SUBROUTINE BB01AD(DEF, NR, DPAR, IPAR, BPAR, CHPAR, VEC, N, M, P,
1 A, LDA, B, LDB, C, LDC, G, LDG, Q, LDQ, X, LDX,
2 DWORK, LDWORK, INFO)
C
C PURPOSE
C
C To generate the benchmark examples for the numerical solution of
C continuous-time algebraic Riccati equations (CAREs) of the form
C
C 0 = Q + A'X + XA - XGX
C
C corresponding to the Hamiltonian matrix
C
C ( A G )
C H = ( T ).
C ( Q -A )
C
C A,G,Q,X are real N-by-N matrices, Q and G are symmetric and may
C be given in factored form
C
C -1 T T
C (I) G = B R B , (II) Q = C W C .
C
C Here, C is P-by-N, W P-by-P, B N-by-M, and R M-by-M, where W
C and R are symmetric. In linear-quadratic optimal control problems,
C usually W is positive semidefinite and R positive definite. The
C factorized form can be used if the CARE is solved using the
C deflating subspaces of the extended Hamiltonian pencil
C
C ( A 0 B ) ( I 0 0 )
C ( T ) ( )
C H - s K = ( Q A 0 ) - s ( 0 -I 0 ) ,
C ( T ) ( )
C ( 0 B R ) ( 0 0 0 )
C
C where I and 0 denote the identity and zero matrix, respectively,
C of appropriate dimensions.
C
C NOTE: the formulation of the CARE and the related matrix (pencils)
C used here does not include CAREs as they arise in robust
C control (H_infinity optimization).
C
C ARGUMENTS
C
C Mode Parameters
C
C DEF CHARACTER
C This parameter specifies if the default parameters are
C to be used or not.
C = 'N' or 'n' : The parameters given in the input vectors
C xPAR (x = 'D', 'I', 'B', 'CH') are used.
C = 'D' or 'd' : The default parameters for the example
C are used.
C This parameter is not meaningful if NR(1) = 1.
C
C Input/Output Parameters
C
C NR (input) INTEGER array, dimension (2)
C This array determines the example for which CAREX returns
C data. NR(1) is the group of examples.
C NR(1) = 1 : parameter-free problems of fixed size.
C NR(1) = 2 : parameter-dependent problems of fixed size.
C NR(1) = 3 : parameter-free problems of scalable size.
C NR(1) = 4 : parameter-dependent problems of scalable size.
C NR(2) is the number of the example in group NR(1).
C Let NEXi be the number of examples in group i. Currently,
C NEX1 = 6, NEX2 = 9, NEX3 = 2, NEX4 = 4.
C 1 <= NR(1) <= 4;
C 1 <= NR(2) <= NEXi , where i = NR(1).
C
C DPAR (input/output) DOUBLE PRECISION array, dimension (7)
C Double precision parameter vector. For explanation of the
C parameters see [1].
C DPAR(1) : defines the parameters
C 'delta' for NR(1) = 3,
C 'q' for NR(1).NR(2) = 4.1,
C 'a' for NR(1).NR(2) = 4.2, and
C 'mu' for NR(1).NR(2) = 4.3.
C DPAR(2) : defines parameters
C 'r' for NR(1).NR(2) = 4.1,
C 'b' for NR(1).NR(2) = 4.2, and
C 'delta' for NR(1).NR(2) = 4.3.
C DPAR(3) : defines parameters
C 'c' for NR(1).NR(2) = 4.2 and
C 'kappa' for NR(1).NR(2) = 4.3.
C DPAR(j), j=4,5,6,7: These arguments are only used to
C generate Example 4.2 and define in
C consecutive order the intervals
C ['beta_1', 'beta_2'],
C ['gamma_1', 'gamma_2'].
C NOTE that if DEF = 'D' or 'd', the values of DPAR entries
C on input are ignored and, on output, they are overwritten
C with the default parameters.
C
C IPAR (input/output) INTEGER array, dimension (4)
C On input, IPAR(1) determines the actual state dimension,
C i.e., the order of the matrix A as follows, where
C NO = NR(1).NR(2).
C NR(1) = 1 or 2.1-2.8: IPAR(1) is ignored.
C NO = 2.9 : IPAR(1) = 1 generates the CARE for
C optimal state feedback (default);
C IPAR(1) = 2 generates the Kalman
C filter CARE.
C NO = 3.1 : IPAR(1) is the number of vehicles
C (parameter 'l' in the description
C in [1]).
C NO = 3.2, 4.1 or 4.2: IPAR(1) is the order of the matrix
C A.
C NO = 4.3 or 4.4 : IPAR(1) determines the dimension of
C the second-order system, i.e., the
C order of the stiffness matrix for
C Examples 4.3 and 4.4 (parameter 'l'
C in the description in [1]).
C
C The order of the output matrix A is N = 2*IPAR(1) for
C Example 4.3 and N = 2*IPAR(1)-1 for Examples 3.1 and 4.4.
C NOTE that IPAR(1) is overwritten for Examples 1.1-2.8. For
C the other examples, IPAR(1) is overwritten if the default
C parameters are to be used.
C On output, IPAR(1) contains the order of the matrix A.
C
C On input, IPAR(2) is the number of colums in the matrix B
C in (I) (in control problems, the number of inputs of the
C system). Currently, IPAR(2) is fixed or determined by
C IPAR(1) for all examples and thus is not referenced on
C input.
C On output, IPAR(2) is the number of columns of the
C matrix B from (I).
C NOTE that currently IPAR(2) is overwritten and that
C rank(G) <= IPAR(2).
C
C On input, IPAR(3) is the number of rows in the matrix C
C in (II) (in control problems, the number of outputs of the
C system). Currently, IPAR(3) is fixed or determined by
C IPAR(1) for all examples and thus is not referenced on
C input.
C On output, IPAR(3) contains the number of rows of the
C matrix C in (II).
C NOTE that currently IPAR(3) is overwritten and that
C rank(Q) <= IPAR(3).
C
C On input, if NR(1) = NR(2) = 4, and other data file than
C that used by default is desired, then IPAR(4) is the
C length of the character string in CHPAR specifying the
C file name.
C
C BPAR (input) BOOLEAN array, dimension (6)
C This array defines the form of the output of the examples
C and the storage mode of the matrices G and Q.
C BPAR(1) = .TRUE. : G is returned.
C BPAR(1) = .FALSE. : G is returned in factored form, i.e.,
C B and R from (I) are returned.
C BPAR(2) = .TRUE. : The matrix returned in array G (i.e.,
C G if BPAR(1) = .TRUE. and R if
C BPAR(1) = .FALSE.) is stored as full
C matrix.
C BPAR(2) = .FALSE. : The matrix returned in array G is
C provided in packed storage mode.
C BPAR(3) = .TRUE. : If BPAR(2) = .FALSE., the matrix
C returned in array G is stored in upper
C packed mode, i.e., the upper triangle
C of a symmetric n-by-n matrix is stored
C by columns, e.g., the matrix entry
C G(i,j) is stored in the array entry
C G(i+j*(j-1)/2) for i <= j.
C Otherwise, this entry is ignored.
