array3D.h

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#ifndef _DLR_ARRAY3D_H_
#define _DLR_ARRAY3D_H_

#include <iostream>
#include <dlrNumeric/array1D.h>
#include <dlrNumeric/array2D.h>
#include <dlrCommon/exception.h>

namespace dlr {

  namespace numeric {
    
    template <class Type>
    class Array3D {
    public:
      /* ******** Public typedefs ******** */

      typedef Type value_type;

      typedef Type* iterator;
    
      typedef const Type* const_iterator;

      /* ******** Public member functions ******** */

      Array3D();

      Array3D(size_t shape0, size_t shape1, size_t shape2);

      explicit
      Array3D(const std::string& inputString);

      Array3D(const Array3D<Type> &source);

      Array3D(size_t shape0, size_t shape1, size_t shape2, Type* const dataPtr);

      virtual
      ~Array3D();

      iterator
      begin() {return m_dataPtr;}

      const_iterator
      begin() const {return m_dataPtr;}

      void
      clear() {this->reinit(0, 0, 0);}


      inline void 
      checkDimension(size_t shape0, size_t shape1, size_t shape2) const;


      Array3D<Type>
      copy() const;

      template <class Type2>
      void
      copy(const Array3D<Type2>& source);

      template <class Type2>
      void
      copy(const Type2* dataPtr);

      Type*
      data() {return m_dataPtr;}

      const Type*
      data() const {return m_dataPtr;}

      Type*
      data(size_t index) {
        checkBounds(index);
        return m_dataPtr + index;
      }

      const Type*
      data(size_t index) const {
        checkBounds(index);
        return m_dataPtr+index;
      }

      Type*
      data(size_t index0, size_t index1, size_t index2) {
        checkBounds(index0, index1, index2);
        return (m_dataPtr + index2 + (index1 * m_shape2)
                + (index0 * m_shape1Times2));
      }

      const Type*
      data(size_t index0, size_t index1, size_t index2) const {
        checkBounds(index0, index1, index2);
        return (m_dataPtr + index2 + (index1 * m_shape2)
                + (index0 * m_shape1Times2));
      }


      bool
      empty() const {return this->size() == 0;}

    
      iterator
      end() {return m_dataPtr + m_size;}

      const_iterator
      end() const {return m_dataPtr + m_size;}


      inline Type
      getElement(size_t index0) const {return this->operator()(index0);}


      Type
      getElement(size_t index0, size_t index1, size_t index2) const {
        return this->operator()(index0, index1, index2);
      }        


      std::istream&
      readFromStream(std::istream& inputStream);
    
      void
      reinit(size_t shape0, size_t shape1, size_t shape2);

      void
      reshape(int shape0, int shape1, int shape2);


      Type&
      setElement(size_t index0, const Type& value) {
        return this->operator()(index0) = value;
      }


      Type&
      setElement(size_t index0, size_t index1, size_t index2,
                 const Type& value) {
        return this->operator()(index0, index1, index2) = value;
      }


      Array1D<size_t>
      shape() const;

      size_t
      shape(size_t axis) const;

      size_t
      shape0() const {return m_shape0;}

      size_t
      shape1() const {return m_shape1;}

      size_t
      shape2() const {return m_shape2;}

      size_t
      size() const {return m_size;}
  
      Array2D<Type>
      slice(size_t index);

      const Array2D<Type>
      slice(size_t index) const;

      Array3D<Type>&
      operator=(const Array3D<Type>& source);

      Array3D<Type>&
      operator=(Type value);

      Type&
      operator()(size_t index) {
        checkBounds(index);
        return m_dataPtr[index];
      }

      Type
      operator()(size_t index) const {
        checkBounds(index);
        return m_dataPtr[index];
      }
    
      Type&
      operator()(size_t index0, size_t index1, size_t index2) {
        checkBounds(index0, index1, index2);
        return m_dataPtr[index2 + (index1 * m_shape2)
                         + (index0 * m_shape1Times2)];
      }

      Type
      operator()(size_t index0, size_t index1, size_t index2) const {
        checkBounds(index0, index1, index2);
        return m_dataPtr[index2 + (index1 * m_shape2)
                         + (index0 * m_shape1Times2)];
      }

      Type&
      operator[](size_t index) {return this->operator()(index);}

      Type
      operator[](size_t index) const {return this->operator()(index);}

      template <class Type2>
      Array3D<Type>&
      operator*=(const Array3D<Type2>& arg);

      template <class Type2>
      Array3D<Type>&
      operator/=(const Array3D<Type2>& arg);

      template <class Type2>
      Array3D<Type>&
      operator+=(const Array3D<Type2>& arg);

      template <class Type2>
      Array3D<Type>&
      operator-=(const Array3D<Type2>& arg);

