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Time for an 2014 update…

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Ingy döt Net 2014-01-17 05:32:22 +00:00
parent 372c577f83
commit 09687c4926
2520 changed files with 34227 additions and 7318 deletions
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15
Task/LU-decomposition/D/lu-decomposition.d
View file

@ -28,13 +28,13 @@ in {
}
/// Creates the pivoting matrix for m.
T[][] pivotize(T)(immutable T[][] m) /*pure nothrow*/
T[][] pivotize(T)(immutable T[][] m) pure nothrow
in {
assert(m.isSquare);
} body {
immutable n = m.length;
auto id = iota(n)
.map!(j=> n.iota.map!(i => cast(T)(i == j)).array)
.map!((in j) => n.iota.map!(i => cast(T)(i == j)).array)
.array;
foreach (immutable i; 0 .. n) {
@ -56,7 +56,7 @@ in {
/// Decomposes a square matrix A by PA=LU and returns L, U and P.
Tuple!(T[][],"L", T[][],"U", const T[][],"P")
lu(T)(immutable T[][] A) /*pure nothrow*/
lu(T)(immutable T[][] A) pure nothrow
in {
assert(A.isSquare);
} body {
@ -68,8 +68,8 @@ in {
U[i][0 .. i] = 0;
}
const P = A.pivotize!T;
const A2 = matrixMul!T(P, A);
immutable P = A.pivotize!T;
immutable A2 = matrixMul!T(P, A);
foreach (immutable j; 0 .. n) {
L[j][j] = 1;
@ -99,8 +99,7 @@ void main() {
[3.0, 17, 18, 1],
[2.0, 5, 7, 1]];
//auto f = "[%([%(%.1f, %)],\n %)]]\n\n".replicate(3);
auto f = std.array.replicate("[%([%(%.1f, %)],\n %)]]\n\n", 3);
foreach (m; [a, b])
auto f = "[%([%(%.1f, %)],\n %)]]\n\n".replicate(3);
foreach (immutable m; [a, b])
writefln(f, lu(m).tupleof);
}

87
Task/LU-decomposition/PL-I/lu-decomposition.pli Normal file
View file

@ -0,0 +1,87 @@
(subscriptrange, fofl, size): /* 2 Nov. 2013 */
LU_Decomposition: procedure options (main);
declare a1(3,3) float (18) initial ( 1, 3, 5,
2, 4, 7,
1, 1, 0);
declare a2(4,4) float (18) initial (11, 9, 24, 2,
1, 5, 2, 6,
3, 17, 18, 1,
2, 5, 7, 1);
call check(a1);
call check(a2);
/* In-situ decomposition */
LU: procedure(a, p);
declare a(*,*) float (18);
declare p(*) fixed binary;
declare (maximum, rtemp) float (18);
declare (n, i, j, k, ii, temp) fixed binary;
n = hbound(a,1);
do i = 1 to n; p(i) = i; end;
do k = 1 to n-1;
maximum = 0; ii = k;
do i = k to n;
if maximum < abs(a(p(i),k)) then
do; maximum = abs(a(p(i),k)); ii = i; end;
end;
if ii ^= k then do; temp = p(k); p(k) = p(ii); p(ii) = temp; end;
do i = k+1 to n; a(p(i),k) = a(p(i),k) / a(p(k),k); end;
do j = k+1 to n;
do i = k+1 to n;
a(p(i),j) = a(p(i),j) - a(p(i),k) * a(p(k),j);
end;
end;
end;
end LU;
CHECK: procedure(a);
declare a(*,*) float (18) nonassignable;
declare aa(hbound(a,1), hbound(a,2)) float (18);
declare L(hbound(a,1), hbound(a,2)) float (18);
declare U(hbound(a,1), hbound(a,2)) float (18);
declare (p(hbound(a,1), hbound(a,2)), ipiv(hbound(a,1)) ) fixed binary;
declare pp(hbound(a,1), hbound(a,2)) fixed binary;
declare (i, j, n, temp(hbound(a,1))) fixed binary;
n = hbound(a,1);
aa = A; /* work with a copy */
P = 0; L = 0; U = 0;
do i = 1 to n;
p(i,i) = 1; L(i,i) = 1; /* convert permutation vector to a matrix */
end;
call LU(aa, ipiv);
do i = 1 to n;
do j = 1 to i-1; L(i,j) = aa(ipiv(i),j); end;
do j = i to n; U(i,j) = aa(ipiv(i),j); end;
end;
pp = p;
do i = 1 to n;
p(ipiv(i), *) = pp(i,*);
end;
put skip list ('A');
put edit (A) (skip, (n) f(10,5));
put skip list ('P');
put edit (P) (skip, (n) f(11));
put skip list ('L');
put edit (L) (skip, (n) f(10,5));
put skip list ('U');
put edit (U) (skip, (n) f(10,5));
end CHECK;
end LU_Decomposition;

2
Task/LU-decomposition/Python/lu-decomposition.py
View file

@ -9,7 +9,7 @@ def pivotize(m):
n = len(m)
ID = [[float(i == j) for i in xrange(n)] for j in xrange(n)]
for j in xrange(n):
row = max(xrange(j, n), key=lambda i: m[i][j])
row = max(xrange(j, n), key=lambda i: abs(m[i][j]))
if j != row:
ID[j], ID[row] = ID[row], ID[j]
return ID