bdschur

Block-diagonal Schur factorization

Syntax

[T,B,BLKS] = bdschur(A,CONDMAX)
[T,B] = bdschur(A,[],BLKS)


Description

[T,B,BLKS] = bdschur(A,CONDMAX) computes a transformation matrix T such that B = T \ A * T is block diagonal and each diagonal block is a quasi upper-triangular Schur matrix.

[T,B] = bdschur(A,[],BLKS) pre-specifies the desired block sizes. The input matrix A should already be in Schur form when you use this syntax.

Input Arguments

• A: Matrix for block-diagonal Schur factorization.

• CONDMAX: Specifies an upper bound on the condition number of T. By default, CONDMAX = 1e4. Use CONDMAX to control the tradeoff between block size and conditioning of T with respect to inversion. When CONDMAX is a larger value, the blocks are smaller and T becomes more ill-conditioned.

Output Arguments

• T: Transformation matrix.

• B: Matrix B = T \ A * T.

• BLKS: Vector of block sizes.

Version History

Introduced in R2008a

R2022a: Default value of CONDMAX input argument changed

The default value of CONDMAX input argument is now 1e4. Previously, the default value was 1/sqrt(eps). Increasing CONDMAX reduces the size of the eigenvalue clusters in the transformed model but also decreases the accuracy of the transformation. The new default value balances the conditioning and transformation accuracy. If you have code that relies on the default value of CONDMAX being 1/sqrt(eps), update your code to explicitly set this input argument.