f# - Microsoft Solver Foundation と F#

Question

私はこのMS Solver Foundation の例を C# から F# に変換しようとしていますが、特にセクション 5 で、C# が double から Rational への暗黙の変換を受け入れ、F# が受け入れない何かの型変換に関する問題に常に遭遇しています。解決する？Rational 型自体は、事前定義された Rational.One または Rational.Zero に設定する以外に初期化することは事実上不可能に思えるため、私にとってパズルです。何か案は？以下の最小限の縮小バージョンを参照してください (配列などを使用していません)。

let main argv = 

printfn "%A" argv
Console.WriteLine("\nBegin Solver demo\n")
let mean = 1.0
let solver = new InteriorPointSolver()
let allocation = ref 0
solver.AddVariable("MSFT", allocation) |> ignore
solver.SetBounds(!allocation, Rational.Zero, Rational.One)

let expRet = ref 0
solver.AddRow("expRet", expRet) |> ignore
solver.SetBounds(!expRet, Rational.Zero, Rational.PositiveInfinity)

let unity = ref 0
solver.AddRow("Investments sum to one", unity) |> ignore
solver.SetBounds(!unity, Rational.One, Rational.One)

solver.SetCoefficient(!expRet, !allocation, Rational.)
solver.SetCoefficient(!unity, !allocation, Rational.One);

Console.WriteLine("\nEnd Solver demo\n")
Console.ReadLine() |> ignore
0 // return an integer exit code

score 0 · Accepted Answer

これは古い投稿ですが、誰も回答していません。この情報は他の人に役立つかもしれません.

私は F# を知りません (知っている人は私の構文を編集してください) が、Rational クラスの次のメソッドが役立つはずです。Microsoft.SolverFoundation.Common 名前空間の BigInteger クラスも必要です。( https://docs.microsoft.com/en-us/previous-versions/visualstudio/ff526610を参照)

まず、ご指摘のとおり、多くの「暗黙の」コンストラクターのいずれかを使用して、他の型から Rational を直接構築できます。

    let Rational rat5 = Rational.op_Implicit(5.0:float)
    let Rational rat2 = Rational.op_Implicit(2:int)

ここで、F# 構文を推測しています。

もう 1 つの非常にわかりやすい例として、金銭的価値 (例: $10.43) が double で正確に表現されることはめったにありません。(倍精度で正確になる「セント」値は、xx.00、xx.25、xx.50、および xx.75 だけであり、他のすべての値は数値エラー/差になります。)金銭的価値を表すと主張する double から有理数を構築します。これは、有理数を構築する別の方法の良いサンプルを提供します。

    let BigInteger bi100 = BigInteger.op_Implicit(100:int)
    let float mv = 1000000000000.43 //I am assuming this gets classified by F# as a double.

    //Now, we assume mv is any double that represents a monetary value, and so should be an even 2 decimal places in base 10
    //I have no idea how to Round in F#, nor how to cast to an integer - I have guessed - but should illustrate the idea if it is not valid F#
    let BigInteger cents = BigInteger.op_Implicit( ( Round(mv * 100.0) ):int ) //get exact monetary value, in cents
    let Rational ratMv = Rational.Get(cents:BigInteger, bi100:BigInteger)

そこで、2 つの BigInteger 型から Rational を作成しました。これは、double として格納された金額 mv を正確に表します。

以下は、c# 構文ではありますが、Rational インターフェース全体です。

namespace Microsoft.SolverFoundation.Common
{
    [CLSCompliant(true)]
    public struct Rational : IComparable, IComparable<Rational>, IEquatable<Rational>, IComparable<BigInteger>, IEquatable<BigInteger>, IComparable<int>, IEquatable<int>, IComparable<uint>, IEquatable<uint>, IComparable<long>, IEquatable<long>, IComparable<ulong>, IEquatable<ulong>, IComparable<double>, IEquatable<double>
    {
        public static readonly Rational NegativeInfinity;
        public static readonly Rational Zero;
        public static readonly Rational One;
        public static readonly Rational PositiveInfinity;
        public static readonly Rational Indeterminate;
        public static readonly Rational UnsignedInfinity;

