complex.h

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/* Copyright (C) 2002-2012 Stefan Buehler <sbuehler@ltu.se>
 
   This program 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.
 
   This program 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 this program; if not, write to the Free Software
   Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
   USA. */
 
#ifndef complex_h
#define complex_h
 
#include <complex>
#include "lapack.h"
#include "matpackI.h"
 
typedef std::complex<Numeric> Complex;
 
inline std::complex<float> operator+(const double& d,
                                     const std::complex<float>& c) {
  return (float(d) + c);
}
inline std::complex<float> operator*(const double& d,
                                     const std::complex<float>& c) {
  return (float(d) * c);
}
 
inline std::complex<float> operator+(const std::complex<float>& c,
                                     const double& d) {
  return (c + float(d));
}
inline std::complex<float> operator*(const std::complex<float>& c,
                                     const double& d) {
  return (c * float(d));
}
 
// Constexpr versions of common Complex operations
 
// Helpers to keep equations readable
#define a1 c.real()
#define b1 c.imag()
#define a2 z.real()
#define b2 z.imag()
 
constexpr Numeric abs2(Complex c) { return a1 * a1 + b1 * b1; }
 
constexpr Complex conj(Complex c) { return Complex(a1, -b1); }
 
// Basic constexpr operations for Complex that don't exist in the standard yet (C++11)
// NOTE: Remove these if there is ever an overload warning updating the C++ compiler version
 
constexpr Complex operator+(Complex c, Numeric n) {
  return Complex(a1 + n, b1);
}
constexpr Complex operator-(Complex c, Numeric n) {
  return Complex(a1 - n, b1);
}
constexpr Complex operator*(Complex c, Numeric n) {
  return Complex(a1 * n, b1 * n);
}
constexpr Complex operator/(Complex c, Numeric n) {
  return Complex(a1 / n, b1 / n);
}
 
constexpr Complex operator+(Numeric n, Complex c) {
  return Complex(n + a1, b1);
}
constexpr Complex operator-(Numeric n, Complex c) {
  return Complex(n - a1, -b1);
}
constexpr Complex operator*(Numeric n, Complex c) {
  return Complex(n * a1, n * b1);
}
constexpr Complex operator/(Numeric n, Complex c) {
  return Complex(n * a1, -n * b1) / abs2(c);
}
 
constexpr Complex operator+(Complex c, Complex z) {
  return Complex(a1 + a2, b1 + b2);
}
constexpr Complex operator-(Complex c, Complex z) {
  return Complex(a1 - a2, b1 - b2);
}
constexpr Complex operator*(Complex c, Complex z) {
  return Complex(a1 * a2 - b1 * b2, a1 * b2 + b1 * a2);
}
constexpr Complex operator/(Complex c, Complex z) {
  return Complex(a1 * a2 + b1 * b2, -a1 * b2 + b1 * a2) / abs2(z);
}
 
// Remove helpers to keep global namespace usable
#undef a1
#undef b1
#undef a2
#undef b2
 
// Basic constexpr operations for different types since C++11 std::complex is lacking conversions
// FIXME: Cannot be template because Eigen interferes, so explicit copies are required for operations
// NOTE: Remove these if there is ever an overload warning updating the C++ compiler version
#define _complex_operations_(T)                   \
  constexpr Complex operator+(Complex c, T x) {   \
    return operator+(c, static_cast<Numeric>(x)); \
  }                                               \
  constexpr Complex operator-(Complex c, T x) {   \
    return operator-(c, static_cast<Numeric>(x)); \
  }                                               \
  constexpr Complex operator*(Complex c, T x) {   \
    return operator*(c, static_cast<Numeric>(x)); \
  }                                               \
  constexpr Complex operator/(Complex c, T x) {   \
    return operator/(c, static_cast<Numeric>(x)); \
  }                                               \
                                                  \
  constexpr Complex operator+(T x, Complex c) {   \
    return operator+(static_cast<Numeric>(x), c); \
  }                                               \
  constexpr Complex operator-(T x, Complex c) {   \
    return operator-(static_cast<Numeric>(x), c); \
  }                                               \
  constexpr Complex operator*(T x, Complex c) {   \
    return operator*(static_cast<Numeric>(x), c); \
  }                                               \
  constexpr Complex operator/(T x, Complex c) {   \
    return operator/(static_cast<Numeric>(x), c); \
  }
 
