRQ(ierr);
ierr = EPSPrintSolution(eps,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve second eigenproblem
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = EPSSetOperators(eps,A2,NULL);CHKERRQ(ierr);
ierr = EPSSolve(eps);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD," - - - Second matrix - - -\n");CHKERRQ(ierr);
ierr = EPSPrintSolution(eps,NULL);CHKERRQ(ierr);
ierr = EPSDestroy(&eps);CHKERRQ(ierr);
ierr = MatDestroy(&A1);CHKERRQ(ierr);
ierr = MatDestroy(&A2);CHKERRQ(ierr);
ierr = SlepcFinalize();
return 0;
}