        public bool IsOne { get; }
        public bool IsFinite { get; }
        public bool IsIndeterminate { get; }
        public bool IsInfinite { get; }
        public bool IsSignedInfinity { get; }
        public bool IsUnsignedInfinity { get; }
        public bool HasSign { get; }
        public bool IsNegativeInfinity { get; }
        public bool IsZero { get; }
        public int BitCount { get; }
        public int Sign { get; }
        public BigInteger Numerator { get; }
        public bool IsPositiveInfinity { get; }
        public BigInteger Denominator { get; }
        public Rational AbsoluteValue { get; }

        public static Rational AddMul(Rational ratAdd, Rational ratMul1, Rational ratMul2);
        public static Rational Get(BigInteger bnNum, BigInteger bnDen);
        public static void Negate(ref Rational num);
        public static bool Power(Rational ratBase, Rational ratExp, out Rational ratRes);
        public void AppendDecimalString(StringBuilder sb, int cchMax);
        public int CompareTo(BigInteger bn);
        [CLSCompliant(false)]
        public int CompareTo(uint u);
        public int CompareTo(Rational rat);
        public int CompareTo(long nn);
        [CLSCompliant(false)]
        public int CompareTo(ulong uu);
        public int CompareTo(double dbl);
        public int CompareTo(int n);
        public int CompareTo(object obj);
        [CLSCompliant(false)]
        public bool Equals(uint u);
        public bool Equals(Rational rat);
        public bool Equals(long nn);
        [CLSCompliant(false)]
        public bool Equals(ulong uu);
        public bool Equals(int n);
        public bool Equals(BigInteger bn);
        public override bool Equals(object obj);
        public bool Equals(double dbl);
        public Rational GetCeiling();
        public Rational GetCeilingResidual();
        public Rational GetFloor();
        public Rational GetFloorResidual();
        public Rational GetFractionalPart();
        public override int GetHashCode();
        public Rational GetIntegerPart();
        public double GetSignedDouble();
        public Rational Invert();
        public bool IsInteger(out BigInteger bn);
        public bool IsInteger();
        public double ToDouble();
        public override string ToString();