_complex_operations_(int) _complex_operations_(float)
    _complex_operations_(Index)
 
#undef _complex_operations_
 
    // Declare existence of the global joker object:
    extern const Joker joker;
 
// Declare the existence of class ConstComplexMatrixView:
class ConstComplexIterator1D;
 
// Declare the existence of class ComplexVectorView:
class ComplexVectorView;
 
// Declare the existence of class ConstComplexVectorView:
class ConstComplexVectorView;
 
// Declare the existence of class ConstMatrixView:
class ConstComplexMatrixView;
 
// Eigen library interactions:
typedef Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>
    ComplexMatrixType;
typedef Eigen::Stride<Eigen::Dynamic, Eigen::Dynamic> ComplexStrideType;
typedef Eigen::Map<ComplexMatrixType, 0, ComplexStrideType>
    ComplexMatrixViewMap;
typedef Eigen::Map<const ComplexMatrixType, 0, ComplexStrideType>
    ComplexConstMatrixViewMap;
 
class ComplexIterator1D {
 public:
  ComplexIterator1D() = default;
 
  ComplexIterator1D(Complex* x, Index stride)
      : mx(x), mstride(stride) { /* Nothing to do here. */
  }
 
  // Operators:
 
  ComplexIterator1D& operator++() {
    mx += mstride;
    return *this;
  }
 
  Complex& operator*() const { return *mx; }
 
  bool operator!=(const ComplexIterator1D& other) const {
    if (mx != other.mx)
      return true;
    else
      return false;
  }
 
  friend void copy(ConstComplexIterator1D origin,
                   const ConstComplexIterator1D& end,
                   ComplexIterator1D target);
 
 private:
  Complex* mx{nullptr};
  Index mstride{0};
};
 
class ConstComplexIterator1D {
 public:
  ConstComplexIterator1D() = default;
 
  ConstComplexIterator1D(Complex* x, Index stride)
      : mx(x), mstride(stride) { /* Nothing to do here. */
  }
 
  // Operators:
  ConstComplexIterator1D& operator++() {
    mx += mstride;
    return *this;
  }
 
  const Complex& operator*() const { return *mx; }
 
  bool operator!=(const ConstComplexIterator1D& other) const {
    if (mx != other.mx)
      return true;
    else
      return false;
  }
 
  friend void copy(ConstComplexIterator1D origin,
                   const ConstComplexIterator1D& end,
                   ComplexIterator1D target);
 
 private:
  const Complex* mx{nullptr};
  Index mstride{0};
};
 
// Declare the complex vector class:
class ComplexVector;
 
// Declare the ComplexMatrixView class
class ComplexMatrixView;
 
class ConstComplexVectorView {
 public:
  constexpr ConstComplexVectorView(const ConstComplexVectorView&) = default;
  constexpr ConstComplexVectorView(ConstComplexVectorView&&) = default;
  ConstComplexVectorView& operator=(const ConstComplexVectorView&) = default;
  ConstComplexVectorView& operator=(ConstComplexVectorView&&) = default;
 
  // Typedef for compatibility with STL
  typedef ConstComplexIterator1D const_iterator;
 
  // Member functions:
  bool empty() const { return (nelem() == 0); }
  Index nelem() const { return mrange.mextent; }
  Complex sum() const;
 
  // Const index operators:
  const Complex& operator[](Index n) const {  // Check if index is valid:
    assert(0 <= n);
    assert(n < mrange.mextent);
    return get(n);
  }
 
  const Complex& get(Index n) const {
    return *(mdata + mrange.mstart + n * mrange.mstride);
  }
 
  const Numeric& get_real(Index n) const {
    return reinterpret_cast<const Numeric(&)[2]>(get(n))[0];
  }
 
  const Numeric& get_imag(Index n) const {
    return reinterpret_cast<const Numeric(&)[2]>(get(n))[1];
  }
  
  ConstVectorView real() const {return ConstVectorView(reinterpret_cast<Numeric *>(mdata), Range(2*mrange.mstart, mrange.mextent, mrange.mstride*2));}
  
