check_Bt_Cpp: Check Matrix B Invertibility with C++ (Internal Function)

In sstvars: Toolkit for Reduced Form and Structural Smooth Transition Vector Autoregressive Models

Check Matrix B Invertibility with C++ (Internal Function)

Description

This internal function takes a cube of matrices (all_Omegas), a matrix of weights (alpha_mt), and a numerical tolerance (posdef_tol) to check the invertibility of weighted sums of the matrices in the cube. For each row in alpha_mt, it computes a weighted sum of matrices, and checks if this sum is invertible by verifying that its determinant is not within the specified tolerance of zero.

Usage

check_Bt_Cpp(all_Omegas, alpha_mt, posdef_tol)

Arguments

all_Omegas	A cube (3D array) of impact matrices, with each slice being an inveritble square matrix.
alpha_mt	A matrix of weights, with as many columns as there are slices in all_Omegas.
posdef_tol	A strictly positive small number used as a tolerance for checking the invertibility of the matrix. The matrix is considered non-invertible if its determinant is less than this tolerance.

Value

A boolean value: 'TRUE' if all weighted sums are invertible up to the specified tolerance, 'FALSE' otherwise.

sstvars documentation built on April 11, 2025, 5:47 p.m.