Exemple #1
0
        public static RationalCoFactorInfo GetCoFactor(RationalSquareMatrix symIn, int Column)
        {
            RationalCoFactorInfo cfi = new RationalCoFactorInfo();

            cfi.Sign = (int)Math.Pow(-1, Column + 1);
            RationalVector col = symIn[Column - 1];

            cfi.CoFactor = col[0];
            List <Rational> symList = new List <Rational>();

            for (int i = 1; i < symIn.Rows; i++)
            {
                for (int j = 0; j < symIn.Columns; j++)
                {
                    if (j + 1 != Column)
                    {
                        symList.Add(symIn[i, j]);
                    }
                }
            }

            cfi.Minor           = new RationalSquareMatrix(symIn.Rows - 1, symIn.Columns - 1, symList);
            cfi.Minor.MinorName = symIn.MinorName;
            return(cfi);
        }
Exemple #2
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        public static RationalSquareMatrix FaddevasMethod(RationalSquareMatrix AIn, out RationalVector CharacteristicEquation)
        {
            RationalSquareMatrix A = AIn.Clone();

            CharacteristicEquation = new RationalVector();

            RationalSquareMatrix A_n  = A;
            Rational             b_n  = 1;
            RationalSquareMatrix B_n  = null;
            RationalSquareMatrix I    = null;
            RationalSquareMatrix AInv = null;
            int i = 0;

            for (i = 1; i < A.Rows; i++)
            {
                b_n = -A_n.Trace() / (i);
                CharacteristicEquation.Add(b_n);
                I = RationalSquareMatrix.IdentityMatrix(A.Rows);

                B_n = A_n + b_n * I;

                A_n = A * B_n;
            }
            b_n = -A_n.Trace() / (i);
            CharacteristicEquation.Add(b_n);

            AInv         = -1 / b_n * B_n;
            AInv.FullRep = A.ToLatex() + "^{-1} = " + AInv.ToLatex();

            return(AInv);
        }
        public static int Test_CramersRule()
        {
            RationalFactory      rf    = new RationalFactory(); //Create rational factory
            RationalSquareMatrix ACopy = rf[3, 3,               //Matrix to solve
                                            "1", "2", "-2",
                                            "-1", "1", "3",
                                            "2", "-1", "2"
                                         ];

            RationalVector rv = new RationalVector {
                -7, 3, 8
            };                                      //values to solve for
            StringBuilder sb = new StringBuilder(); //Start building latex

            sb.Append(@"\begin{aligned}");

            //Start system of linear equations
            sb.AppendFormat(@"&x_1 + 2x_2 - 2x_3 = -7 \\ \\");
            sb.AppendFormat(@"&-x_1 + x_2 + 3x_3 = 3 \\ \\");
            sb.AppendFormat(@"&2x_1 - x_2 + 2x_3 = 8 \\ \\");
            RationalVector rvSolved = ACopy.CramersRule(rv);                                                                           //solve system of linear equations

            sb.AppendFormat(@"&x_1 = {0}, x_2 = {1}, x_3 = {2}", rvSolved[0].ToLatex(), rvSolved[1].ToLatex(), rvSolved[2].ToLatex()); //output values

            sb.Append(@"\end{aligned}");

            HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_CramersRule.html"); //display Latex via mathjax

            return(0);
        }
        public static int Test_RationalSquareMatrix()
        {
            RationalFactory rf  = new RationalFactory();
            RealFactory     rff = new RealFactory();

            RationalSquareMatrix A = rf[3, 3,
                                        "1", "2", "-2",
                                        "-1", "1", "3",
                                        "2", "-1", "2"
                                     ];

            SquareRealMatrix SA = rff[3, 3,
                                      7, 2, -2,
                                      3, 1, 3,
                                      8, -1, 2
                                  ];
            RationalVector rv = rf["7", "3", "8"];

            StringBuilder sb = new StringBuilder();//Start building latex

            sb.Append(@"\begin{aligned}");

            sb.AppendFormat(@"&A = {0}", A.ToLatex() + @" \\ \\"); //display A matrix
            A[0] = rv;
            sb.AppendFormat(@"&Ab = {0}", A.ToLatex());            //display Vec A
            sb.AppendFormat(@"&Det = {0}", SA.Determinant());      //display Vec A
            sb.Append(@"\end{aligned}");

            HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_VecOperator.html"); //display Latex via mathjax

            return(0);
        }
Exemple #5
0
        public RationalSquareMatrix Inverse()
        {
            RationalSquareMatrix Inv = null;
            RationalVector       rv  = new RationalVector();

            Inv = FaddevasMethod(this, out rv);

            return(Inv);
        }
Exemple #6
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        public static RationalVector operator +(Rational value, RationalVector v)
        {
            RationalVector vM = new RationalVector();

            for (int i = 0; i < v.Count; i++)
            {
                vM.Add(value + v[i]);
            }
            return(vM);
        }
Exemple #7
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        public static RationalVector operator /(RationalVector v, Rational value)
        {
            RationalVector vM = new RationalVector();

            for (int i = 0; i < v.Count; i++)
            {
                vM.Add(v[i] / value);
            }
            return(vM);
        }
Exemple #8
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        public static RationalVector operator -(RationalVector v1, RationalVector v2)
        {
            RationalVector vM = new RationalVector();

