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The VARIOGRAM Procedure |

**COMPUTE***computation-options***;**

The COMPUTE statement provides a number of options that control the computation of the semivariogram, the robust semivariogram, and the covariance.

**ANGLETOLERANCE=***angle tolerance***ANGLETOL=***angle tolerance***ATOL=***angle tolerance*-
specifies
the tolerance, in degrees, around the angles determined by the
NDIRECTIONS= specification. The default is
[(180
^{o})/(2×*n*_{d})], where*n*_{d}is the NDIRECTIONS= specification.

See the section "Theoretical and Computational Details of the Semivariogram" for more detailed information. **BANDWIDTH=***bandwidth distance***BANDW=***bandwidth distance*-
specifies the
bandwidth, or perpendicular distance cutoff for determining
the angle class for a given pair of points. The distance
classes define a series of cylindrically shaped areas,
while the
angle classes radially cut these
cylindrically shaped areas. For a given angle class
, as
you proceed out radially, the area encompassed by this
angle class becomes larger. The BANDWIDTH= option
restricts this area by excluding all points with a
perpendicular distance from the line that is greater than the BANDWIDTH= value.

If you do not specify the BANDWIDTH= option, no restriction occurs. See Figure 70.15 for more detailed information. **DEPSILON=***distance value***DEPS=***distance value*-
specifies the
distance value for declaring that two distinct points
are zero distance apart. Such pairs, if they
occur, cause numeric problems.
If you specify DEPSILON=, then
pairs of points
*P*and_{1}*P*for which the distance between them are excluded from the continuity measure calculations. The default value of the DEPSILON= option is 100 times machine epsilon; this product is approximately 1E-10 on most computers._{2} **LAGDISTANCE=***distance unit***LAGDIST=***distance unit***LAGD=***distance unit*-
specifies the basic distance unit defining the lags.
For example, a specification of LAGDISTANCE=
*x*results in lag distance classes that are multiples of*x*. For a given pair of points*P*and_{1}*P*, the distance between them, denoted |_{2}*P*|, is calculated. If |_{1}P_{2}*P*| =_{1}P_{2}*x*, then this pair is in the first lag class. If |*P*| = 2_{1}P_{2}*x*, then this pair is in the second lag class, and so on.

For irregularly spaced data, the pairwise distances are unlikely to fall exactly on multiples of the LAGDISTANCE= value. A distance tolerance of is used to accommodate a spread of distances around multiples of*x*(the LAGTOLERANCE= option specifies the distance tolerance). For example, if |*P*| is within , you would place this pair in the first lag class; if |_{1}P_{2}*P*| is within ,you would place this pair in the second lag class, and so on._{1}P_{2}

You can determine the candidate values for the LAGDISTANCE= option by plotting or displaying the OUTDISTANCE= data set.

A LAGDISTANCE= value is required unless you specify the NOVARIOGRAM option.

See the section "Theoretical and Computational Details of the Semivariogram" for more details. **LAGTOLERANCE=***tolerance number***LAGTOL=***tolerance number***LAGT=***tolerance number*- specifies the
tolerance around the LAGDISTANCE= value for
grouping distance pairs into lag classes.
See the preceding description of the LAGDISTANCE= option
for information on the use
of the LAGTOLERANCE= option, and see
the section "Theoretical and Computational Details of the Semivariogram"
for more details.

If you do not specify the LAGTOLERANCE= option, a default value of (1/2) times the LAGDISTANCE= value is used. **MAXLAGS=***number of lags***MAXLAG=***number of lags***MAXL=***number of lags*-
specifies the
maximum number of lag classes used in constructing
the continuity measures. This option excludes
any
pair of points
*P*and_{1}*P*for which the distance between them, |_{2}*P*|, exceeds the MAXLAGS= value times the LAGDISTANCE= value._{1}P_{2}

You can determine candidate values for the MAXLAGS= option by plotting or displaying the OUTDISTANCE= data set.

A MAXLAGS= value is required unless you specify the NOVARIOGRAM option. **NDIRECTIONS=***number of directions***NDIR=***number of directions***ND=***number of directions*-
specifies the
number of
angle classes to use in computing the
continuity measures. This option is useful when there
is potential anisotropy in the spatial
continuity measures. Anisotropy occurs when the
spatial continuity or dependence between a pair
of points depends on the orientation or angle
between the pair. Isotropy is the absence of this
effect: the spatial continuity or dependence
between a pair of points depends only on the distance
between the points, not the angle.

The angle classes formed from the NDIRECTIONS= option start from N -S and proceed clockwise. For example, NDIRECTIONS=3 produces three angle classes. In terms of compass points, these classes are centered at 0^{o}(or its reciprocal 180^{o}), 60^{o}(or its reciprocal 240^{o}), and 120^{o}(or its reciprocal 300^{o}). For irregularly spaced data, the angles between pairs are unlikely to fall exactly in these directions, so an angle tolerance of is used (the ANGLETOLERANCE= option specifies the angle tolerance). If NDIRECTIONS=*n*_{d}, the base angle is , and the angle classes are

If you do not specify the NDIRECTIONS= option, no angles are formed, and the spatial continuity measures are assumed to be isotropic.

The NDIRECTIONS= option is useful for exploring possible anisotropy. The DIRECTIONS statement, described in the "DIRECTIONS Statement" section, provides greater control over the angle classes. See the section "Theoretical and Computational Details of the Semivariogram" for more detailed information. **NHCLASSES=***number of histogram classes***NHCLASS=***number of histogram classes***NHC=***number of histogram classes*-
specifies the number of distance or histogram classes to
write to the OUTDISTANCE= data set. The actual number
of classes is one more than the NHCLASSES= value since
a special lag 0 class is also computed.
See the OUTDISTANCE= option
and the section "OUTDIST=
*SAS-data-set*" for details.

The default value of the NHCLASSES= option is 10. This option is ignored if you do not specify an OUTDISTANCE= data set. **NOVARIOGRAM**-
prevents the computation of the continuity measures.
This option is useful for preliminary analysis when you require only
the OUTDISTANCE= or OUTPAIR= data sets.
**OUTPDISTANCE=***distance limit***OUTPDIST=***distance limit***OUTPD=***distance limit*-
specifies
the cutoff distance for writing observations to
the OUTPAIR= data set. If you specify OUTPDISTANCE=
*d*_{max}, the distance |*P*| between each pair of points_{1}P_{2}*P*and_{1}*P*is checked against_{2}*d*_{max}. If |*P*| >_{1}P_{2}*d*_{max}, the observation for this pair is not written to the OUTPAIR= data set. If you do not specify the OUTPDISTANCE= option, all distinct pairs are written. This option is ignored if you do not specify an OUTPAIR= data set. **ROBUST**-
requests that a robust version of the semivariogram be calculated
in addition to the regular semivariogram and
covariance.

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