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June 2018 Update

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This commit is contained in:
Ingy döt Net 2018-06-22 20:57:24 +00:00
parent ba8067c3b7
commit 22f33d4004
5278 changed files with 84726 additions and 14379 deletions
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44
Task/Reduced-row-echelon-form/J/reduced-row-echelon-form-1.j
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@ -1,10 +1,36 @@
]mymatrix=: _4]\ 1 2 _1 _4 2 3 _1 _11 _2 0 _3 22
1 2 _1 _4
2 3 _1 _11
_2 0 _3 22
NB.*pivot v Pivot at row, column
NB. form: (row,col) pivot M
pivot=: dyad define
'r c'=. x
col=. c{"1 y
y - (col - r = i.#y) */ (r{y) % r{col
)
require 'math/misc/linear'
gauss_jordan mymatrix
1 0 0 _8
0 1 0 1
0 0 1 _2
NB.*gauss_jordan v Gauss-Jordan elimination (full pivoting)
NB. y is: matrix
NB. x is: optional minimum tolerance, default 1e_15.
NB. If a column below the current pivot has numbers of magnitude all
NB. less then x, it is treated as all zeros.
gauss_jordan=: verb define
1e_15 gauss_jordan y
:
mtx=. y
'r c'=. $mtx
rows=. i.r
i=. j=. 0
max=. i.>./
while. (i<r) *. j<c do.
k=. max col=. | i}. j{"1 mtx
if. 0 < x-k{col do. NB. if all col < tol, set to 0:
mtx=. 0 (<(i}.rows);j) } mtx
else. NB. otherwise sort and pivot:
if. k do.
mtx=. (<i,i+k) C. mtx
end.
mtx=. (i,j) pivot mtx
i=. >:i
end.
j=. >:j
end.
mtx
)

26
Task/Reduced-row-echelon-form/J/reduced-row-echelon-form-2.j
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@ -1,16 +1,10 @@
gauss_jordan 2 0 _1 0 0,1 0 0 _1 0,3 0 0 _2 _1,0 1 0 0 _2,:0 1 _1 0 0
1 0 0 0 _1
0 1 0 0 _2
0 0 1 0 _2
0 0 0 1 _1
0 0 0 0 0
gauss_jordan 1 2 3 4 3 1,2 4 6 2 6 2,3 6 18 9 9 _6,4 8 12 10 12 4,:5 10 24 11 15 _4
1 2 0 0 3 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 0 1
0 0 0 0 0 0
gauss_jordan 0 1,1 2,:0 5
1 0
0 1
0 0
require 'math/misc/linear'
]A=: 1 2 _1 _4 , 2 3 _1 _11 ,: _2 0 _3 22
1 2 _1 _4
2 3 _1 _11
_2 0 _3 22
gauss_jordan A
1 0 0 _8
0 1 0 1
0 0 1 _2

53
Task/Reduced-row-echelon-form/J/reduced-row-echelon-form-3.j
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@ -1,37 +1,16 @@
mat=:".;._2]0 :0
1 0 0 0 0 0 1 0 0 0 0 _1 0 0 0 0 0 0
1 0 0 0 0 0 0 1 0 0 0 0 _1 0 0 0 0 0
1 0 0 0 0 0 0 0 1 0 0 0 0 _1 0 0 0 0
0 1 0 0 0 0 1 0 0 0 0 0 0 0 _1 0 0 0
0 1 0 0 0 0 0 0 1 0 0 _1 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 _1 0
0 0 1 0 0 0 1 0 0 0 0 0 _1 0 0 0 0 0
0 0 1 0 0 0 0 0 0 1 0 0 0 0 _1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 _1 0 0
0 0 0 1 0 0 0 0 0 1 0 0 _1 0 0 0 0 0
0 0 0 0 1 0 0 1 0 0 0 0 0 _1 0 0 0 0
0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 _1 0
0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 _1 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
0 0 0 0 0 1 0 0 0 0 1 0 0 0 _1 0 0 0
)
gauss_jordan mat
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.435897
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.307692
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.512821
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0.717949
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0.487179
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0.205128
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0.282051
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0.333333
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0.512821
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0.641026
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0.717949
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0.769231
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0.512821
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0.820513
gauss_jordan 2 0 _1 0 0,1 0 0 _1 0,3 0 0 _2 _1,0 1 0 0 _2,:0 1 _1 0 0
1 0 0 0 _1
0 1 0 0 _2
0 0 1 0 _2
0 0 0 1 _1
0 0 0 0 0
gauss_jordan 1 2 3 4 3 1,2 4 6 2 6 2,3 6 18 9 9 _6,4 8 12 10 12 4,:5 10 24 11 15 _4
1 2 0 0 3 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 0 1
0 0 0 0 0 0
gauss_jordan 0 1,1 2,:0 5
1 0
0 1
0 0

37
Task/Reduced-row-echelon-form/J/reduced-row-echelon-form-4.j Normal file
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@ -0,0 +1,37 @@
mat=: 0 ". ];._2 noun define
1 0 0 0 0 0 1 0 0 0 0 _1 0 0 0 0 0 0
1 0 0 0 0 0 0 1 0 0 0 0 _1 0 0 0 0 0
1 0 0 0 0 0 0 0 1 0 0 0 0 _1 0 0 0 0
0 1 0 0 0 0 1 0 0 0 0 0 0 0 _1 0 0 0
0 1 0 0 0 0 0 0 1 0 0 _1 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 _1 0
0 0 1 0 0 0 1 0 0 0 0 0 _1 0 0 0 0 0
0 0 1 0 0 0 0 0 0 1 0 0 0 0 _1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 _1 0 0
0 0 0 1 0 0 0 0 0 1 0 0 _1 0 0 0 0 0
0 0 0 0 1 0 0 1 0 0 0 0 0 _1 0 0 0 0
0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 _1 0
0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 _1 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
0 0 0 0 0 1 0 0 0 0 1 0 0 0 _1 0 0 0
)
gauss_jordan mat
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.435897
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.307692
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.512821
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0.717949
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0.487179
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0.205128
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0.282051
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0.333333
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0.512821
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0.641026
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0.717949
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0.769231
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0.512821
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0.820513