TUgridMath TCL UTILITIES USER MANUAL TUgridMath
SYNOPSIS
Grid based math
PACKAGE
TCLUTILS
NAME
TUgridMath
USAGE
TUgridMath  Grid1 Oper Grid2 Grid3 gInfo
INPUT DEFINITIONS
Grid1 - A 2D data grid of data generated through a call to TUdataGrid.
Oper - The grid operation to perform.
+ - Cell by cell addition of Grid1 and Grid2. Summed grid is returned in Grid3
- - Cell by cell subtraction of Grid1 from Grid2. Subtracted grid is returned in Grid3
* - Cell by cell multiplication of Grid1 and Grid2. Multiplied grid is returned in Grid3
/ - Cell by cell division of Grid1 by Grid2. Divided grid is returned in Grid3
DUP - Duplicate Grid1 returning the duplicated grid in Grid3
NORMALIZE - Normalize Grid1 by computing the sum of all the cells and then dividing each cell in the grid by the sum. The normalized grid is returned in Grid3
GRAD - Solve for the rectangular X and Y gradients in a rectangular formatted grid. Grid1 is the input grid and must have X varing along the rows and Y varing along the columns. dG1/dX is returned in Grid2 and dG1/dY in Grid3.
GRADCY - Solve for the cylindrical R and $Phi; gradients in a cylindircal formatted grid. Grid1 is the input grid and must have Φ varing along the rows and R varing along the columns. dG1/Φ is returned in Grid2 and columns. dG1/R; is returned in Grid3.
GRADRCY - Solve for the cylindrical R and $Phi; gradients in a rectangular formatted grid. Grid1 is the input grid and must have X varing along the rows and Y varing along the columns. dG1/Φ is returned in Grid2 and columns. dG1/R; is returned in Grid3.
Grid2 - A 2D data grid of data generated through a call to TUdataGrid. At times input may be either unused or be a return Grid.
Grid3 - The output grid in any operation.
gInfo - The grid information array. This must be the same for both Grid1 and Grid2 and by default will describe the output grid Grid3
RETURN DEFINITION
NONE
DESCRIPTION
TUgridMath performs some basic mathematical operations on data grids. Operations of the type 
	Grid3 = Grid1 Oper Grid2
are peformed cell by cell. As such both Grid1 and Grid2 must be represented by the same grid information array. When Oper is a division a check for division by 0 is made at each instance of the operation. If true the result is set to gInfo(12) which is the grid bad cell value.
ERRORS
None Generated
C BACKING
No
EXAMPLE(S)
EXAMPLE 1:Computing the rectangular and cylindrical gradients in a grid. 
# COMPUTE the rectangulan and cylindrical gradiant of a grid

# SET up the grid information array.  

set gInfo(0) -6.0
set gInfo(1) 6.0
set gInfo(2) -6.0
set gInfo(3) 6.0
set gInfo(4) 100
set gInfo(5) 100
set gInfo(6) POINT
set gInfo(7) POINT
set gInfo(8) COLUMN
set gInfo(9) IGNORE
set gInfo(10) NEW:ADD:END
set gInfo(11) -1
set gInfo(12) -5
set gInfo(13) -1.0e30
set gInfo(14)  1.0e30
set gInfo(15)  NO
set gInfo(16)  NO

# SET up a data set consisting of three Gaussians centered at (-3,-3),
#  (-3, 3) and at (3, 0).  Each has a different intensity.

set nP 0
set nG [expr $gInfo(4) * $gInfo(5)]
for { set I 0 } { $I < $nG } { incr I } {
   TUgridInfo 20 gInfo rV $I
   set X($nP) $rV(2)
   set Y($nP) $rV(3)
   set R [expr ($X($nP)-3.0) * ($X($nP)-3.0) + ($Y($nP)-3.0) * ($Y($nP)-3.0)]
   set A [expr exp(-$R / 6.0)]
   set R [expr ($X($nP)-3.0) * ($X($nP)-3.0) + ($Y($nP)+3.0) * ($Y($nP)+3.0)]
   set B [expr 3.0 * exp(-$R / 6.0)]
   set R [expr ($X($nP)+3.0) * ($X($nP)+3.0) + $Y($nP)*$Y($nP)]
   set C [expr 4.0 * exp(-$R / 6.0)]
   set V($nP) [expr $A + $B - $C ]
   incr nP
}

