ap.h

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/********************************************************************
AP library.
See www.alglib.net or alglib.sources.ru for details.
********************************************************************/
 
#ifndef AP_H
#define AP_H
 
#include <stdlib.h>
#include <math.h>
 
/********************************************************************
Checking of the array boundaries mode.
********************************************************************/
//#define NO_AP_ASSERT
#define AP_ASSERT
 
#ifndef AP_ASSERT
#define NO_AP_ASSERT
#endif
 
#ifdef NO_AP_ASSERT
#ifdef AP_ASSERT
#undef NO_AP_ASSERT
#endif
#endif
 
 
/********************************************************************
This symbol is used for debugging. Do not define it and do not remove
comments.
********************************************************************/
//#define UNSAFE_MEM_COPY
 
 
/********************************************************************
Namespace of a standard library AlgoPascal.
********************************************************************/
namespace ap
{
 
 
/********************************************************************
Exception class.
********************************************************************/
class ap_error
{
public:
    static void make_assertion(bool bClause)
        { if(!bClause) throw ap_error(); };
private:
};
 
/********************************************************************
Class defining a complex number with double precision.
********************************************************************/
class complex;
 
class complex
{
public:
    complex():x(0.0),y(0.0){};
    complex(const double &_x):x(_x),y(0.0){};
    complex(const double &_x, const double &_y):x(_x),y(_y){};
    complex(const complex &z):x(z.x),y(z.y){};
 
    complex& operator= (const double& v){ x  = v; y = 0.0; return *this; };
    complex& operator+=(const double& v){ x += v;          return *this; };
    complex& operator-=(const double& v){ x -= v;          return *this; };
    complex& operator*=(const double& v){ x *= v; y *= v;  return *this; };
    complex& operator/=(const double& v){ x /= v; y /= v;  return *this; };
 
    complex& operator= (const complex& z){ x  = z.x; y  = z.y; return *this; };
    complex& operator+=(const complex& z){ x += z.x; y += z.y; return *this; };
    complex& operator-=(const complex& z){ x -= z.x; y -= z.y; return *this; };
    complex& operator*=(const complex& z){ double t = x*z.x-y*z.y; y = x*z.y+y*z.x; x = t; return *this; };
    complex& operator/=(const complex& z)
    {
        ap::complex result;
        double e;
        double f;
        if( fabs(z.y)<fabs(z.x) )
        {
            e = z.y/z.x;
            f = z.x+z.y*e;
            result.x = (z.x+z.y*e)/f;
            result.y = (z.y-z.x*e)/f;
        }
        else
        {
            e = z.x/z.y;
            f = z.y+z.x*e;
            result.x = (z.y+z.x*e)/f;
            result.y = (-z.x+z.y*e)/f;
        }
        *this = result;
        return *this;
    };
 
    double x, y;
};
 
const complex operator/(const complex& lhs, const complex& rhs);
const bool operator==(const complex& lhs, const complex& rhs);
const bool operator!=(const complex& lhs, const complex& rhs);
const complex operator+(const complex& lhs);
const complex operator-(const complex& lhs);
const complex operator+(const complex& lhs, const complex& rhs);
const complex operator+(const complex& lhs, const double& rhs);
const complex operator+(const double& lhs, const complex& rhs);
const complex operator-(const complex& lhs, const complex& rhs);
const complex operator-(const complex& lhs, const double& rhs);
const complex operator-(const double& lhs, const complex& rhs);
const complex operator*(const complex& lhs, const complex& rhs);
const complex operator*(const complex& lhs, const double& rhs);
const complex operator*(const double& lhs, const complex& rhs);
const complex operator/(const complex& lhs, const complex& rhs);
const complex operator/(const double& lhs, const complex& rhs);
const complex operator/(const complex& lhs, const double& rhs);
const double abscomplex(const complex &z);
const complex conj(const complex &z);
const complex csqr(const complex &z);
 
 
/********************************************************************
Template defining vector in memory. It is used by the basic
subroutines of linear algebra.
 
