## 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'.

```
```  None
```
Example

Program Text

```  None
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Program Data
```  None
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Program Results
```  None
```