SUBROUTINE NF01BU( STOR, UPLO, N, IPAR, LIPAR, DPAR, LDPAR, J,
$ LDJ, JTJ, LDJTJ, DWORK, LDWORK, INFO )
C
C PURPOSE
C
C To compute the matrix J'*J + c*I, for the Jacobian J as received
C from SLICOT Library routine NF01BD:
C
C / dy(1)/dwb(1) | dy(1)/dtheta \
C Jc = | : | : | .
C \ dy(L)/dwb(L) | dy(L)/dtheta /
C
C This is a compressed representation of the actual structure
C
C / J_1 0 .. 0 | L_1 \
C | 0 J_2 .. 0 | L_2 |
C J = | : : .. : | : | .
C | : : .. : | : |
C \ 0 0 .. J_L | L_L /
C
C ARGUMENTS
C
C Mode Parameters
C
C STOR CHARACTER*1
C Specifies the storage scheme for the symmetric
C matrix J'*J + c*I, as follows:
C = 'F' : full storage is used;
C = 'P' : packed storage is used.
C
C UPLO CHARACTER*1
C Specifies which part of the matrix J'*J + c*I is stored,
C as follows:
C = 'U' : the upper triagular part is stored;
C = 'L' : the lower triagular part is stored.
C
C Input/Output Parameters
C
C N (input) INTEGER
C The order of the matrix J'*J + c*I.
C N = BN*BSN + ST >= 0. (See parameter description below.)
C
C IPAR (input) INTEGER array, dimension (LIPAR)
C The integer parameters describing the structure of the
C matrix J, as follows:
C IPAR(1) must contain ST, the number of parameters
C corresponding to the linear part. ST >= 0.
C IPAR(2) must contain BN, the number of blocks, BN = L,
C for the parameters corresponding to the nonlinear
C part. BN >= 0.
C IPAR(3) must contain BSM, the number of rows of the blocks
C J_k = dy(k)/dwb(k), k = 1:BN, if BN > 0, or the
C number of rows of the matrix J, if BN <= 1.
C IPAR(4) must contain BSN, the number of columns of the
C blocks J_k, k = 1:BN. BSN >= 0.
C
C LIPAR (input) INTEGER
C The length of the array IPAR. LIPAR >= 4.
C
C DPAR (input) DOUBLE PRECISION array, dimension (LDPAR)
C The real parameters needed for solving the problem.
C The entry DPAR(1) must contain the real scalar c.
C
C LDPAR (input) INTEGER
C The length of the array DPAR. LDPAR >= 1.
C
C J (input) DOUBLE PRECISION array, dimension (LDJ, NC)
C where NC = N if BN <= 1, and NC = BSN+ST, if BN > 1.
C The leading NR-by-NC part of this array must contain
C the (compressed) representation (Jc) of the Jacobian
C matrix J, where NR = BSM if BN <= 1, and NR = BN*BSM,
C if BN > 1.
C
C LDJ (input) INTEGER
C The leading dimension of array J. LDJ >= MAX(1,NR).
C
C JTJ (output) DOUBLE PRECISION array,
C dimension (LDJTJ,N), if STOR = 'F',
C dimension (N*(N+1)/2), if STOR = 'P'.
C The leading N-by-N (if STOR = 'F'), or N*(N+1)/2 (if
C STOR = 'P') part of this array contains the upper or
C lower triangle of the matrix J'*J + c*I, depending on
C UPLO = 'U', or UPLO = 'L', respectively, stored either as
C a two-dimensional, or one-dimensional array, depending
C on STOR.
C
C LDJTJ INTEGER
C The leading dimension of the array JTJ.
C LDJTJ >= MAX(1,N), if STOR = 'F'.
C LDJTJ >= 1, if STOR = 'P'.
C
C Workspace
C
C DWORK DOUBLE PRECISION array, dimension (LDWORK)
C Currently, this array is not used.
C
C LDWORK INTEGER
C The length of the array DWORK. LDWORK >= 0.
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
C METHOD
C
C The matrix product is computed columnn-wise, exploiting the
C symmetry. BLAS 3 routines DGEMM and DSYRK are used if STOR = 'F',
C and BLAS 2 routine DGEMV is used if STOR = 'P'.
C
C CONTRIBUTORS
C
C V. Sima, Research Institute for Informatics, Bucharest, Apr. 2001.
C
C REVISIONS
C
C V. Sima, Dec. 2001, Mar. 2002.
C
C KEYWORDS
C
C Elementary matrix operations, matrix algebra, matrix operations,
C Wiener system.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
C .. Scalar Arguments ..