Vector consists of Length elements of type T, starting from an element,
which Data is pointed to. Interval between adjacent elements equals
the value of Step.
 
The class provides an access for reading only.
********************************************************************/
template<class T>
class const_raw_vector
{
public:
    const_raw_vector(const T *Data, int Length, int Step):
        pData(const_cast<T*>(Data)),iLength(Length),iStep(Step){};
 
    const T* GetData() const
    { return pData; };
 
    int GetLength() const
    { return iLength; };
 
    int GetStep() const
    { return iStep; };
protected:
    T       *pData;
    int     iLength, iStep;
};
 
 
/********************************************************************
Template defining vector in memory, derived from const_raw_vector.
It is used by the basic subroutines of linear algebra.
 
Vector consists of Length elements of type T, starting from an element,
which Data is pointed to. Interval between adjacent elements equals
the value of Step.
 
The class provides an access both for reading and writing.
********************************************************************/
template<class T>
class raw_vector : public const_raw_vector<T>
{
public:
    raw_vector(T *Data, int Length, int Step):const_raw_vector<T>(Data, Length, Step){};
 
    T* GetData()
    { return const_raw_vector<T>::pData; };
};
 
 
/********************************************************************
Scalar product
********************************************************************/
template<class T>
T vdotproduct(const_raw_vector<T> v1, const_raw_vector<T> v2)
{
    ap_error::make_assertion(v1.GetLength()==v2.GetLength());
    if( v1.GetStep()==1 && v2.GetStep()==1 )
    {
        //
        // fast
        //
        T r = 0;
        const T *p1 = v1.GetData();
        const T *p2 = v2.GetData();
        int imax = v1.GetLength()/4;
        int i;
        for(i=imax; i!=0; i--)
        {
            r += (*p1)*(*p2) + p1[1]*p2[1] + p1[2]*p2[2] + p1[3]*p2[3];
            p1+=4;
            p2+=4;
        }
        for(i=0; i<v1.GetLength()%4; i++)
            r += (*(p1++))*(*(p2++));
        return r;
    }
    else
    {
        //
        // general
        //
        int offset11 = v1.GetStep(), offset12 = 2*offset11, offset13 = 3*offset11, offset14 = 4*offset11;
        int offset21 = v2.GetStep(), offset22 = 2*offset21, offset23 = 3*offset21, offset24 = 4*offset21;
        T r = 0;
        const T *p1 = v1.GetData();
        const T *p2 = v2.GetData();
        int imax = v1.GetLength()/4;
        int i;
        for(i=0; i<imax; i++)
        {
            r += (*p1)*(*p2) + p1[offset11]*p2[offset21] + p1[offset12]*p2[offset22] + p1[offset13]*p2[offset23];
            p1+=offset14;
            p2+=offset24;
        }
        for(i=0; i<v1.GetLength()%4; i++)
        {
            r += (*p1)*(*p2);
            p1+=offset11;
            p2+=offset21;
        }
        return r;
    }
}
 
 
/********************************************************************
Copy one vector into another
********************************************************************/
template<class T>
void vmove(raw_vector<T> vdst, const_raw_vector<T> vsrc)
{
    ap_error::make_assertion(vdst.GetLength()==vsrc.GetLength());
    if( vdst.GetStep()==1 && vsrc.GetStep()==1 )
    {
        //
        // fast
        //
        T *p1 = vdst.GetData();
        const T *p2 = vsrc.GetData();
        int imax = vdst.GetLength()/2;
        int i;
        for(i=imax; i!=0; i--)
        {
            *p1 = *p2;
            p1[1] = p2[1];
            p1 += 2;
            p2 += 2;
        }
        if(vdst.GetLength()%2 != 0)
            *p1 = *p2;
        return;
    }
    else
    {
        //
        // general
        //
        int offset11 = vdst.GetStep(), offset12 = 2*offset11, offset13 = 3*offset11, offset14 = 4*offset11;
        int offset21 = vsrc.GetStep(), offset22 = 2*offset21, offset23 = 3*offset21, offset24 = 4*offset21;
        T *p1 = vdst.GetData();
        const T *p2 = vsrc.GetData();
        int imax = vdst.GetLength()/4;
        int i;
        for(i=0; i<imax; i++)
        {
            *p1 = *p2;
            p1[offset11] = p2[offset21];
            p1[offset12] = p2[offset22];
            p1[offset13] = p2[offset23];
            p1 += offset14;
            p2 += offset24;
        }
        for(i=0; i<vdst.GetLength()%4; i++)
        {
            *p1 = *p2;
            p1 += vdst.GetStep();
            p2 += vsrc.GetStep();
        }
        return;
    }
}
 
