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SUBROUTINE SB10MD( NC, MP, LENDAT, F, ORD, MNB, NBLOCK, ITYPE,
$ QUTOL, A, LDA, B, LDB, C, LDC, D, LDD, OMEGA,
$ TOTORD, AD, LDAD, BD, LDBD, CD, LDCD, DD, LDDD,
$ MJU, IWORK, LIWORK, DWORK, LDWORK, ZWORK,
$ LZWORK, INFO )
C
C SLICOT RELEASE 5.0.
C
C Copyright (c) 2002-2009 NICONET e.V.
C
C This program is free software: you can redistribute it and/or
C modify it under the terms of the GNU General Public License as
C published by the Free Software Foundation, either version 2 of
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program. If not, see
C <http://www.gnu.org/licenses/>.
C
C PURPOSE
C
C To perform the D-step in the D-K iteration. It handles
C continuous-time case.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C NC (input) INTEGER
C The order of the matrix A. NC >= 0.
C
C MP (input) INTEGER
C The order of the matrix D. MP >= 0.
C
C LENDAT (input) INTEGER
C The length of the vector OMEGA. LENDAT >= 2.
C
C F (input) INTEGER
C The number of the measurements and controls, i.e.,
C the size of the block I_f in the D-scaling system.
C F >= 0.
C
C ORD (input/output) INTEGER
C The MAX order of EACH block in the fitting procedure.
C ORD <= LENDAT-1.
C On exit, if ORD < 1 then ORD = 1.
C
C MNB (input) INTEGER
C The number of diagonal blocks in the block structure of
C the uncertainty, and the length of the vectors NBLOCK
C and ITYPE. 1 <= MNB <= MP.
C
C NBLOCK (input) INTEGER array, dimension (MNB)
C The vector of length MNB containing the block structure
C of the uncertainty. NBLOCK(I), I = 1:MNB, is the size of
C each block.
C
C ITYPE (input) INTEGER array, dimension (MNB)
C The vector of length MNB indicating the type of each
C block.
C For I = 1 : MNB,
C ITYPE(I) = 1 indicates that the corresponding block is a
C real block. IN THIS CASE ONLY MJU(JW) WILL BE ESTIMATED
C CORRECTLY, BUT NOT D(S)!
C ITYPE(I) = 2 indicates that the corresponding block is a
C complex block. THIS IS THE ONLY ALLOWED VALUE NOW!
C NBLOCK(I) must be equal to 1 if ITYPE(I) is equal to 1.
C
C QUTOL (input) DOUBLE PRECISION
C The acceptable mean relative error between the D(jw) and
C the frequency responce of the estimated block
C [ADi,BDi;CDi,DDi]. When it is reached, the result is
C taken as good enough.
C A good value is QUTOL = 2.0.
C If QUTOL < 0 then only mju(jw) is being estimated,
C not D(s).
C
C A (input/output) DOUBLE PRECISION array, dimension (LDA,NC)
C On entry, the leading NC-by-NC part of this array must
C contain the A matrix of the closed-loop system.
C On exit, if MP > 0, the leading NC-by-NC part of this
C array contains an upper Hessenberg matrix similar to A.
C
C LDA INTEGER
C The leading dimension of the array A. LDA >= MAX(1,NC).
C
C B (input/output) DOUBLE PRECISION array, dimension (LDB,MP)
C On entry, the leading NC-by-MP part of this array must
C contain the B matrix of the closed-loop system.
C On exit, the leading NC-by-MP part of this array contains
C the transformed B matrix corresponding to the Hessenberg
C form of A.
C
C LDB INTEGER
C The leading dimension of the array B. LDB >= MAX(1,NC).
C
C C (input/output) DOUBLE PRECISION array, dimension (LDC,NC)
C On entry, the leading MP-by-NC part of this array must
C contain the C matrix of the closed-loop system.
C On exit, the leading MP-by-NC part of this array contains
C the transformed C matrix corresponding to the Hessenberg
C form of A.
