workspace.hpp

Go to the documentation of this file.

//
// Copyright (c) 2022 INRIA
//
 
#ifndef PROXSUITE_PROXQP_SPARSE_WORKSPACE_HPP
#define PROXSUITE_PROXQP_SPARSE_WORKSPACE_HPP
 
#include <proxsuite/linalg/dense/core.hpp>
#include <proxsuite/linalg/sparse/core.hpp>
#include <proxsuite/linalg/sparse/factorize.hpp>
#include <proxsuite/linalg/sparse/update.hpp>
#include <proxsuite/linalg/sparse/rowmod.hpp>
#include <proxsuite/proxqp/timings.hpp>
#include <proxsuite/proxqp/settings.hpp>
#include <proxsuite/proxqp/dense/views.hpp>
#include <proxsuite/linalg/veg/vec.hpp>
#include "proxsuite/proxqp/sparse/views.hpp"
#include "proxsuite/proxqp/sparse/model.hpp"
#include "proxsuite/proxqp/results.hpp"
#include "proxsuite/proxqp/sparse/utils.hpp"
 
#include <memory>
#include <Eigen/IterativeLinearSolvers>
#include <unsupported/Eigen/IterativeSolvers>
 
namespace proxsuite {
namespace proxqp {
namespace sparse {
 
template<typename T, typename I>
void
refactorize(Workspace<T, I>& work,
            Results<T> const& results,
            Settings<T> const& settings,
            proxsuite::linalg::sparse::MatMut<T, I> kkt_active,
            proxsuite::linalg::veg::SliceMut<bool> active_constraints,
            Model<T, I> const& data,
            proxsuite::linalg::veg::dynstack::DynStackMut stack,
            proxsuite::linalg::veg::Tag<T>& xtag)
{
  isize n_tot = kkt_active.nrows();
  T mu_eq_neg = -results.info.mu_eq;
  T mu_in_neg(0);
  switch (settings.merit_function_type) {
    case MeritFunctionType::GPDAL:
      mu_in_neg = -settings.alpha_gpdal * results.info.mu_in;
      break;
    case MeritFunctionType::PDAL:
      mu_in_neg = -results.info.mu_in;
      break;
  }
 
  if (work.internal.do_ldlt) {
    proxsuite::linalg::sparse::factorize_symbolic_non_zeros(
      work.internal.ldl.nnz_counts.ptr_mut(),
      work.internal.ldl.etree.ptr_mut(),
      work.internal.ldl.perm_inv.ptr_mut(),
      work.internal.ldl.perm.ptr_mut(),
      kkt_active.symbolic(),
      stack);
 
    isize nnz = 0;
    VEG_ONLY_USED_FOR_DEBUG(nnz);
    for (usize j = 0; j < usize(kkt_active.ncols()); ++j) {
      nnz += usize(kkt_active.col_end(j) - kkt_active.col_start(j));
    }
    VEG_ASSERT(kkt_active.nnz() == nnz);
    auto _diag = stack.make_new_for_overwrite(xtag, n_tot);
    T* diag = _diag.ptr_mut();
 
    for (isize i = 0; i < data.dim; ++i) {
      diag[i] = results.info.rho;
    }
    for (isize i = 0; i < data.n_eq; ++i) {
      diag[data.dim + i] = mu_eq_neg;
    }
    for (isize i = 0; i < data.n_in; ++i) {
      diag[(data.dim + data.n_eq) + i] =
        active_constraints[i] ? mu_in_neg : T(1);
    }
 
    proxsuite::linalg::sparse::factorize_numeric(
      work.internal.ldl.values.ptr_mut(),
      work.internal.ldl.row_indices.ptr_mut(),
      diag,
      work.internal.ldl.perm.ptr_mut(),
      work.internal.ldl.col_ptrs.ptr(),
      work.internal.ldl.etree.ptr_mut(),
      work.internal.ldl.perm_inv.ptr_mut(),
      kkt_active.as_const(),
      stack);
  } else {
    *work.internal.matrix_free_kkt = { { kkt_active.as_const(),
                                         active_constraints.as_const(),
                                         data.dim,
                                         data.n_eq,
                                         data.n_in,
                                         results.info.rho,
                                         results.info.mu_eq_inv,
                                         results.info.mu_in_inv } };
    (*work.internal.matrix_free_solver).compute(*work.internal.matrix_free_kkt);
  }
}
 
