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Sylvester Equations (G Dataflow)

Version:
    Last Modified: March 15, 2017

    Solves the Sylvester matrix equation.

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    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

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    matrix A

    Matrix A 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.

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    matrix B

    Matrix B in the Sylvester equation.

    This input accepts the following data types:

    • 2D array of double-precision, floating point numbers
    • 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.

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    matrix C

    Matrix C in the Sylvester equation.

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    sign

    Form of the Sylvester equation.

    Name Value Description
    Plus 0 op(A)X + X op(B) = aC, 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) = aC, where A is the input matrix A, B is the input matrix B, and C is the input matrix C.

    Default: Plus

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    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.

    error in does not contain an error error in contains an error
    If no error occurred before the node runs, the node begins execution normally.

    If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

    If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

    Default: No error

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    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

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    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

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    matrix X

    Solution of the Sylvester equation.

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    scale

    Scaling factor a of the Sylvester equation.

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    perturbed

    A Boolean that specifies whether this 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.
    False Does not use perturbed values to solve the Sylvester equation.
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    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.

    error in does not contain an error error in contains an error
    If no error occurred before the node runs, the node begins execution normally.

    If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

    If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

    Solving the Sylvester Matrix Equation

    The following equations define the Sylvester matrix equation:

    op(A)X + Xop(B) = aC

    or

    op(A)X - Xop(B) = aC

    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. When the solution of the Sylvester matrix equation is not unique, this node sets perturbed to True and might not return the correct solution.

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: This product does not support FPGA devices


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