Performs the QZ decomposition of a pair of square matrices.
The first square matrix.
This input accepts a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.
Default: Empty array
The second square matrix.
Default: Empty array
Type of decomposition to perform.
Name | Value | Description |
---|---|---|
Generalized Hessenberg | 0 | Uses the generalized Hessenberg method. |
Generalized Schur | 1 | Uses the generalized Schur method. |
Default: Generalized Hessenberg
Method to order the generalized eigenvalues.
This input is available only when decomposition type is Generalized Schur.
Name | Value | Description |
---|---|---|
No Reorder | 0 | Does not change the order of the generalized eigenvalues. |
Real Ascending | 1 | Lists the generalized eigenvalues in ascending order according to the real parts. |
Real Descending | 2 | Lists the generalized eigenvalues in descending order according to the real parts. |
Magnitude Ascending | 3 | Lists the generalized eigenvalues in ascending order according to the magnitudes. |
Magnitude Descending | 4 | Lists the generalized eigenvalues in descending order according to the magnitudes. |
Default: No Reorder
Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.
Default: No error
A complex matrix that contains the generalized eigenvectors in its columns.
The orthogonal matrix.
Conditions for matrix Q when trans(Q) is the transpose matrix of Q
When trans(Q) is the transpose matrix of matrix Q, matrix Q satisfies the following conditions:
where
The orthogonal matrix.
Conditions for matrix Z when trans(Q) is the transpose matrix of Q
When trans(matrix Q) is the transpose matrix of matrix Q, matrix Z satisfies the following conditions:
where A is the input matrix A and Z is the output matrix Z.
Denominators of the generalized eigenvalues of the input matrix pair.
If beta is nonzero, alpha_{i}/beta_{i} is a generalized eigenvalue of the input matrix pair.
The following expressions define the QZ decomposition of a matrix pair (A, B).
A = QHZ^{H}
B = QTZ^{H}
where
If B is singular, matrix pair (A, B) has an infinite generalized eigenvalue. In other words, the output betai is zero. If αA - βB is singular for all α and β, matrix pair (A, B) is singular and has an indeterminate generalized eigenvalue. In other words, both beta_{i} and alpha_{i} are zeros. This node cannot order the generalized eigenvalues if there are indeterminate generalized eigenvalues.
Where This Node Can Run:
Desktop OS: Windows
FPGA: Not supported