        public static Rational operator +(Rational rat1, Rational rat2);
        public static Rational operator -(Rational rat);
        public static Rational operator -(Rational rat1, Rational rat2);
        public static Rational operator *(Rational rat1, Rational rat2);
        public static Rational operator /(Rational rat1, Rational rat2);
        [CLSCompliant(false)]
        public static bool operator ==(uint n, Rational rat);
        [CLSCompliant(false)]
        public static bool operator ==(Rational rat, uint n);
        public static bool operator ==(int n, Rational rat);
        public static bool operator ==(long n, Rational rat);
        public static bool operator ==(Rational rat, BigInteger bn);
        public static bool operator ==(Rational rat, int n);
        public static bool operator ==(Rational rat, long n);
        public static bool operator ==(BigInteger bn, Rational rat);
        public static bool operator ==(double dbl, Rational rat);
        [CLSCompliant(false)]
        public static bool operator ==(Rational rat, ulong n);
        public static bool operator ==(Rational rat1, Rational rat2);
        [CLSCompliant(false)]
        public static bool operator ==(ulong n, Rational rat);
        public static bool operator ==(Rational rat, double dbl);
        [CLSCompliant(false)]
        public static bool operator !=(ulong n, Rational rat);
        [CLSCompliant(false)]
        public static bool operator !=(Rational rat, ulong n);
        [CLSCompliant(false)]
        public static bool operator !=(uint n, Rational rat);
        public static bool operator !=(BigInteger bn, Rational rat);
        [CLSCompliant(false)]
        public static bool operator !=(Rational rat, uint n);
        public static bool operator !=(double dbl, Rational rat);
        public static bool operator !=(int n, Rational rat);
        public static bool operator !=(Rational rat, int n);
        public static bool operator !=(long n, Rational rat);
        public static bool operator !=(Rational rat, BigInteger bn);
        public static bool operator !=(Rational rat1, Rational rat2);
        public static bool operator !=(Rational rat, double dbl);
        public static bool operator !=(Rational rat, long n);
        public static bool operator <(double dbl, Rational rat);
        public static bool operator <(Rational rat, double dbl);
        [CLSCompliant(false)]
        public static bool operator <(ulong n, Rational rat);
        [CLSCompliant(false)]
        public static bool operator <(Rational rat, ulong n);
        [CLSCompliant(false)]
        public static bool operator <(uint n, Rational rat);
        public static bool operator <(Rational rat1, Rational rat2);
        public static bool operator <(Rational rat, BigInteger bn);
        public static bool operator <(long n, Rational rat);
        public static bool operator <(BigInteger bn, Rational rat);
        public static bool operator <(Rational rat, int n);
        public static bool operator <(int n, Rational rat);
        [CLSCompliant(false)]
        public static bool operator <(Rational rat, uint n);
        public static bool operator <(Rational rat, long n);
        public static bool operator >(long n, Rational rat);
        public static bool operator >(Rational rat1, Rational rat2);
        public static bool operator >(Rational rat, BigInteger bn);
        public static bool operator >(BigInteger bn, Rational rat);
        public static bool operator >(Rational rat, int n);
        [CLSCompliant(false)]
        public static bool operator >(Rational rat, uint n);
        public static bool operator >(double dbl, Rational rat);
        [CLSCompliant(false)]
        public static bool operator >(uint n, Rational rat);
        public static bool operator >(int n, Rational rat);
        public static bool operator >(Rational rat, long n);
        public static bool operator >(Rational rat, double dbl);
        [CLSCompliant(false)]
        public static bool operator >(ulong n, Rational rat);
        [CLSCompliant(false)]
        public static bool operator >(Rational rat, ulong n);
        [CLSCompliant(false)]
        public static bool operator <=(ulong n, Rational rat);
        public static bool operator <=(Rational rat, int n);
        public static bool operator <=(Rational rat, BigInteger bn);
        public static bool operator <=(int n, Rational rat);
        [CLSCompliant(false)]
        public static bool operator <=(Rational rat, uint n);
        public static bool operator <=(BigInteger bn, Rational rat);
        [CLSCompliant(false)]
        public static bool operator <=(Rational rat, ulong n);
        public static bool operator <=(Rational rat1, Rational rat2);
        public static bool operator <=(long n, Rational rat);
        public static bool operator <=(Rational rat, double dbl);
        public static bool operator <=(double dbl, Rational rat);
        [CLSCompliant(false)]
        public static bool operator <=(uint n, Rational rat);
        public static bool operator <=(Rational rat, long n);
        public static bool operator >=(Rational rat, BigInteger bn);
        public static bool operator >=(Rational rat1, Rational rat2);
        [CLSCompliant(false)]
        public static bool operator >=(Rational rat, ulong n);
        [CLSCompliant(false)]
        public static bool operator >=(uint n, Rational rat);
        public static bool operator >=(Rational rat, long n);
        public static bool operator >=(int n, Rational rat);
        public static bool operator >=(BigInteger bn, Rational rat);
        public static bool operator >=(Rational rat, int n);
        [CLSCompliant(false)]
        public static bool operator >=(ulong n, Rational rat);
        public static bool operator >=(long n, Rational rat);
        public static bool operator >=(double dbl, Rational rat);
        [CLSCompliant(false)]
        public static bool operator >=(Rational rat, uint n);
        public static bool operator >=(Rational rat, double dbl);

        public static implicit operator Rational(double dbl);
        public static implicit operator Rational(BigInteger bn);
        [CLSCompliant(false)]
        public static implicit operator Rational(uint u);
        public static implicit operator Rational(long nn);
        [CLSCompliant(false)]
        public static implicit operator Rational(ulong uu);
        public static implicit operator Rational(int n);
        public static explicit operator BigInteger(Rational rat);
        public static explicit operator double(Rational rat);
        [CLSCompliant(false)]
        public static explicit operator ulong(Rational rat);
        public static explicit operator long(Rational rat);
        [CLSCompliant(false)]
        public static explicit operator uint(Rational rat);
        public static explicit operator int(Rational rat);
    }
}

上記のリンクで見つけることができる他の非常に有用な情報は、次の表です。

「次の表は、有理数の特殊なケースがどのように表現されるかを示しています。

有理数	表現
非ゼロの有理数	(分子、分母) 分母 > 0
ゼロ	(0, 0)
負の無限大	(-1, 0)
正の無限大	(+1, 0)
符号なし無限大	(+2, 0)
不定 (NaN)	(+3, 0)

ゼロ以外の値をゼロで除算すると、0 は符号なしであるため、符号なし無限大になります。有限値を任意の無限値で除算すると、結果は 0 になります。」

f# - Microsoft Solver Foundation と F#

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