C BPAR(3) = .FALSE. : If BPAR(2) = .FALSE., the matrix
C returned in array G is stored in lower
C packed mode, i.e., the lower triangle
C of a symmetric n-by-n matrix is stored
C by columns, e.g., the matrix entry
C G(i,j) is stored in the array entry
C G(i+(2*n-j)*(j-1)/2) for j <= i.
C Otherwise, this entry is ignored.
C BPAR(4) = .TRUE. : Q is returned.
C BPAR(4) = .FALSE. : Q is returned in factored form, i.e.,
C C and W from (II) are returned.
C BPAR(5) = .TRUE. : The matrix returned in array Q (i.e.,
C Q if BPAR(4) = .TRUE. and W if
C BPAR(4) = .FALSE.) is stored as full
C matrix.
C BPAR(5) = .FALSE. : The matrix returned in array Q is
C provided in packed storage mode.
C BPAR(6) = .TRUE. : If BPAR(5) = .FALSE., the matrix
C returned in array Q is stored in upper
C packed mode (see above).
C Otherwise, this entry is ignored.
C BPAR(6) = .FALSE. : If BPAR(5) = .FALSE., the matrix
C returned in array Q is stored in lower
C packed mode (see above).
C Otherwise, this entry is ignored.
C NOTE that there are no default values for BPAR. If all
C entries are declared to be .TRUE., then matrices G and Q
C are returned in conventional storage mode, i.e., as
C N-by-N arrays where the array element Z(I,J) contains the
C matrix entry Z_{i,j}.
C
C CHPAR (input/output) CHARACTER*255
C On input, this is the name of a data file supplied by the
C user.
C In the current version, only Example 4.4 allows a
C user-defined data file. This file must contain
C consecutively DOUBLE PRECISION vectors mu, delta, gamma,
C and kappa. The length of these vectors is determined by
C the input value for IPAR(1).
C If on entry, IPAR(1) = L, then mu and delta must each
C contain L DOUBLE PRECISION values, and gamma and kappa
C must each contain L-1 DOUBLE PRECISION values.
C On output, this string contains short information about
C the chosen example.
C
C VEC (output) LOGICAL array, dimension (9)
C Flag vector which displays the availability of the output
C data:
C VEC(j), j=1,2,3, refer to N, M, and P, respectively, and
C are always .TRUE.
C VEC(4) refers to A and is always .TRUE.
C VEC(5) is .TRUE. if BPAR(1) = .FALSE., i.e., the factors B
C and R from (I) are returned.
C VEC(6) is .TRUE. if BPAR(4) = .FALSE., i.e., the factors C
C and W from (II) are returned.
C VEC(7) refers to G and is always .TRUE.
C VEC(8) refers to Q and is always .TRUE.
C VEC(9) refers to X and is .TRUE. if the exact solution
C matrix is available.
C NOTE that VEC(i) = .FALSE. for i = 1 to 9 if on exit
C INFO .NE. 0.
C
C N (output) INTEGER
C The order of the matrices A, X, G if BPAR(1) = .TRUE., and
C Q if BPAR(4) = .TRUE.
C
C M (output) INTEGER
C The number of columns in the matrix B (or the dimension of
C the control input space of the underlying dynamical
C system).
C
C P (output) INTEGER
C The number of rows in the matrix C (or the dimension of
C the output space of the underlying dynamical system).
C
C A (output) DOUBLE PRECISION array, dimension (LDA,N)
C The leading N-by-N part of this array contains the
C coefficient matrix A of the CARE.
C
C LDA INTEGER
C The leading dimension of array A. LDA >= N.
C
C B (output) DOUBLE PRECISION array, dimension (LDB,M)
C If (BPAR(1) = .FALSE.), then the leading N-by-M part of
C this array contains the matrix B of the factored form (I)
C of G. Otherwise, B is used as workspace.
C
C LDB INTEGER
C The leading dimension of array B. LDB >= N.
C
C C (output) DOUBLE PRECISION array, dimension (LDC,N)
C If (BPAR(4) = .FALSE.), then the leading P-by-N part of
C this array contains the matrix C of the factored form (II)
C of Q. Otherwise, C is used as workspace.
C
C LDC INTEGER
C The leading dimension of array C.
C LDC >= P, where P is the number of rows of the matrix C,
C i.e., the output value of IPAR(3). (For all examples,
C P <= N, where N equals the output value of the argument
C IPAR(1), i.e., LDC >= LDA is always safe.)
C
C G (output) DOUBLE PRECISION array, dimension (NG)
C If (BPAR(2) = .TRUE.) then NG = LDG*N.
C If (BPAR(2) = .FALSE.) then NG = N*(N+1)/2.
C If (BPAR(1) = .TRUE.), then array G contains the
C coefficient matrix G of the CARE.
C If (BPAR(1) = .FALSE.), then array G contains the 'control
C weighting matrix' R of G's factored form as in (I). (For
C all examples, M <= N.) The symmetric matrix contained in
C array G is stored according to BPAR(2) and BPAR(3).
C
C LDG INTEGER
C If conventional storage mode is used for G, i.e.,
C BPAR(2) = .TRUE., then G is stored like a 2-dimensional
C array with leading dimension LDG. If packed symmetric
C storage mode is used, then LDG is not referenced.
C LDG >= N if BPAR(2) = .TRUE..
C
C Q (output) DOUBLE PRECISION array, dimension (NQ)
C If (BPAR(5) = .TRUE.) then NQ = LDQ*N.
C If (BPAR(5) = .FALSE.) then NQ = N*(N+1)/2.
C If (BPAR(4) = .TRUE.), then array Q contains the
C coefficient matrix Q of the CARE.
C If (BPAR(4) = .FALSE.), then array Q contains the 'output
C weighting matrix' W of Q's factored form as in (II).
C The symmetric matrix contained in array Q is stored
C according to BPAR(5) and BPAR(6).
C
C LDQ INTEGER
C If conventional storage mode is used for Q, i.e.,
C BPAR(5) = .TRUE., then Q is stored like a 2-dimensional
C array with leading dimension LDQ. If packed symmetric
C storage mode is used, then LDQ is not referenced.
C LDQ >= N if BPAR(5) = .TRUE..
C
C X (output) DOUBLE PRECISION array, dimension (LDX,IPAR(1))
C If an exact solution is available (NR = 1.1, 1.2, 2.1,
C 2.3-2.6, 3.2), then the leading N-by-N part of this array
C contains the solution matrix X in conventional storage
C mode. Otherwise, X is not referenced.
C
C LDX INTEGER
C The leading dimension of array X. LDX >= 1, and
C LDX >= N if NR = 1.1, 1.2, 2.1, 2.3-2.6, 3.2.
C
C Workspace
C
C DWORK DOUBLE PRECISION array, dimension (LDWORK)
C
C LDWORK INTEGER
C The length of the array DWORK.
C LDWORK >= N*MAX(4,N).
C
C Error Indicator
C
C INFO INTEGER
C = 0 : successful exit;
C < 0 : if INFO = -i, the i-th argument had an illegal
C value;
C = 1 : data file could not be opened or had wrong format;
C = 2 : division by zero;
C = 3 : G can not be computed as in (I) due to a singular R
C matrix.