 
/********************************************************************
Copy one vector multiplied by -1 into another.
********************************************************************/
template<class T>
void vmoveneg(raw_vector<T> vdst, const_raw_vector<T> vsrc)
{
    ap_error::make_assertion(vdst.GetLength()==vsrc.GetLength());
    if( vdst.GetStep()==1 && vsrc.GetStep()==1 )
    {
        //
        // fast
        //
        T *p1 = vdst.GetData();
        const T *p2 = vsrc.GetData();
        int imax = vdst.GetLength()/2;
        int i;
        for(i=0; i<imax; i++)
        {
            *p1 = -*p2;
            p1[1] = -p2[1];
            p1 += 2;
            p2 += 2;
        }
        if(vdst.GetLength()%2 != 0)
            *p1 = -*p2;
        return;
    }
    else
    {
        //
        // general
        //
        int offset11 = vdst.GetStep(), offset12 = 2*offset11, offset13 = 3*offset11, offset14 = 4*offset11;
        int offset21 = vsrc.GetStep(), offset22 = 2*offset21, offset23 = 3*offset21, offset24 = 4*offset21;
        T *p1 = vdst.GetData();
        const T *p2 = vsrc.GetData();
        int imax = vdst.GetLength()/4;
        int i;
        for(i=imax; i!=0; i--)
        {
            *p1 = -*p2;
            p1[offset11] = -p2[offset21];
            p1[offset12] = -p2[offset22];
            p1[offset13] = -p2[offset23];
            p1 += offset14;
            p2 += offset24;
        }
        for(i=0; i<vdst.GetLength()%4; i++)
        {
            *p1 = -*p2;
            p1 += vdst.GetStep();
            p2 += vsrc.GetStep();
        }
        return;
    }
}
 
 
/********************************************************************
Copy one vector multiplied by a number into another vector.
********************************************************************/
template<class T, class T2>
void vmove(raw_vector<T> vdst, const_raw_vector<T> vsrc, T2 alpha)
{
    ap_error::make_assertion(vdst.GetLength()==vsrc.GetLength());
    if( vdst.GetStep()==1 && vsrc.GetStep()==1 )
    {
        //
        // fast
        //
        T *p1 = vdst.GetData();
        const T *p2 = vsrc.GetData();
        int imax = vdst.GetLength()/4;
        int i;
        for(i=imax; i!=0; i--)
        {
            *p1 = alpha*(*p2);
            p1[1] = alpha*p2[1];
            p1[2] = alpha*p2[2];
            p1[3] = alpha*p2[3];
            p1 += 4;
            p2 += 4;
        }
        for(i=0; i<vdst.GetLength()%4; i++)
            *(p1++) = alpha*(*(p2++));
        return;
    }
    else
    {
        //
        // general
        //
        int offset11 = vdst.GetStep(), offset12 = 2*offset11, offset13 = 3*offset11, offset14 = 4*offset11;
        int offset21 = vsrc.GetStep(), offset22 = 2*offset21, offset23 = 3*offset21, offset24 = 4*offset21;
        T *p1 = vdst.GetData();
        const T *p2 = vsrc.GetData();
        int imax = vdst.GetLength()/4;
        int i;
        for(i=0; i<imax; i++)
        {
            *p1 = alpha*(*p2);
            p1[offset11] = alpha*p2[offset21];
            p1[offset12] = alpha*p2[offset22];
            p1[offset13] = alpha*p2[offset23];
            p1 += offset14;
            p2 += offset24;
        }
        for(i=0; i<vdst.GetLength()%4; i++)
        {
            *p1 = alpha*(*p2);
            p1 += vdst.GetStep();
            p2 += vsrc.GetStep();
        }
        return;
    }
}
 
