public static double ellipsoid_volume(int m, double[] a, double[] v, double r)
//****************************************************************************80
//
// Purpose:
//
// ELLIPSOID_VOLUME returns the volume of an ellipsoid.
//
// Discussion:
//
// The points X in the ellipsoid are described by an M by M
// positive definite symmetric matrix A, an M-dimensional point V,
// and a "radius" R, such that
// (X-V)' * A * (X-V) <= R * R
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 14 August 2014
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int M, the spatial dimension.
//
// Input, double A[M*M], the matrix that describes
// the ellipsoid. A must be symmetric and positive definite.
//
// Input, double V[M], the "center" of the ellipse.
// The value of V is not actually needed by this function.
//
// Input, double R, the "radius" of the ellipse.
//
// Output, double ELLIPSOID_VOLUME, the volume of the ellipsoid.
//
{
int i;
double[] u = typeMethods.r8po_fa(m, a);
double sqrt_det = 1.0;
for (i = 0; i < m; i++)
{
sqrt_det *= u[i + i * m];
}
double volume = Math.Pow(r, m) * Hypersphere.hypersphere_unit_volume(m) / sqrt_det;
return(volume);
}