  ConstVectorView imag() const {return ConstVectorView(reinterpret_cast<Numeric *>(mdata), Range(2*mrange.mstart + 1, mrange.mextent, mrange.mstride*2));}
 
  ConstComplexVectorView operator[](const Range& r) const;
  friend Complex operator*(const ConstComplexVectorView& a,
                           const ConstComplexVectorView& b);
 
  // Functions returning iterators:
  ConstComplexIterator1D begin() const;
  ConstComplexIterator1D end() const;
 
  // Conversion to 1 column matrix:
  operator ConstComplexMatrixView() const;
 
  virtual ~ConstComplexVectorView() = default;
 
  // Friends:
  friend class ComplexVectorView;
  friend class ConstComplexIterator2D;
  friend class ConstComplexMatrixView;
  friend void mult(ComplexVectorView,
                   const ConstComplexMatrixView&,
                   const ConstComplexVectorView&);
 
  friend ComplexConstMatrixViewMap MapToEigen(const ConstComplexVectorView&);
  friend ComplexConstMatrixViewMap MapToEigenCol(const ConstComplexVectorView&);
  friend ComplexMatrixViewMap MapToEigen(ComplexVectorView&);
  friend ComplexMatrixViewMap MapToEigenCol(ComplexVectorView&);
 
  // A special constructor, that allows to make a ConstVectorView of a scalar.
  ConstComplexVectorView(const Complex& a);
 
 protected:
  // Constructors:
  ConstComplexVectorView() = default;
  ConstComplexVectorView(Complex* data, const Range& range);
  ConstComplexVectorView(Complex* data, const Range& p, const Range& n);
 
  // Data members:
  // -------------
  Range mrange{0, 0};
  Complex* mdata{nullptr};
};
 
class ComplexVectorView : public ConstComplexVectorView {
 public:
  // Make const methods visible from base class
  using ConstComplexVectorView::begin;
  using ConstComplexVectorView::end;
  using ConstComplexVectorView::operator[];
  using ConstComplexVectorView::get;
  using ConstComplexVectorView::get_imag;
  using ConstComplexVectorView::get_real;
  using ConstComplexVectorView::imag;
  using ConstComplexVectorView::real;
 
  constexpr ComplexVectorView(const ComplexVectorView&) = default;
  ComplexVectorView(const ComplexVector&);
  ComplexVectorView(ComplexVector& v);
 
  // Typedef for compatibility with STL
  typedef ComplexIterator1D iterator;
 
  Complex& operator[](Index n) {  // Check if index is valid:
    assert(0 <= n);
    assert(n < mrange.mextent);
    return get(n);
  }
 
  Complex& get(Index n) {
    return *(mdata + mrange.mstart + n * mrange.mstride);
  }
 
  Numeric& get_real(Index n) {
    return reinterpret_cast<Numeric(&)[2]>(get(n))[0];
  }
 
  Numeric& get_imag(Index n) {
    return reinterpret_cast<Numeric(&)[2]>(get(n))[1];
  }
  
  VectorView real() {return VectorView(reinterpret_cast<Numeric *>(mdata), Range(2*mrange.mstart, mrange.mextent, mrange.mstride*2));}
  
  VectorView imag() {return VectorView(reinterpret_cast<Numeric *>(mdata), Range(2*mrange.mstart + 1, mrange.mextent, mrange.mstride*2));}
 
  ComplexVectorView operator[](const Range& r);
 
  // ComplexIterators:
  ComplexIterator1D begin();
  ComplexIterator1D end();
 
  // Assignment operators:
  ComplexVectorView& operator=(const ConstComplexVectorView& v);
  ComplexVectorView& operator=(const ComplexVectorView& v);
  ComplexVectorView& operator=(const ComplexVector& v);
  ComplexVectorView& operator=(const Array<Complex>& v);
  ComplexVectorView& operator=(Complex x);
  ComplexVectorView& operator=(const ConstVectorView& v);
  ComplexVectorView& operator=(const VectorView& v);
  ComplexVectorView& operator=(const Vector& v);
  ComplexVectorView& operator=(const Array<Numeric>& v);
  ComplexVectorView& operator=(Numeric x);
 