 
/********************************************************************
Vector addition
********************************************************************/
template<class T>
void vadd(raw_vector<T> vdst, const_raw_vector<T> vsrc)
{
    ap_error::make_assertion(vdst.GetLength()==vsrc.GetLength());
    if( vdst.GetStep()==1 && vsrc.GetStep()==1 )
    {
        //
        // fast
        //
        T *p1 = vdst.GetData();
        const T *p2 = vsrc.GetData();
        int imax = vdst.GetLength()/4;
        int i;
        for(i=imax; i!=0; i--)
        {
            *p1 += *p2;
            p1[1] += p2[1];
            p1[2] += p2[2];
            p1[3] += p2[3];
            p1 += 4;
            p2 += 4;
        }
        for(i=0; i<vdst.GetLength()%4; i++)
            *(p1++) += *(p2++);
        return;
    }
    else
    {
        //
        // general
        //
        int offset11 = vdst.GetStep(), offset12 = 2*offset11, offset13 = 3*offset11, offset14 = 4*offset11;
        int offset21 = vsrc.GetStep(), offset22 = 2*offset21, offset23 = 3*offset21, offset24 = 4*offset21;
        T *p1 = vdst.GetData();
        const T *p2 = vsrc.GetData();
        int imax = vdst.GetLength()/4;
        int i;
        for(i=0; i<imax; i++)
        {
            *p1 += *p2;
            p1[offset11] += p2[offset21];
            p1[offset12] += p2[offset22];
            p1[offset13] += p2[offset23];
            p1 += offset14;
            p2 += offset24;
        }
        for(i=0; i<vdst.GetLength()%4; i++)
        {
            *p1 += *p2;
            p1 += vdst.GetStep();
            p2 += vsrc.GetStep();
        }
        return;
    }
}
 
 
/********************************************************************
Add one vector multiplied by a number to another vector.
********************************************************************/
template<class T, class T2>
void vadd(raw_vector<T> vdst, const_raw_vector<T> vsrc, T2 alpha)
{
    ap_error::make_assertion(vdst.GetLength()==vsrc.GetLength());
    if( vdst.GetStep()==1 && vsrc.GetStep()==1 )
    {
        //
        // fast
        //
        T *p1 = vdst.GetData();
        const T *p2 = vsrc.GetData();
        int imax = vdst.GetLength()/4;
        int i;
        for(i=imax; i!=0; i--)
        {
            *p1 += alpha*(*p2);
            p1[1] += alpha*p2[1];
            p1[2] += alpha*p2[2];
            p1[3] += alpha*p2[3];
            p1 += 4;
            p2 += 4;
        }
        for(i=0; i<vdst.GetLength()%4; i++)
            *(p1++) += alpha*(*(p2++));
        return;
    }
    else
    {
        //
        // general
        //
        int offset11 = vdst.GetStep(), offset12 = 2*offset11, offset13 = 3*offset11, offset14 = 4*offset11;
        int offset21 = vsrc.GetStep(), offset22 = 2*offset21, offset23 = 3*offset21, offset24 = 4*offset21;
        T *p1 = vdst.GetData();
        const T *p2 = vsrc.GetData();
        int imax = vdst.GetLength()/4;
        int i;
        for(i=0; i<imax; i++)
        {
            *p1 += alpha*(*p2);
            p1[offset11] += alpha*p2[offset21];
            p1[offset12] += alpha*p2[offset22];
            p1[offset13] += alpha*p2[offset23];
            p1 += offset14;
            p2 += offset24;
        }
        for(i=0; i<vdst.GetLength()%4; i++)
        {
            *p1 += alpha*(*p2);
            p1 += vdst.GetStep();
            p2 += vsrc.GetStep();
        }
        return;
    }
}
 