template<typename T, typename I>
struct Ldlt
{
  proxsuite::linalg::veg::Vec<I> etree;
  proxsuite::linalg::veg::Vec<I> perm;
  proxsuite::linalg::veg::Vec<I> perm_inv;
  proxsuite::linalg::veg::Vec<I> col_ptrs;
  proxsuite::linalg::veg::Vec<I> nnz_counts;
  proxsuite::linalg::veg::Vec<I> row_indices;
  proxsuite::linalg::veg::Vec<T> values;
};
 
template<typename T, typename I>
struct Workspace
{
 
  struct /* NOLINT */
  {
    // temporary allocations
    proxsuite::linalg::veg::Vec<proxsuite::linalg::veg::mem::byte>
      storage; // memory of the stack with the requirements req which determines
               // its size.
    Ldlt<T, I> ldl;
    bool do_ldlt;
    bool do_symbolic_fact;
    // persistent allocations
 
    Eigen::Matrix<T, Eigen::Dynamic, 1> g_scaled;
    Eigen::Matrix<T, Eigen::Dynamic, 1> b_scaled;
    Eigen::Matrix<T, Eigen::Dynamic, 1> l_scaled;
    Eigen::Matrix<T, Eigen::Dynamic, 1> u_scaled;
    proxsuite::linalg::veg::Vec<I> kkt_nnz_counts;
 
    // stored in unique_ptr because we need a stable address
    std::unique_ptr<detail::AugmentedKkt<T, I>>
      matrix_free_kkt; // view on active part of the KKT which includes the
                       // regularizations
    std::unique_ptr<Eigen::MINRES<detail::AugmentedKkt<T, I>,
                                  Eigen::Upper | Eigen::Lower,
                                  Eigen::IdentityPreconditioner>>
      matrix_free_solver; // eigen based method which takes in entry vector, and
                          // performs matrix vector products
 
    auto stack_mut() -> proxsuite::linalg::veg::dynstack::DynStackMut
    {
      return {
        proxsuite::linalg::veg::from_slice_mut,
        storage.as_mut(),
      };
    } // exploits all available memory in storage
 
    // Whether the workspace is dirty
    bool dirty;
    bool proximal_parameter_update;
    bool is_initialized;
 
  } internal;
  VecBool active_set_up;
  VecBool active_set_low;
  proxsuite::linalg::veg::Vec<bool> active_inequalities;
  isize lnnz;
  void setup_symbolic_factorizaton(
    Model<T, I>& data,
    proxsuite::linalg::sparse::SymbolicMatRef<I> H,
    proxsuite::linalg::sparse::SymbolicMatRef<I> AT,
    proxsuite::linalg::sparse::SymbolicMatRef<I> CT)
  {
    auto& ldl = internal.ldl;
 
    auto& storage = internal.storage;
    auto& do_ldlt = internal.do_ldlt;
    // persistent allocations
 
    data.dim = H.nrows();
    data.n_eq = AT.ncols();
    data.n_in = CT.ncols();
    data.H_nnz = H.nnz();
    data.A_nnz = AT.nnz();
    data.C_nnz = CT.nnz();
 
    using namespace proxsuite::linalg::veg::dynstack;
    using namespace proxsuite::linalg::sparse::util;
    proxsuite::linalg::veg::Tag<I> itag;
 
    isize n = H.nrows();
    isize n_eq = AT.ncols();
    isize n_in = CT.ncols();
    isize n_tot = n + n_eq + n_in;
 
    isize nnz_tot = H.nnz() + AT.nnz() + CT.nnz();
 
    // form the full kkt matrix
    // assuming H, AT, CT are sorted
    // and H is upper triangular
    {
      data.kkt_col_ptrs.resize_for_overwrite(n_tot + 1); //
      data.kkt_row_indices.resize_for_overwrite(nnz_tot);
      data.kkt_values.resize_for_overwrite(nnz_tot);
 
