NF01BW

Matrix-vector product x <-- (J' J + c I) x, for J in a compressed form

Purpose

  To compute the matrix-vector product x <-- (J'*J + c*I)*x, for the
  Jacobian J as received from SLICOT Library routine NF01BD:

       /  dy(1)/dwb(1)  |  dy(1)/dtheta  \
  Jc = |       :        |       :        | .
       \  dy(L)/dwb(L)  |  dy(L)/dtheta  /

  This is a compressed representation of the actual structure

      /   J_1    0    ..   0   |  L_1  \
      |    0    J_2   ..   0   |  L_2  |
  J = |    :     :    ..   :   |   :   | .
      |    :     :    ..   :   |   :   |
      \    0     0    ..  J_L  |  L_L  /

      SUBROUTINE NF01BW( N, IPAR, LIPAR, DPAR, LDPAR, J, LDJ, X, INCX,
     $                   DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
      INTEGER           INCX, INFO, LDJ, LDPAR, LDWORK, LIPAR, N
C     .. Array Arguments ..
      DOUBLE PRECISION  DPAR(*), DWORK(*), J(LDJ,*), X(*)
      INTEGER           IPAR(*)

Input/Output Parameters

  N       (input) INTEGER
          The dimension of the vector x.
          N = BN*BSN + ST >= 0.  (See parameter description below.)

  IPAR    (input) INTEGER array, dimension (LIPAR)
          The integer parameters describing the structure of the
          matrix J, as follows:
          IPAR(1) must contain ST, the number of parameters
                  corresponding to the linear part.  ST >= 0.
          IPAR(2) must contain BN, the number of blocks, BN = L,
                  for the parameters corresponding to the nonlinear
                  part.  BN >= 0.
          IPAR(3) must contain BSM, the number of rows of the blocks
                  J_k = dy(k)/dwb(k), k = 1:BN, if BN > 0, or the
                  number of rows of the matrix J, if BN <= 1.
          IPAR(4) must contain BSN, the number of columns of the
                  blocks J_k, k = 1:BN.  BSN >= 0.

  LIPAR   (input) INTEGER
          The length of the array IPAR.  LIPAR >= 4.

  DPAR    (input) DOUBLE PRECISION array, dimension (LDPAR)
          The real parameters needed for solving the problem.
          The entry DPAR(1) must contain the real scalar c.

  LDPAR   (input) INTEGER
          The length of the array DPAR.  LDPAR >= 1.

  J       (input) DOUBLE PRECISION array, dimension (LDJ, NC)
          where NC = N if BN <= 1, and NC = BSN+ST, if BN > 1.
          The leading NR-by-NC part of this array must contain
          the (compressed) representation (Jc) of the Jacobian
          matrix J, where NR = BSM if BN <= 1, and NR = BN*BSM,
          if BN > 1.

  LDJ     (input) INTEGER
          The leading dimension of array J.  LDJ >= MAX(1,NR).

  X       (input/output) DOUBLE PRECISION array, dimension
          (1+(N-1)*INCX)
          On entry, this incremented array must contain the
          vector x.
          On exit, this incremented array contains the value of the
          matrix-vector product (J'*J + c*I)*x.

  INCX    (input) INTEGER
          The increment for the elements of X.  INCX >= 1.

  DWORK   DOUBLE PRECISION array, dimension (LDWORK)

  LDWORK  INTEGER
          The length of the array DWORK.  LDWORK >= NR.

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value.

  The associativity of matrix multiplications is used; the result
  is obtained as:  x_out = J'*( J*x ) + c*x.

  None

Program Text

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