      Array3D<Type>&
      operator+=(const Type arg);

      Array3D<Type>&
      operator-=(const Type arg);

      Array3D<Type>&
      operator*=(const Type arg);

      Array3D<Type>&
      operator/=(const Type arg);

    private:
      // Private member functions
      void allocate();

      // Optionally throw an exception if index is beyond the range of
      // this array.
      inline void
      checkBounds(size_t index) const;

      // Optionally throw an exception if any index is beyond the range of
      // this array.
      inline void
      checkBounds(size_t index0, size_t index1, size_t index2) const;

      void deAllocate();

      // Constants to help with formatting.  We use the initialization
      // on first use paradigm for the string constants to avoid
      // headaches.

      static const std::string& ioIntro(); 

      static const std::string& ioOutro();

      static const char ioOpening = '[';

      static const char ioClosing = ']';

      static const char ioSeparator = ',';
    
      // Private member variables
      size_t m_shape0;
      size_t m_shape1;
      size_t m_shape2;
      size_t m_shape1Times2;
      size_t m_size;
      Type* m_dataPtr;
      size_t* m_refCountPtr;
      bool m_isAllocated;
    
    };


    /* =========== Non-member functions related to Array3D =========== */

//   /** 
//    * This function returns the maximum element of the an Array3D
//    * instance.
//    * 
//    * @param array This argument is the Array3D instance in which to
//    * search for the largest element.
//    * 
//    * @return The return value is the value of the largest element.
//    */
//   template <class Type> 
//   Type maximum(const Array3D<Type>& array);


//   /** 
//    * This function returns the minimum element of the an Array3D
//    * instance.
//    * 
//    * @param array This argument is the Array3D instance in which to
//    * search for the smallest element.
//    * 
//    * @return The return value is the value of the smallest element.
//    */
//   template <class Type> 
//   Type minimum(const Array3D<Type>& array);


//   /** 
//    * This function computes the sum of the elements of its argument.
//    * The summation is accumulated into a variable of type
//    * NumericTraits<Type>::SumType, which for now defaults to Type, but
//    * ultimately should be a type which (for fixed point and integral
//    * types) has enough bits to hold the sum of at least 65535
//    * elements.
//    * 
//    * @param array0 This argument is the array to be summed.
//    *
//    * @return The summation of all the elements of array0.
//    */
//   template <class Type> 
//   Type sum(const Array3D<Type>& array);


  
    template <class Type>
    Array3D<Type>
    operator+(const Array3D<Type>& array0, const Array3D<Type>& array1);


    template <class Type>
    Array3D<Type>
    operator-(const Array3D<Type>& array0, const Array3D<Type>& array1);


    template <class Type>
    Array3D<Type>
    operator*(const Array3D<Type>& array0, const Array3D<Type>& array1);

  
    template <class Type>
    Array3D<Type>
    operator/(const Array3D<Type>& array0, const Array3D<Type>& array1);


    template <class Type>
    Array3D<Type>
    operator+(const Array3D<Type>& array0, Type scalar);

  
    template <class Type>
    Array3D<Type>
    operator-(const Array3D<Type>& array0, Type scalar);

  
    template <class Type>
    Array3D<Type>
    operator*(const Array3D<Type>& array0, Type scalar);

  
    template <class Type>
    Array3D<Type>
    operator/(const Array3D<Type>& array0, Type scalar);

  
    template <class Type>
    inline Array3D<Type>
    operator+(Type scalar, const Array3D<Type>& array0);

  
    template <class Type>
    inline Array3D<Type>
    operator*(Type scalar, const Array3D<Type>& array0);


    template <class Type>
    Array3D<bool>
    operator==(const Array3D<Type>& array0, const Type arg);

    
    template <class Type>
    Array3D<bool>
    operator==(const Array3D<Type>& array0, const Array3D<Type>& array1);
    

    template <class Type>
    Array3D<bool>
    operator<(const Array3D<Type>& array0, Type arg);

  
    template <class Type>
    Array3D<bool>
    operator<=(const Array3D<Type>& array0, Type arg);


    template <class Type>
    Array3D<bool>
    operator>(const Array3D<Type>& array0, Type arg);

  
    template <class Type>
    Array3D<bool>
    operator>=(const Array3D<Type>& array0, Type arg);


    template <class Type>
    std::ostream& operator<<(std::ostream& stream, const Array3D<Type>& array0);

  
    template <class Type>
    std::istream&
    operator>>(std::istream& stream, Array3D<Type>& array0);
  
  } // namespace numeric

} // namespace dlr


/* ======= Declarations to maintain compatibility with legacy code. ======= */

namespace dlr {

  using numeric::Array3D;

} // namespace dlr


/*******************************************************************
 * Member function definitions follow.  This would be a .C file
 * if it weren't templated.
 *******************************************************************/