 
/********************************************************************
Vector subtraction
********************************************************************/
template<class T>
void vsub(raw_vector<T> vdst, const_raw_vector<T> vsrc)
{
    ap_error::make_assertion(vdst.GetLength()==vsrc.GetLength());
    if( vdst.GetStep()==1 && vsrc.GetStep()==1 )
    {
        //
        // fast
        //
        T *p1 = vdst.GetData();
        const T *p2 = vsrc.GetData();
        int imax = vdst.GetLength()/4;
        int i;
        for(i=imax; i!=0; i--)
        {
            *p1 -= *p2;
            p1[1] -= p2[1];
            p1[2] -= p2[2];
            p1[3] -= p2[3];
            p1 += 4;
            p2 += 4;
        }
        for(i=0; i<vdst.GetLength()%4; i++)
            *(p1++) -= *(p2++);
        return;
    }
    else
    {
        //
        // general
        //
        int offset11 = vdst.GetStep(), offset12 = 2*offset11, offset13 = 3*offset11, offset14 = 4*offset11;
        int offset21 = vsrc.GetStep(), offset22 = 2*offset21, offset23 = 3*offset21, offset24 = 4*offset21;
        T *p1 = vdst.GetData();
        const T *p2 = vsrc.GetData();
        int imax = vdst.GetLength()/4;
        int i;
        for(i=0; i<imax; i++)
        {
            *p1 -= *p2;
            p1[offset11] -= p2[offset21];
            p1[offset12] -= p2[offset22];
            p1[offset13] -= p2[offset23];
            p1 += offset14;
            p2 += offset24;
        }
        for(i=0; i<vdst.GetLength()%4; i++)
        {
            *p1 -= *p2;
            p1 += vdst.GetStep();
            p2 += vsrc.GetStep();
        }
        return;
    }
}
 
 
/********************************************************************
Subtract one vector multiplied by a number from another vector.
********************************************************************/
template<class T, class T2>
void vsub(raw_vector<T> vdst, const_raw_vector<T> vsrc, T2 alpha)
{
    vadd(vdst, vsrc, -alpha);
}
 
 
/********************************************************************
In-place vector multiplication
********************************************************************/
template<class T, class T2>
void vmul(raw_vector<T> vdst, T2 alpha)
{
    if( vdst.GetStep()==1 )
    {
        //
        // fast
        //
        T *p1 = vdst.GetData();
        int imax = vdst.GetLength()/4;
        int i;
        for(i=imax; i!=0; i--)
        {
            *p1 *= alpha;
            p1[1] *= alpha;
            p1[2] *= alpha;
            p1[3] *= alpha;
            p1 += 4;
        }
        for(i=0; i<vdst.GetLength()%4; i++)
            *(p1++) *= alpha;
        return;
    }
    else
    {
        //
        // general
        //
        int offset11 = vdst.GetStep(), offset12 = 2*offset11, offset13 = 3*offset11, offset14 = 4*offset11;
        T *p1 = vdst.GetData();
        int imax = vdst.GetLength()/4;
        int i;
        for(i=0; i<imax; i++)
        {
            *p1 *= alpha;
            p1[offset11] *= alpha;
            p1[offset12] *= alpha;
            p1[offset13] *= alpha;
            p1 += offset14;
        }
        for(i=0; i<vdst.GetLength()%4; i++)
        {
            *p1 *= alpha;
            p1 += vdst.GetStep();
        }
        return;
    }
}
 
