/*************************************************************************
AP library
Copyright (c) 2003-2009 Sergey Bochkanov (ALGLIB project).

>>> LICENSE >>>
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 (www.fsf.org); either version 2 of the
License, 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.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses

>>> END OF LICENSE >>>
*************************************************************************/
using System;
public partial class alglib
{
    /********************************************************************
    Callback definitions for optimizers/fitters/solvers.
    
    Callbacks for unparameterized (general) functions:
    * ndimensional_func         calculates f(arg), stores result to func
    * ndimensional_grad         calculates func = f(arg), 
                                grad[i] = df(arg)/d(arg[i])
    * ndimensional_hess         calculates func = f(arg),
                                grad[i] = df(arg)/d(arg[i]),
                                hess[i,j] = d2f(arg)/(d(arg[i])*d(arg[j]))
    
    Callbacks for systems of functions:
    * ndimensional_fvec         calculates vector function f(arg),
                                stores result to fi
    * ndimensional_jac          calculates f[i] = fi(arg)
                                jac[i,j] = df[i](arg)/d(arg[j])
                                
    Callbacks for  parameterized  functions,  i.e.  for  functions  which 
    depend on two vectors: P and Q.  Gradient  and Hessian are calculated 
    with respect to P only.
    * ndimensional_pfunc        calculates f(p,q),
                                stores result to func
    * ndimensional_pgrad        calculates func = f(p,q),
                                grad[i] = df(p,q)/d(p[i])
    * ndimensional_phess        calculates func = f(p,q),
                                grad[i] = df(p,q)/d(p[i]),
                                hess[i,j] = d2f(p,q)/(d(p[i])*d(p[j]))

    Callbacks for progress reports:
    * ndimensional_rep          reports current position of optimization algo    
    
    Callbacks for ODE solvers:
    * ndimensional_ode_rp       calculates dy/dx for given y[] and x
    
    Callbacks for integrators:
    * integrator1_func          calculates f(x) for given x
                                (additional parameters xminusa and bminusx
                                contain x-a and b-x)
    ********************************************************************/
    public delegate void ndimensional_func (double[] arg, ref double func, object obj);
    public delegate void ndimensional_grad (double[] arg, ref double func, double[] grad, object obj);
    public delegate void ndimensional_hess (double[] arg, ref double func, double[] grad, double[,] hess, object obj);
    
    public delegate void ndimensional_fvec (double[] arg, double[] fi, object obj);
    public delegate void ndimensional_jac  (double[] arg, double[] fi, double[,] jac, object obj);
    
    public delegate void ndimensional_pfunc(double[] p, double[] q, ref double func, object obj);
    public delegate void ndimensional_pgrad(double[] p, double[] q, ref double func, double[] grad, object obj);
    public delegate void ndimensional_phess(double[] p, double[] q, ref double func, double[] grad, double[,] hess, object obj);
    
    public delegate void ndimensional_rep(double[] arg, double func, object obj);

    public delegate void ndimensional_ode_rp (double[] y, double x, double[] dy, object obj);

    public delegate void integrator1_func (double x, double xminusa, double bminusx, ref double f, object obj);

    /********************************************************************
    Class defining a complex number with double precision.
    ********************************************************************/
    public struct complex
    {
        public double x;
        public double y;

