###
Special similarity transformation of a state-space system

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

To apply a special similarity transformation to a system given as
a triple (A,B,C),
A <-- P * A * P, B <-- P * B, C <-- C * P,
where P is a matrix with 1 on the secondary diagonal, and with 0
in the other entries.

**Specification**
SUBROUTINE TB01YD( N, M, P, A, LDA, B, LDB, C, LDC, INFO )
C .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LDC, M, N, P
C .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )

**Arguments**
**Input/Output Parameters**

N (input) INTEGER
The order of the matrix A, the number of rows of matrix B
and the number of columns of matrix C.
N represents the dimension of the state vector. N >= 0.
M (input) INTEGER.
The number of columns of matrix B.
M represents the dimension of input vector. M >= 0.
P (input) INTEGER.
The number of rows of matrix C.
P represents the dimension of output vector. P >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading N-by-N part of this array must
contain the system state matrix A.
On exit, the leading N-by-N part of this array contains
the transformed matrix P*A*P.
LDA INTEGER
The leading dimension of the array A. LDA >= MAX(1,N).
B (input/output) DOUBLE PRECISION array, dimension (LDB,M)
On entry, the leading N-by-M part of this array must
contain the system input matrix B.
On exit, the leading N-by-M part of this array contains
the transformed matrix P*B.
LDB INTEGER
The leading dimension of the array B.
LDB >= MAX(1,N) if M > 0.
LDB >= 1 if M = 0.
C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
On entry, the leading P-by-N part of this array must
contain the system output matrix C.
On exit, the leading P-by-N part of this array contains
the transformed matrix C*P.
LDC INTEGER
The leading dimension of the array C. LDC >= MAX(1,P).

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

**Method**
The rows and/or columns of the matrices of the triplet (A,B,C)
are swapped in a special way.

**Numerical Aspects**
None.

**Further Comments**
None

**Example**
**Program Text**

None

**Program Data**
None

**Program Results**
None

**Return to Supporting Routines index**