bgeot_tensor.h

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/**@file bgeot_tensor.h
   @author  Yves Renard <Yves.Renard@insa-lyon.fr>
   @date October 09, 2000.
   @brief tensor class, used in mat_elem computations.
*/
#ifndef BGEOT_TENSOR_H__
#define BGEOT_TENSOR_H__

#include "bgeot_small_vector.h"
#include "getfem/getfem_omp.h"


namespace bgeot {

  /* ********************************************************************* */
  /*                Class tensor<T>.                                       */
  /* ********************************************************************* */

  typedef size_t size_type;
  typedef gmm::uint16_type short_type;

  class multi_index : public std::vector<size_type> {
  public :

    void incrementation(const multi_index &m) {
      iterator it = begin(), ite = end();
      const_iterator itm = m.begin();
      if (it != ite) {
        ++(*it);
        while (*it >= *itm && it != (ite-1)) { *it = 0; ++it; ++itm; ++(*it); }
      } else resize(1);
    }

    void reset(void) { std::fill(begin(), end(), 0); }

    inline bool finished(const multi_index &m) {
      if (m.size() == 0)
        return  (size() == 1);
      else
        return ((*this)[size()-1] >= m[size()-1]);
    }

    multi_index(size_t n) : std::vector<size_type>(n)
    { std::fill(begin(), end(), size_type(0)); }
    multi_index(size_type i, size_type j)
      : std::vector<size_type>(2)
    { (*this)[0] = i; (*this)[1] = j; }
    multi_index(size_type i, size_type j, size_type k)
      : std::vector<size_type>(3)
    { (*this)[0] = i; (*this)[1] = j; (*this)[2] = k; }
    multi_index(size_type i, size_type j, size_type k, size_type l)
      : std::vector<size_type>(4)
    { (*this)[0] = i; (*this)[1] = j; (*this)[2] = k; (*this)[3] = l; }

    multi_index(void) {}

    bool is_equal(const multi_index &m) const {
      if (this->size() != m.size()) return false;
      for (size_type i = 0; i < m.size(); ++i)
        if (m[i] != (*this)[i]) return false;
      return true;
    }

    size_type total_size(void) const {
      size_type s = 1;
      for (size_type k = 0; k < this->size(); ++k) s *= (*this)[k];
      return s;
    }

    size_type memsize() const {
      return std::vector<size_type>::capacity()*sizeof(size_type) +
        sizeof(multi_index);
    }
  };

  inline std::ostream &operator <<(std::ostream &o,
                                   const multi_index& mi) { /* a compiler ...*/
    multi_index::const_iterator it = mi.begin(), ite = mi.end();
    bool f = true;
    o << "(";
    for ( ; it != ite; ++it)
      { if (!f) o << ", "; o << *it; f = false; }
    o << ")";
    return o;
  }

  template<class T> class tensor : public std::vector<T> {
    protected:

    multi_index sizes_, coeff;

    public:

    typedef typename std::vector<T>::size_type size_type;
    typedef typename std::vector<T>::iterator iterator;
    typedef typename std::vector<T>::const_iterator const_iterator;

    template<class CONT> inline const T& operator ()(const CONT &c) const {
      typename CONT::const_iterator it = c.begin();
      multi_index::const_iterator q = coeff.begin(), e = coeff.end();
#ifndef NDEBUG
      multi_index::const_iterator qv = sizes_.begin();
#endif
      size_type d = 0;
      for ( ; q != e; ++q, ++it) {
        d += (*q) * (*it);
        GMM_ASSERT2(*it < *qv++, "Index out of range.");
      }
      return *(this->begin() + d);
    }

    inline T& operator ()(size_type i, size_type j, size_type k,
                          size_type l) {
      GMM_ASSERT2(order() == 4, "Bad tensor order.");
      size_type d = coeff[0]*i + coeff[1]*j + coeff[2]*k + coeff[3]*l;
      GMM_ASSERT2(d < size(), "Index out of range.");
      return *(this->begin() + d);
    }

    inline T& operator ()(size_type i, size_type j, size_type k) {
      GMM_ASSERT2(order() == 3, "Bad tensor order.");
      size_type d = coeff[0]*i + coeff[1]*j + coeff[2]*k;
      GMM_ASSERT2(d < size(), "Index out of range.");
      return *(this->begin() + d);
    }

    inline T& operator ()(size_type i, size_type j) {
      GMM_ASSERT2(order() == 2, "Bad tensor order");
        size_type d = coeff[0]*i + coeff[1]*j;
        GMM_ASSERT2(d < size(), "Index out of range.");
        return *(this->begin() + d);
    }

