LU decomposition: Difference between revisions

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=={{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]