| 1 | /*************************************************************************
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| 2 | AP library
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| 3 | Copyright (c) 2003-2009 Sergey Bochkanov (ALGLIB project).
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| 4 |
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| 5 | >>> LICENSE >>>
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| 6 | This program is free software; you can redistribute it and/or modify
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| 7 | it under the terms of the GNU General Public License as published by
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| 8 | the Free Software Foundation (www.fsf.org); either version 2 of the
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| 9 | License, or (at your option) any later version.
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| 10 |
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| 11 | This program is distributed in the hope that it will be useful,
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| 12 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 14 | GNU General Public License for more details.
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| 15 |
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| 16 | A copy of the GNU General Public License is available at
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| 17 | http://www.fsf.org/licensing/licenses
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| 18 |
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| 19 | >>> END OF LICENSE >>>
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| 20 | *************************************************************************/
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| 21 | using System;
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| 22 | public partial class alglib
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| 23 | {
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| 24 | /********************************************************************
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| 25 | Callback definitions for optimizers/fitters/solvers.
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| 26 |
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| 27 | Callbacks for unparameterized (general) functions:
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| 28 | * ndimensional_func calculates f(arg), stores result to func
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| 29 | * ndimensional_grad calculates func = f(arg),
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| 30 | grad[i] = df(arg)/d(arg[i])
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| 31 | * ndimensional_hess calculates func = f(arg),
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| 32 | grad[i] = df(arg)/d(arg[i]),
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| 33 | hess[i,j] = d2f(arg)/(d(arg[i])*d(arg[j]))
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| 34 |
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| 35 | Callbacks for systems of functions:
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| 36 | * ndimensional_fvec calculates vector function f(arg),
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| 37 | stores result to fi
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| 38 | * ndimensional_jac calculates f[i] = fi(arg)
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| 39 | jac[i,j] = df[i](arg)/d(arg[j])
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| 40 |
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| 41 | Callbacks for parameterized functions, i.e. for functions which
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| 42 | depend on two vectors: P and Q. Gradient and Hessian are calculated
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| 43 | with respect to P only.
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| 44 | * ndimensional_pfunc calculates f(p,q),
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| 45 | stores result to func
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| 46 | * ndimensional_pgrad calculates func = f(p,q),
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| 47 | grad[i] = df(p,q)/d(p[i])
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| 48 | * ndimensional_phess calculates func = f(p,q),
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| 49 | grad[i] = df(p,q)/d(p[i]),
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| 50 | hess[i,j] = d2f(p,q)/(d(p[i])*d(p[j]))
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| 51 |
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| 52 | Callbacks for progress reports:
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| 53 | * ndimensional_rep reports current position of optimization algo
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| 54 |
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| 55 | Callbacks for ODE solvers:
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| 56 | * ndimensional_ode_rp calculates dy/dx for given y[] and x
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| 57 |
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| 58 | Callbacks for integrators:
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| 59 | * integrator1_func calculates f(x) for given x
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| 60 | (additional parameters xminusa and bminusx
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| 61 | contain x-a and b-x)
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| 62 | ********************************************************************/
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| 63 | public delegate void ndimensional_func (double[] arg, ref double func, object obj);
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| 64 | public delegate void ndimensional_grad (double[] arg, ref double func, double[] grad, object obj);
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| 65 | public delegate void ndimensional_hess (double[] arg, ref double func, double[] grad, double[,] hess, object obj);
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| 66 |
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| 67 | public delegate void ndimensional_fvec (double[] arg, double[] fi, object obj);
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| 68 | public delegate void ndimensional_jac (double[] arg, double[] fi, double[,] jac, object obj);
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| 69 |
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| 70 | public delegate void ndimensional_pfunc(double[] p, double[] q, ref double func, object obj);
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| 71 | public delegate void ndimensional_pgrad(double[] p, double[] q, ref double func, double[] grad, object obj);
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| 72 | public delegate void ndimensional_phess(double[] p, double[] q, ref double func, double[] grad, double[,] hess, object obj);
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| 73 |
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| 74 | public delegate void ndimensional_rep(double[] arg, double func, object obj);
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| 75 |
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| 76 | public delegate void ndimensional_ode_rp (double[] y, double x, double[] dy, object obj);
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| 77 |
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| 78 | public delegate void integrator1_func (double x, double xminusa, double bminusx, ref double f, object obj);
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| 79 |
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| 80 | /********************************************************************
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| 81 | Class defining a complex number with double precision.
