359 lines
11 KiB
FortranFixed
359 lines
11 KiB
FortranFixed
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SUBROUTINE TF01MY( N, M, P, NY, A, LDA, B, LDB, C, LDC, D, LDD,
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$ U, LDU, X, Y, LDY, DWORK, LDWORK, INFO )
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C
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C SLICOT RELEASE 5.0.
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C
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C Copyright (c) 2002-2009 NICONET e.V.
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C
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C This program is free software: you can redistribute it and/or
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C modify it under the terms of the GNU General Public License as
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C published by the Free Software Foundation, either version 2 of
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C the License, or (at your option) any later version.
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C
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C This program is distributed in the hope that it will be useful,
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C but WITHOUT ANY WARRANTY; without even the implied warranty of
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C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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C GNU General Public License for more details.
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C
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C You should have received a copy of the GNU General Public License
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C along with this program. If not, see
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C <http://www.gnu.org/licenses/>.
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C
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C PURPOSE
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C
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C To compute the output sequence of a linear time-invariant
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C open-loop system given by its discrete-time state-space model
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C (A,B,C,D), where A is an N-by-N general matrix.
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C
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C The initial state vector x(1) must be supplied by the user.
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C
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C This routine differs from SLICOT Library routine TF01MD in the
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C way the input and output trajectories are stored.
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C
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C ARGUMENTS
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C
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C Input/Output Parameters
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C
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C N (input) INTEGER
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C The order of the matrix A. N >= 0.
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C
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C M (input) INTEGER
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C The number of system inputs. M >= 0.
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C
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C P (input) INTEGER
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C The number of system outputs. P >= 0.
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C
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C NY (input) INTEGER
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C The number of output vectors y(k) to be computed.
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C NY >= 0.
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C
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C A (input) DOUBLE PRECISION array, dimension (LDA,N)
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C The leading N-by-N part of this array must contain the
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C state matrix A of the system.
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C
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C LDA INTEGER
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C The leading dimension of array A. LDA >= MAX(1,N).
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C
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C B (input) DOUBLE PRECISION array, dimension (LDB,M)
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C The leading N-by-M part of this array must contain the
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C input matrix B of the system.
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C
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C LDB INTEGER
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C The leading dimension of array B. LDB >= MAX(1,N).
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C
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C C (input) DOUBLE PRECISION array, dimension (LDC,N)
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C The leading P-by-N part of this array must contain the
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C output matrix C of the system.
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C
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C LDC INTEGER
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C The leading dimension of array C. LDC >= MAX(1,P).
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C
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C D (input) DOUBLE PRECISION array, dimension (LDD,M)
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C The leading P-by-M part of this array must contain the
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C direct link matrix D of the system.
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C
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C LDD INTEGER
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C The leading dimension of array D. LDD >= MAX(1,P).
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C
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C U (input) DOUBLE PRECISION array, dimension (LDU,M)
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C The leading NY-by-M part of this array must contain the
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C input vector sequence u(k), for k = 1,2,...,NY.
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C Specifically, the k-th row of U must contain u(k)'.
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C
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C LDU INTEGER
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C The leading dimension of array U. LDU >= MAX(1,NY).
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C
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C X (input/output) DOUBLE PRECISION array, dimension (N)
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C On entry, this array must contain the initial state vector
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C x(1) which consists of the N initial states of the system.
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C On exit, this array contains the final state vector
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C x(NY+1) of the N states of the system at instant NY+1.
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C
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C Y (output) DOUBLE PRECISION array, dimension (LDY,P)
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C The leading NY-by-P part of this array contains the output
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C vector sequence y(1),y(2),...,y(NY) such that the k-th
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C row of Y contains y(k)' (the outputs at instant k),
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C for k = 1,2,...,NY.
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C
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C LDY INTEGER
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C The leading dimension of array Y. LDY >= MAX(1,NY).
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C
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C Workspace
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C
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C DWORK DOUBLE PRECISION array, dimension (LDWORK)
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C
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C LDWORK INTEGER
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C The length of the array DWORK. LDWORK >= N.
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C For better performance, LDWORK should be larger.
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C
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C Error Indicator
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C
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C INFO INTEGER
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C = 0: successful exit;
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C < 0: if INFO = -i, the i-th argument had an illegal
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C value.
