Important: The linalg package has been deprecated. Use the superseding packages, LinearAlgebra and VectorCalculus, instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

forwardsub generates a solution vector x to the equation .

If b is omitted, or b is 'false' then L is assumed to be an augmented matrix and the last column of L is used in place of b.

If b is a matrix, then x (the solution) will also be a matrix with the same number of columns.

If L is the result of applying Gaussian elimination to the augmented matrix of a system of linear equations, as might be obtained from LUdecomp, forwardsub completes the solution by forward substitution.  If a solution exists, it is returned as a vector. If no solution exists, an error will be generated.

If the solution is not unique, it will be parameterized in terms of the symbols v[1], v[2], ..., etc. or v[1,k], v[2,k], ... as in the case where b is a matrix. If the third argument v is not specified, the global variable _t will be used.

The input matrix must be in row-echelon form with all zero rows grouped at the top. Such a matrix is produced by obtaining the LU decomposition.

The command with(linalg,forwardsub) allows the use of the abbreviated form of this command.