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| 82 | ********************************************************************/
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| 83 | public struct complex
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| 84 | {
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| 85 | public double x;
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| 86 | public double y;
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| 87 |
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| 88 | public complex(double _x)
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| 89 | {
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| 90 | x = _x;
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| 91 | y = 0;
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| 92 | }
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| 93 | public complex(double _x, double _y)
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| 94 | {
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| 95 | x = _x;
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| 96 | y = _y;
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| 97 | }
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| 98 | public static implicit operator complex(double _x)
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| 99 | {
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| 100 | return new complex(_x);
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| 101 | }
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| 102 | public static bool operator==(complex lhs, complex rhs)
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| 103 | {
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| 104 | return ((double)lhs.x==(double)rhs.x) & ((double)lhs.y==(double)rhs.y);
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| 105 | }
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| 106 | public static bool operator!=(complex lhs, complex rhs)
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| 107 | {
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| 108 | return ((double)lhs.x!=(double)rhs.x) | ((double)lhs.y!=(double)rhs.y);
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| 109 | }
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| 110 | public static complex operator+(complex lhs)
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| 111 | {
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| 112 | return lhs;
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| 113 | }
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| 114 | public static complex operator-(complex lhs)
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| 115 | {
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| 116 | return new complex(-lhs.x,-lhs.y);
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| 117 | }
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| 118 | public static complex operator+(complex lhs, complex rhs)
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| 119 | {
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| 120 | return new complex(lhs.x+rhs.x,lhs.y+rhs.y);
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| 121 | }
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| 122 | public static complex operator-(complex lhs, complex rhs)
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| 123 | {
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| 124 | return new complex(lhs.x-rhs.x,lhs.y-rhs.y);
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| 125 | }
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| 126 | public static complex operator*(complex lhs, complex rhs)
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| 127 | {
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| 128 | return new complex(lhs.x*rhs.x-lhs.y*rhs.y, lhs.x*rhs.y+lhs.y*rhs.x);
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| 129 | }
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| 130 | public static complex operator/(complex lhs, complex rhs)
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| 131 | {
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| 132 | complex result;
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| 133 | double e;
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| 134 | double f;
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| 135 | if( System.Math.Abs(rhs.y)<System.Math.Abs(rhs.x) )
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| 136 | {
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| 137 | e = rhs.y/rhs.x;
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| 138 | f = rhs.x+rhs.y*e;
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| 139 | result.x = (lhs.x+lhs.y*e)/f;
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| 140 | result.y = (lhs.y-lhs.x*e)/f;
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| 141 | }
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| 142 | else
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| 143 | {
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| 144 | e = rhs.x/rhs.y;
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| 145 | f = rhs.y+rhs.x*e;
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| 146 | result.x = (lhs.y+lhs.x*e)/f;
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| 147 | result.y = (-lhs.x+lhs.y*e)/f;
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| 148 | }
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| 149 | return result;
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| 150 | }
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| 151 | public override int GetHashCode()
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| 152 | {
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| 153 | return x.GetHashCode() ^ y.GetHashCode();
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| 154 | }
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| 155 | public override bool Equals(object obj)
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| 156 | {
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| 157 | if( obj is byte)
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| 158 | return Equals(new complex((byte)obj));
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| 159 | if( obj is sbyte)
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| 160 | return Equals(new complex((sbyte)obj));
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| 161 | if( obj is short)
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| 162 | return Equals(new complex((short)obj));
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| 163 | if( obj is ushort)
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| 164 | return Equals(new complex((ushort)obj));
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| 165 | if( obj is int)
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| 166 | return Equals(new complex((int)obj));
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| 167 | if( obj is uint)
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| 168 | return Equals(new complex((uint)obj));
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| 169 | if( obj is long)
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| 170 | return Equals(new complex((long)obj));
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| 171 | if( obj is ulong)
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| 172 | return Equals(new complex((ulong)obj));
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| 173 | if( obj is float)
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| 174 | return Equals(new complex((float)obj));
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| 175 | if( obj is double)
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| 176 | return Equals(new complex((double)obj));
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| 177 | if( obj is decimal)
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| 178 | return Equals(new complex((double)(decimal)obj));
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| 179 | return base.Equals(obj);
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| 180 | }
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| 181 | }
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| 182 |
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| 183 | /********************************************************************
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| 184 | Class defining an ALGLIB exception
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| 185 | ********************************************************************/
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| 186 | public class alglibexception : System.Exception
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| 187 | {
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| 188 | public string msg;
