nittfq2 Interface

Dimension of the problem

Array of length n containing the current $x$ value

Array of length n containing current approximate solution

Vector of of length n containing trial step

Relative residual reduction factor

User-supplied subroutine for evaluating the function the zero of which is sought.

User-supplied subroutine for optionally evaluating $J\vec{v}$ or $P^{-1}\vec{v}$, where $J$ is the Jacobian of $f$ and $P$ is a right preconditioning operator. If neither analytic $J\vec{v}$ evaluations nor right preconditioning is used, this can be a dummy subroutine; if right preconditioning is used but not analytic $J\vec{v}$ evaluations, this need only evaluate $P^{-1}\vec{v}$.

Parameter/work array passed to the f and jacv routines

Parameter/work array passed to the f and jacv routines

Flag for determining method of $J\vec{v}$ evaluation. 0 (default) indicates finite-difference evaluation, while 1 indicates analytic evaluation.

Flag for right preconditioning. 0 indicates no preconditioning, while 1 inidcates right preconditioning.

Maximum allowable number of TFQMR iterations

Order of the finite-difference formula used in TFQMR when J*v products are evaluated using finite-differences. When ijacv = 0 on input to nitsol, ifdord is set to 1, 2, or 4 in nitsol; otherwise, it is irrelevant. When ijacv = 0 on input to this subroutine, ifdord determines the order of the finite-difference formula used at each TFQMR iteration (default 1). In this case, ijacv is set to -1 below to signal to nitjv that the order of the finite-difference formula is to be determined by ifdord. The original value ijacv = 0 is restored on return.

Number of function evaluations

Number of $J\vec{v}$ evaluations

Number of $P^{-1}\vec{v}$ evaluations

Number of linear iterations

Residual vector (for the QMR process)

Residual vector (of the underlying CGS process)

'Shadow' residual vector used in bi-orthogonalization

Vector used in TFQMR

Vector used in TFQMR

Vector used in TFQMR

Vector used in TFQMR

Vector used in TFQMR

Vector used in TFQMR

Work vector, passed on to nitjv

Work vector, passed on to nitjv

TFQMR residual norm on return

Inner-product routine, either user-supplied or BLAS ddot.

Norm routine, either user supplied or BLAS dnrm2.

Termination flag. Values have the following meanings:

0

normal termination: acceptable step found

1

$J\vec{v}$ failure in nitjv

2

$P^{-1}\vec{v}$ failure in nitjv

3

Acceptable step not found in iksmax TFQMR iterations

4

TFQMR breakdown

5

Floating point error (the underlying CGS iteration has probably blown up)