/usr/share/axiom-20140801/input/lupfact.input is in axiom-test 20140801-6.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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)spool lupfact.output
)set message test on
)set message auto off
)clear all
--S 1 of 18
field := Fraction Integer
--R
--R
--R (1) Fraction(Integer)
--R Type: Domain
--E 1
--S 2 of 18
permMat: (INT, INT, INT) -> Matrix field
--R
--R Type: Void
--E 2
--S 3 of 18
permMat(dim, i, j) ==
m : Matrix field :=
diagonalMatrix [(if i = k or j = k then 0 else 1) for k in 1..dim]
m(i,j) := 1
m(j,i) := 1
m
--R
--R Type: Void
--E 3
--S 4 of 18
nonZeroCol: Matrix field -> INT
--R
--R Type: Void
--E 4
--S 5 of 18
nonZeroCol(m) ==
foundit := false
col := 1
for i in 1..ncols(m) while not foundit repeat
for j in 1..nrows(m) while not foundit repeat
if not(m(j,i) = 0) then
col := i
foundit := true
col
--R
--R Type: Void
--E 5
--S 6 of 18
embedMatrix: (Matrix field,NNI,NNI) -> Matrix field
--R
--R Type: Void
--E 6
--S 7 of 18
embedMatrix(m, oldDim, newDim) ==
n := diagonalMatrix([1 for i in 1..newDim])$(Matrix(field))
setsubMatrix!(n,1,1,m)
n
--R
--R Type: Void
--E 7
--S 8 of 18
lupFactorEngine: (Matrix field, INT, INT) -> List Matrix field
--R
--R Type: Void
--E 8
--S 9 of 18
lupFactorEngine(a, m, p) ==
m = 1 =>
l : Matrix field := diagonalMatrix [1]
pm : Matrix field := permMat(p,1,nonZeroCol a)
[l,a*pm,pm]
m2 : NNI := m quo 2
b : Matrix field := subMatrix(a,1,m2,1,p)
c : Matrix field := subMatrix(a,m2+1,m,1,p)
lup := lupFactorEngine(b,m2,p)
l1 := lup.1
u1 := lup.2
pm1 := lup.3
d : Matrix field := c * (inverse(pm1) :: Matrix(field))
e : Matrix field := subMatrix(u1,1,m2,1,m2)
f : Matrix field := subMatrix(d,1,m2,1,m2)
g : Matrix field := d - f * (inverse(e) :: Matrix(field)) * u1
pmin2 : NNI := p - m2
g' : Matrix field := subMatrix(g,1,nrows(g),p - pmin2 + 1,p)
lup := lupFactorEngine(g',m2,pmin2)
l2 := lup.1
u2 := lup.2
pm2 := lup.3
pm3 := horizConcat(zero(pmin2,m2)$(Matrix field), pm2)
pm3 := vertConcat(horizConcat(diagonalMatrix [1 for i in 1..m2],
zero(m2,pmin2)$(Matrix field)),pm3)
h : Matrix field := u1 * (inverse(pm3) :: Matrix(field))
l : Matrix field := horizConcat(l1, zero(m2,m2)$(Matrix field))
l := vertConcat(l,horizConcat(f * (inverse(e) :: Matrix(field)), l2))
u : Matrix field := horizConcat(zero(m2,m2)$(Matrix field), u2)
u := vertConcat(h,u)
pm := pm3 * pm1
[l,u,pm]
--R
--R Type: Void
--E 9
--S 10 of 18
intLog2: NNI -> NNI
--R
--R Type: Void
--E 10
--S 11 of 18
intLog2 n == if n = 1 then 0 else 1 + intLog2(n quo 2)
--R
--R Type: Void
--E 11
--S 12 of 18
lupFactor: Matrix field -> Union(List Matrix field,"failed")
--R
--R Type: Void
--E 12
--S 13 of 18
lupFactor m ==
not((r := nrows m) = ncols m) =>
messagePrint("Matrix must be square")$OUTFORM
"failed"
ilog := intLog2(2)
not(r = 2 ** ilog) =>
m := embedMatrix(m,r,(n := 2 ** (ilog + 1)))
l := lupFactorEngine(m,n,n)
[subMatrix(l.1,1,r,1,r),subMatrix(l.2,1,r,1,r),
subMatrix(l.3,1,r,1,r)]
lupFactorEngine(m,r,r)
--R
--R Type: Void
--E 13
--S 14 of 18
m : Matrix field := zero(4,4)
--R
--R
--R +0 0 0 0+
--R | |
--R |0 0 0 0|
--R (14) | |
--R |0 0 0 0|
--R | |
--R +0 0 0 0+
--R Type: Matrix(Fraction(Integer))
--E 14
--S 15 of 18
for i in 4..1 by -1 repeat m(5-i,i) := i
--R
--R Type: Void
--E 15
--S 16 of 18
m
--R
--R
--R +0 0 0 4+
--R | |
--R |0 0 3 0|
--R (16) | |
--R |0 2 0 0|
--R | |
--R +1 0 0 0+
--R Type: Matrix(Fraction(Integer))
--E 16
--S 17 of 18
lupFactor m
--R
--R Compiling function intLog2 with type NonNegativeInteger ->
--R NonNegativeInteger
--R Compiling function embedMatrix with type (Matrix(Fraction(Integer)),
--R NonNegativeInteger,NonNegativeInteger) -> Matrix(Fraction(Integer
--R ))
--R Compiling function nonZeroCol with type Matrix(Fraction(Integer))
--R -> Integer
--R Compiling function permMat with type (Integer,Integer,Integer) ->
--R Matrix(Fraction(Integer))
--R Compiling function lupFactorEngine with type (Matrix(Fraction(
--R Integer)),Integer,Integer) -> List(Matrix(Fraction(Integer)))
--R Compiling function lupFactor with type Matrix(Fraction(Integer)) ->
--R Union(List(Matrix(Fraction(Integer))),"failed")
--I Compiling function G7376 with type Integer -> Boolean
--R
--R +1 0 0 0+ +4 0 0 0+ +0 0 0 1+
--R | | | | | |
--R |0 1 0 0| |0 3 0 0| |0 0 1 0|
--R (17) [| |,| |,| |]
--R |0 0 1 0| |0 0 2 0| |0 1 0 0|
--R | | | | | |
--R +0 0 0 1+ +0 0 0 1+ +1 0 0 0+
--R Type: Union(List(Matrix(Fraction(Integer))),...)
--E 17
--S 18 of 18
m := [[1,2,3],[2,3,1],[3,1,2]]
--R
--R
--R +1 2 3+
--R | |
--R (18) |2 3 1|
--R | |
--R +3 1 2+
--R Type: Matrix(Fraction(Integer))
--E 18
)spool
)lisp (bye)
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