      I* kktp = data.kkt_col_ptrs.ptr_mut();
      I* kkti = data.kkt_row_indices.ptr_mut();
 
      kktp[0] = 0;
      usize col = 0;
      usize pos = 0;
 
      auto insert_submatrix =
        [&](proxsuite::linalg::sparse::SymbolicMatRef<I> m,
            bool assert_sym_hi) -> void {
        I const* mi = m.row_indices();
        isize ncols = m.ncols();
 
        for (usize j = 0; j < usize(ncols); ++j) {
          usize col_start = m.col_start(j);
          usize col_end = m.col_end(j);
 
          kktp[col + 1] =
            checked_non_negative_plus(kktp[col], I(col_end - col_start));
          ++col;
 
          for (usize p = col_start; p < col_end; ++p) {
            usize i = zero_extend(mi[p]);
            if (assert_sym_hi) {
              VEG_ASSERT(i <= j);
            }
 
            kkti[pos] = proxsuite::linalg::veg::nb::narrow<I>{}(i);
 
            ++pos;
          }
        }
      };
 
      insert_submatrix(H, true);
      insert_submatrix(AT, false);
      insert_submatrix(CT, false);
    }
 
    data.kkt_col_ptrs_unscaled = data.kkt_col_ptrs;
    data.kkt_row_indices_unscaled = data.kkt_row_indices;
 
    storage.resize_for_overwrite( //
      (StackReq::with_len(itag, n_tot) &
       proxsuite::linalg::sparse::factorize_symbolic_req( //
         itag,                                            //
         n_tot,                                           //
         nnz_tot,                                         //
         proxsuite::linalg::sparse::Ordering::amd))       //
        .alloc_req()                                      //
    );
 
    ldl.col_ptrs.resize_for_overwrite(n_tot + 1);
    ldl.perm_inv.resize_for_overwrite(n_tot);
 
    DynStackMut stack = stack_mut();
 
    bool overflow = false;
    {
      ldl.etree.resize_for_overwrite(n_tot);
      auto etree_ptr = ldl.etree.ptr_mut();
 
      using namespace proxsuite::linalg::veg::literals;
      auto kkt_sym = proxsuite::linalg::sparse::SymbolicMatRef<I>{
        proxsuite::linalg::sparse::from_raw_parts,
        n_tot,
        n_tot,
        nnz_tot,
        data.kkt_col_ptrs.ptr(),
        nullptr,
        data.kkt_row_indices.ptr(),
      };
      proxsuite::linalg::sparse::factorize_symbolic_non_zeros( //
        ldl.col_ptrs.ptr_mut() +
          1, // reimplements col counts to get the matrix free version as well
        etree_ptr,
        ldl.perm_inv.ptr_mut(),
        static_cast<I const*>(nullptr),
        kkt_sym,
        stack);
 
      auto pcol_ptrs = ldl.col_ptrs.ptr_mut();
      pcol_ptrs[0] = I(0);
 
      using proxsuite::linalg::veg::u64;
      u64 acc = 0;
 
      for (usize i = 0; i < usize(n_tot); ++i) {
        acc += u64(zero_extend(pcol_ptrs[i + 1]));
        if (acc != u64(I(acc))) {
          overflow = true;
        }
        pcol_ptrs[(i + 1)] = I(acc);
      }
    }
 
    lnnz = isize(zero_extend(ldl.col_ptrs[n_tot]));
 
    // if ldlt is too sparse
    // do_ldlt = !overflow && lnnz < (10000000);
    do_ldlt = !overflow && lnnz < 10000000;
 
    internal.do_symbolic_fact = false;
  }

  template<typename P>
  void setup_impl(const QpView<T, I> qp,
                  Model<T, I>& data,
                  const Settings<T>& settings,
                  bool execute_or_not,
                  P& precond,
                  proxsuite::linalg::veg::dynstack::StackReq precond_req)
  {
 
    auto& ldl = internal.ldl;
 
    auto& storage = internal.storage;
    auto& do_ldlt = internal.do_ldlt;
    // persistent allocations
 
    auto& g_scaled = internal.g_scaled;
    auto& b_scaled = internal.b_scaled;
    auto& l_scaled = internal.l_scaled;
    auto& u_scaled = internal.u_scaled;
    auto& kkt_nnz_counts = internal.kkt_nnz_counts;
 
