NAME
PDL::Graphics::Limits  derive limits for display purposes
DESCRIPTION
Functions to derive limits for data for display purposes
SYNOPSIS
use PDL::Graphics::Limits;
FUNCTIONS
limits
limits derives global limits for one or more multidimensional sets of data for display purposes. It obtains minimum and maximum limits for each dimension based upon one of several algorithms.
@limits = limits( @datasets );
@limits = limits( @datasets, \%attr );
$limits = limits( @datasets );
$limits = limits( @datasets, \%attr );
Data Sets
A data set is represented as a set of one dimensional vectors, one per dimension. All data sets must have the same dimensions. Multidimensional data sets are packaged as arrays or hashs; one dimensional data sets need not be. The different representations may be mixed, as long as the dimensions are presented in the same order. Vectors may be either scalars or ndarrays.
 One dimensional data sets

One dimensional data sets may be passed directly, with no additional packaging:
limits( $scalar, $ndarray );
 Data sets as arrays

If the data sets are represented by arrays, each vectors in each array must have the same order:
@ds1 = ( $x1_pdl, $y1_pdl ); @ds2 = ( $x2_pdl, $y2_pdl );
They are passed by reference:
limits( \@ds1, \@ds2 );
 Data sets as hashes

Hashes are passed by reference as well, but must be further embedded in arrays (also passed by reference), in order that the last one is not confused with the optional trailing attribute hash. For example:
limits( [ \%ds4, \%ds5 ], \%attr );
If each hash uses the same keys to identify the data, the keys should be passed as an ordered array via the
VecKeys
attribute:limits( [ \%h1, \%h2 ], { VecKeys => [ 'x', 'y' ] } );
If the hashes use different keys, each hash must be accompanied by an ordered listing of the keys, embedded in their own anonymous array:
[ \%h1 => ( 'x', 'y' ) ], [ \%h2 => ( 'u', 'v' ) ]
Keys which are not explicitly identified are ignored.
Errors
Error bars must be taken into account when determining limits; care is especially needed if the data are to be transformed before plotting (for logarithmic plots, for example). Errors may be symmetric (a single value indicates the negative and positive going errors for a data point) or asymmetric (two values are required to specify the errors).
If the data set is specified as an array of vectors, vectors with errors should be embedded in an array. For symmetric errors, the error is given as a single vector (ndarray or scalar); for asymmetric errors, there should be two values (one of which may be undef
to indicate a onesided error bar):
@ds1 = ( $x, # no errors
[ $y, $yerr ], # symmetric errors
[ $z, $zn, $zp ], # asymmetric errors
[ $u, undef, $up ], # onesided error bar
[ $v, $vn, undef ], # onesided error bar
);
If the data set is specified as a hash of vectors, the names of the error bar keys are appended to the names of the data keys in the VecKeys
designations. The error bar key names are always prefixed with a character indicating what kind of error they represent:
< negative going errors
> positive going errors
= symmetric errors
(Column names may be separated by commas or white space.)
For example,
%ds1 = ( x => $x, xerr => $xerr, y => $y, yerr => $yerr );
limits( [ \%ds1 ], { VecKeys => [ 'x =xerr', 'y =yerr' ] } );
To specify asymmetric errors, specify both the negative and positive going errors:
%ds1 = ( x => $x, xnerr => $xn, xperr => $xp,
y => $y );
limits( [ \%ds1 ], { VecKeys => [ 'x <xnerr >xperr', 'y' ] } );
For onesided error bars, specify a column just for the side to be plotted:
%ds1 = ( x => $x, xnerr => $xn,
y => $y, yperr => $yp );
limits( [ \%ds1 ], { VecKeys => [ 'x <xnerr', 'y >yperr' ] } );
Data in hashes with different keys follow the same paradigm:
[ \%h1 => ( 'x =xerr', 'y =yerr' ) ], [ \%h2 => ( 'u =uerr', 'v =verr' ) ]
In this case, the column names specific to a single data set override those specified via the VecKeys
option.
limits( [ \%h1 => 'x =xerr' ], { VecKeys => [ 'x <xn >xp' ] } )
In the case of a multidimensional data set, one must specify all of the keys:
limits( [ \%h1 => ( 'x =xerr', 'y =yerr' ) ],
{ VecKeys => [ 'x <xn >xp', 'y <yp >yp' ] } )
One can override only parts of the specifications:
limits( [ \%h1 => ( '=xerr', '=yerr' ) ],
