C# Matrix.Cholesky方法代码示例

        /// <summary>
        /// Initializes a new instance of the <see cref="InverseWishart"/> class.
        /// </summary>
        /// <param name="degreesOfFreedom">The degree of freedom (ν) for the inverse Wishart distribution.</param>
        /// <param name="scale">The scale matrix (Ψ) for the inverse Wishart distribution.</param>
        public InverseWishart(double degreesOfFreedom, Matrix<double> scale)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(degreesOfFreedom, scale))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            _random = SystemRandomSource.Default;
            _freedom = degreesOfFreedom;
            _scale = scale;
            _chol = _scale.Cholesky();
        }

        /// <summary>
        /// Samples a vector normal distributed random variable.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="mean">The mean of the vector normal distribution.</param>
        /// <param name="covariance">The covariance matrix of the vector normal distribution.</param>
        /// <returns>a sequence of samples from defined distribution.</returns>
        static Vector<double> SampleVectorNormal(System.Random rnd, Vector<double> mean, Matrix<double> covariance)
        {
            var chol = covariance.Cholesky();

            // Sample a standard normal variable.
            var v = Vector<double>.Build.Random(mean.Count, new Normal(rnd));

            // Return the transformed variable.
            return mean + (chol.Factor*v);
        }

        /// <summary>
        /// Sets the parameters of the distribution after checking their validity.
        /// </summary>
        /// <param name="degreesOfFreedom">The degree of freedom (ν) for the inverse Wishart distribution.</param>
        /// <param name="scale">The scale matrix (Ψ) for the inverse Wishart distribution.</param>
        /// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
        void SetParameters(double degreesOfFreedom, Matrix<double> scale)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(degreesOfFreedom, scale))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            _freedom = degreesOfFreedom;
            _scale = scale;
            _chol = _scale.Cholesky();
        }

        /// <summary>
        /// Evaluates the probability density function for the inverse Wishart distribution.
        /// </summary>
        /// <param name="x">The matrix at which to evaluate the density at.</param>
        /// <exception cref="ArgumentOutOfRangeException">If the argument does not have the same dimensions as the scale matrix.</exception>
        /// <returns>the density at <paramref name="x"/>.</returns>
        public double Density(Matrix<double> x)
        {
            var p = _scale.RowCount;

            if (x.RowCount != p || x.ColumnCount != p)
            {
                throw new ArgumentOutOfRangeException("x", Resources.ArgumentMatrixDimensions);
            }

            var chol = x.Cholesky();
            var dX = chol.Determinant;
            var sXi = chol.Solve(Scale);

            // Compute the multivariate Gamma function.
            var gp = Math.Pow(Constants.Pi, p*(p - 1.0)/4.0);
            for (var j = 1; j <= p; j++)
            {
                gp *= SpecialFunctions.Gamma((_freedom + 1.0 - j)/2.0);
            }

            return Math.Pow(dX, -(_freedom + p + 1.0)/2.0)
                   *Math.Exp(-0.5*sXi.Trace())
                   *Math.Pow(_chol.Determinant, _freedom/2.0)
                   /Math.Pow(2.0, _freedom*p/2.0)
                   /gp;
        }

        /// <summary>
        /// Samples a Wishart distributed random variable using the method
        ///     Algorithm AS 53: Wishart Variate Generator
        ///     W. B. Smith and R. R. Hocking
        ///     Applied Statistics, Vol. 21, No. 3 (1972), pp. 341-345
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="degreesOfFreedom">The degrees of freedom (n) for the Wishart distribution.</param>
        /// <param name="scale">The scale matrix (V) for the Wishart distribution.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static Matrix<double> Sample(System.Random rnd, double degreesOfFreedom, Matrix<double> scale)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(degreesOfFreedom, scale))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            return DoSample(rnd, degreesOfFreedom, scale, scale.Cholesky());
        }