    // stored in unique_ptr because we need a stable address
    auto& matrix_free_solver = internal.matrix_free_solver;
    auto& matrix_free_kkt = internal.matrix_free_kkt;
 
    data.dim = qp.H.nrows();
    data.n_eq = qp.AT.ncols();
    data.n_in = qp.CT.ncols();
    data.H_nnz = qp.H.nnz();
    data.A_nnz = qp.AT.nnz();
    data.C_nnz = qp.CT.nnz();
 
    data.g = qp.g.to_eigen();
    data.b = qp.b.to_eigen();
    data.l = qp.l.to_eigen();
    data.u = qp.u.to_eigen();
 
    using namespace proxsuite::linalg::veg::dynstack;
    using namespace proxsuite::linalg::sparse::util;
 
    using SR = StackReq;
    proxsuite::linalg::veg::Tag<I> itag;
    proxsuite::linalg::veg::Tag<T> xtag;
 
    isize n = qp.H.nrows();
    isize n_eq = qp.AT.ncols();
    isize n_in = qp.CT.ncols();
    isize n_tot = n + n_eq + n_in;
 
    isize nnz_tot = qp.H.nnz() + qp.AT.nnz() + qp.CT.nnz();
 
    if (internal.do_symbolic_fact) {
 
      // form the full kkt matrix
      // assuming H, AT, CT are sorted
      // and H is upper triangular
      {
        data.kkt_col_ptrs.resize_for_overwrite(n_tot + 1);
        data.kkt_row_indices.resize_for_overwrite(nnz_tot);
        data.kkt_values.resize_for_overwrite(nnz_tot);
 
        I* kktp = data.kkt_col_ptrs.ptr_mut();
        I* kkti = data.kkt_row_indices.ptr_mut();
        T* kktx = data.kkt_values.ptr_mut();
 
        kktp[0] = 0;
        usize col = 0;
        usize pos = 0;
 
        auto insert_submatrix = [&](proxsuite::linalg::sparse::MatRef<T, I> m,
                                    bool assert_sym_hi) -> void {
          I const* mi = m.row_indices();
          T const* mx = m.values();
          isize ncols = m.ncols();
 
          for (usize j = 0; j < usize(ncols); ++j) {
            usize col_start = m.col_start(j);
            usize col_end = m.col_end(j);
 
            kktp[col + 1] =
              checked_non_negative_plus(kktp[col], I(col_end - col_start));
            ++col;
 
            for (usize p = col_start; p < col_end; ++p) {
              usize i = zero_extend(mi[p]);
              if (assert_sym_hi) {
                VEG_ASSERT(i <= j);
              }
 
              kkti[pos] = proxsuite::linalg::veg::nb::narrow<I>{}(i);
              kktx[pos] = mx[p];
 
              ++pos;
            }
          }
        };
 
        insert_submatrix(qp.H, true);
        insert_submatrix(qp.AT, false);
        insert_submatrix(qp.CT, false);
      }
 
      data.kkt_col_ptrs_unscaled = data.kkt_col_ptrs;
      data.kkt_row_indices_unscaled = data.kkt_row_indices;
      data.kkt_values_unscaled = data.kkt_values;
 
      storage.resize_for_overwrite( //
        (StackReq::with_len(itag, n_tot) &
         proxsuite::linalg::sparse::factorize_symbolic_req( //
           itag,                                            //
           n_tot,                                           //
           nnz_tot,                                         //
           proxsuite::linalg::sparse::Ordering::amd))       //
          .alloc_req()                                      //
      );
 
      ldl.col_ptrs.resize_for_overwrite(n_tot + 1);
      ldl.perm_inv.resize_for_overwrite(n_tot);
 
      DynStackMut stack = stack_mut();
 
      bool overflow = false;
      {
        ldl.etree.resize_for_overwrite(n_tot);
        auto etree_ptr = ldl.etree.ptr_mut();
 
        using namespace proxsuite::linalg::veg::literals;
        auto kkt_sym = proxsuite::linalg::sparse::SymbolicMatRef<I>{
          proxsuite::linalg::sparse::from_raw_parts,
          n_tot,
          n_tot,
          nnz_tot,
          data.kkt_col_ptrs.ptr(),
          nullptr,
          data.kkt_row_indices.ptr(),
        };
        proxsuite::linalg::sparse::factorize_symbolic_non_zeros( //
          ldl.col_ptrs.ptr_mut() + 1,
          etree_ptr,
          ldl.perm_inv.ptr_mut(),
          static_cast<I const*>(nullptr),
          kkt_sym,
          stack);
 
