bdschur

Block diagonalization with the Schur factorization.

Syntax

[T,B] = bdschur(A))

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

Inputs

A
A square matrix in the real Schur form.
CONDMAX
The upper limit for the infinity norm of elementary sub-matrices of the individual transformations used for reduction.

Outputs

T
Transformation matrix.
B
Matrix as B = T \ A * T.

Example

Example including the bdschur function: 
A = [ 1.   -1.    1.    2.    3.    1.    2.    3.;
   1.    1.    3.    4.    2.    3.    4.    2.;
   0.    0.    1.   -1.    1.    5.    4.    1.;
   0.    0.    0.    1.   -1.    3.    1.    2.;
   0.    0.    0.    1.    1.    2.    3.   -1.;
   0.    0.    0.    0.    0.    1.    5.    1.;
   0.    0.    0.    0.    0.    0.    0.99999999   -0.99999999;
   0.    0.    0.    0.    0.    0.    0.99999999    0.99999999];
   [T, B] = bdschur(A)

T = [Matrix] 8 x 8 Rows[1:8]
1.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00   9.04534e-01   1.95685e-01
0.00000e+00   1.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00  -3.01511e-01   9.75458e-01
0.00000e+00  -0.00000e+00   8.16497e-01  -2.77556e-17  -5.76811e-01  -1.56454e-02  -3.01511e-01   1.48246e-02
0.00000e+00  -0.00000e+00  -4.08248e-01   7.07107e-01  -5.76811e-01  -1.56454e-02   2.04391e-17  -5.33685e-02
0.00000e+00  -0.00000e+00  -4.08248e-01  -7.07107e-01  -5.76811e-01  -1.56454e-02   4.12647e-17   8.00528e-02
0.00000e+00  -0.00000e+00   0.00000e+00  -0.00000e+00  -2.76132e-02   9.80452e-01   7.15878e-18   2.66843e-02
0.00000e+00  -0.00000e+00   0.00000e+00  -0.00000e+00   3.32343e-02  -6.58864e-03  -1.29651e-18  -1.78170e-18
0.00000e+00  -0.00000e+00   0.00000e+00  -0.00000e+00   1.12423e-03   1.94773e-01   9.76197e-19  -2.28057e-18  
B = [Matrix] 8 x 8
1.00000e+00  -1.00000e+00  -1.22474e+00  -7.07107e-01  -3.41864e+00   1.45772e+00  0.00000e+00   0.00000e+00
1.00000e+00   1.00000e+00   1.66533e-16   1.41421e+00  -5.13895e+00   3.16374e+00  0.00000e+00   0.00000e+00
0.00000e+00   0.00000e+00   1.00000e+00  -1.73205e+00  -1.63479e-03   2.07010e+00  0.00000e+00   0.00000e+00
0.00000e+00   0.00000e+00   5.77350e-01   1.00000e+00   7.51592e-01   1.13790e+00  0.00000e+00   0.00000e+00
0.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00   1.00000e+00  -5.86059e+00  0.00000e+00   0.00000e+00
0.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00   1.70631e-01   1.00000e+00  0.00000e+00   0.00000e+00
0.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00  1.00000e+00  -8.85017e-01
0.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00   0.00000e+00  0.00000e+00   1.00000e+00

Comments

Based on the SLICOT library function mb03rd.