 
/********************************************************************
Template of a dynamical one-dimensional array
********************************************************************/
template<class T>
class template_1d_array
{
public:
    template_1d_array()
    {
        m_Vec=0;
        m_iVecSize = 0;
    };
 
    ~template_1d_array()
    {
        if(m_Vec)
            delete[] m_Vec;
    };
 
    template_1d_array(const template_1d_array &rhs)
    {
        m_iVecSize = rhs.m_iVecSize;
        m_iLow = rhs.m_iLow;
        m_iHigh = rhs.m_iHigh;
        if(rhs.m_Vec)
        {
            m_Vec = new T[m_iVecSize];
            #ifndef UNSAFE_MEM_COPY
            for(int i=0; i<m_iVecSize; i++)
                m_Vec[i] = rhs.m_Vec[i];
            #else
            memcpy(m_Vec, rhs.m_Vec, m_iVecSize*sizeof(T));
            #endif
        }
        else
            m_Vec=0;
    };
 
 
    const template_1d_array& operator=(const template_1d_array &rhs)
    {
        if( this==&rhs )
            return *this;
 
        m_iLow = rhs.m_iLow;
        m_iHigh = rhs.m_iHigh;
        m_iVecSize = rhs.m_iVecSize;
        if(m_Vec)
            delete[] m_Vec;
        if(rhs.m_Vec)
        {
            m_Vec = new T[m_iVecSize];
            #ifndef UNSAFE_MEM_COPY
            for(int i=0; i<m_iVecSize; i++)
                m_Vec[i] = rhs.m_Vec[i];
            #else
            memcpy(m_Vec, rhs.m_Vec, m_iVecSize*sizeof(T));
            #endif
        }
        else
            m_Vec=0;
        return *this;
    };
 
 
    const T& operator()(int i) const
    {
        #ifndef NO_AP_ASSERT
        ap_error::make_assertion(i>=m_iLow && i<=m_iHigh);
        #endif
        return m_Vec[ i-m_iLow ];
    };
 
 
    T& operator()(int i)
    {
        #ifndef NO_AP_ASSERT
        ap_error::make_assertion(i>=m_iLow && i<=m_iHigh);
        #endif
        return m_Vec[ i-m_iLow ];
    };
 
 
    void setbounds( int iLow, int iHigh )
    {
        if(m_Vec)
            delete[] m_Vec;
        m_iLow = iLow;
        m_iHigh = iHigh;
        m_iVecSize = iHigh-iLow+1;
        m_Vec = new T[m_iVecSize];
    };
 
 
    void setcontent( int iLow, int iHigh, const T *pContent )
    {
        setbounds(iLow, iHigh);
        for(int i=iLow; i<=iHigh; i++)
            (*this)(i) = pContent[i-iLow];
    };
 
 
    T* getcontent()
    {
        return m_Vec;
    };
 
    const T* getcontent() const
    {
        return m_Vec;
    };
 
 
    int getlowbound(int iBoundNum = 0) const
    {
        return m_iLow;
    };
 
 
    int gethighbound(int iBoundNum = 0) const
    {
        return m_iHigh;
    };
 
    raw_vector<T> getvector(int iStart, int iEnd)
    {
        if( iStart>iEnd || wrongIdx(iStart) || wrongIdx(iEnd) )
            return raw_vector<T>(0, 0, 1);
        else
            return raw_vector<T>(m_Vec+iStart-m_iLow, iEnd-iStart+1, 1);
    };
 
 
    const_raw_vector<T> getvector(int iStart, int iEnd) const
    {
        if( iStart>iEnd || wrongIdx(iStart) || wrongIdx(iEnd) )
            return const_raw_vector<T>(0, 0, 1);
        else
            return const_raw_vector<T>(m_Vec+iStart-m_iLow, iEnd-iStart+1, 1);
    };
private:
    bool wrongIdx(int i) const { return i<m_iLow || i>m_iHigh; };
 
