223 lines
6.1 KiB
C++
223 lines
6.1 KiB
C++
#include <ulocks.h>
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#include <task.h>
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typedef void (*pfunction)();
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typedef double *pdouble;
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struct gmres_data{
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int nit;
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double **H, **HH, *r, *ap, *xNew, *y, *h1, **q, *inpr;
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};
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void pgmres(int &, int &, double *, double *, Matrix *, gmres_data &);
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//============================================================================
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// This is parallel implementation of the GMRES routine.
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//============================================================================
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void Method::gmres(int n, int &nit, double *x, double *b, int Kmax,Matrix *A){
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/*
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int i,ii, j, k, m;
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double H[Kmax+2][Kmax+1];//, HH[Kmax][Kmax];
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double r[n], ap[n], xNew[n];
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int iter;
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double rNorm, RNorm, y[Kmax], h1[Kmax];
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//if (Kmax > n) Kmax=n;
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//double *q[Kmax+1];
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//for (i=1; i<=Kmax; i++) q[i] = new double[n];
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int np = 1, begin = 0, end = n, p = 0;
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double inpr[1];
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// gmres_data data;
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//double **H, **HH, **q;
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double **q, **HH;
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if (Kmax > n) Kmax=n;
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q = new pdouble[Kmax+1];
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for (i=1; i<=Kmax; i++) q[i] = new double[n];
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//H = new pdouble[Kmax+2];
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//for(i=0; i<(Kmax+2); i++) H[i] = new double[Kmax+1];
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HH = new pdouble[Kmax+1];
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for(i=0; i<Kmax+1; i++) HH[i] = new double[Kmax+1];
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*/
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int i, np = m_get_numprocs();
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//double r[n], ap[n], xNew[n], inpr[np];
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//double y[Kmax], h1[Kmax];
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double *r, *ap, *xNew, *inpr;
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double *y, *h1;
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r = new double[n];
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ap = new double[n];
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xNew = new double[n];
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inpr = new double[np];
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y = new double[Kmax];
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h1 = new double[Kmax];
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gmres_data data;
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if (Kmax > n) Kmax=n;
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data.q = new pdouble[Kmax+1];
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for (i=1; i<=Kmax; i++) data.q[i] = new double[n];
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data.H = new pdouble[Kmax+2];
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for(i=0; i<(Kmax+2); i++) data.H[i] = new double[Kmax+1];
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data.HH = new pdouble[Kmax+1];
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for(i=0; i<=Kmax; i++) data.HH[i] = new double[Kmax+1];
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double **H = data.H, **HH = data.HH, **q = data.q;
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data.nit = nit;
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data.r = r;
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data.ap = ap;
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data.xNew= xNew;
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data.y = y;
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data.h1 = h1;
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data.inpr= inpr;
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m_fork((pfunction)pgmres, &n, &Kmax, x, b, A, &data);
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//pgmres(n, Kmax, x, b, A, data);
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//==========================================================================
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/*
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for (i=1; i<=Kmax; i++) delete []data.q[i];
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delete [] data.q;
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for(i=0; i<(Kmax+2); i++) delete []data.H[i];
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delete [] data.H;
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for(i=0; i<Kmax; i++) delete [] data.HH[i];
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delete [] data.HH;
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*/
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}
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//============================================================================
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void pgmres(int &n,int &Kmax, double *x, double *b, Matrix *A, gmres_data &D){
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int p = m_get_myid(), np = m_get_numprocs();
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//int p = 0, np = 1;
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int begin, end, i, k, m, j, ii, iter, nit = D.nit;
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double rNorm, RNorm;
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double **H = D.H, **HH = D.HH, *r = D.r, *ap = D.ap;
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double *xNew = D.xNew, *y = D.y, *h1 = D.h1, **q = D.q, *inpr = D.inpr;
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if (n%np >= 2){ begin = p*(n/np + 1); end = (p+1)*(n/np+1);}
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else { begin = p*n/np; end = begin + n/np;}
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if (p == (np-1)) end = n;
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//fprintf(stderr,"begin = %d, end = %d\n", begin, end);
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for(iter = 0; iter<nit; iter++){
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A->Action(x, ap, begin, end); // ap = Ax
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fprintf(stderr,"%d\n", p);
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m_sync();
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inpr[p] = 0.;