        public complex(double _x)
        {
            x = _x;
            y = 0;
        }
        public complex(double _x, double _y)
        {
            x = _x;
            y = _y;
        }
        public static implicit operator complex(double _x)
        {
            return new complex(_x);
        }
        public static bool operator==(complex lhs, complex rhs)
        {
            return ((double)lhs.x==(double)rhs.x) & ((double)lhs.y==(double)rhs.y);
        }
        public static bool operator!=(complex lhs, complex rhs)
        {
            return ((double)lhs.x!=(double)rhs.x) | ((double)lhs.y!=(double)rhs.y);
        }
        public static complex operator+(complex lhs)
        {
            return lhs;
        }
        public static complex operator-(complex lhs)
        {
            return new complex(-lhs.x,-lhs.y);
        }
        public static complex operator+(complex lhs, complex rhs)
        {
            return new complex(lhs.x+rhs.x,lhs.y+rhs.y);
        }
        public static complex operator-(complex lhs, complex rhs)
        {
            return new complex(lhs.x-rhs.x,lhs.y-rhs.y);
        }
        public static complex operator*(complex lhs, complex rhs)
        { 
            return new complex(lhs.x*rhs.x-lhs.y*rhs.y, lhs.x*rhs.y+lhs.y*rhs.x);
        }
        public static complex operator/(complex lhs, complex rhs)
        {
            complex result;
            double e;
            double f;
            if( System.Math.Abs(rhs.y)<System.Math.Abs(rhs.x) )
            {
                e = rhs.y/rhs.x;
                f = rhs.x+rhs.y*e;
                result.x = (lhs.x+lhs.y*e)/f;
                result.y = (lhs.y-lhs.x*e)/f;
            }
            else
            {
                e = rhs.x/rhs.y;
                f = rhs.y+rhs.x*e;
                result.x = (lhs.y+lhs.x*e)/f;
                result.y = (-lhs.x+lhs.y*e)/f;
            }
            return result;
        }
        public override int GetHashCode() 
        { 
            return x.GetHashCode() ^ y.GetHashCode(); 
        }
        public override bool Equals(object obj) 
        { 
            if( obj is byte)
                return Equals(new complex((byte)obj));
            if( obj is sbyte)
                return Equals(new complex((sbyte)obj));
            if( obj is short)
                return Equals(new complex((short)obj));
            if( obj is ushort)
                return Equals(new complex((ushort)obj));
            if( obj is int)
                return Equals(new complex((int)obj));
            if( obj is uint)
                return Equals(new complex((uint)obj));
            if( obj is long)
                return Equals(new complex((long)obj));
            if( obj is ulong)
                return Equals(new complex((ulong)obj));
            if( obj is float)
                return Equals(new complex((float)obj));
            if( obj is double)
                return Equals(new complex((double)obj));
            if( obj is decimal)
                return Equals(new complex((double)(decimal)obj));
            return base.Equals(obj); 
        }    
    }    
    
    /********************************************************************
    Class defining an ALGLIB exception
    ********************************************************************/
    public class alglibexception : System.Exception
    {
        public string msg;
        public alglibexception(string s)
        {
            msg = s;
        }
        
    }
    
    /********************************************************************
    reverse communication structure
    ********************************************************************/
    public class rcommstate
    {
        public rcommstate()
        {
            stage = -1;
            ia = new int[0];
            ba = new bool[0];
            ra = new double[0];
            ca = new alglib.complex[0];
        }
        public int stage;
        public int[] ia;
        public bool[] ba;
        public double[] ra;
        public alglib.complex[] ca;
    };

    /********************************************************************
    internal functions
    ********************************************************************/
    public class ap
    {
        public static int len<T>(T[] a)
        { return a.Length; }
        public static int rows<T>(T[,] a)
        { return a.GetLength(0); }
        public static int cols<T>(T[,] a)
        { return a.GetLength(1); }
        public static void swap<T>(ref T a, ref T b)
        {
            T t = a;
            a = b;
            b = t;
        }
        
        public static void assert(bool cond, string s)
        {
            if( !cond )
                throw new alglibexception(s);
        }
        
        public static void assert(bool cond)
        {
            assert(cond, "ALGLIB: assertion failed");
        }
        
        /****************************************************************
        returns dps (digits-of-precision) value corresponding to threshold.
        dps(0.9)  = dps(0.5)  = dps(0.1) = 0
        dps(0.09) = dps(0.05) = dps(0.01) = 1
        and so on
        ****************************************************************/
        public static int threshold2dps(double threshold)
        {
            int result = 0;
            double t;
            for (result = 0, t = 1; t / 10 > threshold*(1+1E-10); result++, t /= 10) ;
            return result;
        }

        /****************************************************************
        prints formatted array
        ****************************************************************/
        public static string format(bool[] a)
        {
            string[] result = new string[len(a)];
            int i;
            for(i=0; i<len(a); i++)
                if( a[i] )
                    result[i] = "true";
                else
                    result[i] = "false";
            return "{"+String.Join(",",result)+"}";
        }
        
        /****************************************************************
        prints formatted array
        ****************************************************************/
        public static string format(int[] a)
        {
            string[] result = new string[len(a)];
            int i;
            for (i = 0; i < len(a); i++)
                result[i] = a[i].ToString();
            return "{" + String.Join(",", result) + "}";
        }