    T         *m_Vec;
    long      m_iVecSize;
    long      m_iLow, m_iHigh;
};
 
 
 
/********************************************************************
Template of a dynamical two-dimensional array
********************************************************************/
template<class T>
class template_2d_array
{
public:
    template_2d_array()
    {
        m_Vec=0;
        m_iVecSize=0;
    };
 
    ~template_2d_array()
    {
        if(m_Vec)
            delete[] m_Vec;
    };
 
    template_2d_array(const template_2d_array &rhs)
    {
        m_iVecSize = rhs.m_iVecSize;
        m_iLow1 = rhs.m_iLow1;
        m_iLow2 = rhs.m_iLow2;
        m_iHigh1 = rhs.m_iHigh1;
        m_iHigh2 = rhs.m_iHigh2;
        m_iConstOffset = rhs.m_iConstOffset;
        m_iLinearMember = rhs.m_iLinearMember;
        if(rhs.m_Vec)
        {
            m_Vec = new T[m_iVecSize];
            #ifndef UNSAFE_MEM_COPY
            for(int i=0; i<m_iVecSize; i++)
                m_Vec[i] = rhs.m_Vec[i];
            #else
            memcpy(m_Vec, rhs.m_Vec, m_iVecSize*sizeof(T));
            #endif
        }
        else
            m_Vec=0;
    };
    const template_2d_array& operator=(const template_2d_array &rhs)
    {
        if( this==&rhs )
            return *this;
 
        m_iLow1 = rhs.m_iLow1;
        m_iLow2 = rhs.m_iLow2;
        m_iHigh1 = rhs.m_iHigh1;
        m_iHigh2 = rhs.m_iHigh2;
        m_iConstOffset = rhs.m_iConstOffset;
        m_iLinearMember = rhs.m_iLinearMember;
        m_iVecSize = rhs.m_iVecSize;
        if(m_Vec)
            delete[] m_Vec;
        if(rhs.m_Vec)
        {
            m_Vec = new T[m_iVecSize];
            #ifndef UNSAFE_MEM_COPY
            for(int i=0; i<m_iVecSize; i++)
                m_Vec[i] = rhs.m_Vec[i];
            #else
            memcpy(m_Vec, rhs.m_Vec, m_iVecSize*sizeof(T));
            #endif
        }
        else
            m_Vec=0;
        return *this;
    };
 
    const T& operator()(int i1, int i2) const
    {
        #ifndef NO_AP_ASSERT
        ap_error::make_assertion(i1>=m_iLow1 && i1<=m_iHigh1);
        ap_error::make_assertion(i2>=m_iLow2 && i2<=m_iHigh2);
        #endif
        return m_Vec[ m_iConstOffset + i2 +i1*m_iLinearMember];
    };
 
    T& operator()(int i1, int i2)
    {
        #ifndef NO_AP_ASSERT
        ap_error::make_assertion(i1>=m_iLow1 && i1<=m_iHigh1);
        ap_error::make_assertion(i2>=m_iLow2 && i2<=m_iHigh2);
        #endif
        return m_Vec[ m_iConstOffset + i2 +i1*m_iLinearMember];
    };
 
    void setbounds( int iLow1, int iHigh1, int iLow2, int iHigh2 )
    {
        if(m_Vec)
            delete[] m_Vec;
        m_iVecSize = (iHigh1-iLow1+1)*(iHigh2-iLow2+1);
        m_Vec = new T[m_iVecSize];
        m_iLow1  = iLow1;
        m_iHigh1 = iHigh1;
        m_iLow2  = iLow2;
        m_iHigh2 = iHigh2;
        m_iConstOffset = -m_iLow2-m_iLow1*(m_iHigh2-m_iLow2+1);
        m_iLinearMember = (m_iHigh2-m_iLow2+1);
    };
 
    void setcontent( int iLow1, int iHigh1, int iLow2, int iHigh2, const T *pContent )
    {
        setbounds(iLow1, iHigh1, iLow2, iHigh2);
        for(int i=0; i<m_iVecSize; i++)
            m_Vec[i]=pContent[i];
    };
 