#include <algorithm>
#include <sstream>
#include <numeric>
#include <functional>
#include <dlrNumeric/numericTraits.h>

namespace dlr {

  namespace numeric {
    
    // Static constant describing how the string representation of an
    // Array3D should start.
    template <class Type>
    const std::string&
    Array3D<Type>::
    ioIntro()
    {
      static const std::string intro = "Array3D(";
      return intro;
    }

  
    // Static constant describing how the string representation of an
    // Array3D should end.
    template <class Type>
    const std::string&
    Array3D<Type>::
    ioOutro()
    {
      static const std::string outro = ")";
      return outro;
    }

    // Non-static member functions below.

    template <class Type>
    Array3D<Type>::
    Array3D()
      : m_shape0(0),
        m_shape1(0),
        m_shape2(0),
        m_shape1Times2(0),
        m_size(0),
        m_dataPtr(0),
        m_refCountPtr(0),
        m_isAllocated(false)
    {
      // Empty.
    }

  
    template <class Type>
    Array3D<Type>::
    Array3D(size_t shape0, size_t shape1, size_t shape2)
      : m_shape0(shape0),
        m_shape1(shape1),
        m_shape2(shape2),
        m_shape1Times2(0), // This will be set in the call to allocate().
        m_size(0),         // This will be set in the call to allocate().
        m_dataPtr(0),      // This will be set in the call to allocate().
        m_refCountPtr(0),  // This will be set in the call to allocate().
        m_isAllocated(false)
    {
      this->allocate();
    }

  
    // Construct from an initialization string.
    template <class Type>
    Array3D<Type>::
    Array3D(const std::string& inputString)
      : m_shape0(0),
        m_shape1(0),
        m_shape2(0),
        m_shape1Times2(0),
        m_size(0),
        m_dataPtr(0),
        m_refCountPtr(0),
        m_isAllocated(false)
    {
      // We'll use the stream input operator to parse the string.
      std::istringstream inputStream(inputString);

      // Now read the string into an array.
      Array3D<Type> inputArray;
      inputStream >> inputArray;
      if(!inputStream) {
        std::ostringstream message;
        message << "Couldn't parse input string: \"" << inputString << "\".";
        DLR_THROW3(ValueException, "Array3D::Array3D(const std::string&)",
                   message.str().c_str());                 
      }

      // If all went well, copy into *this.
      *this = inputArray;
    }


  
    /* When copying from a Array3D do a shallow copy */
    /* Update reference count if the array we're copying has */
    /* valid data. */
    template <class Type>
    Array3D<Type>::
    Array3D(const Array3D<Type>& source)
      : m_shape0(source.m_shape0),
        m_shape1(source.m_shape1),
        m_shape2(source.m_shape2),
        m_shape1Times2(source.m_shape1 * source.m_shape2),
        m_size(source.m_size),
        m_dataPtr(source.m_dataPtr),
        m_refCountPtr(source.m_refCountPtr),
        m_isAllocated(source.m_isAllocated)
    {
      if(m_isAllocated) {
        ++(*m_refCountPtr);
      }
    }


    /* Here's a constructor for getting image data into the array */
    /* cheaply. */
    template <class Type>
    Array3D<Type>::
    Array3D(size_t shape0, size_t shape1, size_t shape2, Type* const dataPtr)
      : m_shape0(shape0),
        m_shape1(shape1),
        m_shape2(shape2),
        m_shape1Times2(shape1 * shape2),
        m_size(shape0 * shape1 * shape2),
        m_dataPtr(dataPtr),
        m_refCountPtr(0),
        m_isAllocated(false)
    {
      // empty
    }

  
    template <class Type>
    Array3D<Type>::
    ~Array3D()
    {
      deAllocate();
    }


    template <class Type>
    inline void Array3D<Type>::
    checkDimension(size_t shape0, size_t shape1, size_t shape2) const
    {
#ifdef _DLRNUMERIC_CHECKBOUNDS_
      if(shape0 != this->shape0()
         || shape1 != this->shape1()
         || shape2 != this->shape2()){
        std::ostringstream message;
        message << "Size mismatch: required dimension is ("
                << shape0 << ", " << shape1 << ", " << shape2 << ") "
                << " while *this has dimension "
                << this->shape0() << ", " << this->shape1() << ", "
                << this->shape2() << ") ";
        DLR_THROW(IndexException, "Array3D::checkDimension()",
                  message.str().c_str());
      }
#endif
    }


    template <class Type>
    Array3D<Type> Array3D<Type>::
    copy() const
    {
      Array3D<Type> newArray(m_shape0, m_shape1, m_shape2);
      newArray.copy(*this);
      return newArray;
    }