  // Other operators:
  ComplexVectorView operator*=(Complex x);
  ComplexVectorView operator/=(Complex x);
  ComplexVectorView operator+=(Complex x);
  ComplexVectorView operator-=(Complex x);
  ComplexVectorView operator*=(Numeric x);
  ComplexVectorView operator/=(Numeric x);
  ComplexVectorView operator+=(Numeric x);
  ComplexVectorView operator-=(Numeric x);
 
  ComplexVectorView operator*=(const ConstComplexVectorView& x);
  ComplexVectorView operator/=(const ConstComplexVectorView& x);
  ComplexVectorView operator+=(const ConstComplexVectorView& x);
  ComplexVectorView operator-=(const ConstComplexVectorView& x);
  ComplexVectorView operator*=(const ConstVectorView& x);
  ComplexVectorView operator/=(const ConstVectorView& x);
  ComplexVectorView operator+=(const ConstVectorView& x);
  ComplexVectorView operator-=(const ConstVectorView& x);
 
  // Conversion to 1 column matrix:
  operator ComplexMatrixView();
  // Conversion to a plain C-array
  const Complex* get_c_array() const;
  Complex* get_c_array();
 
  virtual ~ComplexVectorView() = default;
 
  // Friends:
  friend class ConstComplexIterator2D;
  friend class ComplexIterator2D;
  friend class ComplexMatrixView;
 
  // A special constructor, that allows to make a ComplexVectorView of a scalar.
  ComplexVectorView(Complex& a);
 
 protected:
  // Constructors:
  ComplexVectorView() = default;
  ComplexVectorView(Complex* data, const Range& range);
  ComplexVectorView(Complex* data, const Range& p, const Range& n);
};
 
class ComplexIterator2D {
 public:
  // Constructors:
  ComplexIterator2D() = default;
 
  ComplexIterator2D(const ComplexVectorView& x, Index stride)
      : msv(x), mstride(stride) { /* Nothing to do here. */
  }
 
  // Operators:
  ComplexIterator2D& operator++() {
    msv.mdata += mstride;
    return *this;
  }
 
  bool operator!=(const ComplexIterator2D& other) const {
    if (msv.mdata + msv.mrange.mstart !=
        other.msv.mdata + other.msv.mrange.mstart)
      return true;
    else
      return false;
  }
 
  ComplexVectorView* operator->() { return &msv; }
 
  ComplexVectorView& operator*() { return msv; }
 
 private:
  ComplexVectorView msv;
  Index mstride{0};
};
 
class ConstComplexIterator2D {
 public:
  // Constructors:
  ConstComplexIterator2D() = default;
 
  ConstComplexIterator2D(const ConstComplexVectorView& x, Index stride)
      : msv(x), mstride(stride) { /* Nothing to do here. */
  }
 
  // Operators:
  ConstComplexIterator2D& operator++() {
    msv.mdata += mstride;
    return *this;
  }
 
  bool operator!=(const ConstComplexIterator2D& other) const {
    if (msv.mdata + msv.mrange.mstart !=
        other.msv.mdata + other.msv.mrange.mstart)
      return true;
    else
      return false;
  }
 
  const ConstComplexVectorView* operator->() const { return &msv; }
 
  const ConstComplexVectorView& operator*() const { return msv; }
 
 private:
  ConstComplexVectorView msv;
  Index mstride{0};
};
 
class ComplexVector : public ComplexVectorView {
 public:
  // Constructors:
  ComplexVector();
  explicit ComplexVector(Index n);
  ComplexVector(Index n, Complex fill);
  ComplexVector(Index n, Numeric fill);
  ComplexVector(Complex start, Index extent, Complex stride);
  ComplexVector(Complex start, Index extent, Numeric stride);
  ComplexVector(Numeric start, Index extent, Complex stride);
  ComplexVector(Numeric start, Index extent, Numeric stride);
  ComplexVector(const ConstComplexVectorView& v);
  ComplexVector(const ComplexVector& v);
  ComplexVector(const Vector& v);
  ComplexVector(const std::vector<Complex>&);
  ComplexVector(const std::vector<Numeric>&);
 
  // Assignment operators:
  ComplexVector& operator=(ComplexVector v);
  ComplexVector& operator=(const Array<Complex>& v);
  ComplexVector& operator=(Complex x);
 
  // Resize function:
  void resize(Index n);
 