C
C REFERENCES
C
C [1] Abels, J. and Benner, P.
C CAREX - A Collection of Benchmark Examples for Continuous-Time
C Algebraic Riccati Equations (Version 2.0).
C SLICOT Working Note 1999-14, November 1999. Available from
C http://www.win.tue.nl/niconet/NIC2/reports.html.
C
C This is an updated and extended version of
C
C [2] Benner, P., Laub, A.J., and Mehrmann, V.
C A Collection of Benchmark Examples for the Numerical Solution
C of Algebraic Riccati Equations I: Continuous-Time Case.
C Technical Report SPC 95_22, Fak. f. Mathematik,
C TU Chemnitz-Zwickau (Germany), October 1995.
C
C NUMERICAL ASPECTS
C
C If the original data as taken from the literature is given via
C matrices G and Q, but factored forms are requested as output, then
C these factors are obtained from Cholesky or LDL' decompositions of
C G and Q, i.e., the output data will be corrupted by roundoff
C errors.
C
C FURTHER COMMENTS
C
C Some benchmark examples read data from the data files provided
C with the collection.
C
C CONTRIBUTOR
C
C Peter Benner (Universitaet Bremen), November 15, 1999.
C
C For questions concerning the collection or for the submission of
C test examples, please send e-mail to benner@math.uni-bremen.de.
C
C REVISIONS
C
C V. Sima, 1999, December 23, May 2016.
C
C KEYWORDS
C
C Algebraic Riccati equation, Hamiltonian matrix.
C
C ******************************************************************
C
C .. Parameters ..
C . # of examples available , # of examples with fixed size. .
INTEGER NEX1, NEX2, NEX3, NEX4, NMAX
PARAMETER ( NMAX = 9, NEX1 = 6, NEX2 = 9, NEX3 = 2,
1 NEX4 = 4 )
DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR, PI
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
1 THREE = 3.0D0, FOUR = 4.0D0,
2 PI = .3141592653589793D1 )
C
C .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LDC, LDG, LDQ, LDWORK, LDX, M, N,
$ P
CHARACTER DEF
C
C .. Array Arguments ..
INTEGER IPAR(4), NR(2)
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), DPAR(*), DWORK(*),
1 G(*), Q(*), X(LDX,*)
CHARACTER CHPAR*(*)
LOGICAL BPAR(6), VEC(9)
C
C .. Local Scalars ..
INTEGER GDIMM, I, IOS, ISYMM, J, K, L, MSYMM, NSYMM, POS,
1 PSYMM, QDIMM
DOUBLE PRECISION APPIND, B1, B2, C1, C2, SUM, TEMP, TTEMP
C
C ..Local Arrays ..
INTEGER MDEF(2,NMAX), NDEF(4,NMAX), NEX(4), PDEF(2,NMAX)
DOUBLE PRECISION PARDEF(4,NMAX)
CHARACTER IDENT*4
CHARACTER*255 NOTES(4,NMAX)
C
C .. External Functions ..
C . BLAS .
DOUBLE PRECISION DDOT
EXTERNAL DDOT
C . LAPACK .
LOGICAL LSAME
DOUBLE PRECISION DLAPY2
EXTERNAL LSAME, DLAPY2
C
C .. External Subroutines ..
C . BLAS .
EXTERNAL DCOPY, DGEMV, DSCAL, DSPMV, DSPR, DSYMM, DSYRK
C . LAPACK .
EXTERNAL DLASET, DPPTRF, DPPTRI, DPTTRF, DPTTRS, XERBLA
C . SLICOT .
EXTERNAL MA02DD, MA02ED
C
C .. Intrinsic Functions ..
INTRINSIC COS, DBLE, MAX, MIN, MOD, SQRT
C
C .. Data Statements ..
C . default values for dimensions .
DATA (NEX(I), I = 1, 4) /NEX1, NEX2, NEX3, NEX4/
DATA (NDEF(1,I), I = 1, NEX1) /2, 2, 4, 8, 9, 30/
DATA (NDEF(2,I), I = 1, NEX2) /2, 2, 2, 2, 2, 3, 4, 4, 55/
DATA (NDEF(3,I), I = 1, NEX3) /20, 64/
DATA (NDEF(4,I), I = 1, NEX4) /21, 100, 30, 211/
DATA (MDEF(1,I), I = 1, NEX1) /1, 1, 2, 2, 3, 3/
DATA (MDEF(2,I), I = 1, NEX2) /1, 2, 1, 2, 1, 3, 1, 1, 2/
DATA (PDEF(1,I), I = 1, NEX1) /2, 2, 4, 8, 9, 5/
DATA (PDEF(2,I), I = 1, NEX2) /1, 1, 2, 2, 2, 3, 2, 1, 10/
C . default values for parameters .
DATA (PARDEF(1,I), I = 1, NEX1) /ZERO, ZERO, ZERO, ZERO, ZERO,
1 ZERO/
DATA (PARDEF(2,I), I = 1, NEX2) /.1D-5, .1D-7, .1D7, .1D-6, ZERO,
1 .1D7, .1D-5, .1D-5, .1D1/
DATA (PARDEF(3,I), I = 1, NEX3) /ZERO, ZERO/
DATA (PARDEF(4,I), I = 1, NEX4) /ONE, .1D-1, FOUR, ZERO/
C . comments on examples .
DATA (NOTES(1,I), I = 1, NEX1) /
1'Laub 1979, Ex.1', 'Laub 1979, Ex.2: uncontrollable-unobservable d
2ata', 'Beale/Shafai 1989: model of L-1011 aircraft', 'Bhattacharyy
3a et al. 1983: binary distillation column', 'Patnaik et al. 1980:
4tubular ammonia reactor', 'Davison/Gesing 1978: J-100 jet engine'/
DATA (NOTES(2,I), I = 1, NEX2) /
1'Arnold/Laub 1984, Ex.1: (A,B) unstabilizable as EPS -> 0', 'Arnol
2d/Laub 1984, Ex.3: control weighting matrix singular as EPS -> 0',
3'Kenney/Laub/Wette 1989, Ex.2: ARE ill conditioned for EPS -> oo',
4'Bai/Qian 1994: ill-conditioned Hamiltonian for EPS -> 0', 'Laub 1
5992: H-infinity problem, eigenvalues +/- EPS +/- i', 'Petkov et a
6l. 1987: increasingly badly scaled Hamiltonian as EPS -> oo', 'Cho
7w/Kokotovic 1976: magnetic tape control system', 'Arnold/Laub 1984
8, Ex.2: poor sep. of closed-loop spectrum as EPS -> 0', 'IFAC Benc
9hmark Problem #90-06: LQG design for modified Boing B-767 at flutt
1er condition'/
DATA (NOTES(3,I), I = 1, NEX3) /
1'Laub 1979, Ex.4: string of high speed vehicles', 'Laub 1979, Ex.5
2: circulant matrices'/
DATA (NOTES(4,I), I = 1, NEX4) /
1'Laub 1979, Ex.6: ill-conditioned Riccati equation', 'Rosen/Wang 1
2992: lq control of 1-dimensional heat flow','Hench et al. 1995: co
3upled springs, dashpots and masses','Lang/Penzl 1994: rotating axl
4e' /
C
C .. Executable Statements ..
