1matlab(3)                           MEPACK                           matlab(3)
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NAME

6       matlab - MATLAB / GNU Octave Interface
7
8       MEPACK provides an interface for MATLAB and GNU Octave. The interface
9       is optional and its build need to be enabled separately. See
10       Installation for details. Once upon the interface is build, the files
11       either reside in
12
13       ${BUILDDIR}/matlab/matlab
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15
16        for the MATLAB interface and in
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18       ${BUILDDIR}/matlab/octave
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21        for the GNU Octave interface. These paths need to be added to your
22       MATLAB or GNU Octave search path.
23

Interface Functions

25       The MATLAB and GNU Octave interface provides access to all basic
26       routines of MEPACK. All function provide a detailed help page, which is
27       accessible via
28
29       help mepack_XXXXXX
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31
32       The following interfaces exist for general coefficient matrices:
33
34       • mepack_csylv: Solve the generalized coupled Sylvester equation
35         (CSYLV) $(AR m
36         LB=E,CR m
37         LD = F)$.
38
39       • mepack_csylv_dual: Solve the generalized coupled Sylvester equation
40         (CSYLV_DUAL) $(AR + CL = E, m
41         RB m
42         LD =F)$.
43
44       • mepack_glyap: Solve the generalized Lyapunov equation (GLYAP)
45         $AXB^{T} + BXA^T = Y$.
46
47       • mepack_gstein: Solve the generalized Stein equation (GSTEIN) $AXA^T -
48         EXE^T = Y$.
49
50       • mepack_gsylv: Solve the generalized Sylvester equation (GSYLV) $AXB m
51         CXD = Y$.
52
53       • mepack_lyap: Solve the standard Lyapunov equation (LYAP) $AX + XA^T =
54         Y$.
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56       • mepack_stein: Solve the standard Stein equation (STEIN) $AXA^T - X =
57         Y$.
58
59       • mepack_sylv2: Solve the discrete-time Sylvester equation (SYLV2) $AXB
60         - X = Y$.
61
62       • mepack_sylv: Solve the standard Sylvester equation (SYLV) $AXm
63         XB = Y$.
64
65       The following interfaces are available for (quasi-) triangular
66       coefficient matrices:
67
68       • mepack_tgcsylv: Solve the generalized coupled Sylvester equation
69         (CSYLV) $(AR m
70         LB=E,CR m
71         LD = F)$.
72
73       • mepack_tgcsylv_dual: Solve the generalized coupled Sylvester equation
74         (CSYLV_DUAL) $(AR + CL = E, m
75         RB m
76         LD =F)$.
77
78       • mepack_tglyap: Solve the generalized Lyapunov equation (GLYAP)
79         $AXB^{T} + BXA^T = Y$.
80
81       • mepack_tgstein: Solve the generalized Stein equation (GSTEIN) $AXA^T
82         - EXE^T = Y$.
83
84       • mepack_tgsylv: Solve the generalized Sylvester equation (GSYLV) $AXB
85         m
86         CXD = Y$.
87
88       • mepack_trlyap: Solve the standard Lyapunov equation (LYAP) $AX + XA^T
89         = Y$.
90
91       • mepack_trstein: Solve the standard Stein equation (STEIN) $AXA^T - X
92         = Y$.
93
94       • mepack_trsylv2: Solve the discrete-time Sylvester equation (SYLV2)
95         $AXB - X = Y$.
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97       • mepack_trsylv: Solve the standard Sylvester equation (SYLV) $AXm
98         XB = Y$.
99
100       The following routines implement the iterative refinement strategy:
101
102       • mepack_csylv_refine: Solve the generalized coupled Sylvester equation
103         (CSYLV) $(AR m
104         LB=E,CR m
105         LD = F)$.
106
107       • mepack_csylv_dual_refine: Solve the generalized coupled Sylvester
108         equation (CSYLV_DUAL) $(AR + CL = E, m
109         RB m
110         LD =F)$.
111
112       • mepack_glyap_refine: Solve the generalized Lyapunov equation (GLYAP)
113         $AXB^{T} + BXA^T = Y$.
114
115       • mepack_gstein_refine: Solve the generalized Stein equation (GSTEIN)
116         $AXA^T - EXE^T = Y$.
117
118       • mepack_gsylv_refine: Solve the generalized Sylvester equation (GSYLV)
119         $AXB m
120         CXD = Y$.
121
122       • mepack_lyap_refine: Solve the standard Lyapunov equation (LYAP) $AX +
123         XA^T = Y$.
124
125       • mepack_stein_refine: Solve the standard Stein equation (STEIN) $AXA^T
126         - X = Y$.
127
128       • mepack_sylv2_refine: Solve the discrete-time Sylvester equation
129         (SYLV2) $AXB - X = Y$.
130
131       • mepack_sylv_refine: Solve the standard Sylvester equation (SYLV) $AXm
132         XB = Y$.
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Known Issues

135   MATLAB and OpenMP Codes
136       Due to bugs in MATLABs GNU OpenMP - Intel OpenMP wrapper, algorithms
137       using OpenMP's task dependencies are disable when calling the interface
138       from MATLAB. The algorithms can be enabled at runtime by setting the
139       openmp value in the optional options structure to 1.
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143Version 1.1.0                   Wed Oct 18 2023                      matlab(3)