/*$Id: jbearing2.c 1.78 05/05/12 13:59:03-05:00 sarich@zorak.(none) $*/
/*
Include "tao.h" so we can use TAO solvers with PETSc support.
Include "petscda.h" so that we can use distributed arrays (DAs) for managing
the parallel mesh.
*/
#include "petscda.h"
#include "tao.h"
#include <math.h> /* for cos() sin(0), and atan() */
static char help[]=
"This example demonstrates use of the TAO package to \n\
solve a bound constrained minimization problem. This example is based on \n\
the problem DPJB from the MINPACK-2 test suite. This pressure journal \n\
bearing problem is an example of elliptic variational problem defined over \n\
a two dimensional rectangle. By discretizing the domain into triangular \n\
elements, the pressure surrounding the journal bearing is defined as the \n\
minimum of a quadratic function whose variables are bounded below by zero.\n\
The command line options are:\n\
-mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
-my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
\n";
/*T
Concepts: TAO - Solving a bound constrained minimization problem
Routines: TaoInitialize(); TaoFinalize();
Routines: TaoApplicationCreate(); TaoAppDestroy();
Routines: TaoAppSetObjectiveAndGradientRoutine(); TaoAppSetHessianRoutine();
Routines: TaoAppSetInitialSolutionVec(); TaoAppSetHessianMat();
Routines: TaoCreate(); TaoDestroy();
Routines: TaoSetOptions(); TaoGetKSP()
Routines: TaoSolveApplication(); TaoGetTerminationReason();
Processors: n
T*/
/*
User-defined application context - contains data needed by the
application-provided call-back routines, FormFunctionGradient(),
FormHessian().
*/
typedef struct {
/* problem parameters */
PetscReal ecc; /* test problem parameter */
PetscReal b; /* A dimension of journal bearing */
int nx,ny; /* discretization in x, y directions */
/* Working space */
DA da; /* distributed array data structure */
Mat A; /* Quadratic Objective term */
Vec B; /* Linear Objective term */
} AppCtx;
/* User-defined routines */
static PetscReal p(PetscReal xi, PetscReal ecc);
static int FormFunctionGradient(TAO_APPLICATION, Vec, double *,Vec,void *);
static int FormHessian(TAO_APPLICATION,Vec,Mat *, Mat *, MatStructure *, void *);
static int ComputeB(AppCtx*);
static int ComputeBounds(TAO_APPLICATION, Vec, Vec, void *);
#undef __FUNCT__
#define __FUNCT__ "main"
int main( int argc, char **argv )
{
int info; /* used to check for functions returning nonzeros */
int Nx, Ny; /* number of processors in x- and y- directions */
int m, N; /* number of local and global elements in vectors */
Vec x; /* variables vector */
PetscTruth flg; /* A return variable when checking for user options */
TAO_SOLVER tao; /* TAO_SOLVER solver context */
TaoMethod method = "tao_gpcg";/* default minimization method */
TAO_APPLICATION jbearingapp; /* The PETSc application */
ISLocalToGlobalMapping isltog; /* local-to-global mapping object */
int nloc; /* The number of local elements */
int *ltog; /* mapping of local elements to global elements */
TaoTerminateReason reason;
AppCtx user; /* user-defined work context */
PetscReal zero=0.0; /* lower bound on all variables */
KSP ksp;
/* Initialize PETSC and TAO */
PetscInitialize( &argc, &argv,(char *)0,help );
TaoInitialize( &argc, &argv,(char *)0,help );
/* Set the default values for the problem parameters */
user.nx = 50; user.ny = 50; user.ecc = 0.1; user.b = 10.0;
/* Check for any command line arguments that override defaults */
info = PetscOptionsGetInt(TAO_NULL,"-mx",&user.nx,&flg); CHKERRQ(info);
info = PetscOptionsGetInt(TAO_NULL,"-my",&user.ny,&flg); CHKERRQ(info);
info = PetscOptionsGetReal(TAO_NULL,"-ecc",&user.ecc,&flg); CHKERRQ(info);
info = PetscOptionsGetReal(TAO_NULL,"-b",&user.b,&flg); CHKERRQ(info);
PetscPrintf(MPI_COMM_WORLD,"\n---- Journal Bearing Problem -----\n");
PetscPrintf(MPI_COMM_WORLD,"mx: %d, my: %d, ecc: %4.3f \n\n",
user.nx,user.ny,user.ecc);
/* Calculate any derived values from parameters */
N = user.nx*user.ny;
/* Let Petsc determine the grid division */
Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;
/*
A two dimensional distributed array will help define this problem,
which derives from an elliptic PDE on two dimensional domain. From
the distributed array, Create the vectors.
