gmm_superlu_interface.h

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/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================

 Copyright (C) 2003-2017 Yves Renard

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/**@file gmm_superlu_interface.h
   @author  Yves Renard <Yves.Renard@insa-lyon.fr>
   @date October 17, 2003.
   @brief Interface with SuperLU (LU direct solver for sparse matrices).
*/
#if defined(GMM_USES_SUPERLU) && !defined(GETFEM_VERSION)

#ifndef GMM_SUPERLU_INTERFACE_H
#define GMM_SUPERLU_INTERFACE_H

#include "gmm_kernel.h"

typedef int int_t;

/* because SRC/util.h defines TRUE and FALSE ... */
#ifdef TRUE
# undef TRUE
#endif
#ifdef FALSE
# undef FALSE
#endif

#include "superlu/slu_Cnames.h"
#include "superlu/supermatrix.h"
#include "superlu/slu_util.h"

namespace SuperLU_S {
#include "superlu/slu_sdefs.h"
}
namespace SuperLU_D {
#include "superlu/slu_ddefs.h"
}
namespace SuperLU_C {
#include "superlu/slu_cdefs.h"
}
namespace SuperLU_Z {
#include "superlu/slu_zdefs.h" 
}



namespace gmm {

  /*  interface for Create_CompCol_Matrix */

  inline void Create_CompCol_Matrix(SuperMatrix *A, int m, int n, int nnz,
                             float *a, int *ir, int *jc) {
    SuperLU_S::sCreate_CompCol_Matrix(A, m, n, nnz, a, ir, jc,
                                      SLU_NC, SLU_S, SLU_GE);
  }
  
  inline void Create_CompCol_Matrix(SuperMatrix *A, int m, int n, int nnz,
                             double *a, int *ir, int *jc) {
    SuperLU_D::dCreate_CompCol_Matrix(A, m, n, nnz, a, ir, jc,
                                      SLU_NC, SLU_D, SLU_GE);
  }
  
  inline void Create_CompCol_Matrix(SuperMatrix *A, int m, int n, int nnz,
                             std::complex<float> *a, int *ir, int *jc) {
    SuperLU_C::cCreate_CompCol_Matrix(A, m, n, nnz, (SuperLU_C::complex *)(a),
                                      ir, jc, SLU_NC, SLU_C, SLU_GE);
  }
  
  inline void Create_CompCol_Matrix(SuperMatrix *A, int m, int n, int nnz,
                             std::complex<double> *a, int *ir, int *jc) {
    SuperLU_Z::zCreate_CompCol_Matrix(A, m, n, nnz,
                                      (SuperLU_Z::doublecomplex *)(a), ir, jc,
                                      SLU_NC, SLU_Z, SLU_GE);
  }

  /*  interface for Create_Dense_Matrix */

  inline void Create_Dense_Matrix(SuperMatrix *A, int m, int n, float *a, int k)
  { SuperLU_S::sCreate_Dense_Matrix(A, m, n, a, k, SLU_DN, SLU_S, SLU_GE); }
  inline void Create_Dense_Matrix(SuperMatrix *A, int m, int n, double *a, int k)
  { SuperLU_D::dCreate_Dense_Matrix(A, m, n, a, k, SLU_DN, SLU_D, SLU_GE); }
  inline void Create_Dense_Matrix(SuperMatrix *A, int m, int n,
                           std::complex<float> *a, int k) {
    SuperLU_C::cCreate_Dense_Matrix(A, m, n, (SuperLU_C::complex *)(a),
                                    k, SLU_DN, SLU_C, SLU_GE);
  }
  inline void Create_Dense_Matrix(SuperMatrix *A, int m, int n, 
                           std::complex<double> *a, int k) {
    SuperLU_Z::zCreate_Dense_Matrix(A, m, n, (SuperLU_Z::doublecomplex *)(a),
                                    k, SLU_DN, SLU_Z, SLU_GE);
  }

  /*  interface for gssv */

#define DECL_GSSV(NAMESPACE,FNAME,FLOATTYPE,KEYTYPE) \
  inline void SuperLU_gssv(superlu_options_t *options, SuperMatrix *A, int *p, \
  int *q, SuperMatrix *L, SuperMatrix *U, SuperMatrix *B,               \
  SuperLUStat_t *stats, int *info, KEYTYPE) {                           \
  NAMESPACE::FNAME(options, A, p, q, L, U, B, stats, info);             \
  }

