C++ ADB::derivative方法代码示例

    ADB PolymerPropsAd::effectiveInvWaterVisc(const ADB& c,
	                    				      const double* visc) const
    {
	    const int nc = c.size();
    	V inv_mu_w_eff(nc);
    	V dinv_mu_w_eff(nc);
    	for (int i = 0; i < nc; ++i) {
    	    double im = 0, dim = 0;
    	    polymer_props_.effectiveInvViscWithDer(c.value()(i), visc, im, dim);
    	    inv_mu_w_eff(i) = im;
    	    dinv_mu_w_eff(i) = dim;
    	}
        ADB::M dim_diag = spdiag(dinv_mu_w_eff);
        const int num_blocks = c.numBlocks();
        std::vector<ADB::M> jacs(num_blocks);
        for (int block = 0; block < num_blocks; ++block) {
            jacs[block] = dim_diag * c.derivative()[block];
        }
        return ADB::function(std::move(inv_mu_w_eff), std::move(jacs));
    }

ADB SolventPropsAdFromDeck::makeADBfromTables(const ADB& X_AD,
                                              const Cells& cells,
                                              const std::vector<int>& regionIdx,
                                              const std::vector<NonuniformTableLinear<double>>& tables) const {
    const int n = cells.size();
    assert(X_AD.value().size() == n);
    V x(n);
    V dx(n);
    for (int i = 0; i < n; ++i) {
        const double& X_i = X_AD.value()[i];
        x[i] = tables[regionIdx[cells[i]]](X_i);
        dx[i] = tables[regionIdx[cells[i]]].derivative(X_i);
    }

    ADB::M dx_diag(dx.matrix().asDiagonal());
    const int num_blocks = X_AD.numBlocks();
    std::vector<ADB::M> jacs(num_blocks);
    for (int block = 0; block < num_blocks; ++block) {
        fastSparseProduct(dx_diag, X_AD.derivative()[block], jacs[block]);
    }
    return ADB::function(std::move(x), std::move(jacs));
}

 /// Gas formation volume factor.
 /// \param[in]  pg     Array of n gas pressure values.
 /// \param[in]  cells  Array of n cell indices to be associated with the pressure values.
 /// \return            Array of n formation volume factor values.
 ADB BlackoilPropsAd::bGas(const ADB& pg,
                           const Cells& cells) const
 {
     if (!pu_.phase_used[Gas]) {
         OPM_THROW(std::runtime_error, "Cannot call muGas(): gas phase not present.");
     }
     const int n = cells.size();
     assert(pg.value().size() == n);
     const int np = props_.numPhases();
     Block z = Block::Zero(n, np);
     Block matrix(n, np*np);
     Block dmatrix(n, np*np);
     props_.matrix(n, pg.value().data(), z.data(), cells.data(), matrix.data(), dmatrix.data());
     const int phase_ind = pu_.phase_pos[Gas];
     const int column = phase_ind*np + phase_ind; // Index of our sought diagonal column.
     ADB::M db_diag = spdiag(dmatrix.col(column));
     const int num_blocks = pg.numBlocks();
     std::vector<ADB::M> jacs(num_blocks);
     for (int block = 0; block < num_blocks; ++block) {
         jacs[block] = db_diag * pg.derivative()[block];
     }
     return ADB::function(matrix.col(column), jacs);
 }

 /// Water formation volume factor.
 /// \param[in]  pw     Array of n water pressure values.
 /// \param[in]  cells  Array of n cell indices to be associated with the pressure values.
 /// \return            Array of n formation volume factor values.
 ADB BlackoilPropsAd::bWat(const ADB& pw,
                           const Cells& cells) const
 {
     if (!pu_.phase_used[Water]) {
         THROW("Cannot call muWat(): water phase not present.");
     }
     const int n = cells.size();
     ASSERT(pw.value().size() == n);
     const int np = props_.numPhases();
     Block z = Block::Zero(n, np);
     Block matrix(n, np*np);
     Block dmatrix(n, np*np);
     props_.matrix(n, pw.value().data(), z.data(), cells.data(), matrix.data(), dmatrix.data());
     const int phase_ind = pu_.phase_pos[Water];
     const int column = phase_ind*np + phase_ind; // Index of our sought diagonal column.
     ADB::M db_diag = spdiag(dmatrix.col(column));
     const int num_blocks = pw.numBlocks();
     std::vector<ADB::M> jacs(num_blocks);
     for (int block = 0; block < num_blocks; ++block) {
         jacs[block] = db_diag * pw.derivative()[block];
     }
     return ADB::function(matrix.col(column), jacs);
 }