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C
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C METHOD
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C
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C Given an initial state vector x(1), the output vector sequence
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C y(1), y(2),..., y(NY) is obtained via the formulae
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C
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C x(k+1) = A x(k) + B u(k)
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C y(k) = C x(k) + D u(k),
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C
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C where each element y(k) is a vector of length P containing the
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C outputs at instant k and k = 1,2,...,NY.
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C
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C REFERENCES
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C
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C [1] Luenberger, D.G.
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C Introduction to Dynamic Systems: Theory, Models and
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C Applications.
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C John Wiley & Sons, New York, 1979.
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C
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C NUMERICAL ASPECTS
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C
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C The algorithm requires approximately (N + M) x (N + P) x NY
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C multiplications and additions.
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C
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C FURTHER COMMENTS
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C
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C The implementation exploits data locality and uses BLAS 3
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C operations as much as possible, given the workspace length.
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C
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C CONTRIBUTOR
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C
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C V. Sima, Research Institute for Informatics, Bucharest, Mar. 2001.
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C
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C REVISIONS
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C
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C -
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C
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C KEYWORDS
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C
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C Discrete-time system, multivariable system, state-space model,
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C state-space representation, time response.
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C
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C ******************************************************************
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C
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C .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
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C .. Scalar Arguments ..
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INTEGER INFO, LDA, LDB, LDC, LDD, LDU, LDWORK, LDY, M,
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$ N, NY, P
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C .. Array Arguments ..
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DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*),
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$ DWORK(*), U(LDU,*), X(*), Y(LDY,*)
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C .. Local Scalars ..
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INTEGER IK, IREM, IS, IYL, MAXN, NB, NS
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DOUBLE PRECISION UPD
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C .. External Functions ..
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INTEGER ILAENV
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EXTERNAL ILAENV
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C .. External Subroutines ..
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EXTERNAL DCOPY, DGEMM, DGEMV, DLASET, XERBLA
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C .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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C .. Executable Statements ..
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C
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INFO = 0
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C
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C Test the input scalar arguments.
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C
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MAXN = MAX( 1, N )
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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( M.LT.0 ) THEN
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INFO = -2
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ELSE IF( P.LT.0 ) THEN
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INFO = -3
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ELSE IF( NY.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDA.LT.MAXN ) THEN
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INFO = -6
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ELSE IF( LDB.LT.MAXN ) THEN
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INFO = -8
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ELSE IF( LDC.LT.MAX( 1, P ) ) THEN
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INFO = -10
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ELSE IF( LDD.LT.MAX( 1, P ) ) THEN
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INFO = -12
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ELSE IF( LDU.LT.MAX( 1, NY ) ) THEN
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INFO = -14
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ELSE IF( LDY.LT.MAX( 1, NY ) ) THEN
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INFO = -17
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ELSE IF( LDWORK.LT.N ) THEN
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INFO = -19
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END IF
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C
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IF ( INFO.NE.0 ) THEN
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C
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C Error return.
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C
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CALL XERBLA( 'TF01MY', -INFO )
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RETURN
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END IF
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C
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C Quick return if possible.
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C
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IF ( MIN( NY, P ).EQ.0 ) THEN
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RETURN
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ELSE IF ( N.EQ.0 ) THEN
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C
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C Non-dynamic system: compute the output vectors.
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C
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IF ( M.EQ.0 ) THEN
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CALL DLASET( 'Full', NY, P, ZERO, ZERO, Y, LDY )
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ELSE
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CALL DGEMM( 'No transpose', 'Transpose', NY, P, M, ONE,
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$ U, LDU, D, LDD, ZERO, Y, LDY )
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END IF
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RETURN
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END IF
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C
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C Determine the block size (taken as for LAPACK routine DGETRF).
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C
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NB = ILAENV( 1, 'DGETRF', ' ', NY, MAX( M, P ), -1, -1 )
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C
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C Find the number of state vectors that can be accommodated in
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C the provided workspace and initialize.
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C
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NS = MIN( LDWORK/N, NB*NB/N, NY )
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C
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IF ( NS.LE.1 .OR. NY*MAX( M, P ).LE.NB*NB ) THEN
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C
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C LDWORK < 2*N or small problem:
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C only BLAS 2 calculations are used in the loop
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C for computing the output corresponding to D = 0.
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C One row of the array Y is computed for each loop index value.