C
INFO = 0
DO 5 I = 1, 9
VEC(I) = .FALSE.
5 CONTINUE
C
IF ((NR(1) .NE. 1) .AND. (.NOT. (LSAME(DEF,'N')
1 .OR. LSAME(DEF,'D')))) THEN
INFO = -1
ELSE IF ((NR(1) .LT. 1) .OR. (NR(2) .LT. 1) .OR.
1 (NR(1) .GT. 4) .OR. (NR(2) .GT. NEX(NR(1)))) THEN
INFO = -2
ELSE IF (NR(1) .GT. 2) THEN
IF (.NOT. LSAME(DEF,'N')) IPAR(1) = NDEF(NR(1),NR(2))
IF (NR(1) .EQ. 3) THEN
IF (NR(2) .EQ. 1) THEN
IPAR(2) = IPAR(1)
IPAR(3) = IPAR(1) - 1
IPAR(1) = 2*IPAR(1) - 1
ELSE IF (NR(2) .EQ. 2) THEN
IPAR(2) = IPAR(1)
IPAR(3) = IPAR(1)
ELSE
IPAR(2) = 1
IPAR(3) = 1
END IF
ELSE IF (NR(1) .EQ. 4) THEN
IF (NR(2) .EQ. 3) THEN
L = IPAR(1)
IPAR(2) = 2
IPAR(3) = 2*L
IPAR(1) = 2*L
ELSE IF (NR(2) .EQ. 4) THEN
L = IPAR(1)
IPAR(2) = L
IPAR(3) = L
IPAR(1) = 2*L-1
ELSE
IPAR(2) = 1
IPAR(3) = 1
END IF
END IF
ELSE IF ((NR(1) .EQ. 2) .AND. (NR(2) .EQ. 9) .AND.
1 (IPAR(1) . EQ. 2)) THEN
IPAR(1) = NDEF(NR(1),NR(2))
IPAR(2) = MDEF(NR(1),NR(2))
IPAR(3) = 3
ELSE
IPAR(1) = NDEF(NR(1),NR(2))
IPAR(2) = MDEF(NR(1),NR(2))
IPAR(3) = PDEF(NR(1),NR(2))
END IF
IF (INFO .NE. 0) GOTO 7
C
IF (IPAR(1) .LT. 1) THEN
INFO = -4
ELSE IF (IPAR(1) .GT. LDA) THEN
INFO = -12
ELSE IF (IPAR(1) .GT. LDB) THEN
INFO = -14
ELSE IF (IPAR(3) .GT. LDC) THEN
INFO = -16
ELSE IF (BPAR(2) .AND. (IPAR(1).GT. LDG)) THEN
INFO = -18
ELSE IF (BPAR(5) .AND. (IPAR(1).GT. LDQ)) THEN
INFO = -20
ELSE IF (LDX.LT.1) THEN
INFO = -22
ELSE IF ((NR(1) .EQ. 1) .AND.
$ ((NR(2) .EQ. 1) .OR. (NR(2) .EQ.2))) THEN
IF (IPAR(1) .GT. LDX) INFO = -22
ELSE IF ((NR(1) .EQ. 2) .AND. (NR(2) .EQ. 1)) THEN
IF (IPAR(1) .GT. LDX) INFO = -22
ELSE IF ((NR(1) .EQ. 2) .AND. ((NR(2) .GE. 3) .AND.
1 (NR(2) .LE. 6))) THEN
IF (IPAR(1) .GT. LDX) INFO = -22
ELSE IF ((NR(1) .EQ. 3) .AND. (NR(2) .EQ. 2)) THEN
IF (IPAR(1) .GT. LDX) INFO = -22
ELSE IF (LDWORK .LT. N*(MAX(4,N))) THEN
INFO = -24
END IF
C
7 CONTINUE
IF (INFO .NE. 0) THEN
CALL XERBLA( 'BB01AD', -INFO )
RETURN
END IF
C
NSYMM = (IPAR(1)*(IPAR(1)+1))/2
MSYMM = (IPAR(2)*(IPAR(2)+1))/2
PSYMM = (IPAR(3)*(IPAR(3)+1))/2
IF (.NOT. LSAME(DEF,'N')) DPAR(1) = PARDEF(NR(1),NR(2))
C
CALL DLASET('A', IPAR(1), IPAR(1), ZERO, ZERO, A, LDA)
CALL DLASET('A', IPAR(1), IPAR(2), ZERO, ZERO, B, LDB)
CALL DLASET('A', IPAR(3), IPAR(1), ZERO, ZERO, C, LDC)
CALL DLASET('L', MSYMM, 1, ZERO, ZERO, G, 1)
CALL DLASET('L', PSYMM, 1, ZERO, ZERO, Q, 1)
C
IF (NR(1) .EQ. 1) THEN
IF (NR(2) .EQ. 1) THEN
A(1,2) = ONE
B(2,1) = ONE
Q(1) = ONE
Q(3) = TWO
IDENT = '0101'
CALL DLASET('A', IPAR(1), IPAR(1), ONE, TWO, X, LDX)
C
ELSE IF (NR(2) .EQ. 2) THEN
A(1,1) = FOUR
A(2,1) = -.45D1
A(1,2) = THREE
A(2,2) = -.35D1
CALL DLASET('A', IPAR(1), IPAR(2), -ONE, ONE, B, LDB)
Q(1) = 9.0D0
Q(2) = 6.0D0
Q(3) = FOUR
IDENT = '0101'
TEMP = ONE + SQRT(TWO)
CALL DLASET('A', IPAR(1), IPAR(1), 6.0D0*TEMP, FOUR*TEMP, X,
1 LDX)
X(1,1) = 9.0D0*TEMP
C
ELSE IF ((NR(2) .GE. 3) .AND. (NR(2) .LE. 6)) THEN
WRITE (CHPAR(1:11), '(A,I1,A,I1,A)') 'BB01', NR(1), '0',
1 NR(2) , '.dat'
IF ((NR(2) .EQ. 3) .OR. (NR(2) .EQ. 4)) THEN
IDENT = '0101'
ELSE IF (NR(2) .EQ. 5) THEN
IDENT = '0111'
ELSE IF (NR(2) .EQ. 6) THEN
IDENT = '0011'
END IF
OPEN(1, IOSTAT = IOS, STATUS = 'OLD', FILE = CHPAR(1:11))
IF (IOS .NE. 0) THEN
INFO = 1
ELSE
DO 10 I = 1, IPAR(1)
READ (1, FMT = *, IOSTAT = IOS)
1 (A(I,J), J = 1, IPAR(1))
IF (IOS .NE. 0) INFO = 1
10 CONTINUE
DO 20 I = 1, IPAR(1)
READ (1, FMT = *, IOSTAT = IOS)
1 (B(I,J), J = 1, IPAR(2))
IF (IOS .NE. 0) INFO = 1
20 CONTINUE
IF (NR(2) .LE. 4) THEN
DO 30 I = 1, IPAR(1)