    inline const T& operator ()(size_type i, size_type j, size_type k,
                                size_type l) const {
      GMM_ASSERT2(order() == 4, "Bad tensor order.");
      size_type d = coeff[0]*i + coeff[1]*j + coeff[2]*k + coeff[3]*l;
      GMM_ASSERT2(d < size(), "Index out of range.");
      return *(this->begin() + d);
    }

    inline const T& operator ()(size_type i, size_type j,
                                size_type k) const {
      GMM_ASSERT2(order() == 3, "Bad tensor order.");
      size_type d = coeff[0]*i + coeff[1]*j + coeff[2]*k;
      GMM_ASSERT2(d < size(), "Index out of range.");
      return *(this->begin() + d);
    }

    inline const T& operator ()(size_type i, size_type j) const {
      GMM_ASSERT2(order() == 2, "Bad tensor order.");
      size_type d = coeff[0]*i + coeff[1]*j;
      GMM_ASSERT2(d < size(), "Index out of range.");
      return *(this->begin() + d);
    }

    template<class CONT> inline T& operator ()(const CONT &c) {
      typename CONT::const_iterator it = c.begin();
      multi_index::iterator q = coeff.begin(), e = coeff.end();
      size_type d = 0;
      for ( ; q != e; ++q, ++it) d += (*q) * (*it);
      GMM_ASSERT2(d < size(), "Index out of range.");
      return *(this->begin() + d);
    }

    inline size_type size(void) const { return std::vector<T>::size(); }
    inline size_type size(size_type i) const { return sizes_[i]; }
    inline const multi_index &sizes(void) const { return sizes_; }
    inline size_type order(void) const { return sizes_.size(); }

    void init(const multi_index &c) {
      auto it = c.begin();
      size_type d = 1;
      sizes_ = c; coeff.resize(c.size());
      auto p = coeff.begin(), pe = coeff.end();
      for ( ; p != pe; ++p, ++it) { *p = d; d *= *it; }
      this->resize(d);
    }

    inline void init() { sizes_.resize(0);  coeff.resize(0); this->resize(1); }

    inline void init(size_type i) {
      sizes_.resize(1); sizes_[0] = i; coeff.resize(1); coeff[0] = 1;
      this->resize(i);
    }

    inline void init(size_type i, size_type j) {
      sizes_.resize(2); sizes_[0] = i; sizes_[1] = j;
      coeff.resize(2); coeff[0] = 1; coeff[1] = i;
      this->resize(i*j);
    }

    inline void init(size_type i, size_type j, size_type k) {
      sizes_.resize(3); sizes_[0] = i; sizes_[1] = j; sizes_[2] = k; 
      coeff.resize(3); coeff[0] = 1; coeff[1] = i; coeff[2] = i*j;
      this->resize(i*j*k);
    }

    inline void init(size_type i, size_type j, size_type k, size_type l) {
      sizes_.resize(4);
      sizes_[0] = i; sizes_[1] = j; sizes_[2] = k; sizes_[3] = k; 
      coeff.resize(4);
      coeff[0] = 1; coeff[1] = i; coeff[2] = i*j; coeff[3] = i*j*k;
      this->resize(i*j*k*l);
    }

    inline void adjust_sizes(const multi_index &mi) { init(mi); }
    inline void adjust_sizes(void) { init(); }
    inline void adjust_sizes(size_type i) { init(i); }
    inline void adjust_sizes(size_type i, size_type j) { init(i, j); }
    inline void adjust_sizes(size_type i, size_type j, size_type k)
    { init(i, j, k); }
    inline void adjust_sizes(size_type i, size_type j, size_type k, size_type l)
    { init(i, j, k, l); }
    
    inline size_type adjust_sizes_changing_last(const tensor &t, size_type P) {
      const multi_index &mi = t.sizes_; size_type d = mi.size();
      sizes_.resize(d); coeff.resize(d);
      if (d) {
        std::copy(mi.begin(), mi.end(), sizes_.begin());
        std::copy(t.coeff.begin(), t.coeff.end(), coeff.begin());
        size_type e = coeff.back();
        sizes_.back() = P;
        this->resize(e*P);
        return e;
      } else {
        this->resize(1);
        return 1;
      }
    }

    inline void remove_unit_dim() {
      if (sizes_.size()) {
        size_type i = 0, j = 0;
        for (; i < sizes_.size(); ++i)
          if (sizes_[i] != 1) { sizes_[j]=sizes_[i]; coeff[j]=coeff[i]; ++j; }
        if (!j) ++j;
        sizes_.resize(j);
        coeff.resize(j);
      }
    }

