Table Of Contents
Sylvester Equations (G Dataflow)
Solves the Sylvester matrix equation.
matrix type
Type of matrix A and matrix B.
Specifying the matrix type allows this node to execute more quickly by avoiding unnecessary computations, which could introduce numerical inaccuracy.
| Name | Value | Description |
|---|---|---|
| General | 0 | The input matrix is a matrix that you cannot describe with one of the other categories. |
| Upper Triangular | 3 | The input matrix is upper triangular. |
Default: Upper Triangular
matrix A
matrix B
Matrix B in the Sylvester equation.
This input accepts a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.
This input must be a square matrix or upper quasi-triangular matrix in canonical Schur form.
matrix C
Matrix C in the Sylvester equation.
sign
Form of the Sylvester equation.
| Name | Value | Description |
|---|---|---|
| Plus | 0 | op(A)X + X op(B) = a C, where A is the input matrix A, B is the input matrix B, and C is the input matrix C. |
| Minus | 1 | op(A)X - X op(B) = a C, where A is the input matrix A, B is the input matrix B, and C is the input matrix C. |
Default: Plus
error in
Error conditions that occur before this node runs.
The node responds to this input according to standard error behavior.
Standard Error Behavior
Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.
Default: No error
operation A
Operation this node performs on matrix A in the Sylvester equation.
| Name | Value | Description |
|---|---|---|
| Not Transposed | 0 | op(A) = A, where A is the input matrix A. |
| Transposed | 1 | op(A) = transpose of A, where A is the input matrix A. |
Default: Not Transposed
operation B
Operation this node performs on matrix B in the Sylvester equation.
| Name | Value | Description |
|---|---|---|
| Not Transposed | 0 | op(B) = B, where B is the input matrix B. |
| Transposed | 1 | op(B) = transpose of B, where B is the input matrix B. |
Default: Not Transposed
matrix X
Solution of the Sylvester equation.
scale
Scaling factor a of the Sylvester equation.
perturbed
A Boolean that returns whether the node uses perturbed values to solve the equation.
| True | Uses perturbed values to solve the Sylvester equation. The eigenvalues of matrix A and matrix B are common or close and indicate the solution of the Sylvester equation is not unique. If the solution of the Sylvester equation is not unique, the node might not return the correct solution. |
| False | Does not use perturbed values to solve the Sylvester equation. |
error out
Error information.
The node produces this output according to standard error behavior.
Standard Error Behavior
Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.
Solving the Sylvester Matrix Equation
The following equations define the Sylvester matrix equation:
op(A)X + Xop(B) = a C
or
op(A)X - Xop(B) = a C
where
- op(A) is A or the conjugate transpose of A
- op(B) is B or the conjugate transpose of B
- a is a scaling factor to avoid overflow in X
The Sylvester matrix equation has a unique solution if and only if λ ± β ≠ 0, where λ and β are the eigenvalues of A and B, respectively, and the sign (±) depends on the equation you want to solve.
Where This Node Can Run:
Desktop OS: Windows
FPGA: Not supported
Web Server: Not supported in VIs that run in a web application