        /****************************************************************
        prints formatted array
        ****************************************************************/
        public static string format(double[] a, int dps)
        {
            string fmt = String.Format("{{0:F{0}}}", dps);
            string[] result = new string[len(a)];
            int i;
            for (i = 0; i < len(a); i++)
            {
                result[i] = String.Format(fmt, a[i]);
                result[i] = result[i].Replace(',', '.');
            }
            return "{" + String.Join(",", result) + "}";
        }

        /****************************************************************
        prints formatted array
        ****************************************************************/
        public static string format(complex[] a, int dps)
        {
            string fmtx = String.Format("{{0:F{0}}}", dps);
            string fmty = String.Format("{{0:F{0}}}", dps);
            string[] result = new string[len(a)];
            int i;
            for (i = 0; i < len(a); i++)
            {
                result[i] = String.Format(fmtx, a[i].x) + (a[i].y >= 0 ? "+" : "-") + String.Format(fmty, Math.Abs(a[i].y)) + "i";
                result[i] = result[i].Replace(',', '.');
            }
            return "{" + String.Join(",", result) + "}";
        }

        /****************************************************************
        prints formatted matrix
        ****************************************************************/
        public static string format(bool[,] a)
        {
            int i, j, m, n;
            n = cols(a);
            m = rows(a);
            bool[] line = new bool[n];
            string[] result = new string[m];
            for (i = 0; i < m; i++)
            {
                for (j = 0; j < n; j++)
                    line[j] = a[i, j];
                result[i] = format(line);
            }
            return "{" + String.Join(",", result) + "}";
        }

        /****************************************************************
        prints formatted matrix
        ****************************************************************/
        public static string format(int[,] a)
        {
            int i, j, m, n;
            n = cols(a);
            m = rows(a);
            int[] line = new int[n];
            string[] result = new string[m];
            for (i = 0; i < m; i++)
            {
                for (j = 0; j < n; j++)
                    line[j] = a[i, j];
                result[i] = format(line);
            }
            return "{" + String.Join(",", result) + "}";
        }

        /****************************************************************
        prints formatted matrix
        ****************************************************************/
        public static string format(double[,] a, int dps)
        {
            int i, j, m, n;
            n = cols(a);
            m = rows(a);
            double[] line = new double[n];
            string[] result = new string[m];
            for (i = 0; i < m; i++)
            {
                for (j = 0; j < n; j++)
                    line[j] = a[i, j];
                result[i] = format(line, dps);
            }
            return "{" + String.Join(",", result) + "}";
        }

        /****************************************************************
        prints formatted matrix
        ****************************************************************/
        public static string format(complex[,] a, int dps)
        {
            int i, j, m, n;
            n = cols(a);
            m = rows(a);
            complex[] line = new complex[n];
            string[] result = new string[m];
            for (i = 0; i < m; i++)
            {
                for (j = 0; j < n; j++)
                    line[j] = a[i, j];
                result[i] = format(line, dps);
            }
            return "{" + String.Join(",", result) + "}";
        }

        /****************************************************************
        checks that matrix is symmetric.
        max|A-A^T| is calculated; if it is within 1.0E-14 of max|A|,
        matrix is considered symmetric
        ****************************************************************/
        public static bool issymmetric(double[,] a)
        {
            int i, j, n;
            double err, mx, v1, v2;
            if( rows(a)!=cols(a) )
                return false;
            n = rows(a);
            if( n==0 )
                return true;
            mx = 0;
            err = 0;
            for( i=0; i<n; i++)
            {
                for(j=i+1; j<n; j++)
                {
                    v1 = a[i,j];
                    v2 = a[j,i];
                    if( !math.isfinite(v1) )
                        return false;
                    if( !math.isfinite(v2) )
                        return false;
                    err = Math.Max(err, Math.Abs(v1-v2));
                    mx  = Math.Max(mx,  Math.Abs(v1));
                    mx  = Math.Max(mx,  Math.Abs(v2));
                }
                v1 = a[i,i];
                if( !math.isfinite(v1) )
                    return false;
                mx = Math.Max(mx, Math.Abs(v1));
            }
            if( mx==0 )
                return true;
            return err/mx<=1.0E-14;
        }
        
