add matrix conjugation and adjunction.

compilation fixes in the numeric traits.

src/Manip

@@ -31,5 +31,6 @@
 #include "internal/Block.h"
 #include "internal/Minor.h"
 #include "internal/Transpose.h"
+#include "internal/Conjugate.h"
 
 #endif // EI_MANIP_H

src/internal/Conjugate.h

@@ -0,0 +1,69 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2007 Benoit Jacob <jacob@math.jussieu.fr>
+//
+// Eigen is free software; 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 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 General Public License for more
+// details.
+//
+// You should have received a copy of the GNU General Public License along
+// with Eigen; if not, write to the Free Software Foundation, Inc., 51
+// Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
+//
+// As a special exception, if other files instantiate templates or use macros
+// or functions from this file, or you compile this file and link it
+// with other works to produce a work based on this file, this file does not
+// by itself cause the resulting work to be covered by the GNU General Public
+// License. This exception does not invalidate any other reasons why a work
+// based on this file might be covered by the GNU General Public License.
+
+#ifndef EI_CONJUGATE_H
+#define EI_CONJUGATE_H
+
+template<typename MatrixType> class EiConjugate
+  : public EiObject<typename MatrixType::Scalar, EiConjugate<MatrixType> >
+{
+  public:
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename MatrixType::Ref MatRef;
+    friend class EiObject<Scalar, EiConjugate<MatrixType> >;
+    
+    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+                     ColsAtCompileTime = MatrixType::ColsAtCompileTime;
+
+    EiConjugate(const MatRef& matrix) : m_matrix(matrix) {}
+    
+    EiConjugate(const EiConjugate& other)
+      : m_matrix(other.m_matrix) {}
+    
+    EI_INHERIT_ASSIGNMENT_OPERATORS(EiConjugate)
+    
+  private:
+    EiConjugate& _ref() { return *this; }
+    const EiConjugate& _constRef() const { return *this; }
+    int _rows() const { return m_matrix.rows(); }
+    int _cols() const { return m_matrix.cols(); }
+    
+    Scalar _read(int row, int col) const
+    {
+      return EiConj(m_matrix.read(row, col));
+    }
+    
+  protected:
+    MatRef m_matrix;
+};
+
+template<typename Scalar, typename Derived>
+EiConjugate<Derived>
+EiObject<Scalar, Derived>::conjugate()
+{
+  return EiConjugate<Derived>(static_cast<Derived*>(this)->ref());
+}
+
+#endif // EI_CONJUGATE_H

src/internal/Matrix.h

@@ -127,4 +127,5 @@ EI_MAKE_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
 #include "MatrixOps.h"
 #include "ScalarOps.h"
 
+
 #endif // EI_MATRIX_H

src/internal/Numeric.h

@@ -24,8 +24,8 @@
 // License. This exception does not invalidate any other reasons why a work
 // based on this file might be covered by the GNU General Public License.
 
-#ifndef EI_TRAITS_H
-#define EI_TRAITS_H
+#ifndef EI_NUMERIC_H
+#define EI_NUMERIC_H
 
 template<typename T> struct EiTraits;
 
@@ -35,10 +35,10 @@ template<> struct EiTraits<int>
   typedef double FloatingPoint;
   typedef double RealFloatingPoint;
   
-  static const int Epsilon = 0;
   static const bool IsComplex = false;
   static const bool HasFloatingPoint = false;
   
+  static int epsilon() { return 0; }
   static int real(const int& x) { return x; }
   static int imag(const int& x) { EI_UNUSED(x); return 0; }
   static int conj(const int& x) { return x; }
@@ -50,7 +50,7 @@ template<> struct EiTraits<int>
     // "rand()%21" would be bad. always use the high-order bits, not the low-order bits.
     // note: here (gcc 4.1) static_cast<int> seems to round the nearest int.
     // I don't know if that's part of the standard.
-    return -10 + static_cast<int>(20.0 * (rand() / (RAND_MAX + 1.0)));
+    return -10 + static_cast<int>(rand() / ((RAND_MAX + 1.0)/20.0));
   }
 };
 
@@ -60,10 +60,10 @@ template<> struct EiTraits<float>
   typedef float FloatingPoint;
   typedef float RealFloatingPoint;
   
-  static const float Epsilon;
   static const bool IsComplex = false;
   static const bool HasFloatingPoint = true;
   
+  static float epsilon() { return 1e-5f; }
   static float real(const float& x) { return x; }
   static float imag(const float& x) { EI_UNUSED(x); return 0; }
   static float conj(const float& x) { return x; }
@@ -72,22 +72,20 @@ template<> struct EiTraits<float>
   static float abs2(const float& x) { return x*x; }
   static float random()
   {
-    return 20.0f * rand() / RAND_MAX - 10.0f;
+    return rand() / (RAND_MAX/20.0f) - 10.0f;
   }
 };
 
-const float EiTraits<float>::Epsilon = 1e-5f;
-
 template<> struct EiTraits<double>
 {
   typedef double Real;
   typedef double FloatingPoint;
   typedef double RealFloatingPoint;
   
