codac2_arith_sub.h

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#pragma once
 
#include "codac2_Interval.h"
#include "codac2_IntervalVector.h"
#include "codac2_IntervalMatrix.h"
#include "codac2_AnalyticType.h"
#include "codac2_AnalyticExprWrapper.h"
 
namespace codac2
{
  struct SubOp
  {
    // Unary operations
 
    template<typename X1>
    static std::string str(const X1& x1)
    {
      return "-" + x1->str(!x1->is_str_leaf());
    }
 
    template<typename X1>
    static std::pair<Index,Index> output_shape(const X1& s1) {
      return s1->output_shape();
    }
 
    static Interval fwd(const Interval& x1);
    static ScalarType fwd_natural(const ScalarType& x1);
    static ScalarType fwd_centered(const ScalarType& x1);
    static void bwd(const Interval& y, Interval& x1);
 
    static IntervalVector fwd(const IntervalVector& x1);
    static VectorType fwd_natural(const VectorType& x1);
    static VectorType fwd_centered(const VectorType& x1);
    static void bwd(const IntervalVector& y, IntervalVector& x1);
 
    static IntervalMatrix fwd(const IntervalMatrix& x1);
    static MatrixType fwd_natural(const MatrixType& x1);
    static MatrixType fwd_centered(const MatrixType& x1);
    static void bwd(const IntervalMatrix& y, IntervalMatrix& x1);
 
    // Binary operations
 
    template<typename X1,typename X2>
    static std::string str(const X1& x1, const X2& x2)
    {
      return x1->str(!x1->is_str_leaf()) + "-" + x2->str(!x2->is_str_leaf());
    }
 
    template<typename X1, typename X2>
    static std::pair<Index,Index> output_shape(const X1& s1, [[maybe_unused]] const X2& s2)
    {
      auto shape1 = s1->output_shape();
      assert(shape1 == s2->output_shape());
      return shape1;
    }
 
    static Interval fwd(const Interval& x1, const Interval& x2);
    static ScalarType fwd_natural(const ScalarType& x1, const ScalarType& x2);
    static ScalarType fwd_centered(const ScalarType& x1, const ScalarType& x2);
    static void bwd(const Interval& y, Interval& x1, Interval& x2);
 
    static IntervalVector fwd(const IntervalVector& x1, const IntervalVector& x2);
    static VectorType fwd_natural(const VectorType& x1, const VectorType& x2);
    static VectorType fwd_centered(const VectorType& x1, const VectorType& x2);
    static void bwd(const IntervalVector& y, IntervalVector& x1, IntervalVector& x2);
 
    static IntervalMatrix fwd(const IntervalMatrix& x1, const IntervalMatrix& x2);
    static MatrixType fwd_natural(const MatrixType& x1, const MatrixType& x2);
    static MatrixType fwd_centered(const MatrixType& x1, const MatrixType& x2);
    static void bwd(const IntervalMatrix& y, IntervalMatrix& x1, IntervalMatrix& x2);
  };
 
  // operator- (unary case)
  // The following functions can be used to build analytic expressions.
  
  inline ScalarExpr
  operator-(const ScalarExpr& x1)
  {
    return { std::make_shared<AnalyticOperationExpr<SubOp,ScalarType,ScalarType>>(x1) };
  }
 
  inline VectorExpr
  operator-(const VectorExpr& x1)
  {
    return { std::make_shared<AnalyticOperationExpr<SubOp,VectorType,VectorType>>(x1) };
  }
 
  inline MatrixExpr
  operator-(const MatrixExpr& x1)
  {
    return { std::make_shared<AnalyticOperationExpr<SubOp,MatrixType,MatrixType>>(x1) };
  }
 
  // operator-
  // The following functions can be used to build analytic expressions.
  
  inline ScalarExpr
  operator-(const ScalarExpr& x1, const ScalarExpr& x2)
  {
    return { std::make_shared<AnalyticOperationExpr<SubOp,ScalarType,ScalarType,ScalarType>>(x1,x2) };
  }
 
  inline VectorExpr
  operator-(const VectorExpr& x1, const VectorExpr& x2)
  {
    return { std::make_shared<AnalyticOperationExpr<SubOp,VectorType,VectorType,VectorType>>(x1,x2) };
  }
 
  inline MatrixExpr
  operator-(const MatrixExpr& x1, const MatrixExpr& x2)
  {
    return { std::make_shared<AnalyticOperationExpr<SubOp,MatrixType,MatrixType,MatrixType>>(x1,x2) };
  }
 