        auto pcol_ptrs = ldl.col_ptrs.ptr_mut();
        pcol_ptrs[0] = I(0); // pcol_ptrs +1: pointor towards the nbr of non
                             // zero elts per column of the ldlt
        // we need to compute its cumulative sum below to determine if there
        // could be an overflow
 
        using proxsuite::linalg::veg::u64;
        u64 acc = 0;
 
        for (usize i = 0; i < usize(n_tot); ++i) {
          acc += u64(zero_extend(pcol_ptrs[i + 1]));
          if (acc != u64(I(acc))) {
            overflow = true;
          }
          pcol_ptrs[(i + 1)] = I(acc);
        }
      }
 
      auto lnnz = isize(zero_extend(ldl.col_ptrs[n_tot]));
 
      // if ldlt is too sparse
      // do_ldlt = !overflow && lnnz < (10000000);
      if (settings.sparse_backend == SparseBackend::Automatic) {
        do_ldlt = !overflow && lnnz < 10000000;
      } else if (settings.sparse_backend == SparseBackend::SparseCholesky) {
        do_ldlt = true;
      } else {
        do_ldlt = false;
      }
 
    } else {
      T* kktx = data.kkt_values.ptr_mut();
      usize pos = 0;
      auto insert_submatrix =
        [&](proxsuite::linalg::sparse::MatRef<T, I> m) -> void {
        T const* mx = m.values();
        isize ncols = m.ncols();
 
        for (usize j = 0; j < usize(ncols); ++j) {
          usize col_start = m.col_start(j);
          usize col_end = m.col_end(j);
          for (usize p = col_start; p < col_end; ++p) {
 
            kktx[pos] = mx[p];
 
            ++pos;
          }
        }
      };
 
      insert_submatrix(qp.H);
      insert_submatrix(qp.AT);
      insert_submatrix(qp.CT);
      data.kkt_values_unscaled = data.kkt_values;
    }
#define PROX_QP_ALL_OF(...)                                                    \
  ::proxsuite::linalg::veg::dynstack::StackReq::and_(                          \
    ::proxsuite::linalg::veg::init_list(__VA_ARGS__))
#define PROX_QP_ANY_OF(...)                                                    \
  ::proxsuite::linalg::veg::dynstack::StackReq::or_(                           \
    ::proxsuite::linalg::veg::init_list(__VA_ARGS__))
    //  ? --> if
    auto refactorize_req =
      do_ldlt
        ? PROX_QP_ANY_OF({
            proxsuite::linalg::sparse::factorize_symbolic_req( // symbolic ldl
              itag,
              n_tot,
              nnz_tot,
              proxsuite::linalg::sparse::Ordering::user_provided),
            PROX_QP_ALL_OF({
              SR::with_len(xtag, n_tot),                        // diag
              proxsuite::linalg::sparse::factorize_numeric_req( // numeric ldl
                xtag,
                itag,
                n_tot,
                nnz_tot,
                proxsuite::linalg::sparse::Ordering::user_provided),
            }),
          })
        : PROX_QP_ALL_OF({
            SR::with_len(itag, 0), // compute necessary space for storing n elts
                                   // of type I (n = 0 here)
            SR::with_len(xtag, 0), // compute necessary space for storing n elts
                                   // of type T (n = 0 here)
          });
 
    auto x_vec = [&](isize n) noexcept -> StackReq {
      return proxsuite::linalg::dense::temp_vec_req(xtag, n);
    };
 
    auto ldl_solve_in_place_req = PROX_QP_ALL_OF({
      x_vec(n_tot), // tmp
      x_vec(n_tot), // err
      x_vec(n_tot), // work
    });
 