C
C LDC INTEGER
C The leading dimension of the array C. LDC >= MAX(1,MP).
C
C D (input) DOUBLE PRECISION array, dimension (LDD,MP)
C The leading MP-by-MP part of this array must contain the
C D matrix of the closed-loop system.
C
C LDD INTEGER
C The leading dimension of the array D. LDD >= MAX(1,MP).
C
C OMEGA (input) DOUBLE PRECISION array, dimension (LENDAT)
C The vector with the frequencies.
C
C TOTORD (output) INTEGER
C The TOTAL order of the D-scaling system.
C TOTORD is set to zero, if QUTOL < 0.
C
C AD (output) DOUBLE PRECISION array, dimension (LDAD,MP*ORD)
C The leading TOTORD-by-TOTORD part of this array contains
C the A matrix of the D-scaling system.
C Not referenced if QUTOL < 0.
C
C LDAD INTEGER
C The leading dimension of the array AD.
C LDAD >= MAX(1,MP*ORD), if QUTOL >= 0;
C LDAD >= 1, if QUTOL < 0.
C
C BD (output) DOUBLE PRECISION array, dimension (LDBD,MP+F)
C The leading TOTORD-by-(MP+F) part of this array contains
C the B matrix of the D-scaling system.
C Not referenced if QUTOL < 0.
C
C LDBD INTEGER
C The leading dimension of the array BD.
C LDBD >= MAX(1,MP*ORD), if QUTOL >= 0;
C LDBD >= 1, if QUTOL < 0.
C
C CD (output) DOUBLE PRECISION array, dimension (LDCD,MP*ORD)
C The leading (MP+F)-by-TOTORD part of this array contains
C the C matrix of the D-scaling system.
C Not referenced if QUTOL < 0.
C
C LDCD INTEGER
C The leading dimension of the array CD.
C LDCD >= MAX(1,MP+F), if QUTOL >= 0;
C LDCD >= 1, if QUTOL < 0.
C
C DD (output) DOUBLE PRECISION array, dimension (LDDD,MP+F)
C The leading (MP+F)-by-(MP+F) part of this array contains
C the D matrix of the D-scaling system.
C Not referenced if QUTOL < 0.
C
C LDDD INTEGER
C The leading dimension of the array DD.
C LDDD >= MAX(1,MP+F), if QUTOL >= 0;
C LDDD >= 1, if QUTOL < 0.
C
C MJU (output) DOUBLE PRECISION array, dimension (LENDAT)
C The vector with the upper bound of the structured
C singular value (mju) for each frequency in OMEGA.
C
C Workspace
C
C IWORK INTEGER array, dimension (LIWORK)
C
C LIWORK INTEGER
C The length of the array IWORK.
C LIWORK >= MAX( NC, 4*MNB-2, MP, 2*ORD+1 ), if QUTOL >= 0;
C LIWORK >= MAX( NC, 4*MNB-2, MP ), if QUTOL < 0.
C
C DWORK DOUBLE PRECISION array, dimension (LDWORK)
C On exit, if INFO = 0, DWORK(1) returns the optimal value
C of LDWORK, DWORK(2) returns the optimal value of LZWORK,
C and DWORK(3) returns an estimate of the minimum reciprocal
C of the condition numbers (with respect to inversion) of
C the generated Hessenberg matrices.
C
C LDWORK INTEGER
C The length of the array DWORK.