  DECL_GSSV(SuperLU_S,sgssv,float,float)
  DECL_GSSV(SuperLU_C,cgssv,float,std::complex<float>)
  DECL_GSSV(SuperLU_D,dgssv,double,double)
  DECL_GSSV(SuperLU_Z,zgssv,double,std::complex<double>)

  /*  interface for gssvx */

#define DECL_GSSVX(NAMESPACE,FNAME,FLOATTYPE,KEYTYPE) \
    inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A,      \
                     int *perm_c, int *perm_r, int *etree, char *equed,  \
                     FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L,         \
                     SuperMatrix *U, void *work, int lwork,              \
                     SuperMatrix *B, SuperMatrix *X,                     \
                     FLOATTYPE *recip_pivot_growth,                      \
                     FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr, \
                     SuperLUStat_t *stats, int *info, KEYTYPE) {         \
    NAMESPACE::mem_usage_t mem_usage;                                    \
    NAMESPACE::FNAME(options, A, perm_c, perm_r, etree, equed, R, C, L,  \
                     U, work, lwork, B, X, recip_pivot_growth, rcond,    \
                     ferr, berr, &mem_usage, stats, info);               \
    return mem_usage.for_lu; /* bytes used by the factor storage */     \
  }

  DECL_GSSVX(SuperLU_S,sgssvx,float,float)
  DECL_GSSVX(SuperLU_C,cgssvx,float,std::complex<float>)
  DECL_GSSVX(SuperLU_D,dgssvx,double,double)
  DECL_GSSVX(SuperLU_Z,zgssvx,double,std::complex<double>)

  /* ********************************************************************* */
  /*   SuperLU solve interface                                             */
  /* ********************************************************************* */

  template <typename MAT, typename VECTX, typename VECTB>
  int SuperLU_solve(const MAT &A, const VECTX &X_, const VECTB &B,
                     double& rcond_, int permc_spec = 3) {
    VECTX &X = const_cast<VECTX &>(X_);
    /*
     * Get column permutation vector perm_c[], according to permc_spec:
     *   permc_spec = 0: use the natural ordering 
     *   permc_spec = 1: use minimum degree ordering on structure of A'*A
     *   permc_spec = 2: use minimum degree ordering on structure of A'+A
     *   permc_spec = 3: use approximate minimum degree column ordering
     */
    typedef typename linalg_traits<MAT>::value_type T;
    typedef typename number_traits<T>::magnitude_type R;

    int m = mat_nrows(A), n = mat_ncols(A), nrhs = 1, info = 0;

    csc_matrix<T> csc_A(m, n); gmm::copy(A, csc_A);
    std::vector<T> rhs(m), sol(m);
    gmm::copy(B, rhs);

    int nz = nnz(csc_A);
    if ((2 * nz / n) >= m)
      GMM_WARNING2("CAUTION : it seems that SuperLU has a problem"
                  " for nearly dense sparse matrices");

    superlu_options_t options;
    set_default_options(&options);
    options.ColPerm = NATURAL;
    options.PrintStat = NO;
    options.ConditionNumber = YES;
    switch (permc_spec) {
    case 1 : options.ColPerm = MMD_ATA; break;
    case 2 : options.ColPerm = MMD_AT_PLUS_A; break;
    case 3 : options.ColPerm = COLAMD; break;
    }
    SuperLUStat_t stat;
    StatInit(&stat);

    SuperMatrix SA, SL, SU, SB, SX; // SuperLU format.
    Create_CompCol_Matrix(&SA, m, n, nz, (double *)(&(csc_A.pr[0])),
                          (int *)(&(csc_A.ir[0])), (int *)(&(csc_A.jc[0])));
    Create_Dense_Matrix(&SB, m, nrhs, &rhs[0], m);
    Create_Dense_Matrix(&SX, m, nrhs, &sol[0], m);
    memset(&SL,0,sizeof SL);
    memset(&SU,0,sizeof SU);

    std::vector<int> etree(n);
    char equed[] = "B";
    std::vector<R> Rscale(m),Cscale(n); // row scale factors
    std::vector<R> ferr(nrhs), berr(nrhs);
    R recip_pivot_gross, rcond;
    std::vector<int> perm_r(m), perm_c(n);