    /// Water viscosity.
    /// \param[in]  pw     Array of n water pressure values.
    /// \param[in]  cells  Array of n cell indices to be associated with the pressure values.
    /// \return            Array of n viscosity values.
    ADB BlackoilPropsAdFromDeck::muWat(const ADB& pw,
                                       const Cells& cells) const
    {
        if (!phase_usage_.phase_used[Water]) {
            OPM_THROW(std::runtime_error, "Cannot call muWat(): water phase not present.");
        }
        const int n = cells.size();
        assert(pw.size() == n);
        V mu(n);
        V dmudp(n);
        V dmudr(n);
        const double* rs = 0;

        props_[phase_usage_.phase_pos[Water]]->mu(n, pw.value().data(), rs,
                                                  mu.data(), dmudp.data(), dmudr.data());
        ADB::M dmudp_diag = spdiag(dmudp);
        const int num_blocks = pw.numBlocks();
        std::vector<ADB::M> jacs(num_blocks);
        for (int block = 0; block < num_blocks; ++block) {
            jacs[block] = dmudp_diag * pw.derivative()[block];
        }
        return ADB::function(mu, jacs);
    }

    /// Oil viscosity.
    /// \param[in]  po     Array of n oil pressure values.
    /// \param[in]  rs     Array of n gas solution factor values.
    /// \param[in]  cond   Array of n taxonomies classifying fluid condition.
    /// \param[in]  cells  Array of n cell indices to be associated with the pressure values.
    /// \return            Array of n viscosity values.
    ADB BlackoilPropsAd::muOil(const ADB& po,
                               const ADB& rs,
                               const std::vector<PhasePresence>& cond,
                               const Cells& cells) const
    {
#if 1
        return ADB::constant(muOil(po.value(), rs.value(), cond, cells), po.blockPattern());
#else
        if (!pu_.phase_used[Oil]) {
            OPM_THROW(std::runtime_error, "Cannot call muOil(): oil phase not present.");
        }
        const int n = cells.size();
        assert(po.value().size() == n);
        const int np = props_.numPhases();
        Block z = Block::Zero(n, np);
        if (pu_.phase_used[Gas]) {
            // Faking a z with the right ratio:
            //   rs = zg/zo
            z.col(pu_.phase_pos[Oil]) = V::Ones(n, 1);
            z.col(pu_.phase_pos[Gas]) = rs.value();
        }
        Block mu(n, np);
        Block dmu(n, np);
        props_.viscosity(n, po.value().data(), z.data(), cells.data(), mu.data(), dmu.data());
        ADB::M dmu_diag = spdiag(dmu.col(pu_.phase_pos[Oil]));
        const int num_blocks = po.numBlocks();
        std::vector<ADB::M> jacs(num_blocks);
        for (int block = 0; block < num_blocks; ++block) {
            // For now, we deliberately ignore the derivative with respect to rs,
            // since the BlackoilPropertiesInterface class does not evaluate it.
            // We would add to the next line: + dmu_drs_diag * rs.derivative()[block]
            jacs[block] = dmu_diag * po.derivative()[block];
        }
        return ADB::function(mu.col(pu_.phase_pos[Oil]), jacs);
#endif
    }

//.........这里部分代码省略.........
    std::cerr << "Property arrays " << clock.secsSinceLast() << std::endl;

    // Initial pressure.
    V p0(nc,1);
    p0.fill(200*Opm::unit::barsa);

    // First actual AD usage: defining pressure variable.
    const std::vector<int> bpat = { nc };
    // Could actually write { nc } instead of bpat below,
    // but we prefer a named variable since we will repeat it.
    const ADB p = ADB::variable(0, p0, bpat);
    const ADB ngradp = ops.ngrad*p;
    // We want flux = totmob*trans*(p_i - p_j) for the ij-face.
    const ADB flux = mobtransf*ngradp;
    const ADB residual = ops.div*flux - q;
    std::cerr << "Construct AD residual " << clock.secsSinceLast() << std::endl;

    // It's the residual we want to be zero. We know it's linear in p,
    // so we just need a single linear solve. Since we have formulated
    // ourselves with a residual and jacobian we do this with a single
    // Newton step (hopefully easy to extend later):
    //   p = p0 - J(p0) \ R(p0)
    // Where R(p0) and J(p0) are contained in residual.value() and
    // residual.derived()[0].

#if HAVE_SUITESPARSE_UMFPACK_H
    typedef Eigen::UmfPackLU<S> LinSolver;
#else
    typedef Eigen::BiCGSTAB<S>  LinSolver;
#endif  // HAVE_SUITESPARSE_UMFPACK_H

    LinSolver solver;
    S pmatr;
    residual.derivative()[0].toSparse(pmatr);
    pmatr.coeffRef(0,0) *= 2.0;
    pmatr.makeCompressed();
    solver.compute(pmatr);
    if (solver.info() != Eigen::Success) {
        std::cerr << "Pressure/flow Jacobian decomposition error\n";
        return EXIT_FAILURE;
    }
    // const Eigen::VectorXd dp = solver.solve(residual.value().matrix());
    ADB::V residual_v = residual.value();
    const V dp = solver.solve(residual_v.matrix()).array();
    if (solver.info() != Eigen::Success) {
        std::cerr << "Pressure/flow solve failure\n";
        return EXIT_FAILURE;
    }
    const V p1 = p0 - dp;
    std::cerr << "Solve " << clock.secsSinceLast() << std::endl;
    // std::cout << p1 << std::endl;