C LDWORK >= MAX( 3, LWM, LWD ), where
C LWM = LWA + MAX( NC + MAX( NC, MP-1 ),
C 2*MP*MP*MNB - MP*MP + 9*MNB*MNB +
C MP*MNB + 11*MP + 33*MNB - 11 );
C LWD = LWB + MAX( 2, LW1, LW2, LW3, LW4, 2*ORD ),
C if QUTOL >= 0;
C LWD = 0, if QUTOL < 0;
C LWA = MP*LENDAT + 2*MNB + MP - 1;
C LWB = LENDAT*(MP + 2) + ORD*(ORD + 2) + 1;
C LW1 = 2*LENDAT + 4*HNPTS; HNPTS = 2048;
C LW2 = LENDAT + 6*HNPTS; MN = MIN( 2*LENDAT, 2*ORD+1 );
C LW3 = 2*LENDAT*(2*ORD + 1) + MAX( 2*LENDAT, 2*ORD + 1 ) +
C MAX( MN + 6*ORD + 4, 2*MN + 1 );
C LW4 = MAX( ORD*ORD + 5*ORD, 6*ORD + 1 + MIN( 1, ORD ) ).
C
C ZWORK COMPLEX*16 array, dimension (LZWORK)
C
C LZWORK INTEGER
C The length of the array ZWORK.
C LZWORK >= MAX( LZM, LZD ), where
C LZM = MAX( MP*MP + NC*MP + NC*NC + 2*NC,
C 6*MP*MP*MNB + 13*MP*MP + 6*MNB + 6*MP - 3 );
C LZD = MAX( LENDAT*(2*ORD + 3), ORD*ORD + 3*ORD + 1 ),
C if QUTOL >= 0;
C LZD = 0, if QUTOL < 0.
C
C Error indicator
C
C INFO (output) INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value;
C = 1: if one or more values w in OMEGA are (close to
C some) poles of the closed-loop system, i.e., the
C matrix jw*I - A is (numerically) singular;
C = 2: the block sizes must be positive integers;
C = 3: the sum of block sizes must be equal to MP;
C = 4: the size of a real block must be equal to 1;
C = 5: the block type must be either 1 or 2;
C = 6: errors in solving linear equations or in matrix
C inversion;
C = 7: errors in computing eigenvalues or singular values.
C = 1i: INFO on exit from SB10YD is i. (1i means 10 + i.)
C
C METHOD
C
C I. First, W(jw) for the given closed-loop system is being
C estimated.
C II. Now, AB13MD SLICOT subroutine can obtain the D(jw) scaling
C system with respect to NBLOCK and ITYPE, and colaterally,
C mju(jw).
C If QUTOL < 0 then the estimations stop and the routine exits.
C III. Now that we have D(jw), SB10YD subroutine can do block-by-
C block fit. For each block it tries with an increasing order
C of the fit, starting with 1 until the
C (mean quadratic error + max quadratic error)/2
C between the Dii(jw) and the estimated frequency responce
C of the block becomes less than or equal to the routine
C argument QUTOL, or the order becomes equal to ORD.
C IV. Arrange the obtained blocks in the AD, BD, CD and DD
C matrices and estimate the total order of D(s), TOTORD.
C V. Add the system I_f to the system obtained in IV.
C
C REFERENCES
C
C [1] Balas, G., Doyle, J., Glover, K., Packard, A. and Smith, R.
C Mu-analysis and Synthesis toolbox - User's Guide,
C The Mathworks Inc., Natick, MA, USA, 1998.
C
C CONTRIBUTORS
C
C Asparuh Markovski, Technical University of Sofia, July 2003.
C
C REVISIONS
C
C V. Sima, Research Institute for Informatics, Bucharest, Aug. 2003.
C A. Markovski, V. Sima, October 2003.
C
C KEYWORDS
C
C Frequency response, H-infinity optimal control, robust control,
C structured singular value.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, ONE, TWO, THREE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0,
$ THREE = 3.0D+0 )
INTEGER HNPTS
PARAMETER ( HNPTS = 2048 )
C ..
C .. Scalar Arguments ..
INTEGER F, INFO, LDA, LDAD, LDB, LDBD, LDC, LDCD, LDD,
$ LDDD, LDWORK, LENDAT, LIWORK, LZWORK, MNB, MP,
$ NC, ORD, TOTORD
DOUBLE PRECISION QUTOL
C ..
C .. Array Arguments ..