        /****************************************************************
        checks that matrix is Hermitian.
        max|A-A^H| is calculated; if it is within 1.0E-14 of max|A|,
        matrix is considered Hermitian
        ****************************************************************/
        public static bool ishermitian(complex[,] a)
        {
            int i, j, n;
            double err, mx;
            complex v1, v2, vt;
            if( rows(a)!=cols(a) )
                return false;
            n = rows(a);
            if( n==0 )
                return true;
            mx = 0;
            err = 0;
            for( i=0; i<n; i++)
            {
                for(j=i+1; j<n; j++)
                {
                    v1 = a[i,j];
                    v2 = a[j,i];
                    if( !math.isfinite(v1.x) )
                        return false;
                    if( !math.isfinite(v1.y) )
                        return false;
                    if( !math.isfinite(v2.x) )
                        return false;
                    if( !math.isfinite(v2.y) )
                        return false;
                    vt.x = v1.x-v2.x;
                    vt.y = v1.y+v2.y;
                    err = Math.Max(err, math.abscomplex(vt));
                    mx  = Math.Max(mx,  math.abscomplex(v1));
                    mx  = Math.Max(mx,  math.abscomplex(v2));
                }
                v1 = a[i,i];
                if( !math.isfinite(v1.x) )
                    return false;
                if( !math.isfinite(v1.y) )
                    return false;
                err = Math.Max(err, Math.Abs(v1.y));
                mx = Math.Max(mx, math.abscomplex(v1));
            }
            if( mx==0 )
                return true;
            return err/mx<=1.0E-14;
        }
        
        
        /****************************************************************
        Forces symmetricity by copying upper half of A to the lower one
        ****************************************************************/
        public static bool forcesymmetric(double[,] a)
        {
            int i, j, n;
            if( rows(a)!=cols(a) )
                return false;
            n = rows(a);
            if( n==0 )
                return true;
            for( i=0; i<n; i++)
                for(j=i+1; j<n; j++)
                    a[i,j] = a[j,i];
            return true;
        }
        
        /****************************************************************
        Forces Hermiticity by copying upper half of A to the lower one
        ****************************************************************/
        public static bool forcehermitian(complex[,] a)
        {
            int i, j, n;
            complex v;
            if( rows(a)!=cols(a) )
                return false;
            n = rows(a);
            if( n==0 )
                return true;
            for( i=0; i<n; i++)
                for(j=i+1; j<n; j++)
                {
                    v = a[j,i];
                    a[i,j].x = v.x;
                    a[i,j].y = -v.y;
                }
            return true;
        }
    };
    
    /********************************************************************
    math functions
    ********************************************************************/
    public class math
    {
        //public static System.Random RndObject = new System.Random(System.DateTime.Now.Millisecond);
        public static System.Random rndobject = new System.Random(System.DateTime.Now.Millisecond + 1000*System.DateTime.Now.Second + 60*1000*System.DateTime.Now.Minute);

        public const double machineepsilon = 5E-16;
        public const double maxrealnumber = 1E300;
        public const double minrealnumber = 1E-300;
        
        public static bool isfinite(double d)
        {
            return !System.Double.IsNaN(d) && !System.Double.IsInfinity(d);
        }
        
        public static double randomreal()
        {
            double r = 0;
            lock(rndobject){ r = rndobject.NextDouble(); }
            return r;
        }
        public static int randominteger(int N)
        {
            int r = 0;
            lock(rndobject){ r = rndobject.Next(N); }
            return r;
        }
        public static double sqr(double X)
        {
            return X*X;
        }        
        public static double abscomplex(complex z)
        {
            double w;
            double xabs;
            double yabs;
            double v;
    
            xabs = System.Math.Abs(z.x);
            yabs = System.Math.Abs(z.y);
            w = xabs>yabs ? xabs : yabs;
            v = xabs<yabs ? xabs : yabs; 
            if( v==0 )
                return w;
            else
            {
                double t = v/w;
                return w*System.Math.Sqrt(1+t*t);
            }
        }
        public static complex conj(complex z)
        {
            return new complex(z.x, -z.y); 
        }    
        public static complex csqr(complex z)
        {
            return new complex(z.x*z.x-z.y*z.y, 2*z.x*z.y); 
        }

    }
}