  // Swap function:
  friend void swap(ComplexVector& v1, ComplexVector& v2);
 
  // Destructor:
  virtual ~ComplexVector();
};
 
// Declare class ComplexMatrix:
class ComplexMatrix;
 
class ConstComplexMatrixView {
 public:
  constexpr ConstComplexMatrixView(const ConstComplexMatrixView&) = default;
  constexpr ConstComplexMatrixView(ConstComplexMatrixView&&) = default;
  ConstComplexMatrixView& operator=(const ConstComplexMatrixView&) = default;
  ConstComplexMatrixView& operator=(ConstComplexMatrixView&&) = default;
 
  // Typedef for compatibility with STL
  typedef ConstComplexIterator2D const_iterator;
 
  // Member functions:
  bool empty() const { return not nrows() or not ncols(); }
  Index nrows() const { return mrr.mextent; }
  Index ncols() const { return mcr.mextent; }
 
  // Const index operators:
  Complex operator()(Index r, Index c) const {  // Check if indices are valid:
    assert(0 <= r);
    assert(0 <= c);
    assert(r < mrr.mextent);
    assert(c < mcr.mextent);
 
    return get(r, c);
  }
 
  Complex get(Index r, Index c) const {
    return *(mdata + mrr.mstart + r * mrr.mstride + mcr.mstart +
             c * mcr.mstride);
  }
 
  Numeric get_real(Index r, Index c) const { return get(r, c).real(); }
 
  Numeric get_imag(Index r, Index c) const { return get(r, c).imag(); }
  
  ConstMatrixView real() const {return ConstMatrixView(reinterpret_cast<Numeric *>(mdata), Range(2*mrr.mstart, mrr.mextent, mrr.mstride*2), 
                                                                                           Range(2*mcr.mstart, mcr.mextent, mcr.mstride*2));}
  
  ConstMatrixView imag() const {return ConstMatrixView(reinterpret_cast<Numeric *>(mdata), Range(2*mrr.mstart, mrr.mextent, mrr.mstride*2),
                                                                                           Range(2*mcr.mstart + 1, mcr.mextent, mcr.mstride*2));}
  
  Index get_column_extent() const {return mcr.get_extent();}
 
  ConstComplexMatrixView operator()(const Range& r, const Range& c) const;
  ConstComplexVectorView operator()(const Range& r, Index c) const;
  ConstComplexVectorView operator()(Index r, const Range& c) const;
 
  // Functions returning iterators:
  ConstComplexIterator2D begin() const;
  ConstComplexIterator2D end() const;
 
  // View on diagonal complex vector
  ConstComplexVectorView diagonal() const;
 
  virtual ~ConstComplexMatrixView() = default;
 
  // Friends:
  friend class ComplexMatrixView;
  friend class ConstComplexVectorView;
  friend ConstComplexMatrixView transpose(ConstComplexMatrixView m);
  friend void mult(ComplexVectorView,
                   const ConstComplexMatrixView&,
                   const ConstComplexVectorView&);
  friend void mult(ComplexMatrixView,
                   const ConstComplexMatrixView&,
                   const ConstComplexMatrixView&);
  friend void mult(ComplexMatrixView,
                   const ConstMatrixView&,
                   const ConstComplexMatrixView&);
  friend void mult(ComplexMatrixView,
                   const ConstComplexMatrixView&,
                   const ConstMatrixView&);
  
 
  friend ComplexConstMatrixViewMap MapToEigen(const ConstComplexMatrixView&);
  friend ComplexMatrixViewMap MapToEigen(ComplexMatrixView&);
 
 protected:
  // Constructors:
  ConstComplexMatrixView() = default;
  ConstComplexMatrixView(Complex* data, const Range& r, const Range& c);
  ConstComplexMatrixView(Complex* data,
                         const Range& pr,
                         const Range& pc,
                         const Range& nr,
                         const Range& nc);
 