INTEGER ITYPE(*), IWORK(*), NBLOCK(*)
DOUBLE PRECISION A(LDA, *), AD(LDAD, *), B(LDB, *), BD(LDBD, *),
$ C(LDC, *), CD(LDCD, *), D(LDD, *), DD(LDDD, *),
$ DWORK(*), MJU(*), OMEGA(*)
COMPLEX*16 ZWORK(*)
C ..
C .. Local Scalars ..
CHARACTER BALEIG, INITA
INTEGER CLWMAX, CORD, DLWMAX, I, IC, ICWRK, IDWRK, II,
$ INFO2, IWAD, IWB, IWBD, IWCD, IWDD, IWGJOM,
$ IWIFRD, IWRFRD, IWX, K, LCSIZE, LDSIZE, LORD,
$ LW1, LW2, LW3, LW4, LWA, LWB, MAXCWR, MAXWRK,
$ MN, W
DOUBLE PRECISION MAQE, MEQE, MOD1, MOD2, RCND, RCOND, RQE, TOL,
$ TOLER
COMPLEX*16 FREQ
C ..
C .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
C ..
C .. External Subroutines ..
EXTERNAL AB13MD, DCOPY, DLACPY, DLASET, DSCAL, SB10YD,
$ TB05AD, XERBLA
C ..
C .. Intrinsic Functions ..
INTRINSIC ABS, DCMPLX, INT, MAX, MIN, SQRT
C
C Decode and test input parameters.
C
C @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
C Workspace usage 1.
C
C real
C
IWX = 1 + MP*LENDAT
IWGJOM = IWX + 2*MNB - 1
IDWRK = IWGJOM + MP
LDSIZE = LDWORK - IDWRK + 1
C
C complex
C
IWB = MP*MP + 1
ICWRK = IWB + NC*MP
LCSIZE = LZWORK - ICWRK + 1
C
INFO = 0
IF ( NC.LT.0 ) THEN
INFO = -1
ELSE IF( MP.LT.0 ) THEN
INFO = -2
ELSE IF( LENDAT.LT.2 ) THEN
INFO = -3
ELSE IF( F.LT.0 ) THEN
INFO = -4
ELSE IF( ORD.GT.LENDAT - 1 ) THEN
INFO = -5
ELSE IF( MNB.LT.1 .OR. MNB.GT.MP ) THEN
INFO = -6
ELSE IF( LDA.LT.MAX( 1, NC ) ) THEN
INFO = -11
ELSE IF( LDB.LT.MAX( 1, NC ) ) THEN
INFO = -13
ELSE IF( LDC.LT.MAX( 1, MP ) ) THEN
INFO = -15
ELSE IF( LDD.LT.MAX( 1, MP ) ) THEN
INFO = -17
ELSE IF( LDAD.LT.1 .OR. ( QUTOL.GE.ZERO .AND. LDAD.LT.MP*ORD ) )
$ THEN
INFO = -21
ELSE IF( LDBD.LT.1 .OR. ( QUTOL.GE.ZERO .AND. LDBD.LT.MP*ORD ) )
$ THEN
INFO = -23
ELSE IF( LDCD.LT.1 .OR. ( QUTOL.GE.ZERO .AND. LDCD.LT.MP + F ) )
$ THEN
INFO = -25
ELSE IF( LDDD.LT.1 .OR. ( QUTOL.GE.ZERO .AND. LDDD.LT.MP + F ) )
$ THEN
INFO = -27
ELSE
C
C Compute workspace.