    /** reduction of tensor t with respect to index ni with matrix m:
     *  t(...,j,...) <-- t(...,i,..) m(i, j)
     */
    void mat_reduction(const tensor &t, const gmm::dense_matrix<T> &m, int ni);
    void mat_transp_reduction(const tensor &t, const gmm::dense_matrix<T> &m,
                              int ni);
    /** mm(i,j) = t(i,j,k,l) * m(k,l); For order four tensor. */
    void mat_mult(const gmm::dense_matrix<T> &m, gmm::dense_matrix<T> &mm);

    /** tt = t(...) * t2(...)  */
    void product(const tensor &t2, tensor &tt);
    /** tt = t(...,k) * t2(k,...)  */
    void dot_product(const tensor &t2, tensor &tt);
    void dot_product(const gmm::dense_matrix<T> &m, tensor &tt);
    /** tt = t(...,k,l) * t2(k,l,...)  */
    void double_dot_product(const tensor &t2, tensor &tt);
    void double_dot_product(const gmm::dense_matrix<T> &m, tensor &tt);

    size_type memsize() const {
      return sizeof(T) * this->size()
        + sizeof(*this) + sizes_.memsize() + coeff.memsize();
    }

    std::vector<T> &as_vector(void) { return *this; }
    const std::vector<T> &as_vector(void) const { return *this; }


    tensor<T>& operator +=(const tensor<T>& w)
    { gmm::add(w.as_vector(), this->as_vector()); return *this; }

    tensor<T>& operator -=(const tensor<T>& w) {
      gmm::add(gmm::scaled(w.as_vector(), T(-1)), this->as_vector());
      return *this;
    }

    tensor<T>& operator *=(const scalar_type w)
    { gmm::scale(this->as_vector(), w); return *this; }

    tensor<T>& operator /=(const scalar_type w)
    { gmm::scale(this->as_vector(), scalar_type(1)/w); return *this; }

    tensor &operator =(const tensor &t) {
      if (this->size() != t.size()) this->resize(t.size());
      std::copy(t.begin(), t.end(), this->begin());
      if (sizes_.size() != t.sizes_.size()) sizes_.resize(t.sizes_.size());
      std::copy(t.sizes_.begin(), t.sizes_.end(), sizes_.begin());
      if (coeff.size() != t.coeff.size()) coeff.resize(t.coeff.size());
      std::copy(t.coeff.begin(), t.coeff.end(), coeff.begin());
      return *this;
    }

    tensor(const multi_index &c) { init(c); }
    tensor(size_type i, size_type j, size_type k, size_type l)
    { init(multi_index(i, j, k, l)); }
    tensor(void) {}
  };

  template<class T> void tensor<T>::mat_transp_reduction
  (const tensor &t, const gmm::dense_matrix<T> &m, int ni) {
    /* reduction du tenseur t par son indice ni et la matrice          */
    /* transposee de m.                                                */

    DEFINE_STATIC_THREAD_LOCAL(std::vector<T>, tmp);
    DEFINE_STATIC_THREAD_LOCAL(multi_index, mi);

    mi = t.sizes();
    size_type dimt = mi[ni], dim = m.nrows();

    GMM_ASSERT2(dimt, "Inconsistent dimension.");
    GMM_ASSERT2(dimt == m.ncols(), "Dimensions mismatch.");
    GMM_ASSERT2(&t != this, "Does not work when t and *this are the same.");

    mi[ni] = dim;
    if (tmp.size() < dimt) tmp.resize(dimt);
    adjust_sizes(mi);

    const_iterator pft = t.begin();
    iterator pf = this->begin();
    size_type dd  =   coeff[ni]*(  sizes()[ni]-1)-1, co  =   coeff[ni];
    size_type ddt = t.coeff[ni]*(t.sizes()[ni]-1)-1, cot = t.coeff[ni];
    std::fill(mi.begin(), mi.end(), 0);
    for (;!mi.finished(sizes()); mi.incrementation(sizes()), ++pf, ++pft) {
      if (mi[ni] != 0) {
        for (size_type k = 0; k <= size_type(ni); ++k)
          mi[k] = size_type(sizes()[k] - 1);
        pf += dd; pft += ddt;
      } else {
        const_iterator pl = pft; iterator pt = tmp.begin();
        *pt++ = *pl;
        for(size_type k = 1; k < dimt; ++k, ++pt) { pl += cot; *pt = *pl;}

