Verilog Code for Matrix Inversion for Triangular Matrices

Matrix inversion is very much necessary for solving a linear system y=Ax. But it is difficult to compute inverse of matrix ‘A’ directly. Thus, we take help of either direct technique like Gaussian Elimination (GE) or matrix factorization-based techniques like QR factorization.

In GE method matrix ‘A’ is converted to an upper triangular matrix with unit diagonal. Then inverse of this upper diagonal matrix is computed to estimate the final value of ‘x’ vector. Similarly, in QR factorization, matrix ‘A’ is factored as A=QR, where ‘R’ is an upper triangular matrix. Now, inverse of matrix ‘R’ is computed to compute the inverse of matrix ‘A’.

Here, two architectures are provided to compute the inverse of triangular matrices. First architecture computes inverse of an upper triangular matrix with non-zero diagonal by vector-vector product. Second architecture is for computing inverse of matrices which are upper-triangular with unity diagonal. First architecture is useful in case of QR factorization and second one is useful for GE base linear system solving.

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