NF01BU - SLICOT Library Routine Documentation

## NF01BU

### Computation of the matrix J' J + c I, for the Jacobian J given in a compressed form

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

      To compute the matrix J'*J + c*I, 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  /

Specification

          SUBROUTINE NF01BU( STOR, UPLO, N, IPAR, LIPAR, DPAR, LDPAR, J,
         $                   LDJ, JTJ, LDJTJ, DWORK, LDWORK, INFO )
    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(*)

Arguments

Mode Parameters

      STOR    CHARACTER*1
              Specifies the storage scheme for the symmetric
              matrix J'*J + c*I, as follows:
              = 'F' :  full storage is used;
              = 'P' :  packed storage is used.

      UPLO    CHARACTER*1
              Specifies which part of the matrix J'*J + c*I is stored,
              as follows:
              = 'U' :  the upper triagular part is stored;
              = 'L' :  the lower triagular part is stored.

Input/Output Parameters

      N       (input) INTEGER
              The order of the matrix J'*J + c*I.
              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).

      JTJ     (output) DOUBLE PRECISION array,
                       dimension (LDJTJ,N),    if STOR = 'F',
                       dimension (N*(N+1)/2),  if STOR = 'P'.
              The leading N-by-N (if STOR = 'F'), or N*(N+1)/2 (if
              STOR = 'P') part of this array contains the upper or
              lower triangle of the matrix J'*J + c*I, depending on
              UPLO = 'U', or UPLO = 'L', respectively, stored either as
              a two-dimensional, or one-dimensional array, depending
              on STOR.

      LDJTJ   INTEGER
              The leading dimension of the array JTJ.
              LDJTJ >= MAX(1,N), if STOR = 'F'.
              LDJTJ >= 1,        if STOR = 'P'.

Workspace

      DWORK   DOUBLE PRECISION array, dimension (LDWORK)
              Currently, this array is not used.

      LDWORK  INTEGER
              The length of the array DWORK.  LDWORK >= 0.

Error Indicator

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

Method

      The matrix product is computed columnn-wise, exploiting the
      symmetry. BLAS 3 routines DGEMM and DSYRK are used if STOR = 'F',
      and BLAS 2 routine DGEMV is used if STOR = 'P'.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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