POS = (I-1)*IPAR(1)
READ (1, FMT = *, IOSTAT = IOS) (DWORK(POS+J),
1 J = 1,IPAR(1))
30 CONTINUE
IF (IOS .NE. 0) THEN
INFO = 1
ELSE
CALL MA02DD('Pack', 'Lower', IPAR(1), DWORK, IPAR(1), Q)
END IF
ELSE IF (NR(2) .EQ. 6) THEN
DO 35 I = 1, IPAR(3)
READ (1, FMT = *, IOSTAT = IOS)
1 (C(I,J), J = 1, IPAR(1))
IF (IOS .NE. 0) INFO = 1
35 CONTINUE
END IF
CLOSE(1)
END IF
END IF
C
ELSE IF (NR(1) .EQ. 2) THEN
IF (NR(2) .EQ. 1) THEN
A(1,1) = ONE
A(2,2) = -TWO
B(1,1) = DPAR(1)
CALL DLASET('U', IPAR(3), IPAR(1), ONE, ONE, C, LDC)
IDENT = '0011'
IF (DPAR(1) .NE. ZERO) THEN
TEMP = DLAPY2(ONE, DPAR(1))
X(1,1) = (ONE + TEMP)/DPAR(1)/DPAR(1)
X(2,1) = ONE/(TWO + TEMP)
X(1,2) = X(2,1)
TTEMP = DPAR(1)*X(1,2)
TEMP = (ONE - TTEMP) * (ONE + TTEMP)
X(2,2) = TEMP / FOUR
ELSE
INFO = 2
END IF
C
ELSE IF (NR(2) .EQ. 2) THEN
A(1,1) = -.1D0
A(2,2) = -.2D-1
B(1,1) = .1D0
B(2,1) = .1D-2
B(2,2) = .1D-1
CALL DLASET('L', MSYMM, 1, ONE, ONE, G, MSYMM)
G(1) = G(1) + DPAR(1)
C(1,1) = .1D2
C(1,2) = .1D3
IDENT = '0010'
C
ELSE IF (NR(2) .EQ. 3) THEN
A(1,2) = DPAR(1)
B(2,1) = ONE
IDENT = '0111'
IF (DPAR(1) .NE. ZERO) THEN
TEMP = SQRT(ONE + TWO*DPAR(1))
CALL DLASET('A', IPAR(1), IPAR(1), ONE, TEMP, X, LDX)
X(1,1) = X(1,1)/DPAR(1)
ELSE
INFO = 2
END IF
C
ELSE IF (NR(2) .EQ. 4) THEN
TEMP = DPAR(1) + ONE
CALL DLASET('A', IPAR(1), IPAR(1), ONE, TEMP, A, LDA)
Q(1) = DPAR(1)**2
Q(3) = Q(1)
IDENT = '1101'
X(1,1) = TWO*TEMP + SQRT(TWO)*(SQRT(TEMP**2 + ONE) + DPAR(1))
X(1,1) = X(1,1)/TWO
X(2,2) = X(1,1)
TTEMP = X(1,1) - TEMP
IF (TTEMP .NE. ZERO) THEN
X(2,1) = X(1,1) / TTEMP
X(1,2) = X(2,1)
ELSE
INFO = 2
END IF
C
ELSE IF (NR(2) .EQ. 5) THEN
A(1,1) = THREE - DPAR(1)
A(2,1) = FOUR
A(1,2) = ONE
A(2,2) = TWO - DPAR(1)
CALL DLASET('L', IPAR(1), IPAR(2), ONE, ONE, B, LDB)
Q(1) = FOUR*DPAR(1) - 11.0D0
Q(2) = TWO*DPAR(1) - 5.0D0
Q(3) = TWO*DPAR(1) - TWO
IDENT = '0101'
CALL DLASET('A', IPAR(1), IPAR(1), ONE, ONE, X, LDX)
X(1,1) = TWO
C
ELSE IF (NR(2) .EQ. 6) THEN
IF (DPAR(1) .NE. ZERO) THEN
A(1,1) = DPAR(1)
A(2,2) = DPAR(1)*TWO
A(3,3) = DPAR(1)*THREE
C .. set C = V ..
TEMP = TWO/THREE
CALL DLASET('A', IPAR(3), IPAR(1), -TEMP, ONE - TEMP,
1 C, LDC)
CALL DSYMM('L', 'L', IPAR(1), IPAR(1), ONE, C, LDC, A, LDA,
1 ZERO, DWORK, IPAR(1))
CALL DSYMM('R', 'L', IPAR(1), IPAR(1), ONE, C, LDC, DWORK,
1 IPAR(1), ZERO, A, LDA)
C .. G = R ! ..
G(1) = DPAR(1)
G(4) = DPAR(1)
G(6) = DPAR(1)
Q(1) = ONE/DPAR(1)
Q(4) = ONE
Q(6) = DPAR(1)
IDENT = '1000'
CALL DLASET('A', IPAR(1), IPAR(1), ZERO, ZERO, X, LDX)
TEMP = DPAR(1)**2
X(1,1) = TEMP + SQRT(TEMP**2 + ONE)
X(2,2) = TEMP*TWO + SQRT(FOUR*TEMP**2 + DPAR(1))
X(3,3) = TEMP*THREE + DPAR(1)*SQRT(9.0D0*TEMP + ONE)
CALL DSYMM('L', 'L', IPAR(1), IPAR(1), ONE, C, LDC, X, LDX,
1 ZERO, DWORK, IPAR(1))
CALL DSYMM('R', 'L', IPAR(1), IPAR(1), ONE, C, LDC, DWORK,
1 IPAR(1), ZERO, X, LDX)
ELSE
INFO = 2
END IF
C
ELSE IF (NR(2) .EQ. 7) THEN
IF (DPAR(1) .NE. ZERO) THEN
A(1,2) = .400D0
A(2,3) = .345D0
A(3,2) = -.524D0/DPAR(1)
A(3,3) = -.465D0/DPAR(1)
A(3,4) = .262D0/DPAR(1)
A(4,4) = -ONE/DPAR(1)
B(4,1) = ONE/DPAR(1)
C(1,1) = ONE
C(2,3) = ONE
IDENT = '0011'
ELSE
INFO = 2
END IF
C
ELSE IF (NR(2) .EQ. 8) THEN
A(1,1) = -DPAR(1)
A(2,1) = -ONE
A(1,2) = ONE
A(2,2) = -DPAR(1)
A(3,3) = DPAR(1)
A(4,3) = -ONE
A(3,4) = ONE
A(4,4) = DPAR(1)
CALL DLASET('L', IPAR(1), IPAR(2), ONE, ONE, B, LDB)
CALL DLASET('U', IPAR(3), IPAR(1), ONE, ONE, C, LDC)
IDENT = '0011'
C
ELSE IF (NR(2) .EQ. 9) THEN
IF (IPAR(3) .EQ. 10) THEN
C .. read LQR CARE ...
