Forward Substitution

Solving a system of equations of the form with respect to for the case where is a lower triangular matrix.

forward substitution

Description

Block Forward Substitution solves the system of linear equations by simple direct substitution of variables, where:

- M by M lower triangular matrix; input signal at port L.
- matrix M by N; input signal on port B.
- output matrix M by N; solution of the system of equations.

The block does not check the rank of the inputs. The unit uses only elements above the main diagonal of the matrix and ignores elements below. If the parameter Input L is unit-upper triangular is set, the block assumes that the elements on the main diagonal of are equal to 1. This is useful when the matrix is the result of another operation, such as an LDL decomposition that uses diagonal elements to represent the matrix .

Ports

Input

L is a lower triangular matrix
`matrix M by M

The input lower triangular matrix L is of size M by M. The inputs L and B must have the same number of rows.

Data types: Float64

B - matrix B
matrix M on N | vector M on 1

The matrix B in the equation is of size M by N or a vector of size M by 1.

If an M by 1 vector is given, the block treats it as an M by 1 matrix. The inputs L and B must have the same number of rows.

Data types: Float64

Output

X is a solution to the system of equations
matrix M on N | vector M on 1

The block finds the solution of the equations in the form of a matrix of size M by N or a vector of size M by 1. The size of the matrix X is the same as the size of the matrix B.

Data types: Float64

Parameters

Input L is unit-upper triangular - diagonal elements of input matrix have value 1
` off (by default)` | ` on`

Tick this checkbox only if all elements on the L diagonal have the value 1. This optimises the block’s behaviour by skipping the unnecessary division operation.

Do not select this check box if any elements on the L diagonal are not equal to 1. When you uncheck Input L is unit-upper triangular, the unit always performs the division operation.

Diagonal of complex input L is real - diagonal elements of complex input L are real
Off (by default) | On

Select the checkbox to optimise the simulation speed when the diagonal elements of complex input L are real.

Dependencies

This parameter is only displayed if the Input L is unit-upper triangular parameter is not selected for input L.