C.4.14. Subroutine FMSVAN

PURPOSE

This subroutine provides a collection of vector utilities primarily used in iterative algorithms. Several processing options are included, as determined by the parameter IOPT. Generally {X} represents the solution values and {Y} the change in solution values, or the solution at a different iteration. The norm RNORM is the ratio of solution increment to solution value.

The following options are implemented:

IOPT	IALPHA	{X} on Output	RNORM
0	Not Used	Unchanged	\|\| {X} \|\|
1	-1	{X}={X}-{Y}	\|\| Y(i) / ( X(i)-Y(i) ) \|\|
1	+1	{X}={X}+{Y}	\|\| Y(i) / ( X(i)+Y(i) ) \|\|
2	Not Used	Unchanged	\|\| ( X(i)-Y(i) ) / X(i) \|\|
3	Not Used	{X}={Y}	\|\| ( Y(i)-X(i)) / Y(i) \|\|

SYNOPSIS


CALL FMSVAN (LUX, IALPHA, LUY, INORM, RNORM, IOPT)

INPUT PARAMETERS

LUX(25) = Integer array.
File attributes for the {X} vectors.
IALPHA = Integer.
Scale factor for {Y} vectors.
LUY(25) = Integer array.
File attributes for the {Y} vectors.
INORM = Integer.
Number of the norm to compute:
RNORM = ( SUM( ABS(X(i))**INORM ) )**(1/INORM)

The exception being when INORM=0, the infinity norm is computed.

The implemented norms are:

INORM RNORM

0 MAX(ABS(X(i)))

1 SUM(ABS(X(i)))

2 SQRT(SUM(X(i)**2))
IOPT = Integer.
Processing options.

INORM	RNORM
0	MAX(ABS(X(i)))
1	SUM(ABS(X(i)))
2	SQRT(SUM(X(i)**2))

OUTPUT PARAMETERS:

RNORM = Real.
Vector norm.

DESCRIPTION:

This subroutine is a collection of vector utilities that are typically used in iterative algorithms. The computed norm RNORM may be used to test for convergence.

The parameter IOPT determines if the vector {X} is modified and how the norm is computed. The following options are implemented:

IOPT=0
Compute the norm of {X}. On exit, {X} is unchanged. The parameters IALPHA and LUY are not used.
IOPT=1
{X} is the solution and {Y} is the increment, which may be added (IALPHA=1) to, or subtracted (IALPHA=-1) from {X}. The norm RNORM is the ratio of the increment to the new solution value.
IOPT=2
{X} is the new solution and {Y} is the previous solution. The norm RNORM is the ratio of the change in solution to the new solution value. On exit, {X} is unchanged. The parameter IALPHA is not used.
IOPT=3
{X} is the previous solution and {Y} is the new solution. The norm RNORM is the ratio of the change in solution to the new solution value. On exit, the new solution value {Y} is moved to the previous solution {X}. The parameter IALPHA is not used.