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| 189 | public alglibexception(string s)
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| 190 | {
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| 191 | msg = s;
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| 192 | }
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| 193 |
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| 194 | }
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| 195 |
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| 196 | /********************************************************************
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| 197 | reverse communication structure
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| 198 | ********************************************************************/
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| 199 | public class rcommstate
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| 200 | {
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| 201 | public rcommstate()
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| 202 | {
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| 203 | stage = -1;
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| 204 | ia = new int[0];
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| 205 | ba = new bool[0];
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| 206 | ra = new double[0];
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| 207 | ca = new alglib.complex[0];
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| 208 | }
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| 209 | public int stage;
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| 210 | public int[] ia;
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| 211 | public bool[] ba;
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| 212 | public double[] ra;
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| 213 | public alglib.complex[] ca;
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| 214 | };
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| 215 |
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| 216 | /********************************************************************
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| 217 | internal functions
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| 218 | ********************************************************************/
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| 219 | public class ap
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| 220 | {
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| 221 | public static int len<T>(T[] a)
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| 222 | { return a.Length; }
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| 223 | public static int rows<T>(T[,] a)
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| 224 | { return a.GetLength(0); }
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| 225 | public static int cols<T>(T[,] a)
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| 226 | { return a.GetLength(1); }
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| 227 | public static void swap<T>(ref T a, ref T b)
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| 228 | {
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| 229 | T t = a;
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| 230 | a = b;
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| 231 | b = t;
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| 232 | }
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| 233 |
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| 234 | public static void assert(bool cond, string s)
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| 235 | {
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| 236 | if( !cond )
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| 237 | throw new alglibexception(s);
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| 238 | }
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| 239 |
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| 240 | public static void assert(bool cond)
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| 241 | {
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| 242 | assert(cond, "ALGLIB: assertion failed");
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| 243 | }
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| 244 |
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| 245 | /****************************************************************
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| 246 | returns dps (digits-of-precision) value corresponding to threshold.
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| 247 | dps(0.9) = dps(0.5) = dps(0.1) = 0
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| 248 | dps(0.09) = dps(0.05) = dps(0.01) = 1
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| 249 | and so on
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| 250 | ****************************************************************/
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| 251 | public static int threshold2dps(double threshold)
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| 252 | {
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| 253 | int result = 0;
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| 254 | double t;
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| 255 | for (result = 0, t = 1; t / 10 > threshold*(1+1E-10); result++, t /= 10) ;
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| 256 | return result;
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| 257 | }
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| 258 |
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| 259 | /****************************************************************
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| 260 | prints formatted array
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| 261 | ****************************************************************/
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| 262 | public static string format(bool[] a)
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| 263 | {
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| 264 | string[] result = new string[len(a)];
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| 265 | int i;
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| 266 | for(i=0; i<len(a); i++)
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| 267 | if( a[i] )
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| 268 | result[i] = "true";
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| 269 | else
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| 270 | result[i] = "false";
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| 271 | return "{"+String.Join(",",result)+"}";
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| 272 | }
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| 273 |
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| 274 | /****************************************************************
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| 275 | prints formatted array
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| 276 | ****************************************************************/
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| 277 | public static string format(int[] a)
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| 278 | {
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| 279 | string[] result = new string[len(a)];
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| 280 | int i;
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| 281 | for (i = 0; i < len(a); i++)
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| 282 | result[i] = a[i].ToString();
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| 283 | return "{" + String.Join(",", result) + "}";
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| 284 | }
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| 285 |
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| 286 | /****************************************************************
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| 287 | prints formatted array
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| 288 | ****************************************************************/
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| 289 | public static string format(double[] a, int dps)
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| 290 | {
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| 291 | string fmt = String.Format("{{0:F{0}}}", dps);
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| 292 | string[] result = new string[len(a)];
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| 293 | int i;
