## AG07BD

### Descriptor inverse of a state-space or descriptor representation

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

```  To compute the inverse (Ai-lambda*Ei,Bi,Ci,Di) of a given
descriptor system (A-lambda*E,B,C,D).

```
Specification
```      SUBROUTINE AG07BD( JOBE, N, M, A, LDA, E, LDE, B, LDB, C, LDC,
\$                   D, LDD, AI, LDAI, EI, LDEI, BI, LDBI, CI, LDCI,
\$                   DI, LDDI, INFO )
C     .. Scalar Arguments ..
CHARACTER          JOBE
INTEGER            INFO, LDA, LDAI, LDB, LDBI, LDC, LDCI,
\$                   LDD, LDDI, LDE, LDEI, M, N
C     .. Array Arguments ..
DOUBLE PRECISION   A(LDA,*), AI(LDAI,*), B(LDB,*), BI(LDBI,*),
\$                   C(LDC,*), CI(LDCI,*), D(LDD,*), DI(LDDI,*),
\$                   E(LDE,*), EI(LDEI,*)

```
Arguments

Mode Parameters

```  JOBE    CHARACTER*1
Specifies whether E is a general square or an identity
matrix as follows:
= 'G':  E is a general square matrix;
= 'I':  E is the identity matrix.

```
Input/Output Parameters
```  N       (input) INTEGER
The order of the square matrices A and E;
also the number of rows of matrix B and the number of
columns of matrix C.  N >= 0.

M       (input) INTEGER
The number of system inputs and outputs, i.e., the number
of columns of matrices B and D and the number of rows of
matrices C and D.  M >= 0.

A       (input) DOUBLE PRECISION array, dimension (LDA,N)
The leading N-by-N part of this array must contain the
state matrix A of the original system.

LDA     INTEGER
The leading dimension of the array A.  LDA >= MAX(1,N).

E       (input) DOUBLE PRECISION array, dimension (LDE,N)
If JOBE = 'G', the leading N-by-N part of this array must
contain the descriptor matrix E of the original system.
If JOBE = 'I', then E is assumed to be the identity
matrix and is not referenced.

LDE     INTEGER
The leading dimension of the array E.
LDE >= MAX(1,N), if JOBE = 'G';
LDE >= 1,        if JOBE = 'I'.

B       (input) DOUBLE PRECISION array, dimension (LDB,M)
The leading N-by-M part of this array must contain the
input matrix B of the original system.

LDB     INTEGER
The leading dimension of the array B.  LDB >= MAX(1,N).

C       (input) DOUBLE PRECISION array, dimension (LDC,N)
The leading M-by-N part of this array must contain the
output matrix C of the original system.

LDC     INTEGER
The leading dimension of the array C.  LDC >= MAX(1,M).

D       (input) DOUBLE PRECISION array, dimension (LDD,M)
The leading M-by-M part of this array must contain the
feedthrough matrix D of the original system.

LDD     INTEGER
The leading dimension of the array D.  LDD >= MAX(1,M).

AI      (output) DOUBLE PRECISION array, dimension (LDAI,N+M)
The leading (N+M)-by-(N+M) part of this array contains
the state matrix Ai of the inverse system.
If LDAI = LDA >= N+M, then AI and A can share the same
storage locations.

LDAI    INTEGER
The leading dimension of the array AI.
LDAI >= MAX(1,N+M).

EI      (output) DOUBLE PRECISION array, dimension (LDEI,N+M)
The leading (N+M)-by-(N+M) part of this array contains
the descriptor matrix Ei of the inverse system.
If LDEI = LDE >= N+M, then EI and E can share the same
storage locations.

LDEI    INTEGER
The leading dimension of the array EI.
LDEI >= MAX(1,N+M).

BI      (output) DOUBLE PRECISION array, dimension (LDBI,M)
The leading (N+M)-by-M part of this array contains
the input matrix Bi of the inverse system.
If LDBI = LDB >= N+M, then BI and B can share the same
storage locations.

LDBI    INTEGER
The leading dimension of the array BI.
LDBI >= MAX(1,N+M).

CI      (output) DOUBLE PRECISION array, dimension (LDCI,N+M)
The leading M-by-(N+M) part of this array contains
the output matrix Ci of the inverse system.
If LDCI = LDC, CI and C can share the same storage
locations.

LDCI    INTEGER
The leading dimension of the array CI.  LDCI >= MAX(1,M).

DI      (output) DOUBLE PRECISION array, dimension (LDDI,M)
The leading M-by-M part of this array contains
the feedthrough matrix Di = 0 of the inverse system.
DI and D can share the same storage locations.

LDDI    INTEGER
The leading dimension of the array DI.  LDDI >= MAX(1,M).

```
Error Indicator
```  INFO    INTEGER
= 0:  successful exit;
< 0:  if INFO = -i, the i-th argument had an illegal
value.

```
Method
```  The matrices of the inverse system are computed with the formulas

( E  0 )        ( A  B )         (  0 )
Ei = (      ) , Ai = (      ) ,  Bi = (    ),
( 0  0 )        ( C  D )         ( -I )

Ci = ( 0  I ),  Di = 0.

```
```  The routine does not perform an invertibility test. This check can
be performed by using the SLICOT routines AB08NX or AG08BY.

```
Example

Program Text

```  None
```
Program Data
```  None
```
Program Results
```  None
```