*/
info = DACreate2d(MPI_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,user.nx,
user.ny,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&user.da); CHKERRQ(info);
/*
Extract global and local vectors from DA; the vector user.B is
used solely as work space for the evaluation of the function,
gradient, and Hessian. Duplicate for remaining vectors that are
the same types.
*/
info = DACreateGlobalVector(user.da,&x); CHKERRQ(info); /* Solution */
info = VecDuplicate(x,&user.B); CHKERRQ(info); /* Linear objective */
/* Create matrix user.A to store quadratic, Create a local ordering scheme. */
info = VecGetLocalSize(x,&m); CHKERRQ(info);
info = MatCreateMPIAIJ(MPI_COMM_WORLD,m,m,N,N,5,TAO_NULL,3,TAO_NULL,&user.A); CHKERRQ(info);
info = DAGetGlobalIndices(user.da,&nloc,<og); CHKERRQ(info);
info = ISLocalToGlobalMappingCreate(MPI_COMM_SELF,nloc,ltog,&isltog);
CHKERRQ(info);
info = MatSetLocalToGlobalMapping(user.A,isltog); CHKERRQ(info);
info = ISLocalToGlobalMappingDestroy(isltog); CHKERRQ(info);
/* User defined function -- compute linear term of quadratic */
info = ComputeB(&user); CHKERRQ(info);
/* The TAO code begins here */
/*
Create the optimization solver, Petsc application
Suitable methods: "tao_gpcg","tao_bqpip","tao_tron","tao_blmvm"
*/
info = TaoCreate(MPI_COMM_WORLD,method,&tao); CHKERRQ(info);
info = TaoApplicationCreate(MPI_COMM_WORLD,&jbearingapp); CHKERRQ(info);
/* Set the initial vector */
info = VecSet(x, zero); CHKERRQ(info);
info = TaoAppSetInitialSolutionVec(jbearingapp,x); CHKERRQ(info);
/* Set the user function, gradient, hessian evaluation routines and data structures */
info = TaoAppSetObjectiveAndGradientRoutine(jbearingapp,FormFunctionGradient,(void*) &user);
CHKERRQ(info);
info = TaoAppSetHessianMat(jbearingapp,user.A,user.A); CHKERRQ(info);
info = TaoAppSetHessianRoutine(jbearingapp,FormHessian,(void*)&user);
CHKERRQ(info);
/* Set a routine that defines the bounds */
info = TaoAppSetVariableBoundsRoutine(jbearingapp,ComputeBounds,(void*)&user); CHKERRQ(info);
info = TaoGetKSP(tao,&ksp); CHKERRQ(info);
if (ksp) { /* Modify the PETSc KSP structure */
info = KSPSetType(ksp,KSPCG); CHKERRQ(info);
}
/* Check for any tao command line options */
info = TaoSetOptions(jbearingapp,tao); CHKERRQ(info);
/* Solve the bound constrained problem */
info = TaoSolveApplication(jbearingapp,tao); CHKERRQ(info);
info = TaoGetTerminationReason(tao,&reason); CHKERRQ(info);
if (reason <= 0)
PetscPrintf(MPI_COMM_WORLD,"Try a different TAO method, adjust some parameters, or check the function evaluation routines\n");
/* Free TAO data structures */
info = TaoDestroy(tao); CHKERRQ(info);
info = TaoAppDestroy(jbearingapp); CHKERRQ(info);
/* Free PETSc data structures */
info = VecDestroy(x); CHKERRQ(info);
info = MatDestroy(user.A); CHKERRQ(info);
info = VecDestroy(user.B); CHKERRQ(info);
info = DADestroy(user.da); CHKERRQ(info);
TaoFinalize();
PetscFinalize();
return 0;
}
#undef __FUNCT__
#define __FUNCT__ "ComputeBounds"
static int ComputeBounds(TAO_APPLICATION taoapp, Vec xl, Vec xu, void *ctx){
int info;
PetscReal zero=0.0, d1000=1000;
/* Set the upper and lower bounds */
info = VecSet(xl, zero); CHKERRQ(info);
info = VecSet(xu, d1000); CHKERRQ(info);
return 0;
}
