zgsrfs.c

来自「SuperLU is a general purpose library for」· C语言 代码 · 共 461 行 · 第 1/2 页

    /* NZ = maximum number of nonzero elements in each row of A, plus 1 */
    nz     = A->ncol + 1;
    eps    = dlamch_("Epsilon");
    safmin = dlamch_("Safe minimum");
    /* Set SAFE1 essentially to be the underflow threshold times the
       number of additions in each row. */
    safe1  = nz * safmin;
    safe2  = safe1 / eps;

    /* Compute the number of nonzeros in each row (or column) of A */
    for (i = 0; i < A->nrow; ++i) iwork[i] = 0;
    if ( notran ) {
	for (k = 0; k < A->ncol; ++k)
	    for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) 
		++iwork[Astore->rowind[i]];
    } else {
	for (k = 0; k < A->ncol; ++k)
	    iwork[k] = Astore->colptr[k+1] - Astore->colptr[k];
    }	

    /* Copy one column of RHS B into Bjcol. */
    Bjcol.Stype = B->Stype;
    Bjcol.Dtype = B->Dtype;
    Bjcol.Mtype = B->Mtype;
    Bjcol.nrow  = B->nrow;
    Bjcol.ncol  = 1;
    Bjcol.Store = (void *) SUPERLU_MALLOC( sizeof(DNformat) );
    if ( !Bjcol.Store ) ABORT("SUPERLU_MALLOC fails for Bjcol.Store");
    Bjcol_store = Bjcol.Store;
    Bjcol_store->lda = ldb;
    Bjcol_store->nzval = work; /* address aliasing */
	
    /* Do for each right hand side ... */
    for (j = 0; j < nrhs; ++j) {
	count = 0;
	lstres = 3.;
	Bptr = &Bmat[j*ldb];
	Xptr = &Xmat[j*ldx];

	while (1) { /* Loop until stopping criterion is satisfied. */

	    /* Compute residual R = B - op(A) * X,   
	       where op(A) = A, A**T, or A**H, depending on TRANS. */
	    
#ifdef _CRAY
	    CCOPY(&A->nrow, Bptr, &ione, work, &ione);
#else
	    zcopy_(&A->nrow, Bptr, &ione, work, &ione);
#endif
	    sp_zgemv(transc, ndone, A, Xptr, ione, done, work, ione);

	    /* Compute componentwise relative backward error from formula 
	       max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) )   
	       where abs(Z) is the componentwise absolute value of the matrix
	       or vector Z.  If the i-th component of the denominator is less
	       than SAFE2, then SAFE1 is added to the i-th component of the   
	       numerator before dividing. */

	    for (i = 0; i < A->nrow; ++i) rwork[i] = z_abs1( &Bptr[i] );
	    
	    /* Compute abs(op(A))*abs(X) + abs(B). */
	    if (notran) {
		for (k = 0; k < A->ncol; ++k) {
		    xk = z_abs1( &Xptr[k] );
		    for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
			rwork[Astore->rowind[i]] += z_abs1(&Aval[i]) * xk;
		}
	    } else {
		for (k = 0; k < A->ncol; ++k) {
		    s = 0.;
		    for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
			irow = Astore->rowind[i];
			s += z_abs1(&Aval[i]) * z_abs1(&Xptr[irow]);
		    }
		    rwork[k] += s;
		}
	    }
	    s = 0.;
	    for (i = 0; i < A->nrow; ++i) {
		if (rwork[i] > safe2) {
		    s = SUPERLU_MAX( s, z_abs1(&work[i]) / rwork[i] );
                } else if ( rwork[i] != 0.0 ) {
		    s = SUPERLU_MAX( s, (z_abs1(&work[i]) + safe1) / rwork[i] );
                }
                /* If rwork[i] is exactly 0.0, then we know the true 
                   residual also must be exactly 0.0. */
	    }
	    berr[j] = s;

	    /* Test stopping criterion. Continue iterating if   
	       1) The residual BERR(J) is larger than machine epsilon, and   
	       2) BERR(J) decreased by at least a factor of 2 during the   
	          last iteration, and   
	       3) At most ITMAX iterations tried. */

	    if (berr[j] > eps && berr[j] * 2. <= lstres && count < ITMAX) {
		/* Update solution and try again. */
		zgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
		
#ifdef _CRAY
		CAXPY(&A->nrow, &done, work, &ione,
		       &Xmat[j*ldx], &ione);
#else
		zaxpy_(&A->nrow, &done, work, &ione,
		       &Xmat[j*ldx], &ione);
#endif
		lstres = berr[j];
		++count;
	    } else {
		break;
	    }
        