  
    template <class Type> template <class Type2>
    void Array3D<Type>::
    copy(const Array3D<Type2>& source)
    {
      if(source.size() != m_size) {
        std::ostringstream message;
        message << "Mismatched array sizes. Source array has "
                << source.size() << " elements, while destination array has "
                << m_size << " elements.";
        DLR_THROW3(ValueException, "Array3D::copy(const Array3D&)",
                   message.str().c_str());
      }
      if(m_size != 0) {
        this->copy(source.data());
      }
    }

  
    template <class Type> template <class Type2>
    void Array3D<Type>::
    copy(const Type2* dataPtr)
    {
      if (dataPtr == 0) {
        DLR_THROW(ValueException, "Array3D::copy(const Type2*)",
                  "Argument is a NULL pointer.");
      }
      std::copy(dataPtr, dataPtr + m_size, m_dataPtr);
    }

  
    // This member function sets the value of the array from an input
    // stream.
    template <class Type>
    std::istream&
    Array3D<Type>::
    readFromStream(std::istream& inputStream)
    {
      // Most of the time, InputType will be the same as Type.
      typedef typename NumericTraits<Type>::TextOutputType InputType;

      // If stream is in a bad state, we can't read from it.
      if (!inputStream){
        return inputStream;
      }
    
      // It's a lot easier to use a try block than to be constantly
      // testing whether the IO has succeeded, so we tell inputStream to
      // complain if anything goes wrong.
      std::ios_base::iostate oldExceptionState = inputStream.exceptions();
      inputStream.exceptions(
        std::ios_base::badbit | std::ios_base::failbit | std::ios_base::eofbit);

      // Now on with the show.
      try{
        // Construct an InputStream instance so we can use our
        // convenience functions.
        InputStream stream(inputStream);

        // We won't require the input format to start with "Array3D(", but
        // if it does we read it here.
        bool foundIntro = false;
        if(stream.peek() == ioIntro()[0]) {
          foundIntro = true;
          stream.expect(ioIntro());
        }

        // OK.  We've dispensed with the intro.  What's left should be of
        // the format "[row, row, row, ...]".  We require the square
        // brackets to be there.
        stream.expect(ioOpening);

        // Read the data.  We'll use the Array1D<Type> stream operator to
        // read each row.
        Array2D<Type> inputValue;
        std::vector< Array2D<Type> > inputBuffer;
        while(1) {
          // Read the next row.
          stream >> inputValue;
          inputBuffer.push_back(inputValue);

          // Read the separator, or else the closing character.
          char inChar = 0;
          stream >> inChar;
          if(inChar == ioClosing) {
            // Found a closing.  Stop here.
            break;
          }
          if(inChar != ioSeparator) {
            // Missing separator?  Fail here.
            stream.clear(std::ios_base::failbit);
          }
        }
    
        // If we found an intro, we expect the corresponding outro.
        if(foundIntro) {
          stream.expect(ioOutro());
        }

        // Now we're done with all of the parsing, verify that all slices
        // have the same number of rows and columns.
        size_t shape0 = inputBuffer.size();
        size_t shape1 = ((shape0 != 0) ? inputBuffer[0].rows() : 0);
        size_t shape2 = ((shape0 != 0) ? inputBuffer[0].columns() : 0);
        for(size_t index = 1; index < shape0; ++index) {
          if((inputBuffer[index].rows() != shape1)
             || (inputBuffer[index].columns() != shape2)) {
            // Inconsistent slice sizes!  Fail here.
            stream.clear(std::ios_base::failbit);
          }
        }

        // And finally, copy the data.
        size_t sliceSize = shape1 * shape2;
        this->reinit(shape0, shape1, shape2);
        for(size_t index = 0; index < shape0; ++index) {
          std::copy(inputBuffer[index].begin(), inputBuffer[index].end(),
                    this->begin() + (index * sliceSize));
        }
      } catch(std::ios_base::failure) {
        // Empty
      }
      inputStream.exceptions(oldExceptionState);
      return inputStream;
    }

  
    template <class Type>
    void Array3D<Type>::
    reinit(size_t shape0, size_t shape1, size_t shape2)
    {
      this->deAllocate();
      this->m_shape0 = shape0;
      this->m_shape1 = shape1;
      this->m_shape2 = shape2;
      this->allocate();
    }


