PseudoInverse Matrix (Not in Base Package)

Finds the PseudoInverse Matrix of Input Matrix. You can use this polymorphic VI to find the pseudoinverse matrix of a real rectangular matrix or a complex rectangular matrix. The data type you wire to the Input Matrix input determines the polymorphic instance to use. Details  Example

Real PseudoInverse Matrix

	Input Matrix is a rectangular, real matrix. When Input Matrix is not a square matrix, or when Input Matrix is singular, the inverse of Input Matrix does not exist. You can compute the pseudoinverse of Input Matrix instead. Using the Inverse Matrix VI to compute is more efficient than using this VI.
	tolerance defines a level such that the number of singular values greater than this level is the rank of Input Matrix. The default is –1. If tolerance is negative, the internal tolerance used to determine rank is set as shown in the following equation. tolerance = max(m,n)*||A||*, where A represents the Input Matrix, m represents the number of rows in A, n represents the number of columns in A, ||A|| is the 2-norm of A, is the smallest, floating point number that can be represented by type double, as shown in the following relationship. = 2–52 = 2.22e – 16
	PseudoInverse Matrix is the pseudoinverse matrix of the Input Matrix. If Input Matrix A is square and not singular, then the pseudoinverse is the same as the inverse of a matrix, and the Inverse Matrix VI should be used as a more efficient method of computing the inverse of the Input Matrix.
	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.

Complex Pseudoinverse Matrix

	Input Matrix is usually a rectangular complex matrix. When Input Matrix is not a square matrix, or when Input Matrix is singular, the inverse of Input Matrix does not exist. You can compute the pseudoinverse of Input Matrix instead.
	tolerance defines a level such that the number of singular values greater than this level is the rank of Input Matrix. The default is –1. If tolerance is negative, the internal tolerance used to determine rank is set as shown in the following equation. tolerance = max(m,n)*||A||*, where A represents the Input Matrix, m represents the number of rows in A, n represents the number of columns in A, ||A|| is the 2-norm of A, is the smallest, floating point number that can be represented by type double, as shown in the following relationship. = 2–52 = 2.22e – 16
	PseudoInverse Matrix is the pseudoinverse matrix of Input Matrix. If Input Matrix is square and not singular, then the pseudoinverse is the same as the inverse of a matrix, and the Inverse Matrix VI should be used as a more efficient method of computing the inverse of the Input Matrix.
	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.

PseudoInverse Matrix Details

The VI computes PseudoInverse Matrix A⁺ by using the SVD algorithm. Singular values less than the tolerance are set to zero.

The m-by-n matrix A⁺ is called the pseudoinverse of matrix A if A⁺ satisfies the following four Moore-Penrose conditions:

1. A A⁺ A = A.
2. A⁺ A A⁺ = A⁺.
3. A A⁺ is a symmetric matrix.
4. A⁺ A is a symmetric matrix.

Complex

The Complex Pseudoinverse Matrix A⁺ is computed using the SVD algorithm where the singular values are compared to tolerance before they are used in the PseudoInverse computation.

The m-by-n matrix A⁺ is called the pseudoinverse of matrix A if A⁺ satisfies the following four Moore-Penrose conditions:

Example

Refer to the Linear Algebra Calculator VI in the labview\examples\analysis\linaxmpl.llb directory for an example of using the PseudoInverse Matrix VI.