WEST, Inc.
GRTS for the Average Joe: A
GRTS Sampler for Windows
Trent McDonald
Monitoring Science Symposium
Denver, CO
21-24 Sep 2004
Outline WEST, Inc.
• Motivation for the GRTS sampler
• Description of the sampler, S-Draw
• Examples
• Performance
• Planned modifications
Motivation WEST, Inc.
• Basic hypotheses:
– Average Joe understands the utility of GRTS
samples
– Average Joe does not totally understand the
inner workings of GRTS sampling
– Average Joe could not draw a GRTS sample if
his life depended on it.
Motivation WEST, Inc.
• A GRTS sampler was needed because:
– Average Joe should be able to draw GRTS
samples
– I should be able to draw GRTS samples
S-Draw WEST, Inc.
• Windows application
• Written in Fortran 95
– Amazing speed
– Cross-platform portability
ok
– Cross-language calls easy
(S-Plus, R, C++)
• Used Lahey compiler
• Also S-DrawB
S-Draw WEST, Inc.
• Draws samples of
– Discrete units (finite populations)
– Located in either 1-D or 2-D
• Examples:
– 1-D: River segments located by river mile
– 2-D: Grid cells located in an area
– 2-D: River segments located by coordinates of
their midpoints
S-Draw WEST, Inc.
• Coordinates of units are specified in a
text file
– i.e., the sampling frame is a ASCII file
• Sampling frame can optionally contain
weights and ID’s
S-Draw WEST, Inc.
• Frame Formats:
Sample Structure Data Included in Frame
Pre- Sample Coordin- Order of fields in
defined 1-D 2-D weights ates ID's frame file
Yes Yes Yes Yes x wgt id
Yes Yes Yes No x wgt
Yes Yes No Yes x id
Yes Yes No No x
Yes No Yes Yes wgt id
Yes No Yes No wgt
Yes No No Yes id
Yes No No No [# lines counted]
Yes Yes Yes Yes x y wgt id
Yes Yes Yes No x y wgt
Yes No Yes Yes x y id
Yes No Yes No xy
Yes* Yes - Yes k1 … kK wgt id
Yes* Yes - No k1 … kK wgt
Yes* No - Yes k1 … kK id
Yes* No - No k1 … kK
*K specified on the first line of the frame file
S-Draw WEST, Inc.
• Example frame: Eagle study
STARTPNT_X STARTPNT_Y LINE_ID ID ENDPNT_X ENDPNT_Y
-421014 4572670 1 439 -420245 4572670
-421295 4574670 2 440 -419802 4574670
-421245 4576670 3 441 -419802 4576670
-421196 4578670 4 442 -419802 4578670
-421292 4580670 5 443 -419802 4580670
-421687 4582670 6 444 -419802 4582670
-422806 4584670 7 445 -419802 4584670
-423122 4586670 8 446 -419802 4586670
-422972 4588670 9 447 -419802 4588670
-422836 4590670 10 448 -419802 4590670
-422352 4592670 11 449 -419802 4592670
-421284 4594670 12 450 -419802 4594670
Columns following
frame data ignored
S-Draw WEST, Inc.
• Does the quadrant-recursive mapping
of Stevens and Olsen (2004):
2 4
0 n
1 3 1 4 2 3
2 4
4 3 1 2
1 3
S-Draw WEST, Inc.
• Pixelsize = size of smallest quadrant in
recursive map
• S-Draw allows user to specify
pixelsize
S-Draw WEST, Inc.
• Line segment (0,n] sampled using a
systematic sample
– Random start between (0,1]
– Step size = 1.0
Random start = 0.19
0 1 2 3 n
u1 u2 u3 u4
S-Draw WEST, Inc.
• Reverse-hierarchical ordering of
sample optionally applied
– Convert sample order to base-4: 10010=012004
– Reverse base-4 digits: 012004=002104
– Convert back to base-10: 002104=3610
– Sort sample on base-10 numbers
S-Draw WEST, Inc.
• Users can pre-define the hierarchical
sort keys
• Digits within each level of the
hierarchy are randomly permuted, and
sample is drawn as usual
• Allows use of a general recursive map
– Triangular-recursive
– ID’s like: state.county.watershed.segment
S-Draw WEST, Inc.
• Triangular-recursive mapping:
1 2
4
3
Examples WEST, Inc.
• C:\>s-drawb –n 20 –popsize 100
– Will produce 1-D GRTS sample of size 20 assuming
units are located at coordinates 1, 2, …, 100
• C:\>s-drawb –n 20 –popsize 100 –pixelsize 100
– Will produce a simple random sample of size 20
• C:\>s-drawb –n 20 –popsize 100 –nrand
– Will produce a fixed-size systematic sample
Examples WEST, Inc.
• Golden eagle sample:
– Dense grid of transect start points spaced 2km
north-south, 100km east-west
– “No-fly” transect portions eliminated, new
transect start created
– Frame:
• 27,078 starting points over western US
• 2-D coordinates and ID’s
– Desire sample of 416 transects
• 208 primary, 208 alternate
Examples WEST, Inc.
Coordinates and ID in frame Sample size
2-D
Frame
file
Examples WEST, Inc.
Performance WEST, Inc.
• GRTS sample of size 500 from
100,000 took 4.2 seconds on my laptop
• GRTS sample of size 500 from
1,000,000 took 44.3 seconds
• Algorithms approximately O(N)
• Runs should take ~ 4.45e-5(N) seconds
– N=5,000,000: ~3.7 minutes
Enhancements WEST, Inc.
• An S-Plus and R interface
• Ability to read .e00 file, and ArcGIS
binary files
• Ability to take a true point sample