static PetscReal p(PetscReal xi, PetscReal ecc)
{
PetscReal t=1.0+ecc*cos(xi);
return (t*t*t);
}
#undef __FUNCT__
#define __FUNCT__ "ComputeB"
int ComputeB(AppCtx* user)
{
int i,j,k,info;
int nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
PetscReal two=2.0, pi=4.0*atan(1.0);
PetscReal hx,hy,ehxhy;
PetscReal temp,*b;
PetscReal ecc=user->ecc;
nx=user->nx;
ny=user->ny;
hx=two*pi/(nx+1.0);
hy=two*user->b/(ny+1.0);
ehxhy = ecc*hx*hy;
/*
Get local grid boundaries
*/
info = DAGetCorners(user->da,&xs,&ys,TAO_NULL,&xm,&ym,TAO_NULL); CHKERRQ(info);
info = DAGetGhostCorners(user->da,&gxs,&gys,TAO_NULL,&gxm,&gym,TAO_NULL); CHKERRQ(info);
/* Compute the linear term in the objective function */
info = VecGetArray(user->B,&b); CHKERRQ(info);
for (i=xs; i<xs+xm; i++){
temp=sin((i+1)*hx);
for (j=ys; j<ys+ym; j++){
k=xm*(j-ys)+(i-xs);
b[k]= - ehxhy*temp;
}
}
info = VecRestoreArray(user->B,&b); CHKERRQ(info);
info = PetscLogFlops(5*xm*ym+3*xm); CHKERRQ(info);
return 0;
}
#undef __FUNCT__
#define __FUNCT__ "FormFunctionGradient"
int FormFunctionGradient(TAO_APPLICATION taoapp, Vec X, double *fcn,Vec G,void *ptr)
{
AppCtx* user=(AppCtx*)ptr;
int i,j,k,kk,info;
int col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
PetscReal one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
PetscReal hx,hy,hxhy,hxhx,hyhy;
PetscReal xi,v[5];
PetscReal ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
PetscReal vmiddle, vup, vdown, vleft, vright;
PetscReal tt,f1,f2;
PetscReal *x,*g,zero=0.0;
Vec localX;
nx=user->nx;
ny=user->ny;
hx=two*pi/(nx+1.0);
hy=two*user->b/(ny+1.0);
hxhy=hx*hy;
hxhx=one/(hx*hx);
hyhy=one/(hy*hy);
info = DAGetLocalVector(user->da,&localX);CHKERRQ(info);
info = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
info = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
info = VecSet(G, zero); CHKERRQ(info);
/*
Get local grid boundaries
*/
info = DAGetCorners(user->da,&xs,&ys,TAO_NULL,&xm,&ym,TAO_NULL); CHKERRQ(info);
info = DAGetGhostCorners(user->da,&gxs,&gys,TAO_NULL,&gxm,&gym,TAO_NULL); CHKERRQ(info);
info = VecGetArray(localX,&x); CHKERRQ(info);
info = VecGetArray(G,&g); CHKERRQ(info);
for (i=xs; i< xs+xm; i++){
xi=(i+1)*hx;
trule1=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc) ) / six; /* L(i,j) */
trule2=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc) ) / six; /* U(i,j) */
trule3=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc) ) / six; /* U(i+1,j) */
trule4=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc) ) / six; /* L(i-1,j) */
trule5=trule1; /* L(i,j-1) */
trule6=trule2; /* U(i,j+1) */
vdown=-(trule5+trule2)*hyhy;
vleft=-hxhx*(trule2+trule4);
vright= -hxhx*(trule1+trule3);
vup=-hyhy*(trule1+trule6);
vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);
for (j=ys; j<ys+ym; j++){
row=(j-gys)*gxm + (i-gxs);
v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;
k=0;
if (j>gys){
v[k]=vdown; col[k]=row - gxm; k++;
}
if (i>gxs){
v[k]= vleft; col[k]=row - 1; k++;
}
v[k]= vmiddle; col[k]=row; k++;
if (i+1 < gxs+gxm){
v[k]= vright; col[k]=row+1; k++;
}
if (j+1 <gys+gym){
v[k]= vup; col[k] = row+gxm; k++;
}
tt=0;
for (kk=0;kk<k;kk++){
tt+=v[kk]*x[col[kk]];
}
row=(j-ys)*xm + (i-xs);
g[row]=tt;
}
}
info = VecRestoreArray(localX,&x); CHKERRQ(info);