# GRID the data set

TUdataGrid $nP 1 X X 1 Y Y V gV Norm gInfo

# SET up the plot basics.  There are a total of 5 plots defined here.

set GphInfo(xScrL) 500
set GphInfo(yScrL) 760
GraphicsOn TK ETones SWAP

GenWindow 1 0.0 0.0 0.0 1.0 1.0 0.0  0. 0. 0. 1. 1. 0. XY
set WinInfo(2,corFmt) 1
RelWindow 2 1 177.0 515.0 0. 377. 715. 0. -6. -6. 0. 6. 6. 0.
DefinePlot 2 2 $gInfo(4) $gInfo(5)
set WinInfo(4,corFmt) 1
RelWindow 4 1 75.0 290.0 0. 275. 490. 0. -6. -6. 0. 6. 6. 0.
DefinePlot 4 4 $gInfo(4) $gInfo(5)
set WinInfo(5,corFmt) 1
RelWindow 5 1 280.0 290.0 0. 480. 490. 0. -6. -6. 0. 6. 6. 0.
DefinePlot 5 5 $gInfo(4) $gInfo(5)
set WinInfo(6,corFmt) 1
RelWindow 6 1 75.0 65.0 0. 275. 265. 0. -6. -6. 0. 6. 6. 0.
DefinePlot 6 6 $gInfo(4) $gInfo(5)
set WinInfo(7,corFmt) 1
RelWindow 7 1 280.0 65.0 0. 480. 265. 0. -6. -6. 0. 6. 6. 0.
DefinePlot 7 7 $gInfo(4) $gInfo(5)

# SET up the color map to run from -4.5 to 4.5

PLTcolorMap -4.1 4.1 LINEAR 0 cA

# PLOT the gaussians

Plot3D 2 Xb Yb Dummy Dummy gV AUTO Dummy cA

# COMPUTE the rectangular gradient of the grid and plot both components

TUgridMath gV GRAD gdX gdY gInfo

PLTcolorMap -2.5 2.5 LINEAR 0 cA
Plot3D 4 Xb Yb Dummy Dummy gdX AUTO Dummy cA
Plot3D 5 Xb Yb Dummy Dummy gdY AUTO Dummy cA

# COMPUTE the cylindrical gradient of the grid and plot both components

TUgridMath gV GRADRCY gdP gdR gInfo

PLTcolorMap -5.5 5.5 LINEAR 0 cA
Plot3D 6 Xb Yb Dummy Dummy gdP AUTO Dummy cA
Plot3D 7 Xb Yb Dummy Dummy gdR AUTO Dummy cA

# THROW up the axis.  Only annotate lower left-hand  plot

PlotOutlines 2 [list "" 1.0 "" 1.0] [list NONE NONE BOTH BOTH]
PlotOutlines 4 [list "" 1.0 "" 1.0] [list NONE NONE BOTH BOTH]
PlotOutlines 5 [list "" 1.0 "" 1.0] [list NONE NONE BOTH BOTH]
PlotOutlines 6 [list "X" 1.0 "Y" 1.0] [list BOT BOT BOTH BOTH]
PlotOutlines 7 [list "" 1.0 "" 1.0] [list NONE NONE BOTH BOTH]

# LABEL the plots 

TextProp 12 HOLD HOLD
WinClip 2 0
TexT 2 0.0 6.50 0.0 center "ORIGINAL" $GphInfo(White)
WinClip 4 0
TexT 4 0.0 6.50 0.0 center "dG/dX" $GphInfo(White)
WinClip 5 0
TexT 5 0.0 6.50 0.0 center "dG/dY" $GphInfo(White)
WinClip 6 0
TexT 6 0.0 6.50 0.0 center "(1.0/R)dG/dP" $GphInfo(White)
WinClip 7 0
TexT 7 0.0 6.50 0.0 center "dG/dR" $GphInfo(White)

update
Sept 24, 2006