LU decomposition: Difference between revisions

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std.array, std.conv;

bool isRectangular(T)(in T[][] m) pure nothrow {

bool isRectangular(T)(in T[][] m) pure /*nothrow*/ {

//return !canFind!((r){ return r.length != m[0].length; })(m);

return !canFind!((r){ return r.length != m[0].length; })(m);

foreach (row; m)

if (row.length != m[0].length)

return false;

return true;

}

bool isSquare(T)(in T[][] m) pure nothrow {

bool isSquare(T)(in T[][] m) pure /*nothrow*/ {

return isRectangular(m) && m[0].length == m.length;

}

~~string~~ ~~prettyPrint~~(T)(in T[][] ~~m) {~~

immutable(T[][]) matrixMul(T)(immutable T[][] A,

immutable T[][] B) pure nothrow

//return "[" ~ join(map!text(m), ",\n ") ~ "]";

return "[" ~ array(map!text(m)).join(",\n ") ~ "]";

}

T[][] matrixMul(T)(in T[][] A, in T[][] B) pure nothrow

in {

assert(A.length && B.length &&

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/// Creates the pivoting matrix for m.

T[][] pivotize(T)(in T[][] m) pure nothrow

immutable(T[][]) pivotize(T)(immutable T[][] m) pure nothrow

in {

assert(isSquare(m));

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/// Decomposes a square matrix A by PA=LU and returns L, U and P.

Tuple!(T[][],"L", T[][],"U", const T[][],"P")

lu(T)(in T[][] A) pure nothrow

lu(T)(immutable T[][] A) pure nothrow

in {

assert(isSquare(A));

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}

/*immutable*/ const P = pivotize!T(A);

immutable P = pivotize!T(A);

/*immutable*/ const A2 = matrixMul!T(P, A);

immutable A2 = matrixMul!T(P, A);

foreach (j; 0 .. n) {

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void main() {

~~enum double[][]~~ a = [[1, 3, 5],

immutable a = [[1., 3, 5],

[2, 4, 7],

[2., 4, 7],

[1, 1, 0]];

[1., 1, 0]];

foreach (part; lu(a)~~.tupleof~~)

foreach (part; lu(a))

writeln(~~prettyPrint~~(part), "\n");

writeln("[", join(map!text(part), ",\n "), "]\n");

writeln();

~~enum double[][]~~ b = [[11, 9, 24, 2],

immutable b = [[11., 9, 24, 2],

[1, 5, 2, 6],

[1., 5, 2, 6],

[3, 17, 18, 1],

[3., 17, 18, 1],

[2, 5, 7, 1]];

[2., 5, 7, 1]];

foreach (part; lu(b)~~.tupleof~~)

foreach (part; lu(b))

writeln(~~prettyPrint~~(part), "\n");

writeln("[", join(map!text(part), ",\n "), "]\n");

}</lang>

Output:

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[0, 0, 1, 0],

[0, 1, 0, 0],

[0, 0, 0, 1]]~~</pre>~~

[0, 0, 0, 1]]

</pre>

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