I did not find a method for solving a set of linear equations, apart from
the ones in /math/misc/linear.ijs which did not work for mutual dependent
equations. So I constructed a solution myself.
(See also http://www.jsoftware.com/jwiki/RE%20Boss/J-blog/(De)Convolution )
NB. y is a matrix representing a set of equations given by the multipliers
(}:"1 y) and the results ({:"1 y).
NB. the result is a vector, or a matrix, the minimal set of independent
equations
sle=: 3 : 0 NB. solve linear
equations
Y=. (#"1~ +./@:*)&.|: y NB. eliminate
dependent equations
Y=. \:~ rdeq^:(<:@{:@$)^:_ Y NB. reduce the
equations and sort them in descending order
if. 1 = -~/ $Y do. {:"1 Y return. end. NB. give the
solution in the natural order
Y NB. give the minimal
set of independent equations
)
rdeq=: 3 : 0 NB. reduce equations
y0=. {.y
assert. (0 ~: +./ }:y0) +. 0 = {:y0 NB. conflicting
equations
t=. ((%~<:)@{. , }. % {.) y {"1~ 1 i.~ * | y0 NB. coefficients to
be used
Y=. ({. ,~ }.) t (] - (*/ {.)) y NB. cleaning the
column
(#"1~ +./@:*)&.|: Y NB. eliminate
dependent equations
)
T=:".;._2]0 :0 NB. from
http://www.jsoftware.com/jwiki/RE%20Boss/J-blog/(De)Convolution
6 0 0 0 0 0 0 0 0 0 0 0 30
9 6 0 0 0 0 0 0 0 0 0 0 57
0 9 6 0 0 0 0 0 0 0 0 0 72
6 0 9 6 0 0 0 0 0 0 0 0 141
3 6 0 9 0 0 0 0 0 0 0 0 72
0 3 6 0 0 0 0 0 0 0 0 0 60
0 0 3 6 0 0 0 0 0 0 0 0 57
0 0 0 3 0 0 0 0 0 0 0 0 15
2 0 0 0 6 0 0 0 0 0 0 0 34
9 2 0 0 9 6 0 0 0 0 0 0 85
1 9 2 0 0 9 6 0 0 0 0 0 95
7 1 9 2 6 0 9 6 0 0 0 0 233
3 7 1 9 3 6 0 9 0 0 0 0 95
0 3 7 1 0 3 6 0 0 0 0 0 128
0 0 3 7 0 0 3 6 0 0 0 0 89
0 0 0 3 0 0 0 3 0 0 0 0 15
0 0 0 0 2 0 0 0 6 0 0 0 8
0 0 0 0 9 2 0 0 9 6 0 0 78
0 0 0 0 1 9 2 0 0 9 6 0 139
0 0 0 0 7 1 9 2 6 0 9 6 238
0 0 0 0 3 7 1 9 3 6 0 9 135
0 0 0 0 0 3 7 1 0 3 6 0 138
0 0 0 0 0 0 3 7 0 0 3 6 102
0 0 0 0 0 0 0 3 0 0 0 3 24
0 0 0 0 0 0 0 0 2 0 0 0 0
0 0 0 0 0 0 0 0 9 2 0 0 14
0 0 0 0 0 0 0 0 1 9 2 0 81
0 0 0 0 0 0 0 0 7 1 9 2 104
0 0 0 0 0 0 0 0 3 7 1 9 130
0 0 0 0 0 0 0 0 0 3 7 1 92
0 0 0 0 0 0 0 0 0 0 3 7 83
0 0 0 0 0 0 0 0 0 0 0 3 24
)
sle T
5 2 9 5 4 0 9 0 0 7 9 8
({:"1 T) -: (}:"1 T)(+/@:*"1) sle T
1
R.E. Boss
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