    SuperLU_gssvx(&options, &SA, &perm_c[0], &perm_r[0], 
                  &etree[0] /* output */, equed /* output         */, 
                  &Rscale[0] /* row scale factors (output)        */, 
                  &Cscale[0] /* col scale factors (output)        */,
                  &SL /* fact L (output)*/, &SU /* fact U (output)*/, 
                  NULL /* work                                    */, 
                  0 /* lwork: superlu auto allocates (input)      */, 
                  &SB /* rhs */, &SX /* solution                  */,
                  &recip_pivot_gross /* reciprocal pivot growth   */
                  /* factor max_j( norm(A_j)/norm(U_j) ).         */,  
                  &rcond /*estimate of the reciprocal condition   */
                  /* number of the matrix A after equilibration   */,
                  &ferr[0] /* estimated forward error             */,
                  &berr[0] /* relative backward error             */,
                  &stat, &info, T());
    rcond_ = rcond;
    Destroy_SuperMatrix_Store(&SB);
    Destroy_SuperMatrix_Store(&SX);
    Destroy_SuperMatrix_Store(&SA);
    Destroy_SuperNode_Matrix(&SL);
    Destroy_CompCol_Matrix(&SU);
    StatFree(&stat);
    GMM_ASSERT1(info >= 0, "SuperLU solve failed: info =" << info);
    if (info > 0) GMM_WARNING1("SuperLU solve failed: info =" << info);
    gmm::copy(sol, X);
    return info;
  }

  template <class T> class SuperLU_factor {
    typedef typename number_traits<T>::magnitude_type R;

    csc_matrix<T> csc_A;
    mutable SuperMatrix SA, SL, SB, SU, SX;
    mutable SuperLUStat_t stat;
    mutable superlu_options_t options;
    float memory_used;
    mutable std::vector<int> etree, perm_r, perm_c;
    mutable std::vector<R> Rscale, Cscale;
    mutable std::vector<R> ferr, berr;
    mutable std::vector<T> rhs;
    mutable std::vector<T> sol;
    mutable bool is_init;
    mutable char equed;

  public :
    enum { LU_NOTRANSP, LU_TRANSP, LU_CONJUGATED };
    void free_supermatrix(void);
    template <class MAT> void build_with(const MAT &A,  int permc_spec = 3);
    template <typename VECTX, typename VECTB> 
    /* transp = LU_NOTRANSP   -> solves Ax = B
       transp = LU_TRANSP     -> solves A'x = B
       transp = LU_CONJUGATED -> solves conj(A)X = B */
    void solve(const VECTX &X_, const VECTB &B, int transp=LU_NOTRANSP) const;
    SuperLU_factor(void) { is_init = false; }
    SuperLU_factor(const SuperLU_factor& other) {
      GMM_ASSERT2(!(other.is_init),
                 "copy of initialized SuperLU_factor is forbidden");
      is_init = false;
    }
    SuperLU_factor& operator=(const SuperLU_factor& other) {
      GMM_ASSERT2(!(other.is_init) && !is_init,
                  "assignment of initialized SuperLU_factor is forbidden");
      return *this;
    }
    ~SuperLU_factor() { free_supermatrix(); }
    float memsize() { return memory_used; }
  };


  template <class T> void SuperLU_factor<T>::free_supermatrix(void) {
      if (is_init) {
        if (SB.Store) Destroy_SuperMatrix_Store(&SB);
        if (SX.Store) Destroy_SuperMatrix_Store(&SX);
        if (SA.Store) Destroy_SuperMatrix_Store(&SA);
        if (SL.Store) Destroy_SuperNode_Matrix(&SL);
        if (SU.Store) Destroy_CompCol_Matrix(&SU);
      }
    }

    
    template <class T> template <class MAT>
    void SuperLU_factor<T>::build_with(const MAT &A,  int permc_spec) {
    /*
     * Get column permutation vector perm_c[], according to permc_spec:
     *   permc_spec = 0: use the natural ordering 
     *   permc_spec = 1: use minimum degree ordering on structure of A'*A
     *   permc_spec = 2: use minimum degree ordering on structure of A'+A
     *   permc_spec = 3: use approximate minimum degree column ordering
     */
      free_supermatrix();
      int n = mat_nrows(A), m = mat_ncols(A), info = 0;
      csc_A.init_with(A);

      rhs.resize(m); sol.resize(m);
      gmm::clear(rhs);
      int nz = nnz(csc_A);

      set_default_options(&options);
      options.ColPerm = NATURAL;
      options.PrintStat = NO;
      options.ConditionNumber = NO;
      switch (permc_spec) {
      case 1 : options.ColPerm = MMD_ATA; break;
      case 2 : options.ColPerm = MMD_AT_PLUS_A; break;
      case 3 : options.ColPerm = COLAMD; break;
      }
      StatInit(&stat);

