394 lines
13 KiB
Fortran
394 lines
13 KiB
Fortran
SUBROUTINE SB10VD( N, M, NP, NCON, NMEAS, A, LDA, B, LDB, C, LDC,
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$ F, LDF, H, LDH, X, LDX, Y, LDY, XYCOND, IWORK,
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$ DWORK, LDWORK, BWORK, 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 state feedback and the output injection
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C matrices for an H2 optimal n-state controller for the system
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C
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C | A | B1 B2 | | A | B |
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C P = |----|---------| = |---|---|
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C | C1 | 0 D12 | | C | D |
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C | C2 | D21 D22 |
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C
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C where B2 has as column size the number of control inputs (NCON)
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C and C2 has as row size the number of measurements (NMEAS) being
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C provided to the controller.
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C
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C It is assumed that
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C
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C (A1) (A,B2) is stabilizable and (C2,A) is detectable,
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C
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C (A2) D12 is full column rank with D12 = | 0 | and D21 is
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C | I |
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C full row rank with D21 = | 0 I | as obtained by the
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C SLICOT Library routine SB10UD. Matrix D is not used
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C explicitly.
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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 system. N >= 0.
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C
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C M (input) INTEGER
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C The column size of the matrix B. M >= 0.
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C
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C NP (input) INTEGER
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C The row size of the matrix C. NP >= 0.
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C
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C NCON (input) INTEGER
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C The number of control inputs (M2). M >= NCON >= 0,
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C NP-NMEAS >= NCON.
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C
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C NMEAS (input) INTEGER
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C The number of measurements (NP2). NP >= NMEAS >= 0,
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C M-NCON >= NMEAS.
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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 system state matrix A.
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C
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C LDA INTEGER
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C The leading dimension of the 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 system input matrix B.
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C
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C LDB INTEGER
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C The leading dimension of the 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 NP-by-N part of this array must contain the
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C system output matrix C.
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C
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C LDC INTEGER
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C The leading dimension of the array C. LDC >= max(1,NP).
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C
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C F (output) DOUBLE PRECISION array, dimension (LDF,N)
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C The leading NCON-by-N part of this array contains the
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C state feedback matrix F.
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C
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C LDF INTEGER
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C The leading dimension of the array F. LDF >= max(1,NCON).
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C
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C H (output) DOUBLE PRECISION array, dimension (LDH,NMEAS)
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C The leading N-by-NMEAS part of this array contains the
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C output injection matrix H.
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C
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C LDH INTEGER
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C The leading dimension of the array H. LDH >= max(1,N).
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C
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C X (output) DOUBLE PRECISION array, dimension (LDX,N)
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C The leading N-by-N part of this array contains the matrix
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C X, solution of the X-Riccati equation.
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C
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C LDX INTEGER
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C The leading dimension of the array X. LDX >= max(1,N).
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C
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C Y (output) DOUBLE PRECISION array, dimension (LDY,N)
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C The leading N-by-N part of this array contains the matrix
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C Y, solution of the Y-Riccati equation.
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C
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C LDY INTEGER
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C The leading dimension of the array Y. LDY >= max(1,N).
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C
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C XYCOND (output) DOUBLE PRECISION array, dimension (2)
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C XYCOND(1) contains an estimate of the reciprocal condition
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C number of the X-Riccati equation;
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C XYCOND(2) contains an estimate of the reciprocal condition
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C number of the Y-Riccati equation.
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C
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C Workspace
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C
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C IWORK INTEGER array, dimension max(2*N,N*N)
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C
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C DWORK DOUBLE PRECISION array, dimension (LDWORK)
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C On exit, if INFO = 0, DWORK(1) contains the optimal
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C LDWORK.
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C
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C LDWORK INTEGER
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C The dimension of the array DWORK.
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C LDWORK >= 13*N*N + 12*N + 5.
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C For good performance, LDWORK must generally be larger.
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C
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C BWORK LOGICAL array, dimension (2*N)
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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 = 1: if the X-Riccati equation was not solved
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C successfully;
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C = 2: if the Y-Riccati equation was not solved
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C successfully.
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C
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C METHOD
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C
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C The routine implements the formulas given in [1], [2]. The X-
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C and Y-Riccati equations are solved with condition and accuracy
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C estimates [3].
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C
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C REFERENCES
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C
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C [1] Zhou, K., Doyle, J.C., and Glover, K.
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C Robust and Optimal Control.
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C Prentice-Hall, Upper Saddle River, NJ, 1996.
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C
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C [2] Balas, G.J., Doyle, J.C., Glover, K., Packard, A., and
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C Smith, R.
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C mu-Analysis and Synthesis Toolbox.
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C The MathWorks Inc., Natick, Mass., 1995.