    template <class Type>
    void Array3D<Type>::
    reshape(int shape0, int shape1, int shape2)
    {
      if ((shape0 * shape1 * shape2 != 0)){
        // If one axis is specified as -1, it will be automatically 
        // chosen to match the number of elements in the array.
        if((shape0 == -1) && (shape1 != -1) && (shape2 != -1)) {
          shape0 = static_cast<int>(this->size()) / (shape1 * shape2);
        } else if((shape1 == -1) && (shape0 != -1) && (shape2 != -1)) {
          shape1 = static_cast<int>(this->size()) / (shape0 * shape2);
        } else if((shape2 == -1) && (shape1 != -1) && (shape0 != -1)) {
          shape2 = static_cast<int>(this->size()) / (shape1 * shape0);
        }
      }
      if((shape0 * shape1 * shape2) != static_cast<int>(this->size())) {
        std::ostringstream message;
        message << "Can't reshape a(n) " << this->size()
                << " element array to be " << shape0 << " x " << shape1
                << " x " << shape2 << ".";
        DLR_THROW(ValueException, "Array3D::reshape()", message.str().c_str());
      }

      m_shape0 = static_cast<size_t>(shape0);
      m_shape1 = static_cast<size_t>(shape1);
      m_shape2 = static_cast<size_t>(shape2);
      m_shape1Times2 = shape1 * shape2;
    }

  
    template <class Type>
    Array1D<size_t> Array3D<Type>::
    shape() const
    {
      Array1D<size_t> rc(3);
      rc(0) = this->shape0();
      rc(1) = this->shape1();
      rc(2) = this->shape2();
      return rc;
    }


    template <class Type>
    size_t Array3D<Type>::
    shape(size_t axis) const
    {
      switch(axis) {
      case 0:
        return this->shape0();
        break;
      case 1:
        return this->shape1();
        break;
      case 2:
        return this->shape2();
        break;
      default:
        std::ostringstream message;
        message << "Invalid Axis: "<< axis << ".";
        DLR_THROW(ValueException, "Array3D::shape(size_t)",
                  message.str().c_str());
        break;
      }
      return 0;                     // To keep the darn compiler happy.
    }


    template <class Type>
    Array2D<Type>
    Array3D<Type>::
    slice(size_t index0)
    {
      this->checkBounds(index0, 0, 0);
      return Array2D<Type>(
        m_shape1, m_shape2, m_dataPtr + (index0 * m_shape1Times2));
    }

  
    template <class Type>
    const Array2D<Type>
    Array3D<Type>::
    slice(size_t index0) const
    {
      this->checkBounds(index0, 0, 0);
      return Array2D<Type>(
        m_shape1, m_shape2, m_dataPtr + (index0 * m_shape1Times2));
    }

  
    template <class Type>
    Array3D<Type>& Array3D<Type>::
    operator=(const Array3D<Type>& source)
    {
      // Check for self-assignment
      if(&source != this) {
        this->deAllocate();
        m_shape0 = source.m_shape0;
        m_shape1 = source.m_shape1;
        m_shape2 = source.m_shape2;
        m_shape1Times2 = source.m_shape1Times2;
        m_size = source.m_size;
        m_dataPtr = source.m_dataPtr;
        m_refCountPtr = source.m_refCountPtr;
        m_isAllocated = source.m_isAllocated;
        if(m_isAllocated) {
          ++(*m_refCountPtr);
        }
      }
      return *this;
    }


    template <class Type>
    Array3D<Type>& Array3D<Type>::
    operator=(Type value)
    {
      std::fill(m_dataPtr, m_dataPtr + m_size, value);
      return *this;
    }


    template <class Type> template <class Type2>
    Array3D<Type>& Array3D<Type>::
    operator*=(const Array3D<Type2>& arg)
    {
      if(m_size != arg.size()) {
        std::ostringstream message;
        message << "Mismatched array sizes. Argument array has "
                << arg.size() << " elements, while destination array has "
                << m_size << " elements.";
        DLR_THROW(ValueException, "Array3D::operator*=()",
                  message.str().c_str());
      }
      std::transform(m_dataPtr, m_dataPtr + m_size, arg.data(), m_dataPtr,
                     std::multiplies<Type>());
      return *this;
    }


    template <class Type> template <class Type2>
    Array3D<Type>& Array3D<Type>::
    operator/=(const Array3D<Type2>& arg)
    {
      if(m_size != arg.size()) {
        std::ostringstream message;
        message << "Mismatched array sizes. Argument array has "
                << arg.size() << " elements, while destination array has "
                << m_size << " elements.";
        DLR_THROW(ValueException, "Array3D::operator/=()",
                  message.str().c_str());
      }
      std::transform(m_dataPtr, m_dataPtr + m_size, arg.data(), m_dataPtr,
                     std::divides<Type>());
      return *this;
    }


    template <class Type> template <class Type2>
    Array3D<Type>& Array3D<Type>::
    operator+=(const Array3D<Type2>& arg)
    {
      if(m_size != arg.size()) {
        std::ostringstream message;
        message << "Mismatched array sizes. Argument array has "
                << arg.size() << " elements, while destination array has "
                << m_size << " elements.";
        DLR_THROW(ValueException, "Array3D::operator+=()",
                  message.str().c_str());
      }
      std::transform(m_dataPtr, m_dataPtr + m_size, arg.data(), m_dataPtr,
                     std::plus<Type>());
      return *this;
    }