WRITE (CHPAR(1:12), '(A,I1,A,I1,A)') 'BB01', NR(1), '0',
1 NR(2), '1.dat'
OPEN(1, IOSTAT = IOS, STATUS = 'OLD', FILE = CHPAR(1:12))
IF (IOS .NE. 0) THEN
INFO = 1
ELSE
DO 36 I = 1, 27, 2
READ (1, FMT = *, IOSTAT = IOS)
1 ((A(I+J,I+K), K = 0, 1), J = 0, 1)
IF (IOS .NE. 0) INFO = 1
36 CONTINUE
DO 37 I = 30, 44, 2
READ (1, FMT = *, IOSTAT = IOS)
1 ((A(I+J,I+K), K = 0, 1), J = 0, 1)
IF (IOS .NE. 0) INFO = 1
37 CONTINUE
DO 38 I = 1, IPAR(1)
READ (1, FMT = *, IOSTAT = IOS)
1 (A(I,J), J = 46, IPAR(1))
IF (IOS .NE. 0) INFO = 1
38 CONTINUE
A(29,29) = -.5301D1
B(48,1) = .8D06
B(51,2) = .8D06
G(1) = .3647D03
G(3) = .1459D02
DO 39 I = 1,6
READ (1, FMT = *, IOSTAT = IOS)
1 (C(I,J), J = 1,45)
IF (IOS .NE. 0) INFO = 1
39 CONTINUE
C(7,47) = ONE
C(8,46) = ONE
C(9,50) = ONE
C(10,49) = ONE
Q(11) = .376D-13
Q(20) = .120D-12
Q(41) = .245D-11
END IF
ELSE
C .. read Kalman filter CARE ..
WRITE (CHPAR(1:12), '(A,I1,A,I1,A)') 'BB01', NR(1), '0',
1 NR(2), '2.dat'
OPEN(1, IOSTAT = IOS, STATUS = 'OLD', FILE = CHPAR(1:12))
IF (IOS .NE. 0) THEN
INFO = 1
ELSE
DO 40 I = 1, 27, 2
READ (1, FMT = *, IOSTAT = IOS)
1 ((A(I+K,I+J), K = 0, 1), J = 0, 1)
IF (IOS .NE. 0) INFO = 1
40 CONTINUE
DO 41 I = 30, 44, 2
READ (1, FMT = *, IOSTAT = IOS)
1 ((A(I+K,I+J), K = 0, 1), J = 0, 1)
IF (IOS .NE. 0) INFO = 1
41 CONTINUE
DO 42 I = 1, IPAR(1)
READ (1, FMT = *, IOSTAT = IOS)
1 (A(J,I), J = 46, IPAR(1))
IF (IOS .NE. 0) INFO = 1
42 CONTINUE
A(29,29) = -.5301D1
DO 43 J = 1, IPAR(2)
READ (1, FMT = *, IOSTAT = IOS)
1 (B(I,J), I = 1, IPAR(1))
IF (IOS .NE. 0) INFO = 1
43 CONTINUE
G(1) = .685D-5
G(3) = .373D3
C(1,52) = .3713
C(1,53) = .1245D1
C(2,48) = .8D6
C(2,54) = ONE
C(3,51) = .8D6
C(3,55) = ONE
Q(1) = .28224D5
Q(4) = .2742D-4
Q(6) = .6854D-3
END IF
END IF
CLOSE(1)
IDENT = '0000'
END IF
C
ELSE IF (NR(1) .EQ. 3) THEN
IF (NR(2) .EQ. 1) THEN
DO 45 I = 1, IPAR(1)
IF (MOD(I,2) .EQ. 1) THEN
A(I,I) = -ONE
B(I,(I+1)/2) = ONE
ELSE
A(I,I-1) = ONE
A(I,I+1) = -ONE
C(I/2,I) = ONE
END IF
45 CONTINUE
ISYMM = 1
DO 50 I = IPAR(3), 1, -1
Q(ISYMM) = 10.0D0
ISYMM = ISYMM + I
50 CONTINUE
IDENT = '0001'
C
ELSE IF (NR(2) .EQ. 2) THEN
DO 60 I = 1, IPAR(1)
A(I,I) = -TWO
IF (I .LT. IPAR(1)) THEN
A(I,I+1) = ONE
A(I+1,I) = ONE
END IF
60 CONTINUE
A(1,IPAR(1)) = ONE
A(IPAR(1),1) = ONE
IDENT = '1111'
TEMP = TWO * PI / DBLE(IPAR(1))
DO 70 I = 1, IPAR(1)
DWORK(I) = COS(TEMP*DBLE(I-1))
DWORK(IPAR(1)+I) = -TWO + TWO*DWORK(I) +
1 SQRT(5.0D0 + FOUR*DWORK(I)*(DWORK(I) - TWO))
70 CONTINUE
DO 90 J = 1, IPAR(1)
DO 80 I = 1, IPAR(1)
DWORK(2*IPAR(1)+I) = COS(TEMP*DBLE(I-1)*DBLE(J-1))
80 CONTINUE
X(J,1) = DDOT(IPAR(1), DWORK(IPAR(1)+1), 1,
1 DWORK(2*IPAR(1)+1), 1)/DBLE(IPAR(1))
90 CONTINUE
C .. set up circulant solution matrix ..
DO 100 I = 2, IPAR(1)
CALL DCOPY(IPAR(1)-I+1, X(1,1), 1, X(I,I), 1)
CALL DCOPY(I-1, X(IPAR(1)-I+2,1), 1, X(1,I), 1)
100 CONTINUE
END IF
C
ELSE IF (NR(1) .EQ. 4) THEN
IF (NR(2) .EQ. 1) THEN
C .. set up remaining parameter ..
IF (.NOT. LSAME(DEF,'N')) THEN
DPAR(1) = ONE
DPAR(2) = ONE
END IF
CALL DLASET('A', IPAR(1)-1, IPAR(1)-1, ZERO, ONE, A(1,2), LDA)
B(IPAR(1),1) = ONE
C(1,1) = ONE
Q(1) = DPAR(1)
G(1) = DPAR(2)
IDENT = '0000'
C
ELSE IF (NR(2) .EQ. 2) THEN
C .. set up remaining parameters ..
APPIND = DBLE(IPAR(1) + 1)
IF (.NOT. LSAME(DEF,'N')) THEN
DPAR(1) = PARDEF(NR(1), NR(2))
DPAR(2) = ONE
DPAR(3) = ONE
DPAR(4) = .2D0
DPAR(5) = .3D0
DPAR(6) = .2D0
DPAR(7) = .3D0
END IF
C .. set up stiffness matrix ..
TEMP = -DPAR(1)*APPIND
CALL DLASET('A', IPAR(1), IPAR(1), ZERO, TWO*TEMP, A, LDA)
DO 110 I = 1, IPAR(1) - 1
A(I+1,I) = -TEMP
A(I,I+1) = -TEMP
110 CONTINUE
C .. set up Gramian, stored by diagonals ..
TEMP = ONE/(6.0D0*APPIND)
CALL DLASET('L', IPAR(1), 1, FOUR*TEMP, FOUR*TEMP, DWORK,
1 IPAR(1))
CALL DLASET('L', IPAR(1)-1, 1, TEMP, TEMP, DWORK(IPAR(1)+1),
1 IPAR(1))
CALL DPTTRF(IPAR(1), DWORK(1), DWORK(IPAR(1)+1), INFO)
C .. A = (inverse of Gramian) * (stiffness matrix) ..
CALL DPTTRS(IPAR(1), IPAR(1), DWORK(1), DWORK(IPAR(1)+1),
1 A, LDA, INFO)
C .. compute B, C ..