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C
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C [3] Petkov, P.Hr., Konstantinov, M.M., and Mehrmann, V.
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C DGRSVX and DMSRIC: Fortan 77 subroutines for solving
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C continuous-time matrix algebraic Riccati equations with
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C condition and accuracy estimates.
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C Preprint SFB393/98-16, Fak. f. Mathematik, Tech. Univ.
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C Chemnitz, May 1998.
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C
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C NUMERICAL ASPECTS
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C
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C The precision of the solution of the matrix Riccati equations
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C can be controlled by the values of the condition numbers
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C XYCOND(1) and XYCOND(2) of these equations.
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C
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C FURTHER COMMENTS
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C
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C The Riccati equations are solved by the Schur approach
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C implementing condition and accuracy estimates.
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C
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C CONTRIBUTORS
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C
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C P.Hr. Petkov, D.W. Gu and M.M. Konstantinov, October 1998.
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C
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C REVISIONS
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C
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C V. Sima, Research Institute for Informatics, Bucharest, May 1999.
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C
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C KEYWORDS
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C
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C Algebraic Riccati equation, H2 optimal control, LQG, LQR, optimal
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C regulator, robust control.
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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 = 0.0D+0, ONE = 1.0D+0 )
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C ..
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C .. Scalar Arguments ..
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INTEGER INFO, LDA, LDB, LDC, LDF, LDH, LDWORK, LDX,
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$ LDY, M, N, NCON, NMEAS, NP
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C ..
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C .. Array Arguments ..
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LOGICAL BWORK( * )
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INTEGER IWORK( * )
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DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ),
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$ DWORK( * ), F( LDF, * ), H( LDH, * ),
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$ X( LDX, * ), XYCOND( 2 ), Y( LDY, * )
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C ..
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C .. Local Scalars ..
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INTEGER INFO2, IWG, IWI, IWQ, IWR, IWRK, IWS, IWT, IWV,
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$ LWAMAX, M1, M2, MINWRK, N2, ND1, ND2, NP1, NP2
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DOUBLE PRECISION FERR, SEP
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C ..
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C .. External Functions ..
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C
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DOUBLE PRECISION DLANSY
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EXTERNAL DLANSY
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C ..
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C .. External Subroutines ..
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EXTERNAL DGEMM, DLACPY, DLASET, DSYRK, SB02RD, XERBLA
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C ..
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C .. Intrinsic Functions ..
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INTRINSIC DBLE, INT, MAX
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C ..
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C .. Executable Statements ..
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C
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C Decode and Test input parameters.
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C
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M1 = M - NCON
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M2 = NCON
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NP1 = NP - NMEAS
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NP2 = NMEAS
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C
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INFO = 0
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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( NP.LT.0 ) THEN
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INFO = -3
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ELSE IF( NCON.LT.0 .OR. M1.LT.0 .OR. M2.GT.NP1 ) THEN
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INFO = -4
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ELSE IF( NMEAS.LT.0 .OR. NP1.LT.0 .OR. NP2.GT.M1 ) THEN
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INFO = -5
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -7
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -9
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ELSE IF( LDC.LT.MAX( 1, NP ) ) THEN
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INFO = -11
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ELSE IF( LDF.LT.MAX( 1, NCON ) ) THEN
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INFO = -13
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ELSE IF( LDH.LT.MAX( 1, N ) ) THEN
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INFO = -15
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ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
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INFO = -17
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ELSE IF( LDY.LT.MAX( 1, N ) ) THEN
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INFO = -19
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ELSE
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C
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C Compute workspace.
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C
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MINWRK = 13*N*N + 12*N + 5
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IF( LDWORK.LT.MINWRK )
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$ INFO = -23
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SB10VD', -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( N.EQ.0 .OR. M.EQ.0 .OR. NP.EQ.0 .OR. M1.EQ.0 .OR. M2.EQ.0
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$ .OR. NP1.EQ.0 .OR. NP2.EQ.0 ) THEN
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DWORK( 1 ) = ONE
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XYCOND( 1 ) = ONE
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XYCOND( 2 ) = ONE
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RETURN
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END IF
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C
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ND1 = NP1 - M2
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ND2 = M1 - NP2
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N2 = 2*N
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C
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C Workspace usage.
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C
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IWQ = N*N + 1
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IWG = IWQ + N*N
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IWT = IWG + N*N
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IWV = IWT + N*N
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IWR = IWV + N*N
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IWI = IWR + N2
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IWS = IWI + N2
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IWRK = IWS + 4*N*N
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C
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C Compute Ax = A - B2*D12'*C1 .