            for (int i = 0; i < v1.Count; i++)
            {
                vM.Add(v1[i] - v2[i]);
            }
            return(vM);
        }
        public RationalVector this[params string[] exps]
        {
            get
            {
                RationalVector rv = new RationalVector();
                foreach (string r in exps)
                {
                    rv.Add(Rational.Parse(r));
                }

                return(rv);
            }
        }
Exemple #10
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        public static Rational DotProduct(RationalVector v1, RationalVector v2)
        {
            Rational ret = 0;

            if (v1.Count != v2.Count)
            {
                throw new Exception("Vectors must be equal in length");
            }

            for (int i = 0; i < v1.Count; i++)
            {
                ret += (v1[i] * v2[i]);
            }
            return(ret);
        }
Exemple #11
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        public RationalVector CramersRule(RationalVector VectorToSolve)
        {
            RationalVector Deltas = new RationalVector();

            RationalSquareMatrix A     = this.Clone();
            Rational             Delta = RationalSquareMatrix.Det(A);

            for (int i = 0; i < this.Rows; i++)
            {
                RationalVector rvSave = A[i];
                A[i] = VectorToSolve;
                Deltas.Add(RationalSquareMatrix.Det(A) / Delta);
                A[i] = rvSave;
            }
            return(Deltas);
        }
Exemple #12
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        public RationalVector this[int Column]
        {
            get
            {
                RationalVector ret = new RationalVector();

                for (int i = 0; i < this.Rows; i++)
                {
                    ret.Add(this[i, Column]);
                }

                return(ret);
            }
            set
            {
                for (int i = 0; i < this.Rows; i++)
                {
                    this[i, Column] = value[i];
                }
            }
        }
Exemple #13
0
 public static RationalVector Normalize(RationalVector v)
 {
     return(v / new Rational(Math.Sqrt(DotProduct(v, v).ToDouble())));
 }
        public static int Test_FaddevasMethod()
        {
            RationalFactory rf = new RationalFactory();

            RationalSquareMatrix A = rf[3, 3,
                                        "1", "0", "-2",
                                        "4", "1", "0",
                                        "0", "2", "1"
                                     ];


            RationalVector       rv   = new RationalVector();
            RationalSquareMatrix AInv = RationalSquareMatrix.FaddevasMethod(A, out rv);
            StringBuilder        sb   = new StringBuilder();//Start building latex

            sb.Append(@"A^{-1} = " + AInv.ToLatex());

            HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(AInv.ToString("F"), "Test_FaddevasMethod_Determinant.html"); //display Latex via mathjax


            /*
             * RationalSquareMatrix A1 = A.Clone();
             * StringBuilder sb = new StringBuilder();//Start building latex
             * sb.Append(@"\begin{aligned}");
             * sb.AppendFormat(@"&A1 = {0} \\ \\", A1.ToLatex());
             *
             * Rational b1 = -A1.Trace();
             * sb.AppendFormat(@"&b1 = {0} \\ \\", b1.ToLatex());
             * RationalSquareMatrix I = RationalSquareMatrix.IdentityMatrix(A.Rows);
             *
             * RationalSquareMatrix B1 = A1 + (b1 * I);
             * sb.AppendFormat(@"&B1 = {0} \\ \\", B1.ToLatex());
             *
             * RationalSquareMatrix A2 = A * B1;
             * sb.AppendFormat(@"&A2 = {0} \\ \\", A2.ToLatex());
             *
             * Rational b2 = A2.Trace() / -2;
             * sb.AppendFormat(@"&b2 = {0} \\ \\", b2.ToLatex());
             *
             * I = RationalSquareMatrix.IdentityMatrix(A.Rows);
             * RationalSquareMatrix B2 = A2 + b2 * I;
             * sb.AppendFormat(@"&B2 = {0} \\ \\", B2.ToLatex());
             *
             * RationalSquareMatrix A3 = A * B2;
             * sb.AppendFormat(@"&A3 = {0} \\ \\", A3.ToLatex());
             *
             * Rational b3 = A3.Trace() / -3;
             * sb.AppendFormat(@"&b3 = {0} \\ \\", b3.ToLatex());
             *
             * RationalSquareMatrix AInv = 1/b3 * B2;
             * sb.Append(@"&A^{-1} = " + AInv.ToLatex() + @" \\ \\");
             *
             *
             * RationalSquareMatrix A_n = A;
             * Rational b_n = 1;
             * RationalSquareMatrix B_n = null;
             * int i = 0;
             * for(i = 0; i < A.Rows - 1; i++)
             * {
             *  b_n = -A_n.Trace() / (i + 1);
             *  I = RationalSquareMatrix.IdentityMatrix(A.Rows);
             *
             *  B_n = A_n + b_n * I;
             *  sb.Append(@"&Bn = " + B_n.ToLatex() + @" \\ \\");
             *
             *  A_n = A * B_n;
             *  sb.Append(@"&An = " + A_n.ToLatex() + @" \\ \\");
             * }
             *
             * b_n = -A_n.Trace() / (i + 1);
             * sb.Append(@"&bn = " + b_n.ToLatex() + @" \\ \\");
             *
             * AInv = 1/b_n * B_n;
             * sb.Append(@"&A^{-1} = " + AInv.ToLatex() + @" \\ \\");
             *
             * sb.Append(@"\end{aligned}");
             * HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_FaddevasMethod_Determinant.html"); //display Latex via mathjax
             */

            return(0);
        }