DO 120 I = 1, IPAR(1)
B1 = MAX(DBLE(I-1)/APPIND, DPAR(4))
B2 = MIN(DBLE(I+1)/APPIND, DPAR(5))
C1 = MAX(DBLE(I-1)/APPIND, DPAR(6))
C2 = MIN(DBLE(I+1)/APPIND, DPAR(7))
IF (B1 .GE. B2) THEN
B(I,1) = ZERO
ELSE
B(I,1) = B2 - B1
TEMP = MIN(B2, DBLE(I)/APPIND)
IF (B1 .LT. TEMP) THEN
B(I,1) = B(I,1) + APPIND*(TEMP**2 - B1**2)/TWO
B(I,1) = B(I,1) + DBLE(I)*(B1 - TEMP)
END IF
TEMP = MAX(B1, DBLE(I)/APPIND)
IF (TEMP .LT. B2) THEN
B(I,1) = B(I,1) - APPIND*(B2**2 - TEMP**2)/TWO
B(I,1) = B(I,1) - DBLE(I)*(TEMP - B2)
END IF
END IF
IF (C1 .GE. C2) THEN
C(1,I) = ZERO
ELSE
C(1,I) = C2 - C1
TEMP = MIN(C2, DBLE(I)/APPIND)
IF (C1 .LT. TEMP) THEN
C(1,I) = C(1,I) + APPIND*(TEMP**2 - C1**2)/TWO
C(1,I) = C(1,I) + DBLE(I)*(C1 - TEMP)
END IF
TEMP = MAX(C1, DBLE(I)/APPIND)
IF (TEMP .LT. C2) THEN
C(1,I) = C(1,I) - APPIND*(C2**2 - TEMP**2)/TWO
C(1,I) = C(1,I) - DBLE(I)*(TEMP - C2)
END IF
END IF
120 CONTINUE
CALL DSCAL(IPAR(1), DPAR(2), B(1,1), 1)
CALL DSCAL(IPAR(1), DPAR(3), C(1,1), LDC)
CALL DPTTRS(IPAR(1), 1, DWORK(1), DWORK(IPAR(1)+1), B, LDB,
1 INFO)
IDENT = '0011'
C
ELSE IF (NR(2) .EQ. 3) THEN
C .. set up remaining parameters ..
IF (.NOT. LSAME(DEF,'N')) THEN
DPAR(1) = PARDEF(NR(1),NR(2))
DPAR(2) = FOUR
DPAR(3) = ONE
END IF
IF (DPAR(1) . NE. 0) THEN
CALL DLASET('A', L, L, ZERO, ONE, A(1,L+1), LDA)
TEMP = DPAR(3) / DPAR(1)
A(L+1,1) = -TEMP
A(L+1,2) = TEMP
A(IPAR(1),L-1) = TEMP
A(IPAR(1),L) = -TEMP
TTEMP = TWO*TEMP
DO 130 I = 2, L-1
A(L+I,I) = -TTEMP
A(L+I,I+1) = TEMP
A(L+I,I-1) = TEMP
130 CONTINUE
CALL DLASET('A', L, L, ZERO, -DPAR(2)/DPAR(1), A(L+1,L+1),
1 LDA)
B(L+1,1) = ONE / DPAR(1)
B(IPAR(1),IPAR(2)) = -ONE / DPAR(1)
IDENT = '0111'
ELSE
INFO = 2
END IF
C
ELSE IF (NR(2) .EQ. 4) THEN
IF (.NOT. LSAME(DEF,'N')) THEN
WRITE (CHPAR(1:11), '(A,I1,A,I1,A)')
1 'BB01', NR(1), '0', NR(2), '.dat'
I = 11
ELSE
I = IPAR(4)
END IF
OPEN(1, IOSTAT = IOS, STATUS = 'OLD', FILE = CHPAR(1:I))
IF (IOS .NE. 0) THEN
INFO = 1
ELSE
READ (1, FMT = *, IOSTAT = IOS) (DWORK(I), I = 1, 4*L-2)
IF (IOS .NE. 0) INFO = 1
END IF
CLOSE(1)
IF (INFO .EQ. 0) THEN
CALL DLASET('A', L-1, L-1, ZERO, ONE, A(L+1,2), LDA)
POS = 2*L + 1
A(1,2) = - DWORK(POS) / DWORK(1)
DO 140 I = 2, L
TEMP = DWORK(POS) / DWORK(I-1)
TTEMP = DWORK(POS) / DWORK(I)
IF (I .GT. 2) A(I-1,I) = TEMP
A(I,I) = -(TEMP + TTEMP)
IF (I .LT. L) A(I+1,I) = TTEMP
POS = POS + 1
140 CONTINUE
POS = L
TEMP = DWORK(POS+1) / DWORK(1)
A(1,1) = -TEMP
DO 160 I = 2, L
TTEMP = TEMP
TEMP = DWORK(POS+I) / DWORK(I)
SUM = TTEMP - TEMP
A(I,1) = -SUM
A(I,I) = A(I,I) - TEMP
DO 150 J = 2, I-2
A(I,J) = SUM
150 CONTINUE
IF (I .GT. 2) A(I,I-1) = A(I,I-1) + SUM
160 CONTINUE
POS = 3*L
A(1,L+1) = -DWORK(3*L)/DWORK(1)
DO 170 I = 2, L
TEMP = DWORK(POS) / DWORK(I-1)
TTEMP = DWORK(POS) / DWORK(I)
IF (I .GT. 2) A(I-1,L+I-1) = TEMP
A(I,L+I-1) = -(TEMP + TTEMP)
IF (I .LT. L) A(I+1,L+I-1) = TTEMP
POS = POS + 1
170 CONTINUE
B(1,1) = ONE/DWORK(1)
DO 180 I = 1, L
TEMP = ONE/DWORK(I)
IF (I .GT. 1) B(I,I) = -TEMP
IF (I .LT. L) B(I+1,I) = TEMP
180 CONTINUE
C(1,1) = ONE
Q(1) = ONE
POS = 2*L - 1
ISYMM = L + 1
DO 190 I = 2, L
TEMP = DWORK(POS+I)
TTEMP = DWORK(POS+L+I-1)
C(I,I) = TEMP
C(I,L+I-1) = TTEMP
Q(ISYMM) = ONE / (TEMP*TEMP + TTEMP*TTEMP)
ISYMM = ISYMM + L - I + 1
190 CONTINUE
IDENT = '0001'
END IF
END IF
END IF
C
IF (INFO .NE. 0) GOTO 2001
C .. set up data in required format ..
C
IF (BPAR(1)) THEN
C .. G is to be returned in product form ..
GDIMM = IPAR(1)
IF (IDENT(4:4) .EQ. '0') THEN
C .. invert R using Cholesky factorization, store in G ..
CALL DPPTRF('L', IPAR(2), G, INFO)
IF (INFO .EQ. 0) THEN
CALL DPPTRI('L', IPAR(2), G, INFO)
IF (IDENT(1:1) .EQ. '0') THEN
C .. B is not identity matrix ..
