Matrix data
Syntax: |
CONTOUR { x y } v nctr { min { incr }}
|
Qualifiers: |
\SPECIFIC, \INTERPSIZE, \POLAR, \LEGEND, \COLOURS, \PARTIAL, \RESET,
\BORDER, \AXES, \COORDINATES, \AREAS, \VOLUMES
|
Defaults: |
X=[1;2;3;...], y=[1;2;3;...], \-SPECIFIC, \-INTERPSIZE, \-POLAR, \-LEGEND, \-COLOURS,
\-RESET, \-AREAS, \-VOLUMES, \BORDER, \-COORDINATES, \AXES
|
Suppose that v
is a matrix which has n columns and m rows. The vectors
x
and y
are optional, and if entered, are used for scaling the axes.
Each matrix element, v[i,j]
, is associated with the coordinates
(x[j],y[i])
. The length of x
must be greater than or equal to n
and the length of y
must be greater than or equal to m.
If x
and y
are not entered, x
defaults to the set
[1;2;3;...;n]
, and y
defaults to the set
[1;2;3;...;m]
, so that matrix element m[i,j]
is
associated with the coordinates (j,i)
.
Minimum and maximum contour coordinates
The minimum and maximum x value for each contour are automatically
stored in vectors named CXMIN
and
CXMAX
; the minimum and maximum
y value for each contour are automatically stored in vectors named
CYMIN
and
CYMAX
. These vectors are then
available to the user for plotting and/or manipulation. Each time the
CONTOUR
command is entered, these
vectors are emptied and replaced, so if you wish to keep them, they should
be renamed or copied into other vectors.
Volume
If the \VOLUMES
qualifier is used, the volume contained within each contour is
calculated as a percentage of the total volume. The volume percentages are automatically stored
in a vector named CVOLM
. Each time the
CONTOUR
command is entered, this vector is emptied and replaced, so if you wish to
keep it, it should be renamed or copied into another vector.
Area
If the \AREAS
qualifier is used, the area contained within each contour is calculated
as a percentage of the total area. The area percentages are automatically stored in a vector
named CAREA
. Each time the
CONTOUR
command is entered, this vector is emptied and replaced, so if you wish to
keep it, it should be renamed or copied into another vector.
Area and volume calculation
The areas and volumes are calculated in the following way. Two dimensional, four point linear interpolation is used to calculate a fine mesh overlayed on the matrix, see the figure below. Suppose the matrix has n columns and m rows and the size of the fine mesh is n1 columns by m1 rows. The total area is n1·m1 and the total volume is the sum of the interpolated values. Each point of the fine mesh is tested against the contour levels, and if a mesh point has a value greater than the contour level, a one is binned for the area vector and the mesh point value is binned for the volume vector. Finally, the area and volume vectors are normalized by conversion to percentages.
Interpolation size
Syntax: |
CONTOUR\INTERPSIZE ntrp { x y } v num { min { incr }}
|
Suppose the matrix has n columns and m rows. The total size of the fine mesh, n1 columns by m1 rows, is defined by the following:
n1 = (n-1)ix + 1
m1 = (m-1)iy + 1
where ix-1
is the number of interpolation
points between matrix points in the x-direction, and
iy-1
is the number of interpolation points
between matrix points in the y-direction. The defaults are as
below:
|
|
To over-ride these defaults, use the \INTERPSIZE
qualifier, and
enter ntrp
as the first parameter. Both ix and iy
will be set to ntrp
.
Matrix boundary
By default, the boundary of the matrix is outlined within the axes. If this
boundary is not desired, use the \-BORDER
qualifier.