Owning Palette: Linear Algebra VIs
Requires: Full Development System
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.
Use the pull-down menu to select an instance of this VI.
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A is a symmetric positive definite matrix. If A is not symmetric, this VI uses only the upper triangular portion of A. |
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Cholesky contains the factored, upper triangular matrix R. |
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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. |
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A is a Hermitian positive definite matrix. If A is not Hermitian, this VI uses only the upper triangular portion of A. |
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Cholesky R contains the factored upper triangular matrix R. |
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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.
Refer to the Linear Algebra Calculator VI in the labview\examples\Mathematics\Linear Algebra directory for an example of using the Cholesky Factorization VI.
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