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| 294 | for (i = 0; i < len(a); i++)
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| 295 | {
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| 296 | result[i] = String.Format(fmt, a[i]);
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| 297 | result[i] = result[i].Replace(',', '.');
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| 298 | }
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| 299 | return "{" + String.Join(",", result) + "}";
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| 300 | }
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| 301 |
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| 302 | /****************************************************************
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| 303 | prints formatted array
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| 304 | ****************************************************************/
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| 305 | public static string format(complex[] a, int dps)
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| 306 | {
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| 307 | string fmtx = String.Format("{{0:F{0}}}", dps);
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| 308 | string fmty = String.Format("{{0:F{0}}}", dps);
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| 309 | string[] result = new string[len(a)];
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| 310 | int i;
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| 311 | for (i = 0; i < len(a); i++)
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| 312 | {
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| 313 | result[i] = String.Format(fmtx, a[i].x) + (a[i].y >= 0 ? "+" : "-") + String.Format(fmty, Math.Abs(a[i].y)) + "i";
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| 314 | result[i] = result[i].Replace(',', '.');
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| 315 | }
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| 316 | return "{" + String.Join(",", result) + "}";
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| 317 | }
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| 318 |
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| 319 | /****************************************************************
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| 320 | prints formatted matrix
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| 321 | ****************************************************************/
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| 322 | public static string format(bool[,] a)
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| 323 | {
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| 324 | int i, j, m, n;
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| 325 | n = cols(a);
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| 326 | m = rows(a);
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| 327 | bool[] line = new bool[n];
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| 328 | string[] result = new string[m];
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| 329 | for (i = 0; i < m; i++)
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| 330 | {
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| 331 | for (j = 0; j < n; j++)
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| 332 | line[j] = a[i, j];
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| 333 | result[i] = format(line);
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| 334 | }
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| 335 | return "{" + String.Join(",", result) + "}";
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| 336 | }
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| 337 |
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| 338 | /****************************************************************
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| 339 | prints formatted matrix
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| 340 | ****************************************************************/
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| 341 | public static string format(int[,] a)
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| 342 | {
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| 343 | int i, j, m, n;
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| 344 | n = cols(a);
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| 345 | m = rows(a);
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| 346 | int[] line = new int[n];
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| 347 | string[] result = new string[m];
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| 348 | for (i = 0; i < m; i++)
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| 349 | {
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| 350 | for (j = 0; j < n; j++)
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| 351 | line[j] = a[i, j];
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| 352 | result[i] = format(line);
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| 353 | }
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| 354 | return "{" + String.Join(",", result) + "}";
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| 355 | }
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| 356 |
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| 357 | /****************************************************************
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| 358 | prints formatted matrix
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| 359 | ****************************************************************/
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| 360 | public static string format(double[,] a, int dps)
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| 361 | {
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| 362 | int i, j, m, n;
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| 363 | n = cols(a);
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| 364 | m = rows(a);
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| 365 | double[] line = new double[n];
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| 366 | string[] result = new string[m];
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| 367 | for (i = 0; i < m; i++)
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| 368 | {
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| 369 | for (j = 0; j < n; j++)
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| 370 | line[j] = a[i, j];
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| 371 | result[i] = format(line, dps);
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| 372 | }
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| 373 | return "{" + String.Join(",", result) + "}";
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| 374 | }
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| 375 |
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| 376 | /****************************************************************
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| 377 | prints formatted matrix
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| 378 | ****************************************************************/
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| 379 | public static string format(complex[,] a, int dps)
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| 380 | {
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| 381 | int i, j, m, n;
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| 382 | n = cols(a);
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| 383 | m = rows(a);
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| 384 | complex[] line = new complex[n];
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| 385 | string[] result = new string[m];
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| 386 | for (i = 0; i < m; i++)
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| 387 | {
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| 388 | for (j = 0; j < n; j++)
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| 389 | line[j] = a[i, j];
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| 390 | result[i] = format(line, dps);
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| 391 | }
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| 392 | return "{" + String.Join(",", result) + "}";
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| 393 | }
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| 394 |
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| 395 | /****************************************************************
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| 396 | checks that matrix is symmetric.