CHARACTER STOR, UPLO
INTEGER INFO, LDJ, LDJTJ, LDPAR, LDWORK, LIPAR, N
C .. Array Arguments ..
DOUBLE PRECISION DPAR(*), DWORK(*), J(LDJ,*), JTJ(*)
INTEGER IPAR(*)
C .. Local Scalars ..
LOGICAL FULL, UPPER
INTEGER BN, BSM, BSN, I1, IBSM, IBSN, II, JL, K, M,
$ NBSN, NTHS, ST
DOUBLE PRECISION C
C .. Local Arrays ..
DOUBLE PRECISION TMP(1)
INTEGER ITMP(1)
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL DCOPY, DGEMM, DGEMV, DLASET, DSYRK, NF01BV,
$ XERBLA
C .. Intrinsic Functions ..
INTRINSIC MAX, MIN
C ..
C .. Executable Statements ..
C
INFO = 0
C
FULL = LSAME( STOR, 'F' )
UPPER = LSAME( UPLO, 'U' )
C
IF( .NOT.( FULL .OR. LSAME( STOR, 'P' ) ) ) THEN
INFO = -1
ELSEIF ( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
INFO = -2
ELSEIF ( N.LT.0 ) THEN
INFO = -3
ELSEIF ( LIPAR.LT.4 ) THEN
INFO = -5
ELSEIF ( LDPAR.LT.1 ) THEN
INFO = -7
ELSEIF ( LDJTJ.LT.1 .OR. ( FULL .AND. LDJTJ.LT.N ) ) THEN
INFO = -11
ELSEIF ( LDWORK.LT.0 ) THEN
INFO = -13
ELSE
ST = IPAR(1)
BN = IPAR(2)
BSM = IPAR(3)
BSN = IPAR(4)
NTHS = BN*BSN
IF ( BN.GT.1 ) THEN
M = BN*BSM
ELSE
M = BSM
END IF
IF ( MIN( ST, BN, BSM, BSN ).LT.0 ) THEN
INFO = -4
ELSEIF ( N.NE.NTHS + ST ) THEN
INFO = -3
ELSEIF ( LDJ.LT.MAX( 1, M ) ) THEN
INFO = -9
END IF
ENDIF
C
C Return if there are illegal arguments.
C
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'NF01BU', -INFO )
RETURN
ENDIF
C
C Quick return if possible.
C
IF ( N.EQ.0 )
$ RETURN
C
C = DPAR(1)
C
IF ( BN.LE.1 .OR. BSN.EQ.0 .OR. BSM.EQ.0 ) THEN
C
C Special case, l <= 1 or BSN = 0 or BSM = 0: the Jacobian is
C represented as a full matrix.
C
ITMP(1) = M
CALL NF01BV( STOR, UPLO, N, ITMP, 1, DPAR, 1, J, LDJ, JTJ,
$ LDJTJ, DWORK, LDWORK, INFO )
RETURN
END IF
C
C General case: l > 1, BSN > 0, BSM > 0.
C
JL = BSN + 1
C
IF ( FULL ) THEN
C
NBSN = N*BSN
C
IF ( UPPER ) THEN
C
C Compute the leading upper triangular part (full storage).
C
CALL DLASET( UPLO, BSN, BSN, ZERO, C, JTJ, LDJTJ )
CALL DSYRK( UPLO, 'Transpose', BSN, BSM, ONE, J, LDJ, ONE,
$ JTJ, LDJTJ )
IBSN = BSN
I1 = NBSN + 1
C
DO 10 IBSM = BSM + 1, M, BSM
II = I1 + IBSN
CALL DLASET( 'Full', IBSN, BSN, ZERO, ZERO, JTJ(I1),
$ LDJTJ )
I1 = I1 + NBSN
CALL DLASET( UPLO, BSN, BSN, ZERO, C, JTJ(II), LDJTJ )
CALL DSYRK( UPLO, 'Transpose', BSN, BSM, ONE, J(IBSM,1),
$ LDJ, ONE, JTJ(II), LDJTJ )
IBSN = IBSN + BSN
10 CONTINUE
C
IF ( ST.GT.0 ) THEN
C
C Compute the last block column.
