The base data type in PASSaGE is the rectangular matrix (also called a data matrix; these terms are used interchangeably throughout the manual). These matrices may have any number of rows and columns, containing either numeric or text values. These data matrices generally have two forms. In the first, each column represents a variable, with each row representing the location where the variable was measured. The coordinates of the locations will often be found in an associated Coordinate Matrix.
|
Length |
Width |
Mass |
Color |
Point 1 |
1.2 |
1.5 |
124.4 |
Red |
Point 2 |
1.5 |
2.3 |
142.6 |
Blue |
Point 3 |
2.9 |
3.1 |
179.8 |
Red |
etc. |
|
|
|
|
Example of a rectangular matrix where each column represents a variable measured at a location specified by the row.
In the second form of a rectangular matrix, the rows and columns represent relative locations of a contiguously measured variable and the specific cell (quadrat) contains the value at the location specified by both the row and column. One-dimensional contiguous data are often called transects, and would be represented by a specific column within the data matrix, with the xth row equivalent to the xth position of the transect. Two-dimensional contiguous data are often called surfaces, and consist of the entire matrix with the xth column and yth row representing the (x,y) position of the surface. Thus the value in cell [1,1] of a rectangular matrix represents the value of the surface at x = 1, y = 1, and the value in cell [2,10] represents the value of the surface at x = 2, y = 10, etc. Three-dimensional contiguous data sets are contained in special three-dimensional matrices.
|
X1 |
X2 |
X3 |
|
X1 |
X2 |
X3 |
||
Y3 |
1,3 |
2,3 |
3,3 |
Row 1 = Y1 |
1,1 |
2,1 |
3,1 |
||
Y2 |
1,2 |
2,2 |
3,2 |
Row 2 = Y2 |
1,2 |
2,2 |
3,2 |
||
| (A) | Y1 |
1,1 |
2,1 |
3,1 |
(B) |
Row 3 = Y3 |
1,3 |
2,3 |
3,3 |
Surface layout showing the contrast between (A) the map layout and (B) the matrix layout. The coordinates representing the lower left corner of the map [1,1] are found in the upper left corner of the data matrix (row 1, column 1).
Note that matrices are viewed (and read) from top to bottom, such that the first row (y = 1) is at the top of the matrix and the nth row is at the bottom of the matrix. However, locations are often measured with y = 0 at the bottom of the map and y = n at the top of the map. Thus the locations along the y-axis of a surface as viewed in matrix form are inverted from the locations as drawn on a map.