        iterator pff = pf;
        for (size_type k = 0; k < dim; ++k) {
          if (k) pff += co;
          *pff = T(0); pt = tmp.begin(); pl = m.begin() + k;
          *pff += (*pl) * (*pt); ++pt;
          for (size_type l = 1; l < dimt; ++l, ++pt) {
            pl += dim;
            *pff += (*pl) * (*pt);
          }
        }
      }
    }
  }

  template<class T> void tensor<T>::mat_mult(const gmm::dense_matrix<T> &m,
                                             gmm::dense_matrix<T> &mm) {
    GMM_ASSERT2(order() == 4,
                "This operation is for order four tensors only.");
    GMM_ASSERT2(sizes_[2] == gmm::mat_nrows(m) &&
                sizes_[3] == gmm::mat_ncols(m), "Dimensions mismatch.");
    mm.base_resize(sizes_[0], sizes_[1]);
    gmm::clear(mm);

    const_iterator pt = this->begin();
    const_iterator pm = m.begin();
    for (size_type l = 0; l < sizes_[3]; ++l)
      for (size_type k = 0; k < sizes_[2]; ++k) {
        iterator pmm = mm.begin();
        for (size_type j = 0; j < sizes_[1]; ++j)
          for (size_type i = 0; i < sizes_[0]; ++i)
            *pmm++ += *pt++ * (*pm);
        ++pm;
      }
  }

  template<class T> void tensor<T>::mat_reduction
  (const tensor &t, const gmm::dense_matrix<T> &m, int ni) {
    /* reduction du tenseur t par son indice ni et la matrice m.       */
    DEFINE_STATIC_THREAD_LOCAL(std::vector<T>, tmp);
    DEFINE_STATIC_THREAD_LOCAL(multi_index, mi);
    
    mi = t.sizes();
    size_type dimt = mi[ni], dim = m.ncols();
    GMM_ASSERT2(dimt, "Inconsistent dimension.");
    GMM_ASSERT2(dimt == m.nrows(), "Dimensions mismatch.");
    GMM_ASSERT2(&t != this, "Does not work when t and *this are the same.");

    mi[ni] = dim;
    if (tmp.size() < dimt) tmp.resize(dimt);
    adjust_sizes(mi);
    const_iterator pft = t.begin();
    iterator pf = this->begin();
    size_type dd  =   coeff[ni]*(  sizes()[ni]-1)-1, co  =   coeff[ni];
    size_type ddt = t.coeff[ni]*(t.sizes()[ni]-1)-1, cot = t.coeff[ni];
    std::fill(mi.begin(), mi.end(), 0);
    for (;!mi.finished(sizes()); mi.incrementation(sizes()), ++pf, ++pft) {
      if (mi[ni] != 0) {
        for (size_type k = 0; k <= size_type(ni); ++k)
          mi[k] = size_type(sizes()[k] - 1);
        pf += dd; pft += ddt;
      }
      else {
        const_iterator pl = pft; iterator pt = tmp.begin();
        *pt++ = *pl;
        for(size_type k = 1; k < dimt; ++k, ++pt) { pl += cot; *pt = *pl; }

        iterator pff = pf; pl = m.begin();
        for (size_type k = 0; k < dim; ++k) {
          if (k) pff += co;
          *pff = T(0); pt = tmp.begin();
          for (size_type l = 0; l < dimt; ++l, ++pt, ++pl)
            *pff += (*pl) * (*pt);
        }
      }
    }
  }


  template<class T> void tensor<T>::product(const tensor<T> &t2,
                                            tensor<T> &tt) {
    size_type res_order = order() + t2.order();
    multi_index res_size(res_order);
    for (size_type i = 0 ; i < this->order(); ++i) res_size[i] = this->size(i);
    for (size_type i = 0 ; i < t2.order(); ++i) res_size[order() + i] = t2.size(i);
    tt.adjust_sizes(res_size);
    gmm::clear(tt.as_vector());

    size_type size1 = this->size();
    size_type size2 = t2.size();
    const_iterator pt2 = t2.begin();
    iterator ptt = tt.begin();
    for (size_type j = 0; j < size2; ++j, ++pt2) {
      const_iterator pt1 = this->begin();
      for (size_type i = 0; i < size1; ++i, ++pt1, ++ptt)
        *ptt += *pt1 * (*pt2);
    }
  }


