Performs the LU factorization of A so that PA = LU. Wire data to the A input to determine the polymorphic instance to use or manually select the instance.


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The LU Factorization VI factors an m × n matrix A into the following types of matrices so that PA = LU:

  • L is an m × min(m, n) matrix. When m ≤ n, L is a lower triangular matrix with ones on the diagonal. When m > n, L is a lower trapezoidal matrix with ones on the diagonal.
  • U is a min(m, n) × n matrix. When m ≥ n, U is an upper triangular matrix. When m < n, U is an upper trapezoidal matrix.
  • P is an m × m permutation matrix, which serves as the identity matrix with some rows exchanged.

For a singular matrix, the VI completes the factorization and returns a warning, and there is at least one zero at the diagonal of U.

The following equation illustrates one useful property of LU factorization when A is a square matrix:

where det(A) is the determinant of A.

LU factorization serves as a key step for inverting a matrix, computing the determinant of a matrix, and solving a linear equation.

Examples

Refer to the following example files included with LabVIEW.

  • labview\examples\Mathematics\Linear Algebra\Linear Algebra Calculator.vi