C
II = MAX( NC, 4*MNB - 2, MP )
MN = MIN( 2*LENDAT, 2*ORD + 1 )
LWA = IDWRK - 1
LWB = LENDAT*( MP + 2 ) + ORD*( ORD + 2 ) + 1
LW1 = 2*LENDAT + 4*HNPTS
LW2 = LENDAT + 6*HNPTS
LW3 = 2*LENDAT*( 2*ORD + 1 ) + MAX( 2*LENDAT, 2*ORD + 1 ) +
$ MAX( MN + 6*ORD + 4, 2*MN + 1 )
LW4 = MAX( ORD*ORD + 5*ORD, 6*ORD + 1 + MIN( 1, ORD ) )
C
DLWMAX = LWA + MAX( NC + MAX( NC, MP - 1 ),
$ 2*MP*MP*MNB - MP*MP + 9*MNB*MNB + MP*MNB +
$ 11*MP + 33*MNB - 11 )
C
CLWMAX = MAX( ICWRK - 1 + NC*NC + 2*NC,
$ 6*MP*MP*MNB + 13*MP*MP + 6*MNB + 6*MP - 3 )
C
IF ( QUTOL.GE.ZERO ) THEN
II = MAX( II, 2*ORD + 1 )
DLWMAX = MAX( DLWMAX,
$ LWB + MAX( 2, LW1, LW2, LW3, LW4, 2*ORD ) )
CLWMAX = MAX( CLWMAX, LENDAT*( 2*ORD + 3 ),
$ ORD*( ORD + 3 ) + 1 )
END IF
IF ( LIWORK.LT.II ) THEN
INFO = -30
ELSE IF ( LDWORK.LT.MAX( 3, DLWMAX ) ) THEN
INFO = -32
ELSE IF ( LZWORK.LT.CLWMAX ) THEN
INFO = -34
END IF
END IF
C
IF ( INFO.NE.0 ) THEN
C
C Error return.
C
CALL XERBLA( 'SB10MD', -INFO )
RETURN
END IF
C
ORD = MAX( 1, ORD )
TOTORD = 0
C
C Quick return if possible.
C
IF( NC.EQ.0 .OR. MP.EQ.0 ) THEN
DWORK(1) = THREE
DWORK(2) = ZERO
DWORK(3) = ONE
RETURN
END IF
C
TOLER = SQRT( DLAMCH( 'Epsilon' ) )
C
BALEIG = 'C'
RCOND = ONE
MAXCWR = CLWMAX
C
C @@@ 1. Estimate W(jw) for the closed-loop system, @@@
C @@@ D(jw) and mju(jw) for each frequency. @@@
C
DO 30 W = 1, LENDAT
FREQ = DCMPLX( ZERO, OMEGA(W) )
IF ( W.EQ.1 ) THEN
INITA = 'G'
ELSE
INITA = 'H'
END IF
C
C Compute C*inv(jw*I-A)*B.
C Integer workspace: need NC.
C Real workspace: need LWA + NC + MAX(NC,MP-1);
C prefer larger,
C where LWA = MP*LENDAT + 2*MNB + MP - 1.
C Complex workspace: need MP*MP + NC*MP + NC*NC + 2*NC.
C
CALL TB05AD( BALEIG, INITA, NC, MP, MP, FREQ, A, LDA, B, LDB,
$ C, LDC, RCND, ZWORK, MP, DWORK, DWORK, ZWORK(IWB),
$ NC, IWORK, DWORK(IDWRK), LDSIZE, ZWORK(ICWRK),
$ LCSIZE, INFO2 )
C
IF ( INFO2.GT.0 ) THEN
INFO = 1
RETURN
END IF
C
RCOND = MIN( RCOND, RCND )
IF ( W.EQ.1 )
$ MAXWRK = INT( DWORK(IDWRK) + IDWRK - 1 )
IC = 0
C
C D + C*inv(jw*I-A)*B
C
DO 20 K = 1, MP
DO 10 I = 1, MP
IC = IC + 1
ZWORK(IC) = ZWORK(IC) + DCMPLX ( D(I,K), ZERO )
10 CONTINUE
20 CONTINUE
C
C Estimate D(jw) and mju(jw).
C Integer workspace: need MAX(4*MNB-2,MP).
C Real workspace: need LWA + 2*MP*MP*MNB - MP*MP + 9*MNB*MNB
C + MP*MNB + 11*MP + 33*MNB - 11;
C prefer larger.