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for(i=begin; i<end; i++){ // r = b-Ax
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r[i] = b[i]-ap[i]; // inpr = (r, r)
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inpr[p] += r[i]*r[i];
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}
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m_sync();
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if (p==0){
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for(i=1; i<np; i++)
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inpr[0]+=inpr[i];
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H[1][0] = sqrt(inpr[0]);
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}
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m_sync();
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//fprintf(stderr,"1. %d\n", p);
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for(k=1; k<=Kmax; k++) {
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for(i=begin; i<end; i++) // q[k] = 1.0/H[k][k-1] r
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q[k][i] = r[i]/H[k][k-1];
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m_sync();
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//fprintf(stderr,"2. %d\n", p);
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A->Action( q[k], ap, begin, end); // ap = A q[k]
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for(i=begin;i<end;i++) r[i] = ap[i]; // r = ap
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for(ii=1; ii<=k; ii++) {
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inpr[p] = 0;
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for(i=begin; i<end; i++) // H[ii][k] = q[ii] . ap
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inpr[p] += q[ii][i]*ap[i];
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m_sync();
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//fprintf(stderr,"3. %d\n", p);
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if (p==0){
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for(i=1; i<np; i++)
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inpr[0] += inpr[i];
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H[ii][k] = inpr[0];
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}
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m_sync();
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//fprintf(stderr,"4. %d\n", p);
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for(i=begin; i<end; i++) // r = r-H[ii][k] q[ii]
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r[i] -= H[ii][k] * q[ii][i];
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}
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inpr[p] = 0;
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for(i=begin; i<end; i++) // inpr = r . r
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inpr[p] += r[i]*r[i];
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m_sync();
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//fprintf(stderr,"5. %d\n", p);
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if (p==0){
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for(i=1; i<np; i++)
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inpr[0]+=inpr[i];
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H[k+1][k]=sqrt(inpr[0]); // H[k+1][k] = sqrt(r . r)
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// Minimization of || b-Ax || in K_k
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for (i=1; i<=k; i++) {
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HH[k][i] = 0.0;
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for (j=1; j<=i+1; j++)
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HH[k][i] += H[j][k] * H[j][i];
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}
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h1[k] = H[1][k]*H[1][0];
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if (k != 1)
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for (i=1; i<k; i++) {
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HH[k][i] = HH[k][i]/HH[i][i];
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for (m=i+1; m<=k; m++)
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HH[k][m] -= HH[k][i] * HH[m][i] * HH[i][i];
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h1[k] -= h1[i] * HH[k][i];
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}
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y[k] = h1[k]/HH[k][k];
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if (k != 1)
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for (i=k-1; i>=1; i--) {
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y[i] = h1[i]/HH[i][i];
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for (j=i+1; j<=k; j++)
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y[i] -= y[j] * HH[j][i];
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}
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// Minimization Done
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}
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m_sync();
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rNorm = fabs(H[k+1][k]);
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//fprintf(stderr,"6. %d\n", p);
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if (rNorm < TOLERANCE || k == Kmax){
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for(i=begin; i<end; i++) xNew[i]=x[i]; // xNew = x
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for (ii=1; ii<=k; ii++)
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for(i=begin; i<end; i++) // xNew += y[ii]*q[ii]
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xNew[i] += y[ii]*q[ii][i];
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break;
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}
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}
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A->Action(xNew, ap, begin, end); // ap = A xNew
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m_sync();
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//fprintf(stderr,"7. %d\n", p);
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inpr[p] = 0.;
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for(i=begin; i<end; i++){ // ap = b - ap
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ap[i] = b[i] - ap[i];
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inpr[p] += ap[i]*ap[i];
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}
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m_sync();
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//fprintf(stderr,"8. %d\n", p);
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if (p==0){
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for(i=1; i<np; i++)
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inpr[0]+=inpr[i];
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fprintf(stderr, "Iteration %d done!\n", iter);
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fprintf(stderr, "The current residual RNorm = %e\n", RNorm);
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}
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m_sync();
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RNorm = sqrt(inpr[0]); // RNorm = sqrt(ap . ap)
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if (rNorm < TOLERANCE) break;
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if (RNorm < TOLERANCE) break;
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for(i=begin;i<end;i++) x[i] = xNew[i]; // x = xNew
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}
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}
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