schur

swordfish.function.schur()

Compute the Schur decomposition of a square matrix.

Suppose the input is the square matrix A:

• If sort is not specified, return 2 matrices: T (Schur form of A, an upper triangular matrix) and an unitary matrix Z (the transpose matrix of Z is equal to its inverse matrix), so that A = Z*T*Z-1.

• If sort is specified, the function will also return an integer indicating the number of eigenvalues that meet the sorting conditions.

Parameters:

• obj (Constant) – A square matrix.

• sort (Constant, optional) –

  A string, by default DFLT.

  It is used to reorder the factors according to a specified ordering of the eigenvalues. The value can be ‘lhp’ (eigenvalue is a negative real number), ‘rhp’ (eigenvalue is a positive real number), ‘iuc’ (the absolute value of a complex eigenvalue<=1.0), ‘ouc’ (the absolute value of a complex eigenvalue>1.0).