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| 397 | max|A-A^T| is calculated; if it is within 1.0E-14 of max|A|,
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| 398 | matrix is considered symmetric
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| 399 | ****************************************************************/
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| 400 | public static bool issymmetric(double[,] a)
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| 401 | {
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| 402 | int i, j, n;
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| 403 | double err, mx, v1, v2;
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| 404 | if( rows(a)!=cols(a) )
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| 405 | return false;
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| 406 | n = rows(a);
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| 407 | if( n==0 )
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| 408 | return true;
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| 409 | mx = 0;
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| 410 | err = 0;
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| 411 | for( i=0; i<n; i++)
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| 412 | {
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| 413 | for(j=i+1; j<n; j++)
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| 414 | {
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| 415 | v1 = a[i,j];
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| 416 | v2 = a[j,i];
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| 417 | if( !math.isfinite(v1) )
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| 418 | return false;
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| 419 | if( !math.isfinite(v2) )
|
|---|
| 420 | return false;
|
|---|
| 421 | err = Math.Max(err, Math.Abs(v1-v2));
|
|---|
| 422 | mx = Math.Max(mx, Math.Abs(v1));
|
|---|
| 423 | mx = Math.Max(mx, Math.Abs(v2));
|
|---|
| 424 | }
|
|---|
| 425 | v1 = a[i,i];
|
|---|
| 426 | if( !math.isfinite(v1) )
|
|---|
| 427 | return false;
|
|---|
| 428 | mx = Math.Max(mx, Math.Abs(v1));
|
|---|
| 429 | }
|
|---|
| 430 | if( mx==0 )
|
|---|
| 431 | return true;
|
|---|
| 432 | return err/mx<=1.0E-14;
|
|---|
| 433 | }
|
|---|
| 434 |
|
|---|
| 435 | /****************************************************************
|
|---|
| 436 | checks that matrix is Hermitian.
|
|---|
| 437 | max|A-A^H| is calculated; if it is within 1.0E-14 of max|A|,
|
|---|
| 438 | matrix is considered Hermitian
|
|---|
| 439 | ****************************************************************/
|
|---|
| 440 | public static bool ishermitian(complex[,] a)
|
|---|
| 441 | {
|
|---|
| 442 | int i, j, n;
|
|---|
| 443 | double err, mx;
|
|---|
| 444 | complex v1, v2, vt;
|
|---|
| 445 | if( rows(a)!=cols(a) )
|
|---|
| 446 | return false;
|
|---|
| 447 | n = rows(a);
|
|---|
| 448 | if( n==0 )
|
|---|
| 449 | return true;
|
|---|
| 450 | mx = 0;
|
|---|
| 451 | err = 0;
|
|---|
| 452 | for( i=0; i<n; i++)
|
|---|
| 453 | {
|
|---|
| 454 | for(j=i+1; j<n; j++)
|
|---|
| 455 | {
|
|---|
| 456 | v1 = a[i,j];
|
|---|
| 457 | v2 = a[j,i];
|
|---|
| 458 | if( !math.isfinite(v1.x) )
|
|---|
| 459 | return false;
|
|---|
| 460 | if( !math.isfinite(v1.y) )
|
|---|
| 461 | return false;
|
|---|
| 462 | if( !math.isfinite(v2.x) )
|
|---|
| 463 | return false;
|
|---|
| 464 | if( !math.isfinite(v2.y) )
|
|---|
| 465 | return false;
|
|---|
| 466 | vt.x = v1.x-v2.x;
|
|---|
| 467 | vt.y = v1.y+v2.y;
|
|---|
| 468 | err = Math.Max(err, math.abscomplex(vt));
|
|---|
| 469 | mx = Math.Max(mx, math.abscomplex(v1));
|
|---|
| 470 | mx = Math.Max(mx, math.abscomplex(v2));
|
|---|
| 471 | }
|
|---|
| 472 | v1 = a[i,i];
|
|---|
| 473 | if( !math.isfinite(v1.x) )
|
|---|
| 474 | return false;
|
|---|
| 475 | if( !math.isfinite(v1.y) )
|
|---|
| 476 | return false;
|
|---|
| 477 | err = Math.Max(err, Math.Abs(v1.y));
|
|---|
| 478 | mx = Math.Max(mx, math.abscomplex(v1));