info = VecRestoreArray(G,&g); CHKERRQ(info);
info = DARestoreLocalVector(user->da,&localX); CHKERRQ(info);
info = VecDot(X,G,&f1); CHKERRQ(info);
info = VecDot(user->B,X,&f2); CHKERRQ(info);
info = VecAXPY(G, one, user->B); CHKERRQ(info);
*fcn = f1/2.0 + f2;
info = PetscLogFlops((91 + 10*ym) * xm); CHKERRQ(info);
return 0;
}
#undef __FUNCT__
#define __FUNCT__ "FormHessian"
/*
FormHessian computes the quadratic term in the quadratic objective function
Notice that the objective function in this problem is quadratic (therefore a constant
hessian). If using a nonquadratic solver, then you might want to reconsider this function
*/
int FormHessian(TAO_APPLICATION taoapp,Vec X,Mat *H, Mat *Hpre, MatStructure *flg, void *ptr)
{
AppCtx* user=(AppCtx*)ptr;
int i,j,k,info;
int col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
PetscReal one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
PetscReal hx,hy,hxhy,hxhx,hyhy;
PetscReal xi,v[5];
PetscReal ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
PetscReal vmiddle, vup, vdown, vleft, vright;
Mat hes=*H;
PetscTruth assembled;
nx=user->nx;
ny=user->ny;
hx=two*pi/(nx+1.0);
hy=two*user->b/(ny+1.0);
hxhy=hx*hy;
hxhx=one/(hx*hx);
hyhy=one/(hy*hy);
*flg=SAME_NONZERO_PATTERN;
/*
Get local grid boundaries
*/
info = DAGetCorners(user->da,&xs,&ys,TAO_NULL,&xm,&ym,TAO_NULL); CHKERRQ(info);
info = DAGetGhostCorners(user->da,&gxs,&gys,TAO_NULL,&gxm,&gym,TAO_NULL); CHKERRQ(info);
info = MatAssembled(hes,&assembled); CHKERRQ(info);
if (assembled){info = MatZeroEntries(hes); CHKERRQ(info);}
for (i=xs; i< xs+xm; i++){
xi=(i+1)*hx;
trule1=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc) ) / six; /* L(i,j) */
trule2=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc) ) / six; /* U(i,j) */
trule3=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc) ) / six; /* U(i+1,j) */
trule4=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc) ) / six; /* L(i-1,j) */
trule5=trule1; /* L(i,j-1) */
trule6=trule2; /* U(i,j+1) */
vdown=-(trule5+trule2)*hyhy;
vleft=-hxhx*(trule2+trule4);
vright= -hxhx*(trule1+trule3);
vup=-hyhy*(trule1+trule6);
vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);
v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;
for (j=ys; j<ys+ym; j++){
row=(j-gys)*gxm + (i-gxs);
k=0;
if (j>gys){
v[k]=vdown; col[k]=row - gxm; k++;
}
if (i>gxs){
v[k]= vleft; col[k]=row - 1; k++;
}
v[k]= vmiddle; col[k]=row; k++;
if (i+1 < gxs+gxm){
v[k]= vright; col[k]=row+1; k++;
}
if (j+1 <gys+gym){
v[k]= vup; col[k] = row+gxm; k++;
}
info = MatSetValuesLocal(hes,1,&row,k,col,v,INSERT_VALUES); CHKERRQ(info);
}
}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd().
By placing code between these two statements, computations can be
done while messages are in transition.
*/
info = MatAssemblyBegin(hes,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
info = MatAssemblyEnd(hes,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
/*
Tell the matrix we will never add a new nonzero location to the
matrix. If we do it will generate an error.
*/
info = MatSetOption(hes,MAT_NEW_NONZERO_LOCATION_ERR); CHKERRQ(info);
info = MatSetOption(hes,MAT_SYMMETRIC); CHKERRQ(info);
info = PetscLogFlops(9*xm*ym+49*xm); CHKERRQ(info);
return 0;
}