  // Inline functions
 
  inline Interval SubOp::fwd(const Interval& x1)
  {
    return -x1;
  }
 
  inline ScalarType SubOp::fwd_natural(const ScalarType& x1)
  {
    return {
      fwd(x1.a),
      x1.def_domain
    };
  }
 
  inline ScalarType SubOp::fwd_centered(const ScalarType& x1)
  {
    return {
      fwd(x1.m),
      fwd(x1.a),
      -x1.da,
      x1.def_domain
    };
  }
 
  inline void SubOp::bwd(const Interval& y, Interval& x1)
  {
    Interval x2_(0.);
    SubOp::bwd(y, x2_, x1);
  }
 
  inline IntervalVector SubOp::fwd(const IntervalVector& x1)
  {
    return -x1;
  }
 
  inline VectorType SubOp::fwd_natural(const VectorType& x1)
  {
    return {
      fwd(x1.a),
      x1.def_domain
    };
  }
 
  inline VectorType SubOp::fwd_centered(const VectorType& x1)
  {
    return {
      fwd(x1.m),
      fwd(x1.a),
      -x1.da,
      x1.def_domain
    };
  }
 
  inline void SubOp::bwd(const IntervalVector& y, IntervalVector& x1)
  {
    assert(y.size() == x1.size());
    for(Index i = 0 ; i < y.size() ; i++)
      bwd(y[i], x1[i]);
  }
 
  inline IntervalMatrix SubOp::fwd(const IntervalMatrix& x1)
  {
    return -x1;
  }
 
  inline MatrixType SubOp::fwd_natural(const MatrixType& x1)
  {
    return {
      fwd(x1.a),
      x1.def_domain
    };
  }
 
  inline MatrixType SubOp::fwd_centered(const MatrixType& x1)
  {
    return {
      fwd(x1.m),
      fwd(x1.a),
      -x1.da, 
      x1.def_domain
    };
  }
 
  inline void SubOp::bwd(const IntervalMatrix& y, IntervalMatrix& x1)
  {
    assert(y.size() == x1.size());
    for(Index i = 0 ; i < y.size() ; i++)
      SubOp::bwd(*(y.data()+i), *(x1.data()+i));
  }
 
  inline Interval SubOp::fwd(const Interval& x1, const Interval& x2)
  {
    return x1 - x2;
  }
 
  inline ScalarType SubOp::fwd_natural(const ScalarType& x1, const ScalarType& x2)
  {
    return {
      fwd(x1.a, x2.a),
      x1.def_domain && x2.def_domain
    };
  }
 
  inline ScalarType SubOp::fwd_centered(const ScalarType& x1, const ScalarType& x2)
  {
    if(centered_form_not_available_for_args(x1,x2))
      return fwd_natural(x1,x2);
 
    assert(x1.da.rows() == x2.da.rows() && x1.da.cols() == x2.da.cols());
    return {
      fwd(x1.m, x2.m),
      fwd(x1.a, x2.a),
      x1.da - x2.da,
      x1.def_domain && x2.def_domain
    };
  }
 
  inline void SubOp::bwd(const Interval& y, Interval& x1, Interval& x2)
  {
    if((x1 &= y+x2).is_empty())
      x2.set_empty();
 
    else if((x2 &= x1-y).is_empty())
      x1.set_empty();
  }
 
  inline IntervalVector SubOp::fwd(const IntervalVector& x1, const IntervalVector& x2)
  {
    assert(x1.size() == x2.size());
    return x1 - x2;
  }
 
  inline VectorType SubOp::fwd_natural(const VectorType& x1, const VectorType& x2)
  {
    return {
      fwd(x1.a, x2.a),
      x1.def_domain && x2.def_domain
    };
  }
 
  inline VectorType SubOp::fwd_centered(const VectorType& x1, const VectorType& x2)
  {
    if(centered_form_not_available_for_args(x1,x2))
      return fwd_natural(x1,x2);
 
    assert(x1.da.rows() == x2.da.rows() && x1.da.cols() == x2.da.cols());
    return {
      fwd(x1.m, x2.m),
      fwd(x1.a, x2.a),
      x1.da - x2.da,
      x1.def_domain && x2.def_domain
    };
  }
 
  inline void SubOp::bwd(const IntervalVector& y, IntervalVector& x1, IntervalVector& x2)
  {
    assert(y.size() == x1.size() && y.size() == x2.size());
    for(Index i = 0 ; i < y.size() ; i++)
      SubOp::bwd(y[i], x1[i], x2[i]);
  }
 
  inline IntervalMatrix SubOp::fwd(const IntervalMatrix& x1, const IntervalMatrix& x2)
  {
    assert(x1.size() == x2.size());
    return x1 - x2;
  }
 
  inline MatrixType SubOp::fwd_natural(const MatrixType& x1, const MatrixType& x2)
  {
    assert(x1.a.cols() == x2.a.cols() && x1.a.rows() == x2.a.rows());
    return {
      fwd(x1.a, x2.a),
      x1.def_domain && x2.def_domain
    };
  }
 
  inline MatrixType SubOp::fwd_centered(const MatrixType& x1, const MatrixType& x2)
  {
    assert(x1.a.cols() == x2.a.cols() && x1.a.rows() == x2.a.rows());
    return {
      fwd(x1.m, x2.m),
      fwd(x1.a, x2.a),
      x1.da - x2.da, 
      x1.def_domain && x2.def_domain
    };
  }
 
  inline void SubOp::bwd(const IntervalMatrix& y, IntervalMatrix& x1, IntervalMatrix& x2)
  {
    assert(y.size() == x1.size() && y.size() == x2.size());
    for(Index i = 0 ; i < y.size() ; i++)
      SubOp::bwd(*(y.data()+i), *(x1.data()+i), *(x2.data()+i));
  }
}