TF01MY

Output sequence of a linear time-invariant open-loop system (variant)

Purpose

  To compute the output sequence of a linear time-invariant
  open-loop system given by its discrete-time state-space model
  (A,B,C,D), where A is an N-by-N general matrix.

  The initial state vector x(1) must be supplied by the user.

  This routine differs from SLICOT Library routine TF01MD in the
  way the input and output trajectories are stored.

      SUBROUTINE TF01MY( N, M, P, NY, A, LDA, B, LDB, C, LDC, D, LDD,
     $                   U, LDU, X, Y, LDY, DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
      INTEGER           INFO, LDA, LDB, LDC, LDD, LDU, LDWORK, LDY, M,
     $                  N, NY, P
C     .. Array Arguments ..
      DOUBLE PRECISION  A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*),
     $                  DWORK(*), U(LDU,*), X(*), Y(LDY,*)

Input/Output Parameters

  N       (input) INTEGER
          The order of the matrix A.  N >= 0.

  M       (input) INTEGER
          The number of system inputs.  M >= 0.

  P       (input) INTEGER
          The number of system outputs.  P >= 0.

  NY      (input) INTEGER
          The number of output vectors y(k) to be computed.
          NY >= 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 system.

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

  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 system.

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

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

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

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

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

  U       (input) DOUBLE PRECISION array, dimension (LDU,M)
          The leading NY-by-M part of this array must contain the
          input vector sequence u(k), for k = 1,2,...,NY.
          Specifically, the k-th row of U must contain u(k)'.

  LDU     INTEGER
          The leading dimension of array U.  LDU >= MAX(1,NY).

  X       (input/output) DOUBLE PRECISION array, dimension (N)
          On entry, this array must contain the initial state vector
          x(1) which consists of the N initial states of the system.
          On exit, this array contains the final state vector
          x(NY+1) of the N states of the system at instant NY+1.

  Y       (output) DOUBLE PRECISION array, dimension (LDY,P)
          The leading NY-by-P part of this array contains the output
          vector sequence y(1),y(2),...,y(NY) such that the k-th
          row of Y contains y(k)' (the outputs at instant k),
          for k = 1,2,...,NY.

  LDY     INTEGER
          The leading dimension of array Y.  LDY >= MAX(1,NY).

  DWORK   DOUBLE PRECISION array, dimension (LDWORK)
          On exit, if INFO = 0, DWORK(1) returns the optimal LDWORK.

  LDWORK  INTEGER
          The length of the array DWORK.  LDWORK >= MAX(1,N).
          For better performance, LDWORK should be larger.

          If LDWORK = -1, then a workspace query is assumed;
          the routine only calculates the optimal size of the
          DWORK array, returns this value as the first entry of
          the DWORK array, and no error message related to LDWORK
          is issued by XERBLA.

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

  Given an initial state vector x(1), the output vector sequence
  y(1), y(2),..., y(NY) is obtained via the formulae

     x(k+1) = A x(k) + B u(k)
     y(k)   = C x(k) + D u(k),

  where each element y(k) is a vector of length P containing the
  outputs at instant k and k = 1,2,...,NY.

  [1] Luenberger, D.G.
      Introduction to Dynamic Systems: Theory, Models and
      Applications.
      John Wiley & Sons, New York, 1979.

  The algorithm requires approximately (N + M) x (N + P) x NY
  multiplications and additions.

  The implementation exploits data locality and uses BLAS 3
  operations as much as possible, given the workspace length.

Program Text

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