Purpose
To compute (J'*J + c*I)*x, where J is an m-by-n real matrix, c is a real scalar, I is the n-by-n identity matrix, and x is a real n-vector. NOTE: this routine must have the same arguments as SLICOT Library routine NF01BW.Specification
SUBROUTINE NF01BX( 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 ..
INTEGER IPAR(*)
DOUBLE PRECISION DPAR(*), DWORK(*), J(LDJ,*), X(*)
Arguments
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).
X (input/output) DOUBLE PRECISION array, dimension
(1+(N-1)*abs(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 <> 0.
Workspace
DWORK DOUBLE PRECISION array, dimension (LDWORK)
LDWORK INTEGER
The length of the array DWORK. LDWORK >= M.
Error Indicator
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
Method
The associativity of matrix multiplications is used; the result is obtained as: x_out = J'*( J*x ) + c*x.Further Comments
NoneExample
Program Text
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