{ Analytica Model Flattening_triangula, encoding="UTF-8" }
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Model Flattening_triangula
Title: Flattening triangular matrix
Description: Challenge Problem: Flattening a triangular matrix, keeping on those elements above the diagonal.
Author: Lonnie Chrisman
Date: Thu, Aug 30, 2007 12:32 PM
DefaultSize: 48,24
DiagState: 2,1,0,483,345,17
DiagramColor: 52428,52428,52428
FontStyle: Arial, 15
FileInfo: 0,Model Flattening_triangula,2,2,0,0,C:\Temp\Flattening_triangular_matrix.ana
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Index I
Title: I
Definition: 1..5
NodeLocation: 96,56,1
NodeSize: 48,24

Index J
Title: J
Definition: 1..5
NodeLocation: 208,56,1
NodeSize: 48,24

Variable A
Title: A
Definition: min([I,J])*10 + max([I,J])
NodeLocation: 96,120,1
NodeSize: 48,24
ValueState: 2,45,8,416,303,0,MIDM
Aliases: Alias Al641068275
ReformDef: [J,I]
ReformVal: [J,I]

Text Te1
Description: Challenge: Define B to be a vector containing the elements of A above the diagonal.  Define C to be a 1-D array that includes the diagonal and the elements above.
NodeLocation: 384,110,-1
NodeSize: 88,74

Variable B
Title: B
NodeLocation: 208,120,1
NodeSize: 48,24

Variable C
Title: C
NodeLocation: 208,176,1
NodeSize: 48,24

Module Solution_1
Title: Solution 1
Description: This solution flattens the entire 2-D array, then subsets to keep only those elements above the diagonal.
Author: Lonnie Chrisman
Date: Thu, Jan 30, 2025 11:32 AM
DefaultSize: 48,24
NodeLocation: 96,272,1
NodeSize: 48,24
DiagState: 2,617,40,534,165,17

Variable B1
Title: B
Definition: LocalIndex K1 := 1..size(I)*size(J);~
LocalIndex L := ['I','J','A'];~
Local full [K1,L] := MdArrayToTable(A,K1,L);~
Localindex K2 := subset( full[ L='I'] < full [L='J'] );~
{ This step is optional -- but just producing informative labels in K }~
Localindex K := full[K1=K2,L='I'] & "," & full[K1=K2,L='J'];~
full[ L='A', K1=K2, @K2=@K ]
NodeLocation: 88,64,1
NodeSize: 48,24
ValueState: 2,493,54,416,303,0,MIDM
ReformVal: [Sys_LocalIndex('K'),Sys_LocalIndex('L')]

Variable C1
Title: C
Definition: LocalIndex K1 := 1..size(I)*size(J);~
LocalIndex L := ['I','J','A'];~
Local full [K1,L] := MdArrayToTable(A,K1,L);~
Localindex K2 := subset( full[ L='I'] <= full [L='J'] );~
{ This step is optional -- but just producing informative labels in K }~
LocalIndex K := full[K1=K2,L='I'] & "," & full[K1=K2,L='J'];~
full[ L='A', K1=K2, @K2=@K ]
NodeLocation: 200,64,1
NodeSize: 48,24
ReformVal: [Sys_LocalIndex('L'),Sys_LocalIndex('K')]

Close Solution_1

Module Solution_2
Title: Solution 2
Description: This solution accesses the elements directly by computing the I and J coordinates of the K'th element in the result.
Author: Lonnie Chrisman
Date: Thu, Jan 30, 2025 11:32 AM
DefaultSize: 48,24
NodeLocation: 208,272,1
NodeSize: 48,24
DiagState: 2,460,39,534,261,17
WindState: 2,102,90,474,224

Index Kth
Title: Kth
Description: Indexes for the elements of B, not including the diagonal.
Definition: 1.. (size(J)-1 +  size(J)-size(I)) * size(I)/2
NodeLocation: 72,56,1
NodeSize: 48,24

Variable I_pos
Title: i pos
Definition: StepInterp( cumulate( size(J)-@I, I), @I, Kth, I )
NodeLocation: 184,56,1
NodeSize: 48,24
ValueState: 2,568,339,416,303,0,MIDM

Variable J_pos
Title: j pos
Definition: Local before := cumulate( size(J)-@I, I);~
before := before - before[@I=1];~
@Kth-before[I=i_pos]+1
NodeLocation: 288,56,1
NodeSize: 48,24
ValueState: 2,105,324,647,303,0,MIDM
ReformVal: [Kth,I]

Variable B2
Title: B
Definition: A[@i=i_pos,@j=j_pos]
NodeLocation: 184,112,1
NodeSize: 48,24
ValueState: 2,545,293,416,303,0,MIDM

Index Kth2
Title: Kth2
Description: Position index for element on or above the diagonal.  This one includes the diagonal
Definition: 1.. (size(J) +  size(J)-size(I)+1) * size(I)/2
NodeLocation: 72,192,1
NodeSize: 48,24
WindState: 2,37,447,476,224

Variable I_pos2
Title: i_pos2
Definition: StepInterp( cumulate( size(J)-@I+1, I), @I, Kth2, I )
NodeLocation: 192,192,1
NodeSize: 48,24
ValueState: 2,545,352,416,303,0,MIDM

Variable J_pos2
Title: j pos2
Definition: Local before := cumulate( size(J)-@I+1, I);~
before := before - before[@I=1];~
@Kth2-before[I=i_pos2]
NodeLocation: 296,192,1
NodeSize: 48,24

Variable C2
Title: C
Definition: A[ @I=i_pos2, @J=j_pos2 ]
NodeLocation: 192,248,1
NodeSize: 48,24

Close Solution_2

Module Solution_3
Title: Solution 3
Description: A third solution (most elegant) using the «condition» parameter of Flatten.
Author: Lonnie Chrisman, Ph.D.~
Lumina Decision Systems
Date: Thu, Jan 30, 2025 11:38 AM
NodeLocation: 320,272,1
NodeSize: 48,24
DiagState: 2,593,25,491,293,17

Variable B3
Title: B
Description: Flattened elements above the diagonal, uses a local index .K.
Definition: Flatten( A, I,J, condition: I<J)
NodeLocation: 216,64,1
NodeSize: 48,24

Variable C3
Title: C
Description: Flattened elements above and including the diagonal, uses a local index .K that has meaningful labels.
Definition: LocalIndex K := CopyIndex(Flatten( f"{I},{J}", I,J, condition:I<=J));  { Meaningful labels }~
Flatten( A, I,J, condition: I<=J, resultIndex:K)
NodeLocation: 216,136,1
NodeSize: 48,24

Alias Al641068275
Title: A
Definition: 1
NodeLocation: 72,64,1
NodeSize: 48,24
Original: A

Close Solution_3

Close Flattening_triangula