From 0170eb0dbecb69814716e3c89263d472dbd363ec Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Wed, 1 Apr 2009 14:43:37 +0000
Subject: add an auto-diff module in unsupported. it is similar to adolc's
 forward mode but the advantage of using Eigen's expression template to
 compute the derivatives (unless you nest an AutoDiffScalar into an Eigen's
 matrix).

---
 unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h | 321 ++++++++++++++++++++++++
 1 file changed, 321 insertions(+)
 create mode 100644 unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h

(limited to 'unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h')

diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
new file mode 100644
index 000000000..852b43bf5
--- /dev/null
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
@@ -0,0 +1,321 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_AUTODIFF_SCALAR_H
+#define EIGEN_AUTODIFF_SCALAR_H
+
+namespace Eigen {
+
+/** \class AutoDiffScalar
+  * \brief A scalar type replacement with automatic differentation capability
+  *
+  * \param DerType the vector type used to store/represent the derivatives (e.g. Vector3f)
+  *
+  * This class represents a scalar value while tracking its respective derivatives.
+  *
+  * It supports the following list of global math function:
+  *  - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos, 
+  *  - ei_abs, ei_sqrt, ei_pow, ei_exp, ei_log, ei_sin, ei_cos,
+  *  - ei_conj, ei_real, ei_imag, ei_abs2.
+  *
+  * AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However,
+  * in that case, the expression template mechanism only occurs at the top Matrix level,
+  * while derivatives are computed right away.
+  *
+  */
+template<typename DerType>
+class AutoDiffScalar
+{
+  public:
+    typedef typename ei_traits<DerType>::Scalar Scalar;
+    
+    inline AutoDiffScalar() {}
+    
+    inline AutoDiffScalar(const Scalar& value)
+      : m_value(value)
+    {
+      if(m_derivatives.size()>0)
+        m_derivatives.setZero();
+    }
+    
+    inline AutoDiffScalar(const Scalar& value, const DerType& der)
+      : m_value(value), m_derivatives(der)
+    {}
+    
+    template<typename OtherDerType>
+    inline AutoDiffScalar(const AutoDiffScalar<OtherDerType>& other)
+      : m_value(other.value()), m_derivatives(other.derivatives())
+    {}
+    
+    inline AutoDiffScalar(const AutoDiffScalar& other)
+      : m_value(other.value()), m_derivatives(other.derivatives())
+    {}
+    
+    template<typename OtherDerType>
+    inline AutoDiffScalar& operator=(const AutoDiffScalar<OtherDerType>& other)
+    {
+      m_value = other.value();
+      m_derivatives = other.derivatives();
+      return *this;
+    }
+    
+    inline AutoDiffScalar& operator=(const AutoDiffScalar& other)
+    {
+      m_value = other.value();
+      m_derivatives = other.derivatives();
+      return *this;
+    }
+    
+//     inline operator const Scalar& () const { return m_value; }
+//     inline operator Scalar& () { return m_value; }
+
+    inline const Scalar& value() const { return m_value; }
+    inline Scalar& value() { return m_value; }
+    
+    inline const DerType& derivatives() const { return m_derivatives; }
+    inline DerType& derivatives() { return m_derivatives; }
+    
+    template<typename OtherDerType>
+    inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,OtherDerType> >
+    operator+(const AutoDiffScalar<OtherDerType>& other) const
+    {
+      return AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,OtherDerType> >(
+        m_value + other.value(),
+        m_derivatives + other.derivatives());
+    }
+    
+    template<typename OtherDerType>
+    inline AutoDiffScalar&
+    operator+=(const AutoDiffScalar<OtherDerType>& other)
+    {
+      (*this) = (*this) + other;
+      return *this;
+    }
+    
+    template<typename OtherDerType>
+    inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,OtherDerType> >
+    operator-(const AutoDiffScalar<OtherDerType>& other) const
+    {
+      return AutoDiffScalar<CwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,OtherDerType> >(
+        m_value - other.value(),
+        m_derivatives - other.derivatives());
+    }
+    
+    template<typename OtherDerType>
+    inline AutoDiffScalar&
+    operator-=(const AutoDiffScalar<OtherDerType>& other)
+    {
+      *this = *this - other;
+      return *this;
+    }
+    
+    template<typename OtherDerType>
+    inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType> >
+    operator-() const
+    {
+      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType> >(
+        -m_value,
+        -m_derivatives);
+    }
+    
+    inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
+    operator*(const Scalar& other) const
+    {
+      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
+        m_value * other,
+        (m_derivatives * other));
+    }
+    
+    friend inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
+    operator*(const Scalar& other, const AutoDiffScalar& a)
+    {
+      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
+        a.value() * other,
+        a.derivatives() * other);
+    }
+    
+    inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
+    operator/(const Scalar& other) const
+    {
+      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
+        m_value / other,
+        (m_derivatives * (Scalar(1)/other)));
+    }
+    
+    friend inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
+    operator/(const Scalar& other, const AutoDiffScalar& a)
+    {
+      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
+        other / a.value(),