    // ------ Transport solve ------

    // Now we'll try to do a transport step as well.
    // Residual formula is
    //   R_w = s_w - s_w^0 + dt/pv * (div v_w)
    // where
    //   v_w = f_w v
    // and f_w is (for now) based on averaged mobilities, not upwind.

    double res_norm = 1e100;
    const V sw0 = s0.leftCols<1>();
    // V sw1 = sw0;
    V sw1 = 0.5*V::Ones(nc,1);
    const V ndp = (ops.ngrad * p1.matrix()).array();

VFPProdProperties::ADB VFPProdProperties::bhp(const std::vector<int>& table_id,
                                              const ADB& aqua,
                                              const ADB& liquid,
                                              const ADB& vapour,
                                              const ADB& thp_arg,
                                              const ADB& alq) const {
    const int nw = thp_arg.size();

    std::vector<int> block_pattern = detail::commonBlockPattern(aqua, liquid, vapour, thp_arg, alq);

    assert(static_cast<int>(table_id.size()) == nw);
    assert(aqua.size()     == nw);
    assert(liquid.size()   == nw);
    assert(vapour.size()   == nw);
    assert(thp_arg.size()      == nw);
    assert(alq.size()      == nw);

    //Allocate data for bhp's and partial derivatives
    ADB::V value = ADB::V::Zero(nw);
    ADB::V dthp = ADB::V::Zero(nw);
    ADB::V dwfr = ADB::V::Zero(nw);
    ADB::V dgfr = ADB::V::Zero(nw);
    ADB::V dalq = ADB::V::Zero(nw);
    ADB::V dflo = ADB::V::Zero(nw);

    //Get the table for each well
    std::vector<const VFPProdTable*> well_tables(nw, nullptr);
    for (int i=0; i<nw; ++i) {
        if (table_id[i] >= 0) {
            well_tables[i] = detail::getTable(m_tables, table_id[i]);
        }
    }

    //Get the right FLO/GFR/WFR variable for each well as a single ADB
    const ADB flo = detail::combineADBVars<VFPProdTable::FLO_TYPE>(well_tables, aqua, liquid, vapour);
    const ADB wfr = detail::combineADBVars<VFPProdTable::WFR_TYPE>(well_tables, aqua, liquid, vapour);
    const ADB gfr = detail::combineADBVars<VFPProdTable::GFR_TYPE>(well_tables, aqua, liquid, vapour);

    //Compute the BHP for each well independently
    for (int i=0; i<nw; ++i) {
        const VFPProdTable* table = well_tables[i];
        if (table != nullptr) {
            //First, find the values to interpolate between
            //Value of FLO is negative in OPM for producers, but positive in VFP table
            auto flo_i = detail::findInterpData(-flo.value()[i], table->getFloAxis());
            auto thp_i = detail::findInterpData( thp_arg.value()[i], table->getTHPAxis());
            auto wfr_i = detail::findInterpData( wfr.value()[i], table->getWFRAxis());
            auto gfr_i = detail::findInterpData( gfr.value()[i], table->getGFRAxis());
            auto alq_i = detail::findInterpData( alq.value()[i], table->getALQAxis());

            detail::VFPEvaluation bhp_val = detail::interpolate(table->getTable(), flo_i, thp_i, wfr_i, gfr_i, alq_i);

            value[i] = bhp_val.value;
            dthp[i] = bhp_val.dthp;
            dwfr[i] = bhp_val.dwfr;
            dgfr[i] = bhp_val.dgfr;
            dalq[i] = bhp_val.dalq;
            dflo[i] = bhp_val.dflo;
        }
        else {
            value[i] = -1e100; //Signal that this value has not been calculated properly, due to "missing" table
        }
    }

    //Create diagonal matrices from ADB::Vs
    ADB::M dthp_diag(dthp.matrix().asDiagonal());
    ADB::M dwfr_diag(dwfr.matrix().asDiagonal());
    ADB::M dgfr_diag(dgfr.matrix().asDiagonal());
    ADB::M dalq_diag(dalq.matrix().asDiagonal());
    ADB::M dflo_diag(dflo.matrix().asDiagonal());

    //Calculate the Jacobians
    const int num_blocks = block_pattern.size();
    std::vector<ADB::M> jacs(num_blocks);
    for (int block = 0; block < num_blocks; ++block) {
        //Could have used fastSparseProduct and temporary variables
        //but may not save too much on that.
        jacs[block] = ADB::M(nw, block_pattern[block]);

        if (!thp_arg.derivative().empty()) {
            jacs[block] += dthp_diag * thp_arg.derivative()[block];
        }
        if (!wfr.derivative().empty()) {
            jacs[block] += dwfr_diag * wfr.derivative()[block];
        }
        if (!gfr.derivative().empty()) {
            jacs[block] += dgfr_diag * gfr.derivative()[block];
        }
        if (!alq.derivative().empty()) {
            jacs[block] += dalq_diag * alq.derivative()[block];
        }
        if (!flo.derivative().empty()) {
            jacs[block] -= dflo_diag * flo.derivative()[block];
        }
    }

    ADB retval = ADB::function(std::move(value), std::move(jacs));
    return retval;
}