	} /* end while */

	stat->RefineSteps = count;

	/* Bound error from formula:
	   norm(X - XTRUE) / norm(X) .le. FERR = norm( abs(inv(op(A)))*   
	   ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X)   
          where   
            norm(Z) is the magnitude of the largest component of Z   
            inv(op(A)) is the inverse of op(A)   
            abs(Z) is the componentwise absolute value of the matrix or
	       vector Z   
            NZ is the maximum number of nonzeros in any row of A, plus 1   
            EPS is machine epsilon   

          The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B))   
          is incremented by SAFE1 if the i-th component of   
          abs(op(A))*abs(X) + abs(B) is less than SAFE2.   

          Use ZLACON to estimate the infinity-norm of the matrix   
             inv(op(A)) * diag(W),   
          where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
	
	for (i = 0; i < A->nrow; ++i) rwork[i] = z_abs1( &Bptr[i] );
	
	/* Compute abs(op(A))*abs(X) + abs(B). */
	if ( notran ) {
	    for (k = 0; k < A->ncol; ++k) {
		xk = z_abs1( &Xptr[k] );
		for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
		    rwork[Astore->rowind[i]] += z_abs1(&Aval[i]) * xk;
	    }
	} else {
	    for (k = 0; k < A->ncol; ++k) {
		s = 0.;
		for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
		    irow = Astore->rowind[i];
		    xk = z_abs1( &Xptr[irow] );
		    s += z_abs1(&Aval[i]) * xk;
		}
		rwork[k] += s;
	    }
	}
	
	for (i = 0; i < A->nrow; ++i)
	    if (rwork[i] > safe2)
		rwork[i] = z_abs(&work[i]) + (iwork[i]+1)*eps*rwork[i];
	    else
		rwork[i] = z_abs(&work[i])+(iwork[i]+1)*eps*rwork[i]+safe1;
	kase = 0;

	do {
	    zlacon_(&A->nrow, &work[A->nrow], work,
		    &ferr[j], &kase);
	    if (kase == 0) break;

	    if (kase == 1) {
		/* Multiply by diag(W)*inv(op(A)**T)*(diag(C) or diag(R)). */
		if ( notran && colequ )
		    for (i = 0; i < A->ncol; ++i) {
		        zd_mult(&work[i], &work[i], C[i]);
	            }
		else if ( !notran && rowequ )
		    for (i = 0; i < A->nrow; ++i) {
		        zd_mult(&work[i], &work[i], R[i]);
                    }

		zgstrs (transt, L, U, perm_c, perm_r, &Bjcol, stat, info);
		
		for (i = 0; i < A->nrow; ++i) {
		    zd_mult(&work[i], &work[i], rwork[i]);
	 	}
	    } else {
		/* Multiply by (diag(C) or diag(R))*inv(op(A))*diag(W). */
		for (i = 0; i < A->nrow; ++i) {
		    zd_mult(&work[i], &work[i], rwork[i]);
		}
		
		zgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
		
		if ( notran && colequ )
		    for (i = 0; i < A->ncol; ++i) {
		        zd_mult(&work[i], &work[i], C[i]);
		    }
		else if ( !notran && rowequ )
		    for (i = 0; i < A->ncol; ++i) {
		        zd_mult(&work[i], &work[i], R[i]);  
		    }
	    }
	    
	} while ( kase != 0 );

	/* Normalize error. */
	lstres = 0.;
 	if ( notran && colequ ) {
	    for (i = 0; i < A->nrow; ++i)
	    	lstres = SUPERLU_MAX( lstres, C[i] * z_abs1( &Xptr[i]) );
  	} else if ( !notran && rowequ ) {
	    for (i = 0; i < A->nrow; ++i)
	    	lstres = SUPERLU_MAX( lstres, R[i] * z_abs1( &Xptr[i]) );
	} else {
	    for (i = 0; i < A->nrow; ++i)
	    	lstres = SUPERLU_MAX( lstres, z_abs1( &Xptr[i]) );
	}
	if ( lstres != 0. )
	    ferr[j] /= lstres;

    } /* for each RHS j ... */
    
    SUPERLU_FREE(work);
    SUPERLU_FREE(rwork);
    SUPERLU_FREE(iwork);
    SUPERLU_FREE(Bjcol.Store);

    return;

} /* zgsrfs */