  // Data members:
  // -------------
  Range mrr{0, 0, 1};
  Range mcr{0, 0, 1};
  Complex* mdata{nullptr};
};
 
class ComplexMatrixView : public ConstComplexMatrixView {
 public:
  // Make const methods visible from base class
  using ConstComplexMatrixView::begin;
  using ConstComplexMatrixView::end;
  using ConstComplexMatrixView::operator();
  using ConstComplexMatrixView::get;
  using ConstComplexMatrixView::get_imag;
  using ConstComplexMatrixView::get_real;
  using ConstComplexMatrixView::imag;
  using ConstComplexMatrixView::real;
  using ConstComplexMatrixView::diagonal;
 
  constexpr ComplexMatrixView(const ComplexMatrixView&) = default;
 
  // Typedef for compatibility with STL
  typedef ComplexIterator2D iterator;
 
  // Index Operators:
  Complex& operator()(Index r, Index c) {  // Check if indices are valid:
    assert(0 <= r);
    assert(0 <= c);
    assert(r < mrr.mextent);
    assert(c < mcr.mextent);
 
    return get(r, c);
  }
 
  Complex& get(Index r, Index c) {
    return *(mdata + mrr.mstart + r * mrr.mstride + mcr.mstart +
             c * mcr.mstride);
  }
 
  Numeric& get_real(Index r, Index c) {
    return reinterpret_cast<Numeric(&)[2]>(get(r, c))[0];
  }
 
  Numeric& get_imag(Index r, Index c) {
    return reinterpret_cast<Numeric(&)[2]>(get(r, c))[1];
  }
  
  MatrixView real() {return MatrixView(reinterpret_cast<Numeric *>(mdata), Range(2*mrr.mstart, mrr.mextent, mrr.mstride*2), 
                                                                           Range(2*mcr.mstart, mcr.mextent, mcr.mstride*2));}
  
  MatrixView imag() {return MatrixView(reinterpret_cast<Numeric *>(mdata), Range(2*mrr.mstart, mrr.mextent, mrr.mstride*2),
                                                                           Range(2*mcr.mstart + 1, mcr.mextent, mcr.mstride*2));}
 
  ComplexMatrixView operator()(const Range& r, const Range& c);
  ComplexVectorView operator()(const Range& r, Index c);
  ComplexVectorView operator()(Index r, const Range& c);
 
  // Functions returning iterators:
  ComplexIterator2D begin();
  ComplexIterator2D end();
  
  // View on diagonal complex vector
  ComplexVectorView diagonal();
 
  // Assignment operators:
  ComplexMatrixView& operator=(const ConstComplexMatrixView& v);
  ComplexMatrixView& operator=(const ComplexMatrixView& v);
  ComplexMatrixView& operator=(const ComplexMatrix& v);
  ComplexMatrixView& operator=(const ConstComplexVectorView& v);
  ComplexMatrixView& operator=(Complex x);
 
  // Other operators:
  ComplexMatrixView& operator*=(Complex x);
  ComplexMatrixView& operator/=(Complex x);
  ComplexMatrixView& operator+=(Complex x);
  ComplexMatrixView& operator-=(Complex x);
  ComplexMatrixView& operator*=(Numeric x);
  ComplexMatrixView& operator/=(Numeric x);
  ComplexMatrixView& operator+=(Numeric x);
  ComplexMatrixView& operator-=(Numeric x);
 
  ComplexMatrixView& operator*=(const ConstComplexMatrixView& x);
  ComplexMatrixView& operator/=(const ConstComplexMatrixView& x);
  ComplexMatrixView& operator+=(const ConstComplexMatrixView& x);
  ComplexMatrixView& operator-=(const ConstComplexMatrixView& x);
 
  ComplexMatrixView& operator*=(const ConstMatrixView& x);
  ComplexMatrixView& operator/=(const ConstMatrixView& x);
  ComplexMatrixView& operator+=(const ConstMatrixView& x);
  ComplexMatrixView& operator-=(const ConstMatrixView& x);
 
  ComplexMatrixView& operator*=(const ConstComplexVectorView& x);
  ComplexMatrixView& operator/=(const ConstComplexVectorView& x);
  ComplexMatrixView& operator+=(const ConstComplexVectorView& x);
  ComplexMatrixView& operator-=(const ConstComplexVectorView& x);
 
  // Conversion to a plain C-array
  const Complex* get_c_array() const;
  Complex* get_c_array();
 
  virtual ~ComplexMatrixView() = default;
 