    template <class Type> template <class Type2>
    Array3D<Type>& Array3D<Type>::
    operator-=(const Array3D<Type2>& arg)
    {
      if(m_size != arg.size()) {
        std::ostringstream message;
        message << "Mismatched array sizes. Argument array has "
                << arg.size() << " elements, while destination array has "
                << m_size << " elements.";
        DLR_THROW(ValueException, "Array3D::operator-=()",
                  message.str().c_str());
      }
      std::transform(m_dataPtr, m_dataPtr + m_size, arg.data(), m_dataPtr,
                     std::minus<Type>());
      return *this;
    }


    template <class Type>
    Array3D<Type>& Array3D<Type>::
    operator+=(const Type arg)
    {
      std::transform(m_dataPtr, m_dataPtr + m_size, m_dataPtr,
                     std::bind2nd(std::plus<Type>(), arg));
      return *this;
    }


    template <class Type>
    Array3D<Type>& Array3D<Type>::
    operator-=(const Type arg)
    {
      std::transform(m_dataPtr, m_dataPtr + m_size, m_dataPtr,
                     std::bind2nd(std::minus<Type>(), arg));
      return *this;
    }


    template <class Type>
    Array3D<Type>& Array3D<Type>::
    operator*=(const Type arg)
    {
      std::transform(m_dataPtr, m_dataPtr + m_size, m_dataPtr,
                     std::bind2nd(std::multiplies<Type>(), arg));
      return *this;
    }


    template <class Type>
    Array3D<Type>& Array3D<Type>::
    operator/=(const Type arg)
    {
      std::transform(m_dataPtr, m_dataPtr + m_size, m_dataPtr,
                     std::bind2nd(std::divides<Type>(), arg));
      return *this;
    }


    template <class Type>
    void Array3D<Type>::
    allocate()
    {
      m_shape1Times2  = m_shape1 * m_shape2;
      m_size = m_shape0 * m_shape1 * m_shape2;
      if(m_shape0 > 0 && m_shape1 > 0 && m_shape2 > 0) {
        m_dataPtr = new(Type[m_size]); // should throw an exeption
        m_refCountPtr = new size_t;      // if we're out of memory.
        *m_refCountPtr = 1;
        m_isAllocated = true;
        return;
      }
      m_dataPtr = 0;
      m_refCountPtr = 0;
      m_isAllocated = false;
      return;
    }


    template <class Type>
    inline void Array3D<Type>::
    checkBounds(size_t index) const
    {
#ifdef _DLRNUMERIC_CHECKBOUNDS_
      if(index >= m_size) {
        std::ostringstream message;
        message << "Index " << index << " is invalid for a(n) " << m_size
                << " element array.";
        DLR_THROW(IndexException, "Array3D::checkBounds(size_t)",
                  message.str().c_str());
      }
#endif
    }

  
    template <class Type>
    inline void Array3D<Type>::
    checkBounds(size_t index0, size_t index1, size_t index2) const
    {
#ifdef _DLRNUMERIC_CHECKBOUNDS_
      if(index0 >= m_shape0) {
        std::ostringstream message;
        message << "index0 should be less than " << m_shape0
                << ", but is actually " << index0 << ".";
        DLR_THROW3(IndexException, "Array3D::checkBounds()",
                   message.str().c_str());
      }
      if(index1 >= m_shape1) {
        std::ostringstream message;
        message << "index1 should be less than " << m_shape1
                << ", but is actually " << index1 << ".";
        DLR_THROW3(IndexException, "Array3D::checkBounds()",
                   message.str().c_str());
      }
      if(index2 >= m_shape2) {
        std::ostringstream message;
        message << "index2 should be less than " << m_shape2
                << ", but is actually " << index2 << ".";
        DLR_THROW3(IndexException, "Array3D::checkBounds()",
                   message.str().c_str());
      }
#endif
    }

  
    template <class Type>
    void Array3D<Type>::
    deAllocate()
    {
      if(m_isAllocated == true) {
        if(--(*m_refCountPtr) == 0) {
          delete[] m_dataPtr;
          delete m_refCountPtr;
          m_isAllocated = false;
          m_dataPtr = 0;
          m_refCountPtr = 0;
        }
      } else {
        m_dataPtr = 0;
        m_refCountPtr = 0;
      }
    }

  
    /* Non-member functions which will ultimately wind up in a different file */
//   template <class Type> 
//   Type maximum(const Array3D<Type>& array)
//   {
//     return *std::max_element(array.data(), array.data() + array.size());
//   }

