blob: 1d5d3170ccfa32c080e87eee56950016c44b181e (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
|
#
# ludcmp.rb
#
module LUSolve
def ludecomp(a,n,zero=0,one=1)
prec = BigDecimal.limit(nil)
ps = []
scales = []
for i in 0...n do # pick up largest(abs. val.) element in each row.
ps <<= i
nrmrow = zero
ixn = i*n
for j in 0...n do
biggst = a[ixn+j].abs
nrmrow = biggst if biggst>nrmrow
end
if nrmrow>zero then
scales <<= one.div(nrmrow,prec)
else
raise "Singular matrix"
end
end
n1 = n - 1
for k in 0...n1 do # Gaussian elimination with partial pivoting.
biggst = zero;
for i in k...n do
size = a[ps[i]*n+k].abs*scales[ps[i]]
if size>biggst then
biggst = size
pividx = i
end
end
raise "Singular matrix" if biggst<=zero
if pividx!=k then
j = ps[k]
ps[k] = ps[pividx]
ps[pividx] = j
end
pivot = a[ps[k]*n+k]
for i in (k+1)...n do
psin = ps[i]*n
a[psin+k] = mult = a[psin+k].div(pivot,prec)
if mult!=zero then
pskn = ps[k]*n
for j in (k+1)...n do
a[psin+j] -= mult.mult(a[pskn+j],prec)
end
end
end
end
raise "Singular matrix" if a[ps[n1]*n+n1] == zero
ps
end
def lusolve(a,b,ps,zero=0.0)
prec = BigDecimal.limit(nil)
n = ps.size
x = []
for i in 0...n do
dot = zero
psin = ps[i]*n
for j in 0...i do
dot = a[psin+j].mult(x[j],prec) + dot
end
x <<= b[ps[i]] - dot
end
(n-1).downto(0) do |i|
dot = zero
psin = ps[i]*n
for j in (i+1)...n do
dot = a[psin+j].mult(x[j],prec) + dot
end
x[i] = (x[i]-dot).div(a[psin+i],prec)
end
x
end
end
|
