## NF01BV

### Computation of the matrix J' J + c I, for a full Jacobian J (one output variable)

[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 NF01BY, for one output variable.

      NOTE: this routine must have the same arguments as SLICOT Library
      routine NF01BU.

Specification

          SUBROUTINE NF01BV( 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 ..
          INTEGER           IPAR(*)
          DOUBLE PRECISION  DPAR(*), DWORK(*), J(LDJ,*), JTJ(*)

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 number of columns of the Jacobian matrix J.  N >= 0.

      IPAR    (input) INTEGER array, dimension (LIPAR)
              The integer parameters describing the structure of the
              matrix J, as follows:
              IPAR(1) must contain the number of rows M of the Jacobian
                      matrix J.  M >= 0.
              IPAR is provided for compatibility with SLICOT Library
              routine MD03AD.

      LIPAR   (input) INTEGER
              The length of the array IPAR.  LIPAR >= 1.

      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,N)
              The leading M-by-N part of this array must contain the
              Jacobian matrix J.

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

      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 routine DSYRK is 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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