//   template <class Type> 
//   Type minimum(const Array3D<Type>& array)
//   {
//     return *std::min_element(array.data(), array.data() + array.size());
//   }

//   template <class Type> 
//   Type sum(const Array3D<Type>& array)
//   {
//     return std::accumulate(array.data(), array.data() + array.size(),
//                            static_cast<Type>(0));
//   }
  
    template <class Type>
    Array3D<Type> operator+(const Array3D<Type>& array0,
                            const Array3D<Type>& array1)
    {
      if((array0.shape0() != array1.shape0())
         || (array0.shape1() != array1.shape1())        
         || (array0.shape2() != array1.shape2())) {
        std::ostringstream message;
        message << "Array sizes do not match.  Array0 is "
                << array0.shape0() << " x " << array0.shape1()
                << " x " << array0.shape2()
                << ", while array1 is "
                << array1.shape0() << " x " << array1.shape1()
                << " x " << array1.shape2() << ".";
        DLR_THROW(ValueException, "Array3D::operator+()", message.str().c_str());
      }
      Array3D<Type> result(array0.shape0(), array0.shape1(), array0.shape2());
      std::transform(array0.begin(), array0.end(), array1.begin(),
                     result.begin(), std::plus<Type>());
      return result;
    }


    template <class Type>
    Array3D<Type> operator-(const Array3D<Type>& array0,
                            const Array3D<Type>& array1)
    {
      if((array0.shape0() != array1.shape0())
         || (array0.shape1() != array1.shape1())        
         || (array0.shape2() != array1.shape2())) {
        std::ostringstream message;
        message << "Array sizes do not match.  Array0 is "
                << array0.shape0() << " x " << array0.shape1()
                << " x " << array0.shape2()
                << ", while array1 is "
                << array1.shape0() << " x " << array1.shape1()
                << " x " << array1.shape2() << ".";
        DLR_THROW(ValueException, "Array3D::operator-()", message.str().c_str());
      }
      Array3D<Type> result(array0.shape0(), array0.shape1(), array0.shape2());
      std::transform(array0.begin(), array0.end(), array1.begin(),
                     result.begin(), std::minus<Type>());
      return result;
    }

  
    template <class Type>
    Array3D<Type> operator*(const Array3D<Type>& array0,
                            const Array3D<Type>& array1)
    {
      if((array0.shape0() != array1.shape0())
         || (array0.shape1() != array1.shape1())        
         || (array0.shape2() != array1.shape2())) {
        std::ostringstream message;
        message << "Array sizes do not match.  Array0 is "
                << array0.shape0() << " x " << array0.shape1()
                << " x " << array0.shape2()
                << ", while array1 is "
                << array1.shape0() << " x " << array1.shape1()
                << " x " << array1.shape2() << ".";
        DLR_THROW(ValueException, "Array3D::operator*()", message.str().c_str());
      }
      Array3D<Type> result(array0.shape0(), array0.shape1(), array0.shape2());
      std::transform(array0.begin(), array0.end(), array1.begin(),
                     result.begin(), std::multiplies<Type>());
      return result;
    }
  

    template <class Type>
    Array3D<Type> operator/(const Array3D<Type>& array0,
                            const Array3D<Type>& array1)
    {
      if((array0.shape0() != array1.shape0())
         || (array0.shape1() != array1.shape1())        
         || (array0.shape2() != array1.shape2())) {
        std::ostringstream message;
        message << "Array sizes do not match.  Array0 is "
                << array0.shape0() << " x " << array0.shape1()
                << " x " << array0.shape2()
                << ", while array1 is "
                << array1.shape0() << " x " << array1.shape1()
                << " x " << array1.shape2() << ".";
        DLR_THROW(ValueException, "Array3D::operator/()", message.str().c_str());
      }
      Array3D<Type> result(array0.shape0(), array0.shape1(), array0.shape2());
      std::transform(array0.begin(), array0.end(), array1.begin(), result.begin(),
                     std::divides<Type>());
      return result;
    }


    template <class Type>
    Array3D<Type> operator+(const Array3D<Type>& array0, Type scalar)
    {
      Array3D<Type> result(array0.shape0(), array0.shape1(), array0.shape2());
      std::transform(array0.begin(), array0.end(), result.begin(),
                     std::bind2nd(std::plus<Type>(), scalar));
      return result;
    }


    template <class Type>
    Array3D<Type> operator-(const Array3D<Type>& array0, Type scalar)
    {
      Array3D<Type> result(array0.shape0(), array0.shape1(), array0.shape2()); 
      std::transform(array0.begin(), array0.end(), result.begin(),
                     std::bind2nd(std::minus<Type>(), scalar));
      return result;
    }