    auto unscaled_primal_dual_residual_req = x_vec(n); // Hx
    auto line_search_req = PROX_QP_ALL_OF({
      x_vec(2 * n_in), // alphas
      x_vec(n),        // Cdx_active
      x_vec(n_in),     // active_part_z
      x_vec(n_in),     // tmp_lo
      x_vec(n_in),     // tmp_up
    });
    // define memory needed for primal_dual_newton_semi_smooth
    // PROX_QP_ALL_OF --> need to store all argument inside
    // PROX_QP_ANY_OF --> au moins un de  ceux en entrée
    auto primal_dual_newton_semi_smooth_req = PROX_QP_ALL_OF({
      x_vec(n_tot), // dw
      PROX_QP_ANY_OF({
        ldl_solve_in_place_req,
        PROX_QP_ALL_OF({
          SR::with_len(proxsuite::linalg::veg::Tag<bool>{},
                       n_in), // active_set_lo
          SR::with_len(proxsuite::linalg::veg::Tag<bool>{},
                       n_in), // active_set_up
          SR::with_len(proxsuite::linalg::veg::Tag<bool>{},
                       n_in), // new_active_constraints
          (do_ldlt && n_in > 0) ? PROX_QP_ANY_OF({
                                    proxsuite::linalg::sparse::add_row_req(
                                      xtag, itag, n_tot, false, n, n_tot),
                                    proxsuite::linalg::sparse::delete_row_req(
                                      xtag, itag, n_tot, n_tot),
                                  })
                                : refactorize_req,
        }),
        PROX_QP_ALL_OF({
          x_vec(n),    // Hdx
          x_vec(n_eq), // Adx
          x_vec(n_in), // Cdx
          x_vec(n),    // ATdy
          x_vec(n),    // CTdz
        }),
      }),
      line_search_req,
    });
 
    auto iter_req = PROX_QP_ANY_OF({
      PROX_QP_ALL_OF({ x_vec(n_eq), // primal_residual_eq_scaled
                       x_vec(n_in), // primal_residual_in_scaled_lo
                       x_vec(n_in), // primal_residual_in_scaled_up
                       x_vec(n_in), // primal_residual_in_scaled_up
                       x_vec(n),    // dual_residual_scaled
                       PROX_QP_ANY_OF({
                         unscaled_primal_dual_residual_req,
                         PROX_QP_ALL_OF({
                           x_vec(n),    // x_prev
                           x_vec(n_eq), // y_prev
                           x_vec(n_in), // z_prev
                           primal_dual_newton_semi_smooth_req,
                         }),
                       }) }),
      refactorize_req, // mu_update
    });
 
    auto req = //
      PROX_QP_ALL_OF({
        x_vec(n),    // g_scaled
        x_vec(n_eq), // b_scaled
        x_vec(n_in), // l_scaled
        x_vec(n_in), // u_scaled
        SR::with_len(proxsuite::linalg::veg::Tag<bool>{},
                     n_in),        // active constr
        SR::with_len(itag, n_tot), // kkt nnz counts
        refactorize_req,
        PROX_QP_ANY_OF({
          precond_req,
          PROX_QP_ALL_OF({
            do_ldlt ? PROX_QP_ALL_OF({
                        SR::with_len(itag, n_tot), // perm
                        SR::with_len(itag, n_tot), // etree
                        SR::with_len(itag, n_tot), // ldl nnz counts
                        SR::with_len(itag, lnnz),  // ldl row indices
                        SR::with_len(xtag, lnnz),  // ldl values
                      })
                    : PROX_QP_ALL_OF({
                        SR::with_len(itag, 0),
                        SR::with_len(xtag, 0),
                      }),
            iter_req,
          }),
        }),
      });
 
    storage.resize_for_overwrite(
      req.alloc_req()); // defines the maximal storage size
    // storage.resize(n): if it is done twice in a row, the second times it does
    // nothing, as the same resize has been asked
 
    // preconditioner
    auto kkt = data.kkt_mut();
    auto kkt_top_n_rows = detail::top_rows_mut_unchecked(
      proxsuite::linalg::veg::unsafe,
      kkt,
      n); //  top_rows_mut_unchecked: take a view of sparse matrix for n first
          //  lines ; the function assumes all others lines are zeros;
    /*
            H AT CT
            A
            C
 
            here we store the upper triangular part below
 
            tirSup(H) AT CT
            0 0 0
            0 0 0
 
            proxsuite::linalg::veg::unsafe:  precises that the function has
       undefined behavior if upper condition is not respected.
    */
 
    proxsuite::linalg::sparse::MatMut<T, I> H_scaled =
      detail::middle_cols_mut(kkt_top_n_rows, 0, n, data.H_nnz);
 
    proxsuite::linalg::sparse::MatMut<T, I> AT_scaled =
      detail::middle_cols_mut(kkt_top_n_rows, n, n_eq, data.A_nnz);
 
