topic Re: Matching Spatially Inhomogeneous Data in Discussions

Matching Spatially Inhomogeneous Data

Resonator_Drift — Fri, 09 Jun 2023 17:01:32 GMT

I have two data tables of values that are spatially mapped, but the coordinates of one table are not the same coordinates as the second. I would like to "Join" these tables but have the data match by coordinate so I can compare the spatially variant values between the two tables.

Does anyone know if there's an easy way to do this instead of just brute force calculating for every value? There looks to be some interesting matrix functions but I am unfamiliar with the mathematical concepts behind them.

I have a mockup of the process shown below that hopefully conveys what I want to have happen.

X	Y	V
0	0	0
1	0	1
2	0	2
0	1	1
1	1	2
2	2	3
0	2	2
1	2	3
2	2	4

X	Y
0.5	0.5
1.5	0.5
0.5	1.5
1.5	1.5

X	Y	I V
0.5	0.5	1
1.5	0.5	2
0.5	1.5	2
1.5	1.5	3

Re: Matching Spatially Inhomogeneous Data

jthi — Wed, 15 Jun 2022 20:25:17 GMT

~~I think VPTree() or Distance() could work here (maybe KDTable()), but what do you do in ties?~~

Not looking for closest points but rather points in same line and interpolation after that if I understood correct.y.

Re: Matching Spatially Inhomogeneous Data

txnelson — Wed, 15 Jun 2022 19:39:55 GMT

I do not understand how you come up with the value for IV. Could you please explain the rules you are using?

Re: Matching Spatially Inhomogeneous Data

Resonator_Drift — Wed, 15 Jun 2022 20:02:13 GMT

IV was the interpolated value of XYV (Table 1) from the table, using the coordinates from the XY (Table 2) table

Re: Matching Spatially Inhomogeneous Data

jthi — Wed, 15 Jun 2022 20:44:40 GMT

Maybe this would be helpful

There also seems to be Scripting Guide > JSL Building Blocks > Conditional Functions > Interpolate > Bilinear Interpolation (jmp.com) but I haven't used that.

Re: Matching Spatially Inhomogeneous Data

txnelson — Thu, 16 Jun 2022 17:13:05 GMT

If the polygon layout data table is regular and complete

Names Default To Here( 1 );

// Create the example data tables
New Table( "Data",
	Add Rows( 4 ),
	New Column( "x", Numeric, "Continuous", Format( "Best", 12 ), Set Values( [0.5, 1.5, 0.5, 1.5] ) ),
	New Column( "y", Numeric, "Continuous", Format( "Best", 12 ), Set Values( [0.5, 0.5, 1.5, 1.5] ) )
);

New Table( "Layout",
	Add Rows( 9 ),
	New Column( "X", Numeric, "Continuous", Format( "Best", 12 ), Set Values( [0, 1, 2, 0, 1, 2, 0, 1, 2] ) ),
	New Column( "Y", Numeric, "Continuous", Format( "Best", 12 ), Set Values( [0, 0, 0, 1, 1, 1, 2, 2, 2] ) ),
	New Column( "V", Numeric, "Continuous", Format( "Best", 12 ), Set Values( [0, 1, 2, 1, 2, 3, 2, 3, 4] ) ),
	Set Row States( [8, 8, 8, 8, 8, 8, 8, 8, 8] ),
	Set Label Columns( :V )
);

// Calculate the IV data
dtLookup = Data Table( "Layout" );
dtData = Data Table( "Data" );

dtData << New Column( "IV" );
For( i = 1, i <= N Rows( dtData ), i++, 

	xVal = dtData:X[i];
	yVal = dtData:Y[i];

	yMin = Col Max( If( dtLookup:Y < yVal, dtLookup:Y, . ) );
	yMax = Col Min( If( dtLookup:Y > yVal, dtLookup:Y, . ) );
	xMin = Col Max( If( dtLookup:X < xVal, dtLookup:X, . ) );
	xMax = Col Min( If( dtLookup:X > xVal, dtLookup:X, . ) );

	botLeft = dtLookup:V[(dtLookup << get rows where( :X == xMin & :Y == yMin ))[1]];
	botRight = dtLookup:V[(dtLookup << get rows where( :X == xMax & :Y == yMin ))[1]];
	topLeft = dtLookup:V[(dtLookup << get rows where( :X == xMin & :Y == yMax ))[1]];
	topRight = dtLookup:V[(dtLookup << get rows where( :X == xMax & :Y == yMax ))[1]];
	dtData:IV[i] = Mean( botLeft, botRight, topLeft, topRight );
);