C Complex workspace: need 6*MP*MP*MNB + 13*MP*MP + 6*MNB +
C 6*MP - 3.
C
CALL AB13MD( 'N', MP, ZWORK, MP, MNB, NBLOCK, ITYPE,
$ DWORK(IWX), MJU(W), DWORK((W-1)*MP+1),
$ DWORK(IWGJOM), IWORK, DWORK(IDWRK), LDSIZE,
$ ZWORK(IWB), LZWORK-IWB+1, INFO2 )
C
IF ( INFO2.NE.0 ) THEN
INFO = INFO2 + 1
RETURN
END IF
C
IF ( W.EQ.1 ) THEN
MAXWRK = MAX( MAXWRK, INT( DWORK(IDWRK) ) + IDWRK - 1 )
MAXCWR = MAX( MAXCWR, INT( ZWORK(IWB) ) + IWB - 1 )
END IF
C
C Normalize D(jw) through it's last entry.
C
IF ( DWORK(W*MP).NE.ZERO )
$ CALL DSCAL( MP, ONE/DWORK(W*MP), DWORK((W-1)*MP+1), 1 )
C
30 CONTINUE
C
C Quick return if needed.
C
IF ( QUTOL.LT.ZERO ) THEN
DWORK(1) = MAXWRK
DWORK(2) = MAXCWR
DWORK(3) = RCOND
RETURN
END IF
C
C @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
C Workspace usage 2.
C
C real
C
IWRFRD = IWX
IWIFRD = IWRFRD + LENDAT
IWAD = IWIFRD + LENDAT
IWBD = IWAD + ORD*ORD
IWCD = IWBD + ORD
IWDD = IWCD + ORD
IDWRK = IWDD + 1
LDSIZE = LDWORK - IDWRK + 1
C
C complex
C
ICWRK = ORD + 2
LCSIZE = LZWORK - ICWRK + 1
INITA = 'H'
C
C Use default tolerance for SB10YD.
C
TOL = -ONE
C
C @@@ 2. Clear imag parts of D(jw) for SB10YD. @@@
C
DO 40 I = 1, LENDAT
DWORK(IWIFRD+I-1) = ZERO
40 CONTINUE
C
C @@@ 3. Clear AD, BD, CD and initialize DD with I_(mp+f). @@@
C
CALL DLASET( 'Full', MP*ORD, MP*ORD, ZERO, ZERO, AD, LDAD )
CALL DLASET( 'Full', MP*ORD, MP+F, ZERO, ZERO, BD, LDBD )
CALL DLASET( 'Full', MP+F, MP*ORD, ZERO, ZERO, CD, LDCD )
CALL DLASET( 'Full', MP+F, MP+F, ZERO, ONE, DD, LDDD )
C
C @@@ 4. Block by block frequency identification. @@@
C
DO 80 II = 1, MP
C
CALL DCOPY( LENDAT, DWORK(II), MP, DWORK(IWRFRD), 1 )
C
C Increase CORD from 1 to ORD for every block, if needed.
C
CORD = 1
C
50 CONTINUE
LORD = CORD
C
C Now, LORD is the desired order.
C Integer workspace: need 2*N+1, where N = LORD.
C Real workspace: need LWB + MAX( 2, LW1, LW2, LW3, LW4),
C where
C LWB = LENDAT*(MP+2) +
C ORD*(ORD+2) + 1,
C HNPTS = 2048, and
C LW1 = 2*LENDAT + 4*HNPTS;
C LW2 = LENDAT + 6*HNPTS;
C MN = min( 2*LENDAT, 2*N+1 )
C LW3 = 2*LENDAT*(2*N+1) +
C max( 2*LENDAT, 2*N+1 ) +
C max( MN + 6*N + 4, 2*MN+1 );
C LW4 = max( N*N + 5*N,
C 6*N + 1 + min( 1,N ) );
C prefer larger.
C Complex workspace: need LENDAT*(2*N+3).