+        a.derivatives() * (-Scalar(1)/other));
+    }
+    
+    template<typename OtherDerType>
+    inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
+        NestByValue<CwiseBinaryOp<ei_scalar_difference_op<Scalar>,
+          NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
+          NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > > > >
+    operator/(const AutoDiffScalar<OtherDerType>& other) const
+    {
+      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
+        NestByValue<CwiseBinaryOp<ei_scalar_difference_op<Scalar>,
+          NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
+          NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > > > >(
+        m_value / other.value(),
+          ((m_derivatives * other.value()).nestByValue() - (m_value * other.derivatives()).nestByValue()).nestByValue()
+        * (Scalar(1)/(other.value()*other.value())));
+    }
+    
+    template<typename OtherDerType>
+    inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,
+        NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
+        NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > >
+    operator*(const AutoDiffScalar<OtherDerType>& other) const
+    {
+      return AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,
+        NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
+        NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > >(
+        m_value * other.value(),
+        (m_derivatives * other.value()).nestByValue() + (m_value * other.derivatives()).nestByValue());
+    }
+    
+    inline AutoDiffScalar& operator*=(const Scalar& other)
+    {
+      *this = *this * other;
+      return *this;
+    }
+    
+    template<typename OtherDerType>
+    inline AutoDiffScalar& operator*=(const AutoDiffScalar<OtherDerType>& other)
+    {
+      *this = *this * other;
+      return *this;
+    }
+    
+  protected:
+    Scalar m_value;
+    DerType m_derivatives;
+    
+};
+
+}
+
+#define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \
+  template<typename DerType> \
+  inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType> > \
+  FUNC(const AutoDiffScalar<DerType>& x) { \
+    typedef typename ei_traits<DerType>::Scalar Scalar; \
+    typedef AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> > ReturnType; \
+    CODE; \
+  }
+
+namespace std
+{
+  EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs,
+    return ReturnType(std::abs(x.value()), x.derivatives() * (sign(x.value())));)
+  
+  EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sqrt,
+    Scalar sqrtx = std::sqrt(x.value());
+    return ReturnType(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)
+  
+  EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cos,
+    return ReturnType(std::cos(x.value()), x.derivatives() * (-std::sin(x.value())));)
+  
+  EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sin,
+    return ReturnType(std::sin(x.value()),x.derivatives() * std::cos(x.value()));)
+  
+  EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(exp,
+    Scalar expx = std::exp(x.value());
+    return ReturnType(expx,x.derivatives() * expx);)
+
+  EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_log,
+    return ReturnType(std::log(x.value),x.derivatives() * (Scalar(1).x.value()));)
+  
+  template<typename DerType>
+  inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType> >
+  pow(const AutoDiffScalar<DerType>& x, typename ei_traits<DerType>::Scalar y)
+  {
+    typedef typename ei_traits<DerType>::Scalar Scalar;
+    return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
+      std::pow(x.value(),y),
+      x.derivatives() * (y * std::pow(x.value(),y-1)));
+  }
+  
+}
+
+namespace Eigen {
+
+template<typename DerType>
+inline const AutoDiffScalar<DerType>& ei_conj(const AutoDiffScalar<DerType>& x)  { return x; }
+template<typename DerType>
+inline const AutoDiffScalar<DerType>& ei_real(const AutoDiffScalar<DerType>& x)  { return x; }
+template<typename DerType>
+inline typename DerType::Scalar ei_imag(const AutoDiffScalar<DerType>&)    { return 0.; }
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_abs,
+  return ReturnType(ei_abs(x.value()), x.derivatives() * (sign(x.value())));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_abs2,
+  return ReturnType(ei_abs2(x.value()), x.derivatives() * (Scalar(2)*x.value()));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_sqrt,
+  Scalar sqrtx = ei_sqrt(x.value());
+  return ReturnType(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_cos,
+  return ReturnType(ei_cos(x.value()), x.derivatives() * (-ei_sin(x.value())));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_sin,
+  return ReturnType(ei_sin(x.value()),x.derivatives() * ei_cos(x.value()));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_exp,
+  Scalar expx = ei_exp(x.value());
+  return ReturnType(expx,x.derivatives() * expx);)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_log,
+  return ReturnType(ei_log(x.value),x.derivatives() * (Scalar(1).x.value()));)
+
+template<typename DerType>
+inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType> >
+ei_pow(const AutoDiffScalar<DerType>& x, typename ei_traits<DerType>::Scalar y)
+{ return std::pow(x,y);}
+
+#undef EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY
+
+template<typename DerType> struct NumTraits<AutoDiffScalar<DerType> >
+{
+  typedef typename DerType::Scalar Real;
+  typedef AutoDiffScalar<DerType> FloatingPoint;
+  enum {
+    IsComplex = 0,
+    HasFloatingPoint = 1,
+    ReadCost = 1,
+    AddCost = 1,
+    MulCost = 1
+  };
+};
+
+}
+
+#endif // EIGEN_AUTODIFF_SCALAR_H
-- 
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