    template <class Type>
    Array3D<Type> operator*(const Array3D<Type>& array0, Type scalar)
    {
      Array3D<Type> result(array0.shape0(), array0.shape1(), array0.shape2()); 
      std::transform(array0.begin(), array0.end(), result.begin(),
                     std::bind2nd(std::multiplies<Type>(), scalar));
      return result;
    }


    template <class Type>
    Array3D<Type> operator/(const Array3D<Type>& array0, Type scalar)
    {
      Array3D<Type> result(array0.shape0(), array0.shape1(), array0.shape2()); 
      std::transform(array0.begin(), array0.end(), result.begin(),
                     std::bind2nd(std::divides<Type>(), scalar));
      return result;
    }


    template <class Type>
    inline Array3D<Type> operator+(Type scalar, const Array3D<Type>& array0)
    {
      return array0 + scalar;
    }


    template <class Type>
    inline Array3D<Type> operator*(Type scalar, const Array3D<Type>& array0)
    {
      return array0 * scalar;
    }


    // Elementwise comparison of an Array3D with a constant.
    template <class Type>
    Array3D<bool>
    operator==(const Array3D<Type>& array0, const Type arg)
    {
      Array3D<bool> result(array0.shape0(), array0.shape1(), array0.shape2());
      std::transform(array0.begin(), array0.end(), result.data(),
                     std::bind2nd(std::equal_to<Type>(), arg));
      return result;
    }

    
    // Elementwise comparison of an Array3D with another array.
    template <class Type>
    Array3D<bool>
    operator==(const Array3D<Type>& array0, const Array3D<Type>& array1)
    {
      array0.checkDimension(array1.shape0(), array1.shape1(), array1.shape2());
      Array3D<bool> result(array0.shape0(), array0.shape1(), array0.shape2());
      std::transform(array0.begin(), array0.end(), array1.begin(),
                     result.begin(), std::equal_to<Type>());
      return result;
    }

    
    template <class Type>
    Array3D<bool> operator>(const Array3D<Type>& array0, Type arg)
    {
      Array3D<bool> result(array0.shape0(), array0.shape1(), array0.shape2()); 
      std::transform(array0.begin(), array0.end(), result.begin(),
                     std::bind2nd(std::greater<Type>(), arg));
      return result;
    }


    template <class Type>
    Array3D<bool> operator<(const Array3D<Type>& array0, Type arg)
    {
      Array3D<bool> result(array0.shape0(), array0.shape1(), array0.shape2()); 
      std::transform(array0.begin(), array0.end(), result.begin(),
                     std::bind2nd(std::less<Type>(), arg));
      return result;
    }

  
    template <class Type>
    Array3D<bool> operator>=(const Array3D<Type>& array0, Type arg)
    {
      Array3D<bool> result(array0.shape0(), array0.shape1(), array0.shape2()); 
      std::transform(array0.begin(), array0.end(), result.begin(),
                     std::bind2nd(std::greater_equal<Type>(), arg));
      return result;
    }

  
    template <class Type>
    Array3D<bool> operator<=(const Array3D<Type>& array0, Type arg)
    {
      Array3D<bool> result(array0.shape0(), array0.shape1(), array0.shape2()); 
      std::transform(array0.begin(), array0.end(), result.begin(),
                     std::bind2nd(std::less_equal<Type>(), arg));
      return result;
    }


    // This operator outputs a text representation of an Array3D
    // instance to a std::ostream.
    template <class Type>  
    std::ostream& operator<<(std::ostream& stream, const Array3D<Type>& array0)
    {
      // Most of the time, OutputType will be the same as Type.
      typedef typename NumericTraits<Type>::TextOutputType OutputType;

      size_t index0, index1, index2;
      stream << "Array3D([";
      for(index0 = 0; index0 < array0.shape0(); ++index0) {
        if(index0 != 0) {
          stream << "         ";
        }
        stream << "[";
        for(index1 = 0; index1 < array0.shape1(); ++index1) {
          if(index1 != 0) {
            stream << "          ";     
          }
          stream << "[";
          for(index2 = 0; index2 < array0.shape2(); ++index2) {
            stream << static_cast<OutputType>(array0(index0, index1, index2));
            if(index2 != array0.shape2() - 1) {
              stream << ", ";
            }
          }
          stream << "]";
          if(index1 != array0.shape1() - 1) {
            stream << ",\n";
          }     
        }
        stream << "]";
        if(index0 != array0.shape0() - 1) {
          stream << ",\n";
        }
      }
      stream << "])\n";
      stream.flush();
      return stream;
    }


    template <class Type>
    std::istream&
    operator>>(std::istream& inputStream, Array3D<Type>& array0)
    {
      return array0.readFromStream(inputStream);
    }
  
  } // namespace numeric

} // namespace dlr

#endif /* #ifdef _DLR_ARRAY3D_H_ */

---