  // Friends:
  friend class ComplexVectorView;
  friend ConstComplexMatrixView transpose(ConstComplexMatrixView m);
  friend ComplexMatrixView transpose(ComplexMatrixView m);
 
 protected:
  // Constructors:
  ComplexMatrixView();
  ComplexMatrixView(Complex* data, const Range& r, const Range& c);
  ComplexMatrixView(Complex* data,
                    const Range& pr,
                    const Range& pc,
                    const Range& nr,
                    const Range& nc);
};
 
class ComplexMatrix : public ComplexMatrixView {
 public:
  // Constructors:
  ComplexMatrix() = default;
  ComplexMatrix(Index r, Index c);
  ComplexMatrix(Index r, Index c, Complex fill);
  ComplexMatrix(Index r, Index c, Numeric fill);
  ComplexMatrix(const ConstComplexMatrixView& v);
  ComplexMatrix(const ComplexMatrix& v);
 
  // Assignment operators:
  ComplexMatrix& operator=(ComplexMatrix x);
  ComplexMatrix& operator=(Complex x);
  ComplexMatrix& operator=(const ConstComplexVectorView& v);
  
  // Inverse in place
  ComplexMatrix& inv(const lapack_help::Inverse<Complex>& help=lapack_help::Inverse<Complex>{0});
 
  // Resize function:
  void resize(Index r, Index c);
 
  // Swap function:
  friend void swap(ComplexMatrix& m1, ComplexMatrix& m2);
 
  // Destructor:
  virtual ~ComplexMatrix();
 
  Complex* get_raw_data() { return mdata; }
};
 
// Function declarations:
// ----------------------
 
ConstComplexMatrixView transpose(ConstComplexMatrixView m);
 
ComplexMatrixView transpose(ComplexMatrixView m);
 
void copy(ConstComplexIterator1D origin,
          const ConstComplexIterator1D& end,
          ComplexIterator1D target);
 
void copy(Complex x, ComplexIterator1D target, const ComplexIterator1D& end);
 
void copy(ConstComplexIterator2D origin,
          const ConstComplexIterator2D& end,
          ComplexIterator2D target);
 
void copy(Complex x, ComplexIterator2D target, const ComplexIterator2D& end);
 
void mult(ComplexVectorView y,
          const ConstComplexMatrixView& M,
          const ConstComplexVectorView& x);
 
void mult(ComplexMatrixView A,
          const ConstComplexMatrixView& B,
          const ConstComplexMatrixView& C);
void mult(ComplexMatrixView A,
          const ConstMatrixView& B,
          const ConstComplexMatrixView& C);
void mult(ComplexMatrixView A,
          const ConstComplexMatrixView& B,
          const ConstMatrixView& C);
void mult(ComplexMatrixView A,
          const ConstMatrixView& B,
          const ConstMatrixView& C);
 
Complex operator*(const ConstComplexVectorView& a,
                  const ConstComplexVectorView& b);
 
std::ostream& operator<<(std::ostream& os, const ConstComplexVectorView& v);
 
std::ostream& operator<<(std::ostream& os, const ConstComplexMatrixView& v);
 
// Converts constant matrix to constant eigen map
ComplexConstMatrixViewMap MapToEigen(const ConstComplexMatrixView& A);
// Converts constant vector to constant eigen row-view
ComplexConstMatrixViewMap MapToEigen(const ConstComplexVectorView& A);
// Converts constant vector to constant eigen row-view
ComplexConstMatrixViewMap MapToEigenRow(const ConstComplexVectorView& A);
// Converts constant vector to constant eigen column-view
ComplexConstMatrixViewMap MapToEigenCol(const ConstComplexVectorView& A);
// Converts matrix to eigen map
ComplexMatrixViewMap MapToEigen(ComplexMatrixView& A);
// Converts vector to eigen map row-view
ComplexMatrixViewMap MapToEigen(ComplexVectorView& A);
// Converts vector to eigen map row-view
ComplexMatrixViewMap MapToEigenRow(ComplexVectorView& A);
// Converts vector to eigen map column-view
ComplexMatrixViewMap MapToEigenCol(ComplexVectorView& A);
 
typedef Array<ComplexVector> ArrayOfComplexVector;
typedef Array<ComplexMatrix> ArrayOfComplexMatrix;
 
#endif