SUBROUTINE NF01BV( 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 NF01BY, for one output variable.
C
C NOTE: this routine must have the same arguments as SLICOT Library
C routine NF01BU.
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 number of columns of the Jacobian matrix J. N >= 0.
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 the number of rows M of the Jacobian
C matrix J. M >= 0.
C IPAR is provided for compatibility with SLICOT Library
C routine MD03AD.
C
C LIPAR (input) INTEGER
C The length of the array IPAR. LIPAR >= 1.
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,N)
C The leading M-by-N part of this array must contain the
C Jacobian matrix J.
C
C LDJ INTEGER
C The leading dimension of the array J. LDJ >= MAX(1,M).
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 routine DSYRK is used if STOR = 'F', and BLAS 2
C 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, March 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 ..
INTEGER IPAR(*)
DOUBLE PRECISION DPAR(*), DWORK(*), J(LDJ,*), JTJ(*)
C .. Local Scalars ..
LOGICAL FULL, UPPER
INTEGER I, II, M
DOUBLE PRECISION C
C .. Local Arrays ..
DOUBLE PRECISION DUM(1)
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL DCOPY, DGEMV, DLASET, DSYRK, XERBLA
C .. Intrinsic Functions ..
INTRINSIC MAX
C ..
C .. Executable Statements ..
C
INFO = 0
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.1 ) 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
M = IPAR(1)
IF ( M.LT.0 ) THEN
INFO = -4
ELSEIF ( LDJ.LT.MAX( 1, M ) ) THEN
INFO = -9
ENDIF
ENDIF
C
C Return if there are illegal arguments.
C
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'NF01BV', -INFO )
RETURN
ENDIF
C
C Quick return if possible.
C
C = DPAR(1)
IF ( N.EQ.0 ) THEN
RETURN
ELSE IF ( M.EQ.0 ) THEN
IF ( FULL ) THEN
CALL DLASET( UPLO, N, N, ZERO, C, JTJ, LDJTJ )
ELSE
DUM(1) = ZERO
CALL DCOPY( ( N*( N + 1 ) )/2, DUM, 0, JTJ, 1 )
IF ( UPPER ) THEN
II = 0
C
DO 10 I = 1, N
II = II + I
JTJ(II) = C
10 CONTINUE
C
ELSE
II = 1
C
DO 20 I = N, 1, -1
JTJ(II) = C
II = II + I
20 CONTINUE
C
ENDIF
ENDIF
RETURN
ENDIF
C
C Build a triangle of the matrix J'*J + c*I.
C
IF ( FULL ) THEN
CALL DLASET( UPLO, N, N, ZERO, C, JTJ, LDJTJ )
CALL DSYRK( UPLO, 'Transpose', N, M, ONE, J, LDJ, ONE, JTJ,
$ LDJTJ )
ELSEIF ( UPPER ) THEN
II = 0
C
DO 30 I = 1, N
CALL DGEMV( 'Transpose', M, I, ONE, J, LDJ, J(1,I), 1, ZERO,
$ JTJ(II+1), 1 )
II = II + I
JTJ(II) = JTJ(II) + C
30 CONTINUE
C
ELSE
II = 1
C
DO 40 I = N, 1, -1
CALL DGEMV( 'Transpose', M, I, ONE, J(1,N-I+1), LDJ,
$ J(1,N-I+1), 1, ZERO, JTJ(II), 1 )
JTJ(II) = JTJ(II) + C
II = II + I
40 CONTINUE
C
ENDIF
C
RETURN
C
C *** Last line of NF01BV ***
END