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C
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DO 10 IK = 1, NY
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CALL DGEMV( 'No transpose', P, N, ONE, C, LDC, X, 1, ZERO,
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$ Y(IK,1), LDY )
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C
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CALL DGEMV( 'No transpose', N, N, ONE, A, LDA, X, 1, ZERO,
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$ DWORK, 1 )
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CALL DGEMV( 'No transpose', N, M, ONE, B, LDB, U(IK,1), LDU,
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$ ONE, DWORK, 1 )
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C
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CALL DCOPY( N, DWORK, 1, X, 1 )
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10 CONTINUE
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C
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ELSE
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C
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C LDWORK >= 2*N and large problem:
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C some BLAS 3 calculations can also be used.
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C
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IYL = ( NY/NS )*NS
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IF ( M.EQ.0 ) THEN
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UPD = ZERO
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ELSE
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UPD = ONE
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END IF
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C
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CALL DCOPY( N, X, 1, DWORK, 1 )
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C
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DO 30 IK = 1, IYL, NS
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C
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C Compute the current NS-1 state vectors in the workspace.
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C
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CALL DGEMM( 'No transpose', 'Transpose', N, NS-1, M, ONE,
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$ B, LDB, U(IK,1), LDU, ZERO, DWORK(N+1), MAXN )
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C
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DO 20 IS = 1, NS - 1
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CALL DGEMV( 'No transpose', N, N, ONE, A, LDA,
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$ DWORK((IS-1)*N+1), 1, UPD, DWORK(IS*N+1), 1 )
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20 CONTINUE
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C
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C Initialize the current NS output vectors.
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C
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CALL DGEMM( 'Transpose', 'Transpose', NS, P, N, ONE, DWORK,
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$ MAXN, C, LDC, ZERO, Y(IK,1), LDY )
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C
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C Prepare the next iteration.
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C
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CALL DGEMV( 'No transpose', N, M, ONE, B, LDB,
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$ U(IK+NS-1,1), LDU, ZERO, DWORK, 1 )
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CALL DGEMV( 'No transpose', N, N, ONE, A, LDA,
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$ DWORK((NS-1)*N+1), 1, UPD, DWORK, 1 )
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30 CONTINUE
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C
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IREM = NY - IYL
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C
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IF ( IREM.GT.1 ) THEN
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C
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C Compute the last IREM output vectors.
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C First, compute the current IREM-1 state vectors.
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C
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IK = IYL + 1
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CALL DGEMM( 'No transpose', 'Transpose', N, IREM-1, M, ONE,
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$ B, LDB, U(IK,1), LDU, ZERO, DWORK(N+1), MAXN )
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C
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DO 40 IS = 1, IREM - 1
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CALL DGEMV( 'No transpose', N, N, ONE, A, LDA,
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$ DWORK((IS-1)*N+1), 1, UPD, DWORK(IS*N+1), 1 )
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40 CONTINUE
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C
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C Initialize the last IREM output vectors.
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C
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CALL DGEMM( 'Transpose', 'Transpose', IREM, P, N, ONE,
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$ DWORK, MAXN, C, LDC, ZERO, Y(IK,1), LDY )
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C
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C Prepare the final state vector.
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C
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CALL DGEMV( 'No transpose', N, M, ONE, B, LDB,
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$ U(IK+IREM-1,1), LDU, ZERO, DWORK, 1 )
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CALL DGEMV( 'No transpose', N, N, ONE, A, LDA,
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$ DWORK((IREM-1)*N+1), 1, UPD, DWORK, 1 )
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C
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ELSE IF ( IREM.EQ.1 ) THEN
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C
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C Compute the last 1 output vectors.
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C
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CALL DGEMV( 'No transpose', P, N, ONE, C, LDC, DWORK, 1,
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$ ZERO, Y(IK,1), LDY )
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C
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C Prepare the final state vector.
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C
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CALL DCOPY( N, DWORK, 1, DWORK(N+1), 1 )
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CALL DGEMV( 'No transpose', N, M, ONE, B, LDB,
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$ U(IK,1), LDU, ZERO, DWORK, 1 )
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CALL DGEMV( 'No transpose', N, N, ONE, A, LDA,
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$ DWORK(N+1), 1, UPD, DWORK, 1 )
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END IF
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C
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C Set the final state vector.
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C
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CALL DCOPY( N, DWORK, 1, X, 1 )
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C
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END IF
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C
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C Add the direct contribution of the input to the output vectors.
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C
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CALL DGEMM( 'No transpose', 'Transpose', NY, P, M, ONE, U, LDU,
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$ D, LDD, ONE, Y, LDY )
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C
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RETURN
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C *** Last line of TF01MY ***
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END
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