  template<class T> void tensor<T>::dot_product(const tensor<T> &t2,
                                                tensor<T> &tt) {
    GMM_ASSERT2(size(order()-1) == t2.size(0),
                "Dimensions mismatch between last dimension of first tensor "
                "and first dimension of second tensor.");
    size_type res_order = order() + t2.order() - 2;
    multi_index res_size(res_order);
    for (size_type i = 0 ; i < this->order() - 1; ++i) res_size[i] = this->size(i);
    for (size_type i = 0 ; i < t2.order() - 1; ++i) res_size[order() - 1 + i] = t2.size(i);
    tt.adjust_sizes(res_size);
    gmm::clear(tt.as_vector());

    size_type size0 = t2.size(0);
    size_type size1 = this->size()/size0;
    size_type size2 = t2.size()/size0;
    const_iterator pt2 = t2.begin();
    iterator ptt = tt.begin();
    for (size_type j = 0; j < size2; ++j) {
      const_iterator pt1 = this->begin();
      iterator ptt0 = ptt;
      for (size_type q = 0; q < size0; ++q, ++pt2) {
        ptt = ptt0;
        for (size_type i = 0; i < size1; ++i, ++pt1, ++ptt)
          *ptt += *pt1 * (*pt2);
      }
    }
  }

  template<class T> void tensor<T>::dot_product(const gmm::dense_matrix<T> &m,
                                                tensor<T> &tt) {
    GMM_ASSERT2(size(order()-1) == gmm::mat_nrows(m),
                "Dimensions mismatch between last dimensions of tensor "
                "and rows of the matrix.");
    tensor<T> t2(multi_index(gmm::mat_nrows(m),gmm::mat_ncols(m)));
    gmm::copy(m.as_vector(), t2.as_vector());
    dot_product(t2, tt);
  }


  template<class T> void tensor<T>::double_dot_product(const tensor<T> &t2,
                                                       tensor<T> &tt) {
    GMM_ASSERT2(order() >= 2 && t2.order() >= 2,
                "Tensors of wrong size. Tensors of order two or higher are required.");
    GMM_ASSERT2(size(order()-2) == t2.size(0) && size(order()-1) == t2.size(1),
                "Dimensions mismatch between last two dimensions of first tensor "
                "and first two dimensions of second tensor.");
    size_type res_order = order() + t2.order() - 4;
    multi_index res_size(res_order);
    for (size_type i = 0 ; i < this->order() - 2; ++i) res_size[i] = this->size(i);
    for (size_type i = 0 ; i < t2.order() - 2; ++i) res_size[order() - 2 + i] = t2.size(i);
    tt.adjust_sizes(res_size);
    gmm::clear(tt.as_vector());

    size_type size0 = t2.size(0)*t2.size(1);
    size_type size1 = this->size()/size0;
    size_type size2 = t2.size()/size0;
    const_iterator pt2 = t2.begin();
    iterator ptt = tt.begin();
    for (size_type j = 0; j < size2; ++j) {
      const_iterator pt1 = this->begin();
      iterator ptt0 = ptt;
      for (size_type q = 0; q < size0; ++q, ++pt2) {
        ptt = ptt0;
        for (size_type i = 0; i < size1; ++i, ++pt1, ++ptt)
          *ptt += *pt1 * (*pt2);
      }
    }
  }

  template<class T> void tensor<T>::double_dot_product(const gmm::dense_matrix<T> &m,
                                                       tensor<T> &tt) {
    GMM_ASSERT2(order() >= 2,
                "Tensor of wrong size. Tensor of order two or higher is required.");
    GMM_ASSERT2(size(order()-2) == gmm::mat_nrows(m) &&
                size(order()-1) == gmm::mat_ncols(m),
                "Dimensions mismatch between last two dimensions of tensor "
                "and dimensions of the matrix.");
    tensor<T> t2(multi_index(gmm::mat_nrows(m),gmm::mat_ncols(m)));
    gmm::copy(m.as_vector(), t2.as_vector());
    double_dot_product(t2, tt);
  }


  template<class T> std::ostream &operator <<
    (std::ostream &o, const tensor<T>& t) {
    o << "sizes " << t.sizes() << " " << vref(t.as_vector());
    return o;
  }

  typedef tensor<scalar_type> base_tensor;
  typedef tensor<complex_type> base_complex_tensor;


}  /* end of namespace bgeot.                                              */


#endif  /* BGEOT_TENSOR_H */