C
CALL SB10YD( 0, 1, LENDAT, DWORK(IWRFRD), DWORK(IWIFRD),
$ OMEGA, LORD, DWORK(IWAD), ORD, DWORK(IWBD),
$ DWORK(IWCD), DWORK(IWDD), TOL, IWORK,
$ DWORK(IDWRK), LDSIZE, ZWORK, LZWORK, INFO2 )
C
C At this point, LORD is the actual order reached by SB10YD,
C 0 <= LORD <= CORD.
C [ADi,BDi; CDi,DDi] is a minimal realization with ADi in
C upper Hessenberg form.
C The leading LORD-by-LORD part of ORD-by-ORD DWORK(IWAD)
C contains ADi, the leading LORD-by-1 part of ORD-by-1
C DWORK(IWBD) contains BDi, the leading 1-by-LORD part of
C 1-by-ORD DWORK(IWCD) contains CDi, DWORK(IWDD) contains DDi.
C
IF ( INFO2.NE.0 ) THEN
INFO = 10 + INFO2
RETURN
END IF
C
C Compare the original D(jw) with the fitted one.
C
MEQE = ZERO
MAQE = ZERO
C
DO 60 W = 1, LENDAT
FREQ = DCMPLX( ZERO, OMEGA(W) )
C
C Compute CD*inv(jw*I-AD)*BD.
C Integer workspace: need LORD.
C Real workspace: need LWB + 2*LORD;
C prefer larger.
C Complex workspace: need 1 + ORD + LORD*LORD + 2*LORD.
C
CALL TB05AD( BALEIG, INITA, LORD, 1, 1, FREQ,
$ DWORK(IWAD), ORD, DWORK(IWBD), ORD,
$ DWORK(IWCD), 1, RCND, ZWORK, 1,
$ DWORK(IDWRK), DWORK(IDWRK), ZWORK(2), ORD,
$ IWORK, DWORK(IDWRK), LDSIZE, ZWORK(ICWRK),
$ LCSIZE, INFO2 )
C
IF ( INFO2.GT.0 ) THEN
INFO = 1
RETURN
END IF
C
RCOND = MIN( RCOND, RCND )
IF ( W.EQ.1 )
$ MAXWRK = MAX( MAXWRK, INT( DWORK(IDWRK) ) + IDWRK - 1)
C
C DD + CD*inv(jw*I-AD)*BD
C
ZWORK(1) = ZWORK(1) + DCMPLX( DWORK(IWDD), ZERO )
C
MOD1 = ABS( DWORK(IWRFRD+W-1) )
MOD2 = ABS( ZWORK(1) )
RQE = ABS( ( MOD1 - MOD2 )/( MOD1 + TOLER ) )
MEQE = MEQE + RQE
MAQE = MAX( MAQE, RQE )
C
60 CONTINUE
C
MEQE = MEQE/LENDAT
C
IF ( ( ( MEQE + MAQE )/TWO.LE.QUTOL ) .OR.
$ ( CORD.EQ.ORD ) ) THEN
GOTO 70
END IF
C
CORD = CORD + 1
GOTO 50
C
70 TOTORD = TOTORD + LORD
C
C Copy ad(ii), bd(ii) and cd(ii) to AD, BD and CD, respectively.
C
CALL DLACPY( 'Full', LORD, LORD, DWORK(IWAD), ORD,
$ AD(TOTORD-LORD+1,TOTORD-LORD+1), LDAD )
CALL DCOPY( LORD, DWORK(IWBD), 1, BD(TOTORD-LORD+1,II), 1 )
CALL DCOPY( LORD, DWORK(IWCD), 1, CD(II,TOTORD-LORD+1), LDCD )
C
C Copy dd(ii) to DD.
C
DD(II,II) = DWORK(IWDD)
C
80 CONTINUE
C
DWORK(1) = MAXWRK
DWORK(2) = MAXCWR
DWORK(3) = RCOND
RETURN
C
C *** Last line of SB10MD ***
END
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