{ VecKeys => [ 'x <xn >xp', 'y <yp >yp' ] } )
Use undef
as a placeholder for those keys for which nothing need by overridden:
limits( [ \%h1 => undef, 'y =yerr' ],
{ VecKeys => [ 'x <xn >xp', 'y <yp >yp' ] } )
Data Transformation
Normally the data passed to limits should be in their final, transformed, form. For example, if the data will be displayed on a logarithmic scale, the logarithm of the data should be passed to limits. However, if error bars are also to be displayed, the untransformed data must be passed, as
log(data) + log(error) != log(data + error)
Since the ranges must be calculated for the transformed values, range must be given the transformation function.
If all of the data sets will undergo the same transformation, this may be done with the Trans attribute, which is given a list of subroutine references, one for each element of a data set. An undef
value may be used to indicate no transformation is to be performed. For example,
@ds1 = ( $x, $y );
# take log of $x
limits( \@ds1, { trans => [ \&log10 ] } );
# take log of $y
limits( \@ds1, { trans => [ undef, \&log10 ] } );
If each data set has a different transformation, things are a bit more complicated. If the data sets are specified as arrays of vectors, vectors with transformations should be embedded in an array, with the last element the subroutine reference:
@ds1 = ( [ $x, \&log10 ], $y );
With error bars, this looks like this:
@ds1 = ( [ $x, $xerr, \&log10 ], $y );
@ds1 = ( [ $x, $xn, $xp, \&log10 ], $y );
If the Trans
attribute is used in conjunction with individual data set transformations, the latter will override it. To explicitly indicate that a specific data set element has no transformation (normally only needed if Trans
is used to specify a default) set the transformation subroutine reference to undef
. In this case, the entire quad of data element, negative error, positive error, and transformation subroutine must be specified to avoid confusion:
[ $x, $xn, $xp, undef ]
Note that $xn and $xp may be undef. For symmetric errors, simply set both $xn
and $xp
to the same value.
For data sets passed as hashes, the subroutine reference is an element in the hashes; the name of the corresponding key is added to the list of keys, preceded by the &
character:
%ds1 = ( x => $x, xerr => $xerr, xtrans => \&log10,
y => $y, yerr => $yerr );
limits( [ \%ds1, \%ds2 ],
{ VecKeys => [ 'x =xerr &xtrans', 'y =yerr' ] });
limits( [ \%ds1 => 'x =xerr &xtrans', 'y =yerr' ] );
If the Trans
attribute is specified, and a key name is also specified via the VecKeys
attribute or individually for a data set element, the latter will take precedence. For example,
$ds1{trans1} = \&log10;
$ds1{trans2} = \&sqrt;
# resolves to exp
limits( [ \%ds1 ], { Trans => [ \&exp ] });
# resolves to sqrt
limits( [ \%ds1 ], { Trans => [ \&exp ],
VecKeys => [ 'x =xerr &trans2' ] });
# resolves to log10
limits( [ \%ds1 => '&trans1' ], { Trans => [ \&exp ],
VecKeys => [ 'x =xerr &trans2' ] });
To indicate that a particular vector should have no transformation, use a blank key:
limits( [ \%ds1 => ( 'x =xerr &', 'y =yerr' ) ], [\%ds2],
{ Trans => [ \&log10 ] } );
or set the hash element to undef
:
$ds1{xtrans} = undef;
Range Algorithms
Sometimes all you want is to find the minimum and maximum values. However, for display purposes, it's often nice to have "clean" range bounds. To that end, limits produces a range in two steps. First it determines the bounds, then it cleans them up.
To specify the bounding algorithm, set the value of the Bounds
key in the %attr
hash to one of the following values:
 MinMax

This indicates the raw minima and maxima should be used. This is the default.
 Zscale

This is valid for two dimensional data only. The
Y
values are sorted, then fit to a line. The minimum and maximum values of the evaluated line are used for theY
bounds; the raw minimum and maximum values of theX
data are used for theX
bounds. This method is good in situations where there are "spurious" spikes in theY
data which would generate too large a dynamic range in the bounds. (Note that theZscale
algorithm is found in IRAF and DS9; its true origin is unknown to the author).
To specify the cleaning algorithm, set the value of the Clean
key in the %attr
hash to one of the following values:
 None

