Performs Cholesky factorization on a symmetric or Hermitian positive definite matrix. Wire data to the A input to determine the polymorphic instance to use or manually select the instance.


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Inputs/Outputs

  • c2ddbl.png A —

    A is a symmetric positive definite matrix.

    If A is not symmetric, this VI uses only the upper triangular portion of A.

  • i2ddbl.png Cholesky —

    Cholesky contains the factored, upper triangular matrix R.

  • ii32.png error —

    error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

    • The following equations show the factorization of A for real cases and complex cases, respectively:

    A = RTR A = RHR

    where R is an upper triangular matrix, and all the diagonal elements of R are positive.

    The Cholesky factorization exists only if the matrix A is positive definite and either symmetric or Hermitian. If A is not symmetric or Hermitian, this VI uses only the upper triangular portion of A. If A is not positive definite, this VI returns an error.

    You can use Cholesky factorization to solve linear equations. For example, to solve the linear equation Ax = b, where A is a positive symmetric matrix and A = RTR, you can derive the following equations: Rx = h, and h = R–Tb. Then you can use the triangular property of matrix R to solve the equations.

    Examples

    Refer to the following example files included with LabVIEW.

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