SCIP in C++11 ― 1.3.3節 その3

問題1.36

問題1.35のコードに標準ストリームへの出力を1行混ぜるだけなのだが、

まあ一応全部。

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const double fixedPoint

(const function<double(double)>& f,

 const double firstGuess)

{

    const double tolerance(0.00001);

    const function<bool(double,double)> isCloseEnough

        =[tolerance](const double v1,const double v2)

        {return(abs(v1-v2)<tolerance);};

    function<double(double)> Try;

    Try=[&f,&isCloseEnough,&Try](const double guess)->const double{

        cout<<setprecision(16)<<"guess="<<guess<<endl;

        const double next(f(guess));

        if(isCloseEnough(guess,next)){return(next);}

        else{return(Try(next));}

    };

    return(Try(firstGuess));

}

const function<double(double,double)> average

=[](const double a,const double b){return((a+b)/2.0);};

const function<double(double)> xPowXEquation

=[](const double x){return(log(1000.0)/log(x));};

const function<double(void)> xPowXFixedRaw=[](void)

{

    return(fixedPoint(xPowXEquation,2.0));

};

const function<double(void)> xPowXFixedAverageDamped=[](void){

    return(fixedPoint([](const double x)

    {

        return(average(x,xPowXEquation(x)));

    },2.0));

};

int main(int argc, char** argv)

{

    cout<<"without average damping:"<<endl;

    cout<<setprecision(16)<<"Solution="

         <<xPowXFixedRaw()<<endl<<endl;

    cout<<"with average damping:"<<endl;

    cout<<setprecision(16)<<"Solution="

         <<xPowXFixedAverageDamped()<<endl;

    return(0);

}

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出力

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without average damping:

guess=2

guess=9.965784284662087

guess=3.004472209841214

guess=6.279195757507157

guess=3.759850702401539

guess=5.215843784925895

guess=4.182207192401397

guess=4.827765098344591

guess=4.387593384662677

guess=4.671250085763899

guess=4.481403616895052

guess=4.6053657460929

guess=4.523084967871887

guess=4.577114682047341

guess=4.541382480151454

guess=4.564903245230833

guess=4.549372679303342

guess=4.559606491913287

guess=4.552853875788271

guess=4.557305529748263

guess=4.554369064436181

guess=4.556305311532999

guess=4.555028263573554

guess=4.555870396702851

guess=4.555315001192079

guess=4.555681263543327

guess=4.555439715736846

guess=4.555599009998291

guess=4.555493957531389

guess=4.555563237292884

guess=4.555517548417651

guess=4.555547679306398

guess=4.555527808516254

guess=4.555540912917957

Solution=4.555532270803653

with average damping:

guess=2

guess=5.982892142331043

guess=4.922168721308343

guess=4.628224318195455

guess=4.568346513136242

guess=4.5577305909237

guess=4.555909809045131

guess=4.555599411610624

guess=4.555546552147367

Solution=4.555537551999825