|
|---|
| 479 | }
|
|---|
| 480 | if( mx==0 )
|
|---|
| 481 | return true;
|
|---|
| 482 | return err/mx<=1.0E-14;
|
|---|
| 483 | }
|
|---|
| 484 |
|
|---|
| 485 |
|
|---|
| 486 | /****************************************************************
|
|---|
| 487 | Forces symmetricity by copying upper half of A to the lower one
|
|---|
| 488 | ****************************************************************/
|
|---|
| 489 | public static bool forcesymmetric(double[,] a)
|
|---|
| 490 | {
|
|---|
| 491 | int i, j, n;
|
|---|
| 492 | if( rows(a)!=cols(a) )
|
|---|
| 493 | return false;
|
|---|
| 494 | n = rows(a);
|
|---|
| 495 | if( n==0 )
|
|---|
| 496 | return true;
|
|---|
| 497 | for( i=0; i<n; i++)
|
|---|
| 498 | for(j=i+1; j<n; j++)
|
|---|
| 499 | a[i,j] = a[j,i];
|
|---|
| 500 | return true;
|
|---|
| 501 | }
|
|---|
| 502 |
|
|---|
| 503 | /****************************************************************
|
|---|
| 504 | Forces Hermiticity by copying upper half of A to the lower one
|
|---|
| 505 | ****************************************************************/
|
|---|
| 506 | public static bool forcehermitian(complex[,] a)
|
|---|
| 507 | {
|
|---|
| 508 | int i, j, n;
|
|---|
| 509 | complex v;
|
|---|
| 510 | if( rows(a)!=cols(a) )
|
|---|
| 511 | return false;
|
|---|
| 512 | n = rows(a);
|
|---|
| 513 | if( n==0 )
|
|---|
| 514 | return true;
|
|---|
| 515 | for( i=0; i<n; i++)
|
|---|
| 516 | for(j=i+1; j<n; j++)
|
|---|
| 517 | {
|
|---|
| 518 | v = a[j,i];
|
|---|
| 519 | a[i,j].x = v.x;
|
|---|
| 520 | a[i,j].y = -v.y;
|
|---|
| 521 | }
|
|---|
| 522 | return true;
|
|---|
| 523 | }
|
|---|
| 524 | };
|
|---|
| 525 |
|
|---|
| 526 | /********************************************************************
|
|---|
| 527 | math functions
|
|---|
| 528 | ********************************************************************/
|
|---|
| 529 | public class math
|
|---|
| 530 | {
|
|---|
| 531 | //public static System.Random RndObject = new System.Random(System.DateTime.Now.Millisecond);
|
|---|
| 532 | public static System.Random rndobject = new System.Random(System.DateTime.Now.Millisecond + 1000*System.DateTime.Now.Second + 60*1000*System.DateTime.Now.Minute);
|
|---|
| 533 |
|
|---|
| 534 | public const double machineepsilon = 5E-16;
|
|---|
| 535 | public const double maxrealnumber = 1E300;
|
|---|
| 536 | public const double minrealnumber = 1E-300;
|
|---|
| 537 |
|
|---|
| 538 | public static bool isfinite(double d)
|
|---|
| 539 | {
|
|---|
| 540 | return !System.Double.IsNaN(d) && !System.Double.IsInfinity(d);
|
|---|
| 541 | }
|
|---|
| 542 |
|
|---|
| 543 | public static double randomreal()
|
|---|
| 544 | {
|
|---|
| 545 | double r = 0;
|
|---|
| 546 | lock(rndobject){ r = rndobject.NextDouble(); }
|
|---|
| 547 | return r;
|
|---|
| 548 | }
|
|---|
| 549 | public static int randominteger(int N)
|
|---|
| 550 | {
|
|---|
| 551 | int r = 0;
|
|---|
| 552 | lock(rndobject){ r = rndobject.Next(N); }
|
|---|
| 553 | return r;
|
|---|
| 554 | }
|
|---|
| 555 | public static double sqr(double X)
|
|---|
| 556 | {
|
|---|
| 557 | return X*X;
|
|---|
| 558 | }
|
|---|
| 559 | public static double abscomplex(complex z)
|
|---|
| 560 | {
|
|---|
| 561 | double w;
|
|---|
| 562 | double xabs;
|
|---|
| 563 | double yabs;
|
|---|
| 564 | double v;
|
|---|
| 565 |
|
|---|
| 566 | xabs = System.Math.Abs(z.x);
|
|---|
| 567 | yabs = System.Math.Abs(z.y);
|
|---|
| 568 | w = xabs>yabs ? xabs : yabs;
|
|---|
| 569 | v = xabs<yabs ? xabs : yabs;
|
|---|
| 570 | if( v==0 )
|
|---|
| 571 | return w;
|
|---|
| 572 | else
|
|---|
| 573 | {
|
|---|
| 574 | double t = v/w;
|
|---|
| 575 | return w*System.Math.Sqrt(1+t*t);
|
|---|
| 576 | }
|
|---|
| 577 | }
|
|---|
| 578 | public static complex conj(complex z)
|
|---|
| 579 | {
|
|---|
| 580 | return new complex(z.x, -z.y);
|
|---|
| 581 | }
|
|---|
| 582 | public static complex csqr(complex z)
|
|---|
| 583 | {
|
|---|
| 584 | return new complex(z.x*z.x-z.y*z.y, 2*z.x*z.y);
|
|---|
| 585 | }
|
|---|
| 586 |
|
|---|
| 587 | }
|
|---|
| 588 | }
|
|---|