Perform no cleaning of the bounds.
 RangeFrac

This is based upon the
PGPLOT
pgrnge function. It symmetrically expands the bounds (determined above) by a fractional amount:$expand = $frac * ( $axis>{max}  $axis>{min} ); $min = $axis>{min}  $expand; $max = $axis>{max} + $expand;
The fraction may be specified in the
%attr
hash with theRangeFrac
key. It defaults to0.05
.Because this is a symmetric expansion, a limit of
0.0
may be transformed into a negative number, which may be inappropriate. If theZeroFix
key is set to a nonzero value in the%attr
hash, the cleaned boundary is set to0.0
if it is on the other side of0.0
from the above determined bounds. For example, If the minimum boundary value is0.1
, and the cleaned boundary value is0.1
, the cleaned value will be set to0.0
. Similarly, if the maximum value is0.1
and the cleaned value is0.1
, it will be set to0.0
.This is the default clean algorithm.
 RoundPow

This is based upon the
PGPLOT
pgrnd routine. It determines a "nice" value, where "nice" is the closest round number to the boundary value, where a round number is 1, 2, or 5 times a power of 10.
User Specified Limits
To fully or partially override the automatically determined limits, use the Limits attribute. These values are used as input to the range algorithms.
The Limits attribute value may be either an array of arrayrefs, or a hash.
 Arrays

The Limits value may be a reference to an array of arrayrefs, one per dimension, which contain the requested limits.
The dimensions should be ordered in the same way as the datasets. Each arrayref should contain two ordered values, the minimum and maximum limits for that dimension. The limits may have the undefined value if that limit is to be automatically determined. The limits should be transformed (or not) in the same fashion as the data.
For example, to specify that the second dimension's maximum limit should be fixed at a specified value:
Limits => [ [ undef, undef ], [ undef, $max ] ]
Note that placeholder values are required for leading dimensions which are to be handled automatically. For convenience, if limits for a dimension are to be fully automatically determined, the placeholder arrayref may be empty. Also, trailing undefined limits may be omitted. The above example may be rewritten as:
Limits => [ [], [ undef, $max ] ]
If the minimum value was specified instead of the maximum, the following would be acceptable:
Limits => [ [], [ $min ] ]
If the data has but a single dimension, nested arrayrefs are not required:
Limits => [ $min, $max ]
 Hashes

Th Limits attribute value may be a hash; this can only be used in conjunction with the VecKeys attribute. If the data sets are represented by hashes which do not have common keys, then the user defined limits should be specified with arrays. The keys in the Limits hash should be the names of the data vectors in the VecKeys. Their values should be hashes with keys
min
andmax
, representing the minimum and maximum limits. Limits which have the valueundef
or which are not specified will be determined from the data. For example,Limits => { x => { min => 30 }, y => { max => 22 } }
Return Values
When called in a list context, it returns the minimum and maximum bounds for each axis:
@limits = ( $min_1, $max_1, $min_2, $max_2, ... );
which makes life easier when using the env method:
$window>env( @limits );
When called in a scalar context, it returns a hashref with the keys
axis1, ... axisN
where axisN
is the name of the Nth axis. If axis names have not been specified via the VecKeys
element of %attr
, names are concocted as q1
, q2
, etc. The values are hashes with keys min
and max
. For example:
{ q1 => { min => 1, max => 2},
q2 => { min => 33, max => 33 } }
Miscellaneous
Normally limits complains if hash data sets don't contain specific keys for error bars or transformation functions. If, however, you'd like to specify default values using the %attr
argument, but there are data sets which don't have the data and you'd rather not have to explicitly indicate that, set the KeyCroak
attribute to zero. For example,
limits( [ { x => $x }, { x => $x1, xerr => $xerr } ],
{ VecKeys => [ 'x =xerr' ] } );
will generate an error because the first data set does not have an xerr
key. Resetting KeyCroak
will fix this:
limits( [ { x => $x }, { x => $x1, xerr => $xerr } ],
{ VecKeys => [ 'x =xerr' ], KeyCroak => 0 } );
AUTHOR
Diab Jerius, <djerius@cpan.org>
COPYRIGHT AND LICENSE
Copyright (C) 2004 by the Smithsonian Astrophysical Observatory
This software is released under the GNU General Public License. You may find a copy at http://www.fsf.org/copyleft/gpl.html.