    proxsuite::linalg::sparse::MatMut<T, I> CT_scaled =
      detail::middle_cols_mut(kkt_top_n_rows, n + n_eq, n_in, data.C_nnz);
 
    g_scaled = data.g;
    b_scaled = data.b;
    u_scaled =
      (data.u.array() <= T(1.E20))
        .select(data.u,
                Eigen::Matrix<T, Eigen::Dynamic, 1>::Zero(data.n_in).array() +
                  T(1.E20));
    l_scaled =
      (data.l.array() >= T(-1.E20))
        .select(data.l,
                Eigen::Matrix<T, Eigen::Dynamic, 1>::Zero(data.n_in).array() -
                  T(1.E20));
 
    QpViewMut<T, I> qp_scaled = {
      H_scaled,
      { proxsuite::linalg::sparse::from_eigen, g_scaled },
      AT_scaled,
      { proxsuite::linalg::sparse::from_eigen, b_scaled },
      CT_scaled,
      { proxsuite::linalg::sparse::from_eigen, l_scaled },
      { proxsuite::linalg::sparse::from_eigen, u_scaled },
    };
 
    DynStackMut stack = stack_mut();
    precond.scale_qp_in_place(qp_scaled,
                              execute_or_not,
                              settings.primal_infeasibility_solving,
                              settings.preconditioner_max_iter,
                              settings.preconditioner_accuracy,
                              stack);
    kkt_nnz_counts.resize_for_overwrite(n_tot);
 
    proxsuite::linalg::sparse::MatMut<T, I> kkt_active = {
      proxsuite::linalg::sparse::from_raw_parts,
      n_tot,
      n_tot,
      data.H_nnz +
        data.A_nnz, // these variables are not used for the matrix vector
                    // product in augmented KKT with Min res algorithm (to be
                    // exact, it should depend of the initial guess)
      kkt.col_ptrs_mut(),
      kkt_nnz_counts.ptr_mut(),
      kkt.row_indices_mut(),
      kkt.values_mut(),
    };
 
    using MatrixFreeSolver = Eigen::MINRES<detail::AugmentedKkt<T, I>,
                                           Eigen::Upper | Eigen::Lower,
                                           Eigen::IdentityPreconditioner>;
    matrix_free_solver = std::unique_ptr<MatrixFreeSolver>{
      new MatrixFreeSolver,
    };
    matrix_free_kkt = std::unique_ptr<detail::AugmentedKkt<T, I>>{
      new detail::AugmentedKkt<T, I>{
        {
          kkt_active.as_const(),
          {},
          n,
          n_eq,
          n_in,
          {},
          {},
          {},
        },
      }
    };
 
    auto zx = proxsuite::linalg::sparse::util::zero_extend; // ?
    auto max_lnnz = isize(zx(ldl.col_ptrs[n_tot]));
    isize ldlt_ntot = do_ldlt ? n_tot : 0;
    isize ldlt_lnnz = do_ldlt ? max_lnnz : 0;
 
    ldl.nnz_counts.resize_for_overwrite(ldlt_ntot);
    ldl.row_indices.resize_for_overwrite(ldlt_lnnz);
    ldl.values.resize_for_overwrite(ldlt_lnnz);
 
    ldl.perm.resize_for_overwrite(ldlt_ntot);
    if (do_ldlt) {
      // compute perm from perm_inv
      for (isize i = 0; i < n_tot; ++i) {
        ldl.perm[isize(zx(ldl.perm_inv[i]))] = I(i);
      }
    }
 
    internal.dirty = false;
  }
  Timer<T> timer;
  Workspace() = default;
 
  auto ldl_col_ptrs() const -> I const* { return internal.ldl.col_ptrs.ptr(); }
  auto ldl_col_ptrs_mut() -> I* { return internal.ldl.col_ptrs.ptr_mut(); }
  auto stack_mut() -> proxsuite::linalg::veg::dynstack::DynStackMut
  {
    return internal.stack_mut();
  }
 
  void set_dirty() { internal.dirty = true; }
};
 
} // namespace sparse
} // namespace proxqp
} // namespace proxsuite
 
#endif /* end of include guard PROXSUITE_PROXQP_SPARSE_WORKSPACE_HPP */