DO 200 I = 1, IPAR(1)
CALL DSPMV('L', IPAR(2), ONE, G, B(I,1), LDB, ZERO,
1 DWORK((I-1)*IPAR(1)+1), 1)
200 CONTINUE
CALL DGEMV('T', IPAR(2), IPAR(1), ONE, DWORK, IPAR(1),
1 B(1,1), LDB, ZERO, G, 1)
ISYMM = IPAR(1) + 1
DO 210 I = 2, IPAR(1)
CALL DGEMV('T', IPAR(2), IPAR(1), ONE, DWORK, IPAR(1),
1 B(I,1), LDB, ZERO, B(1,1), LDB)
CALL DCOPY(IPAR(1) - I + 1, B(1,I), LDB, G(ISYMM), 1)
ISYMM = ISYMM + (IPAR(1) - I + 1)
210 CONTINUE
END IF
ELSE
IF (INFO .GT. 0) THEN
INFO = 3
GOTO 2001
END IF
END IF
ELSE
C .. R = identity ..
IF (IDENT(1:1) .EQ. '0') THEN
C .. B is not identity matrix ..
IF (IPAR(2) .EQ. 1) THEN
CALL DLASET('L', NSYMM, 1, ZERO, ZERO, G, 1)
CALL DSPR('L', IPAR(1), ONE, B, 1, G)
ELSE
CALL DSYRK('L', 'N', IPAR(1), IPAR(2), ONE,
1 B, LDB, ZERO, DWORK, IPAR(1))
CALL MA02DD('Pack', 'Lower', IPAR(1), DWORK, IPAR(1), G)
END IF
ELSE
C .. B = R = identity ..
ISYMM = 1
DO 220 I = IPAR(1), 1, -1
G(ISYMM) = ONE
ISYMM = ISYMM + I
220 CONTINUE
END IF
END IF
ELSE
GDIMM = IPAR(2)
IF (IDENT(1:1) .EQ. '1')
1 CALL DLASET('A', IPAR(1), IPAR(2), ZERO, ONE, B, LDB)
IF (IDENT(4:4) .EQ. '1') THEN
ISYMM = 1
DO 230 I = IPAR(2), 1, -1
G(ISYMM) = ONE
ISYMM = ISYMM + I
230 CONTINUE
END IF
END IF
C
IF (BPAR(4)) THEN
C .. Q is to be returned in product form ..
QDIMM = IPAR(1)
IF (IDENT(3:3) .EQ. '0') THEN
IF (IDENT(2:2) .EQ. '0') THEN
C .. C is not identity matrix ..
DO 240 I = 1, IPAR(1)
CALL DSPMV('L', IPAR(3), ONE, Q, C(1,I), 1, ZERO,
1 DWORK((I-1)*IPAR(1)+1), 1)
240 CONTINUE
C .. use Q(1:IPAR(1)) as workspace and compute the first column
C of Q in the end ..
ISYMM = IPAR(1) + 1
DO 250 I = 2, IPAR(1)
CALL DGEMV('T', IPAR(3), IPAR(1), ONE, DWORK, IPAR(1),
1 C(1,I), 1, ZERO, Q(1), 1)
CALL DCOPY(IPAR(1) - I + 1, Q(I), 1, Q(ISYMM), 1)
ISYMM = ISYMM + (IPAR(1) - I + 1)
250 CONTINUE
CALL DGEMV('T', IPAR(3), IPAR(1), ONE, DWORK, IPAR(1),
1 C(1,1), 1, ZERO, Q, 1)
END IF
ELSE
C .. Q = identity ..
IF (IDENT(2:2) .EQ. '0') THEN
C .. C is not identity matrix ..
IF (IPAR(3) .EQ. 1) THEN
CALL DLASET('L', NSYMM, 1, ZERO, ZERO, Q, 1)
CALL DSPR('L', IPAR(1), ONE, C, LDC, Q)
ELSE
CALL DSYRK('L', 'T', IPAR(1), IPAR(3), ONE, C, LDC,
1 ZERO, DWORK, IPAR(1))
CALL MA02DD('Pack', 'Lower', IPAR(1), DWORK, IPAR(1), Q)
END IF
ELSE
C .. C = Q = identity ..
ISYMM = 1
DO 260 I = IPAR(1), 1, -1
Q(ISYMM) = ONE
ISYMM = ISYMM + I
260 CONTINUE
END IF
END IF
ELSE
QDIMM = IPAR(3)
IF (IDENT(2:2) .EQ. '1')
1 CALL DLASET('A', IPAR(3), IPAR(1), ZERO, ONE, C, LDC)
IF (IDENT(3:3) .EQ. '1') THEN
ISYMM = 1
DO 270 I = IPAR(3), 1, -1
Q(ISYMM) = ONE
ISYMM = ISYMM + I
270 CONTINUE
END IF
END IF
C
C .. unpack symmetric matrices if desired ..
IF (BPAR(2)) THEN
ISYMM = (GDIMM * (GDIMM + 1)) / 2
CALL DCOPY(ISYMM, G, 1, DWORK, 1)
CALL MA02DD('Unpack', 'Lower', GDIMM, G, LDG, DWORK)
CALL MA02ED('Lower', GDIMM, G, LDG)
ELSE IF (BPAR(3)) THEN
CALL MA02DD('Unpack', 'Lower', GDIMM, DWORK, GDIMM, G)
CALL MA02ED('Lower', GDIMM, DWORK, GDIMM)
CALL MA02DD('Pack', 'Upper', GDIMM, DWORK, GDIMM, G)
END IF
IF (BPAR(5)) THEN
ISYMM = (QDIMM * (QDIMM + 1)) / 2
CALL DCOPY(ISYMM, Q, 1, DWORK, 1)
CALL MA02DD('Unpack', 'Lower', QDIMM, Q, LDQ, DWORK)
CALL MA02ED('Lower', QDIMM, Q, LDQ)
ELSE IF (BPAR(6)) THEN
CALL MA02DD('Unpack', 'Lower', QDIMM, DWORK, QDIMM, Q)
CALL MA02ED('Lower', QDIMM, DWORK, QDIMM)
CALL MA02DD('Pack', 'Upper', QDIMM, DWORK, QDIMM, Q)
END IF
C
C ...set VEC...
VEC(1) = .TRUE.
VEC(2) = .TRUE.
VEC(3) = .TRUE.
VEC(4) = .TRUE.
VEC(5) = .NOT. BPAR(1)
VEC(6) = .NOT. BPAR(4)
VEC(7) = .TRUE.
VEC(8) = .TRUE.
IF (NR(1) .EQ. 1) THEN
IF ((NR(2) .EQ. 1) .OR. (NR(2) .EQ. 2)) VEC(9) = .TRUE.
ELSE IF (NR(1) .EQ. 2) THEN
IF ((NR(2) .EQ. 1) .OR. ((NR(2) .GE. 3) .AND. (NR(2) .LE. 6)))
1 VEC(9) = .TRUE.
ELSE IF (NR(1) .EQ. 3) THEN
IF (NR(2) .EQ. 2) VEC(9) = .TRUE.
END IF
CHPAR = NOTES(NR(1),NR(2))
N = IPAR(1)
M = IPAR(2)
P = IPAR(3)
2001 CONTINUE
RETURN
C *** Last line of BB01AD ***
END