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C
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CALL DLACPY ('Full', N, N, A, LDA, DWORK, N )
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CALL DGEMM( 'N', 'N', N, N, M2, -ONE, B( 1, M1+1 ), LDB,
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$ C( ND1+1, 1), LDC, ONE, DWORK, N )
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C
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C Compute Cx = C1'*C1 - C1'*D12*D12'*C1 .
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C
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IF( ND1.GT.0 ) THEN
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CALL DSYRK( 'L', 'T', N, ND1, ONE, C, LDC, ZERO, DWORK( IWQ ),
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$ N )
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ELSE
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CALL DLASET( 'L', N, N, ZERO, ZERO, DWORK( IWQ ), N )
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END IF
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C
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C Compute Dx = B2*B2' .
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C
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CALL DSYRK( 'L', 'N', N, M2, ONE, B( 1, M1+1 ), LDB, ZERO,
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$ DWORK( IWG ), N )
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C
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C Solution of the Riccati equation Ax'*X + X*Ax + Cx - X*Dx*X = 0 .
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C Workspace: need 13*N*N + 12*N + 5;
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C prefer larger.
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C
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CALL SB02RD( 'All', 'Continuous', 'NotUsed', 'NoTranspose',
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$ 'Lower', 'GeneralScaling', 'Stable', 'NotFactored',
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$ 'Original', N, DWORK, N, DWORK( IWT ), N,
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$ DWORK( IWV ), N, DWORK( IWG ), N, DWORK( IWQ ), N,
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$ X, LDX, SEP, XYCOND( 1 ), FERR, DWORK( IWR ),
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$ DWORK( IWI ), DWORK( IWS ), N2, IWORK,
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$ DWORK( IWRK ), LDWORK-IWRK+1, BWORK, INFO2 )
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IF( INFO2.GT.0 ) THEN
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INFO = 1
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RETURN
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END IF
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C
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LWAMAX = INT( DWORK( IWRK ) ) + IWRK - 1
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C
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C Compute F = -D12'*C1 - B2'*X .
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C
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CALL DLACPY( 'Full', M2, N, C( ND1+1, 1 ), LDC, F, LDF )
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CALL DGEMM( 'T', 'N', M2, N, N, -ONE, B( 1, M1+1 ), LDB, X, LDX,
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$ -ONE, F, LDF )
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C
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C Compute Ay = A - B1*D21'*C2 .
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C
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CALL DLACPY( 'Full', N, N, A, LDA, DWORK, N )
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CALL DGEMM( 'N', 'N', N, N, NP2, -ONE, B( 1, ND2+1 ), LDB,
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$ C( NP1+1, 1 ), LDC, ONE, DWORK, N )
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C
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C Compute Cy = B1*B1' - B1*D21'*D21*B1' .
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C
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IF( ND2.GT.0 ) THEN
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CALL DSYRK( 'U', 'N', N, ND2, ONE, B, LDB, ZERO, DWORK( IWQ ),
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$ N )
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ELSE
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CALL DLASET( 'U', N, N, ZERO, ZERO, DWORK( IWQ ), N )
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END IF
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C
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C Compute Dy = C2'*C2 .
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C
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CALL DSYRK( 'U', 'T', N, NP2, ONE, C( NP1+1, 1 ), LDC, ZERO,
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$ DWORK( IWG ), N )
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C
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C Solution of the Riccati equation Ay*Y + Y*Ay' + Cy - Y*Dy*Y = 0 .
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C Workspace: need 13*N*N + 12*N + 5;
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C prefer larger.
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C
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CALL SB02RD( 'All', 'Continuous', 'NotUsed', 'Transpose',
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$ 'Upper', 'GeneralScaling', 'Stable', 'NotFactored',
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$ 'Original', N, DWORK, N, DWORK( IWT ), N,
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$ DWORK( IWV ), N, DWORK( IWG ), N, DWORK( IWQ ), N,
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$ Y, LDY, SEP, XYCOND( 2 ), FERR, DWORK( IWR ),
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$ DWORK( IWI ), DWORK( IWS ), N2, IWORK,
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$ DWORK( IWRK ), LDWORK-IWRK+1, BWORK, INFO2 )
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IF( INFO2.GT.0 ) THEN
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INFO = 2
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RETURN
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END IF
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C
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LWAMAX = MAX( INT( DWORK( IWRK ) ) + IWRK - 1, LWAMAX )
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C
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C Compute H = -B1*D21' - Y*C2' .
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C
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CALL DLACPY( 'Full', N, NP2, B( 1, ND2+1 ), LDB, H, LDH )
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CALL DGEMM( 'N', 'T', N, NP2, N, -ONE, Y, LDY, C( NP1+1, 1 ), LDC,
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$ -ONE, H, LDH )
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C
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DWORK( 1 ) = DBLE( LWAMAX )
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RETURN
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C *** Last line of SB10VD ***
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END
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