-  static const double Epsilon;
   static const bool IsComplex = false;
   static const bool HasFloatingPoint = true;
   
+  static double epsilon() { return 1e-11; }
   static double real(const double& x) { return x; }
   static double imag(const double& x) { EI_UNUSED(x); return 0; }
   static double conj(const double& x) { return x; }
@@ -96,12 +94,10 @@ template<> struct EiTraits<double>
   static double abs2(const double& x) { return x*x; }
   static double random()
   {
-    return 20.0 * rand() / RAND_MAX - 10.0;
+    return rand() / (RAND_MAX/20.0) - 10.0;
   }
 };
 
-const double EiTraits<double>::Epsilon = 1e-11;
-
 template<typename _Real> struct EiTraits<std::complex<_Real> >
 {
   typedef _Real Real;
@@ -109,10 +105,10 @@ template<typename _Real> struct EiTraits<std::complex<_Real> >
   typedef std::complex<double> FloatingPoint;
   typedef typename EiTraits<Real>::FloatingPoint RealFloatingPoint;
   
-  static const Real Epsilon;
   static const bool IsComplex = true;
   static const bool HasFloatingPoint = EiTraits<Real>::HasFloatingPoint;
   
+  static Real epsilon() { return EiTraits<Real>::epsilon(); }
   static Real real(const Complex& x) { return std::real(x); }
   static Real imag(const Complex& x) { return std::imag(x); }
   static Complex conj(const Complex& x) { return std::conj(x); }
@@ -128,10 +124,6 @@ template<typename _Real> struct EiTraits<std::complex<_Real> >
   }
 };
 
-template<typename _Real>
-const _Real EiTraits<std::complex<_Real> >::Epsilon
-  = EiTraits<_Real>::Epsilon;
-
 template<typename T> typename EiTraits<T>::Real EiReal(const T& x)
 { return EiTraits<T>::real(x); }
 
@@ -155,13 +147,13 @@ template<typename T> T EiRandom()
 
 template<typename T> bool EiNegligible(const T& a, const T& b)
 {
-  return(EiAbs(a) <= EiAbs(b) * EiTraits<T>::Epsilon);
+  return(EiAbs(a) <= EiAbs(b) * EiTraits<T>::epsilon());
 }
 
 template<typename T> bool EiApprox(const T& a, const T& b)
 {
   if(EiTraits<T>::IsFloat)
-    return(EiAbs(a - b) <= std::min(EiAbs(a), EiAbs(b)) * EiTraits<T>::Epsilon);
+    return(EiAbs(a - b) <= std::min(EiAbs(a), EiAbs(b)) * EiTraits<T>::epsilon());
   else
     return(a == b);
 }
@@ -174,4 +166,4 @@ template<typename T> bool EiLessThanOrApprox(const T& a, const T& b)
     return(a <= b);
 }
 
-#endif // EI_TRAITS_H
+#endif // EI_NUMERIC_H

src/internal/Object.h

@@ -95,6 +95,8 @@ template<typename Scalar, typename Derived> class EiObject
     EiMinor<Derived> minor(int row, int col);
     EiBlock<Derived> block(int startRow, int endRow, int startCol, int endCol);
     EiTranspose<Derived> transpose();
+    EiConjugate<Derived> conjugate();
+    EiTranspose<EiConjugate<Derived> > adjoint() { return conjugate().transpose(); }
     
     template<typename OtherDerived>
     EiMatrixProduct<Derived, OtherDerived>

src/internal/Util.h

@@ -49,6 +49,7 @@ template<typename MatrixType> class EiColumn;
 template<typename MatrixType> class EiMinor;
 template<typename MatrixType> class EiBlock;
 template<typename MatrixType> class EiTranspose;
+template<typename MatrixType> class EiConjugate;
 template<typename Lhs, typename Rhs> class EiSum;
 template<typename Lhs, typename Rhs> class EiDifference;
 template<typename Lhs, typename Rhs> class EiMatrixProduct;

test/main.h

@@ -47,11 +47,13 @@ class EigenTest : public QObject
     void testMatrixManip();
 };
 
-template<typename T> T TestEpsilon();
-template<> int TestEpsilon<int>() { return 0; }
-template<> float TestEpsilon<float>() { return 1e-2f; }
-template<> double TestEpsilon<double>() { return 1e-4; }
-template<typename T> T TestEpsilon<std::complex<T> >() { return TestEpsilon<T>(); }
+template<typename T> inline typename EiTraits<T>::Real TestEpsilon();
+template<> inline int TestEpsilon<int>() { return 0; }
+template<> inline float TestEpsilon<float>() { return 1e-2f; }
+template<> inline double TestEpsilon<double>() { return 1e-4; }
+template<> inline int TestEpsilon<std::complex<int> >() { return TestEpsilon<int>(); }
+template<> inline float TestEpsilon<std::complex<float> >() { return TestEpsilon<float>(); }
+template<> inline double TestEpsilon<std::complex<double> >() { return TestEpsilon<double>(); }
 
 template<typename T> bool TestNegligible(const T& a, const T& b)
 {