Пример #1
0
        /// <summary>
        /// Evaluates the probability density function for the 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 Matrix.DimensionsDontMatch <ArgumentOutOfRangeException>(x, _scale, "x");
            }

            var dX  = x.Determinant();
            var siX = _chol.Solve(x);

            // 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((_degreesOfFreedom + 1.0 - j) / 2.0);
            }

            return(Math.Pow(dX, (_degreesOfFreedom - p - 1.0) / 2.0)
                   * Math.Exp(-0.5 * siX.Trace())
                   / Math.Pow(2.0, _degreesOfFreedom * p / 2.0)
                   / Math.Pow(_chol.Determinant, _degreesOfFreedom / 2.0)
                   / gp);
        }
Пример #2
0
        /// <summary>
        /// Evaluates the probability density function for the 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 = _s.RowCount;

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

            var dX  = x.Determinant();
            var siX = _chol.Solve(x);

            // 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((_nu + 1.0 - j) / 2.0);
            }

            return(Math.Pow(dX, (_nu - p - 1.0) / 2.0)
                   * Math.Exp(-0.5 * siX.Trace())
                   / Math.Pow(2.0, _nu * p / 2.0)
                   / Math.Pow(_chol.Determinant, _nu / 2.0)
                   / gp);
        }
Пример #3
0
        public void ShouldSolve()
        {
            var a = new double[, ]
            {
                { 6.0, 15.0, 55.0 },
                { 15.0, 55.0, 225.0 },
                { 55.0, 225.0, 979.0 }
            };

            var rhs = new double[] { 9.5, 50.0, 237.0 };

            var solution = Cholesky.Solve(a, rhs);
            var expected = new double[] { -0.5, -1.0, 0.5 };

            Assert.AreEqual(expected.Length, solution.Length);
            for (var i = 0; i < solution.Length; ++i)
            {
                Assert.AreEqual(expected[i], solution[i], 0.000001);
            }
        }