LU decomposition: Difference between revisions
Added 11l
Alextretyak (talk | contribs) (Added 11l) |
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0 1 0 0
0 0 0 1
</pre>
=={{header|11l}}==
{{trans|Python}}
<lang 11l>F pprint(m)
L(row) m
print(row)
F matrix_mul(a, b)
V result = [[0.0] * a.len] * a.len
L(j) 0 .< a.len
L(i) 0 .< a.len
V r = 0.0
L(k) 0 .< a.len
r += a[i][k] * b[k][j]
result[i][j] = r
R result
F pivotize(m)
‘Creates the pivoting matrix for m.’
V n = m.len
V ID = (0 .< n).map(j -> (0 .< @n).map(i -> Float(i == @j)))
L(j) 0 .< n
V row = max(j .< n, key' i -> abs(@m[i][@j]))
I j != row
swap(&ID[j], &ID[row])
R ID
F lu(A)
‘Decomposes a nxn matrix A by PA=lU and returns l, U and P.’
V n = A.len
V l = [[0.0] * n] * n
V U = [[0.0] * n] * n
V P = pivotize(A)
V A2 = matrix_mul(P, A)
L(j) 0 .< n
l[j][j] = 1.0
L(i) 0 .. j
V s1 = sum((0 .< i).map(k -> @U[k][@j] * @l[@i][k]))
U[i][j] = A2[i][j] - s1
L(i) j .< n
V s2 = sum((0 .< j).map(k -> @U[k][@j] * @l[@i][k]))
l[i][j] = (A2[i][j] - s2) / U[j][j]
R (l, U, P)
V a = [[1, 3, 5], [2, 4, 7], [1, 1, 0]]
L(part) lu(a)
pprint(part)
print()
print()
V b = [[11, 9, 24, 2], [1, 5, 2, 6], [3, 17, 18, 1], [2, 5, 7, 1]]
L(part) lu(b)
pprint(part)
print()</lang>
{{out}}
<pre>
[1, 0, 0]
[0.5, 1, 0]
[0.5, -1, 1]
[2, 4, 7]
[0, 1, 1.5]
[0, 0, -2]
[0, 1, 0]
[1, 0, 0]
[0, 0, 1]
[1, 0, 0, 0]
[0.272727, 1, 0, 0]
[0.0909091, 0.2875, 1, 0]
[0.181818, 0.23125, 0.00359712, 1]
[11, 9, 24, 2]
[0, 14.5455, 11.4545, 0.454545]
[0, 0, -3.475, 5.6875]
[0, 0, 0, 0.510791]
[1, 0, 0, 0]
[0, 0, 1, 0]
[0, 1, 0, 0]
[0, 0, 0, 1]
</pre>
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