R: Systematic Scenario Selection for Stress Testing

# Systematic Scenario Selection for Stress Testing

## Documentation for package ‘SyScSelection’ version 1.0.2

- DESCRIPTION file
- User guides, package vignettes and other documentation
- Package README

## Help Pages

baseb_expansion | Adds the next base-b element to an existing base-b sequence
calc_mesh_size | Calculates the number of points in a mesh of fineness phi, covering a hypercube in d dimensions
center_at_origin | Creates a new ellipsoid object equivalent to the given hyperellipsoid (hellipse), but centered at the origin.
fill_adj_2Dface | Creates a phi x phi grid (i.e., the mesh on a single two-dimensional face of a larger hypercube) of d-dimensional points, where the regularity of the grid has been adjusted to avoid clustering in the corners.
fill_adj_2Dface_beta | Calculates the factor, beta in [0, 1], that interpolates the pth equidistant point between the two endpoints, z_one and z_phi, for and adjusted 2D mesh of fineness phi in d dimensions.
fill_corners | Systematically fills a given mesh array (cmesh) with d-dimensional points representing every corner of a d-dimensional hypercube. The function fills the successive dimensions of each point via depth-first recursion across all d dimensions.
get | Get hyperellipsoid property from the specified object and return the value. Property names are: center, shape, and size
hypercube_mesh | Generates a Cartesian mesh of d-dimensional scenarios based on the given ellipsoid. This function does not assume that the ellipsoid is centered at the origin.
hyperellipsoid | Hyperellipsoid class constructor
make_corners | Fills a mesh (corn_mesh) with d-dimensional points representing all corners of a d-dimensional cube encompassing a d-dimensional unit spheroid.
make_edges | Fills a mesh with d-dimensional points representing all non-corner edge points of a d-dimensional cube encompassing a d-dimensional unit spheroid.
make_ellipsoid_from_vertices | Constructs a new d-dimensional ellipsoid with the given "positive vertices", and size parameter, c. The constructed ellipsoid is centered at the origin.Note that the input vertices (i.e., the columns of V) must therefore be orthogonal vectors, themselves centered at the origin.The size parameter, c, may be needed because the points alone only determine the eigenvalues up to a positive constant. For vertices which fall on the constructed ellipsoid, choose as the size parameterc = 1.The new ellipsoid is centered at the origin.
make_faces | Fills a mesh with d-dimensional points representing all non-edge face points of a d-dimensional cube encompassing a d-dimensional unit spheroid.
new_baseb_expansion | Creates a new base-b sequence of a designated length
rotate_to_coordaxes | Rotates the ellipsoid (hellip) so its principal axes align with the coordinate axes. Both ellipsoids are centered at the origin. Note that there are (2^d)*d! valid ways to rotate the ellipsoid to the axes. This algorithm does not prescribe which solution will be provided.
sizeparam_normal_distn | Calculates the size paramater for a d-dimensional hyperellipsoid conforming to a normal (i.e., Gaussian) distribution.
sizeparam_t_distn | Calculates the size paramater for a d-dimensional hyperellipsoid conforming to a Student's t distribution.
spheroid_mesh | Generates a Cartesian mesh of d-dimensional scenarios based on the given ellipsoid. This function does not assume that the ellipsoid is centered at the origin.
stretch_to_unitspheroid | Stretches the ellipsoid (hellip) to the unit spheroid of the same dimension. Both the input ellipsoid and unit spheroid are centered at the origin.
transform_ellipsoid | Applies the given linear transformation, tfm, to the given ellipsoid. The ellipsoid (hellip) must be centered at the origin.
univariate_shocks | Calculates 2d d-dimensional univariate shocks (up and down in each of the d dimensions) based on the given ellipsoid. Univariate shocks are points on the surface of the ellipsoid that differ from the center of the ellipsoid in only one dimension. Thus, for an ellipsoid centered at the origin, only one element of a d-dimensional shock will be non-zero.This function does not assume that the ellipsoid is centered at the origin.
vertices | Finds the d d-dimensional positive vertices for the given ellipsoid. A "positive" vertex is one where a principal axis for the ellipsoid intersects the surface of the ellipsoid in the direction of the corresponding eigenvector. (Recall that each of the eigenvectors of the ellipsoid's shape matrix is collinear with one of the principal axes.) This function does not assume that the ellipsoid is centered at the origin. Because the direction of each unit eigenvector is arbitrary (i.e., multiplication by -1 still yields a unit eigenvector), a simple algorithm is used to pick a consistent orientation for the vertex points.