    T* getcontent()
    {
        return m_Vec;
    };
 
    const T* getcontent() const
    {
        return m_Vec;
    };
 
    int getlowbound(int iBoundNum) const
    {
        return iBoundNum==1 ? m_iLow1 : m_iLow2;
    };
 
    int gethighbound(int iBoundNum) const
    {
        return iBoundNum==1 ? m_iHigh1 : m_iHigh2;
    };
 
    raw_vector<T> getcolumn(int iColumn, int iRowStart, int iRowEnd)
    {
        if( (iRowStart>iRowEnd) || wrongColumn(iColumn) || wrongRow(iRowStart) ||wrongRow(iRowEnd) )
            return raw_vector<T>(0, 0, 1);
        else
            return raw_vector<T>(&((*this)(iRowStart, iColumn)), iRowEnd-iRowStart+1, m_iLinearMember);
    };
 
    raw_vector<T> getrow(int iRow, int iColumnStart, int iColumnEnd)
    {
        if( (iColumnStart>iColumnEnd) || wrongRow(iRow) || wrongColumn(iColumnStart) || wrongColumn(iColumnEnd))
            return raw_vector<T>(0, 0, 1);
        else
            return raw_vector<T>(&((*this)(iRow, iColumnStart)), iColumnEnd-iColumnStart+1, 1);
    };
 
    const_raw_vector<T> getcolumn(int iColumn, int iRowStart, int iRowEnd) const
    {
        if( (iRowStart>iRowEnd) || wrongColumn(iColumn) || wrongRow(iRowStart) ||wrongRow(iRowEnd) )
            return const_raw_vector<T>(0, 0, 1);
        else
            return const_raw_vector<T>(&((*this)(iRowStart, iColumn)), iRowEnd-iRowStart+1, m_iLinearMember);
    };
 
    const_raw_vector<T> getrow(int iRow, int iColumnStart, int iColumnEnd) const
    {
        if( (iColumnStart>iColumnEnd) || wrongRow(iRow) || wrongColumn(iColumnStart) || wrongColumn(iColumnEnd))
            return const_raw_vector<T>(0, 0, 1);
        else
            return const_raw_vector<T>(&((*this)(iRow, iColumnStart)), iColumnEnd-iColumnStart+1, 1);
    };
private:
    bool wrongRow(int i) const { return i<m_iLow1 || i>m_iHigh1; };
    bool wrongColumn(int j) const { return j<m_iLow2 || j>m_iHigh2; };
 
    T           *m_Vec;
    long        m_iVecSize;
    long        m_iLow1, m_iLow2, m_iHigh1, m_iHigh2;
    long        m_iConstOffset, m_iLinearMember;
};
 
 
typedef template_1d_array<int>     integer_1d_array;
typedef template_1d_array<double>  real_1d_array;
typedef template_1d_array<complex> complex_1d_array;
typedef template_1d_array<bool>    boolean_1d_array;
typedef template_2d_array<int>     integer_2d_array;
typedef template_2d_array<double>  real_2d_array;
typedef template_2d_array<complex> complex_2d_array;
typedef template_2d_array<bool>    boolean_2d_array;
 
 
/********************************************************************
Constants and functions introduced for compatibility with AlgoPascal
********************************************************************/
extern const double machineepsilon;
extern const double maxrealnumber;
extern const double minrealnumber;
 
int sign(double x);
double randomreal();
int randominteger(int maxv);
int round(double x);
int trunc(double x);
int ifloor(double x);
int iceil(double x);
double pi();
double sqr(double x);
int maxint(int m1, int m2);
int minint(int m1, int m2);
double maxreal(double m1, double m2);
double minreal(double m1, double m2);
 
};//namespace ap
 
 
#endif