      Create_CompCol_Matrix(&SA, m, n, nz, (double *)(&(csc_A.pr[0])),
                            (int *)(&(csc_A.ir[0])), (int *)(&(csc_A.jc[0])));

      Create_Dense_Matrix(&SB, m, 0, &rhs[0], m);
      Create_Dense_Matrix(&SX, m, 0, &sol[0], m);
      memset(&SL,0,sizeof SL);
      memset(&SU,0,sizeof SU);
      equed = 'B';
      Rscale.resize(m); Cscale.resize(n); etree.resize(n);
      ferr.resize(1); berr.resize(1);
      R recip_pivot_gross, rcond;
      perm_r.resize(m); perm_c.resize(n);
      memory_used = SuperLU_gssvx(&options, &SA, &perm_c[0], &perm_r[0], 
                    &etree[0] /* output */, &equed /* output        */, 
                    &Rscale[0] /* row scale factors (output)        */, 
                    &Cscale[0] /* col scale factors (output)        */,
                    &SL /* fact L (output)*/, &SU /* fact U (output)*/, 
                    NULL /* work                                    */, 
                    0 /* lwork: superlu auto allocates (input)      */, 
                    &SB /* rhs */, &SX /* solution                  */,
                    &recip_pivot_gross /* reciprocal pivot growth   */
                    /* factor max_j( norm(A_j)/norm(U_j) ).         */,  
                    &rcond /*estimate of the reciprocal condition   */
                    /* number of the matrix A after equilibration   */,
                    &ferr[0] /* estimated forward error             */,
                    &berr[0] /* relative backward error             */,
                    &stat, &info, T());
      
      Destroy_SuperMatrix_Store(&SB);
      Destroy_SuperMatrix_Store(&SX);
      Create_Dense_Matrix(&SB, m, 1, &rhs[0], m);
      Create_Dense_Matrix(&SX, m, 1, &sol[0], m);
      StatFree(&stat);

      GMM_ASSERT1(info == 0, "SuperLU solve failed: info=" << info);
      is_init = true;
    }
    
    template <class T> template <typename VECTX, typename VECTB> 
    void SuperLU_factor<T>::solve(const VECTX &X_, const VECTB &B,
                                  int transp) const {
      VECTX &X = const_cast<VECTX &>(X_);
      gmm::copy(B, rhs);
      options.Fact = FACTORED;
      options.IterRefine = NOREFINE;
      switch (transp) {
      case LU_NOTRANSP: options.Trans = NOTRANS; break;
      case LU_TRANSP: options.Trans = TRANS; break;
      case LU_CONJUGATED: options.Trans = CONJ; break;
      default: GMM_ASSERT1(false, "invalid value for transposition option");
      }
      StatInit(&stat);
      int info = 0;
      R recip_pivot_gross, rcond;
      SuperLU_gssvx(&options, &SA, &perm_c[0], &perm_r[0], 
                    &etree[0] /* output */, &equed /* output        */, 
                    &Rscale[0] /* row scale factors (output)        */, 
                    &Cscale[0] /* col scale factors (output)        */,
                    &SL /* fact L (output)*/, &SU /* fact U (output)*/, 
                    NULL /* work                                    */, 
                    0 /* lwork: superlu auto allocates (input)      */, 
                    &SB /* rhs */, &SX /* solution                  */,
                    &recip_pivot_gross /* reciprocal pivot growth   */
                    /* factor max_j( norm(A_j)/norm(U_j) ).         */,  
                    &rcond /*estimate of the reciprocal condition   */
                    /* number of the matrix A after equilibration   */,
                    &ferr[0] /* estimated forward error             */,
                    &berr[0] /* relative backward error             */,
                    &stat, &info, T());
     StatFree(&stat);
     GMM_ASSERT1(info == 0, "SuperLU solve failed: info=" << info);
     gmm::copy(sol, X);
    }

  template <typename T, typename V1, typename V2> inline
  void mult(const SuperLU_factor<T>& P, const V1 &v1, const V2 &v2) {
    P.solve(v2,v1);
  }

  template <typename T, typename V1, typename V2> inline
  void transposed_mult(const SuperLU_factor<T>& P,const V1 &v1,const V2 &v2) {
    P.solve(v2, v1, SuperLU_factor<T>::LU_TRANSP);
  }

}

  
#endif // GMM_SUPERLU_INTERFACE_H

#endif // GMM_USES_SUPERLU