C
DO 20 IBSM = 1, M, BSM
CALL DGEMM( 'Transpose', 'NoTranspose', BSN, ST, BSM,
$ ONE, J(IBSM,1), LDJ, J(IBSM,JL), LDJ,
$ ZERO, JTJ(I1), LDJTJ )
I1 = I1 + BSN
20 CONTINUE
C
CALL DLASET( UPLO, ST, ST, ZERO, C, JTJ(I1), LDJTJ )
CALL DSYRK( UPLO, 'Transpose', ST, M, ONE, J(1,JL),
$ LDJ, ONE, JTJ(I1), LDJTJ )
END IF
C
ELSE
C
C Compute the leading lower triangular part (full storage).
C
IBSN = NTHS
II = 1
C
DO 30 IBSM = 1, M, BSM
I1 = II + BSN
CALL DLASET( UPLO, BSN, BSN, ZERO, C, JTJ(II), LDJTJ )
CALL DSYRK( UPLO, 'Transpose', BSN, BSM, ONE, J(IBSM,1),
$ LDJ, ONE, JTJ(II), LDJTJ )
IBSN = IBSN - BSN
CALL DLASET( 'Full', IBSN, BSN, ZERO, ZERO, JTJ(I1),
$ LDJTJ )
II = I1 + NBSN
IF ( ST.GT.0 )
$ CALL DGEMM( 'Transpose', 'NoTranspose', ST, BSN, BSM,
$ ONE, J(IBSM,JL), LDJ, J(IBSM,1), LDJ,
$ ZERO, JTJ(I1+IBSN), LDJTJ )
30 CONTINUE
C
IF ( ST.GT.0 ) THEN
C
C Compute the last diagonal block.
C
CALL DLASET( UPLO, ST, ST, ZERO, C, JTJ(II), LDJTJ )
CALL DSYRK( UPLO, 'Transpose', ST, M, ONE, J(1,JL),
$ LDJ, ONE, JTJ(II), LDJTJ )
END IF
C
END IF
C
ELSE
C
TMP(1) = ZERO
C
IF ( UPPER ) THEN
C
C Compute the leading upper triangular part (packed storage).
C
IBSN = 0
I1 = 1
C
DO 50 IBSM = 1, M, BSM
C
DO 40 K = 1, BSN
II = I1 + IBSN
CALL DCOPY( IBSN, TMP, 0, JTJ(I1), 1 )
CALL DGEMV( 'Transpose', BSM, K, ONE, J(IBSM,1), LDJ,
$ J(IBSM,K), 1, ZERO, JTJ(II), 1 )
I1 = II + K
JTJ(I1-1) = JTJ(I1-1) + C
40 CONTINUE
C
IBSN = IBSN + BSN
50 CONTINUE
C
C Compute the last block column.
C
DO 70 K = 1, ST
C
DO 60 IBSM = 1, M, BSM
CALL DGEMV( 'Transpose', BSM, BSN, ONE, J(IBSM,1),
$ LDJ, J(IBSM,BSN+K), 1, ZERO, JTJ(I1), 1 )
I1 = I1 + BSN
60 CONTINUE
C
CALL DGEMV( 'Transpose', M, K, ONE, J(1,JL), LDJ,
$ J(1,BSN+K), 1, ZERO, JTJ(I1), 1 )
I1 = I1 + K
JTJ(I1-1) = JTJ(I1-1) + C
70 CONTINUE
C
ELSE
C
C Compute the leading lower triangular part (packed storage).
C
IBSN = NTHS
II = 1
C
DO 90 IBSM = 1, M, BSM
IBSN = IBSN - BSN
C
DO 80 K = 1, BSN
I1 = II + BSN - K + 1
CALL DCOPY( IBSN, TMP, 0, JTJ(I1), 1 )
CALL DGEMV( 'Transpose', BSM, BSN-K+1, ONE, J(IBSM,K),
$ LDJ, J(IBSM,K), 1, ZERO, JTJ(II), 1 )
JTJ(II) = JTJ(II) + C
I1 = I1 + IBSN
II = I1 + ST
IF ( ST.GT.0 )
$ CALL DGEMV( 'Transpose', BSM, ST, ONE, J(IBSM,JL),
$ LDJ, J(IBSM,K), 1, ZERO, JTJ(I1), 1 )
80 CONTINUE
C
90 CONTINUE
C
C Compute the last diagonal block.
C
DO 100 K = 1, ST
CALL DGEMV( 'Transpose', M, ST-K+1, ONE, J(1,BSN+K), LDJ,
$ J(1,BSN+K), 1, ZERO, JTJ(II), 1 )
JTJ(II) = JTJ(II) + C
II = II + ST - K + 1
100 CONTINUE
C
END IF
C
END IF
C
RETURN
C
C *** Last line of NF01BU ***
END