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Ingy döt Net 2013-10-27 22:24:23 +00:00
parent 6f050a029e
commit 776bba907c
3887 changed files with 59894 additions and 7280 deletions
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3
Task/QR-decomposition/Ada/qr-decomposition.ada
View file

@ -9,7 +9,8 @@ procedure QR is
for row in mat'Range (1) loop
for col in mat'Range (2) loop
FIO.Put (mat (row, col), Exp => 0, Aft => 4, Fore => 5);
end loop; New_Line;
end loop;
New_Line;
end loop;
end Show;

63
Task/QR-decomposition/D/qr-decomposition.d
View file

@ -1,43 +1,37 @@
import std.stdio, std.math, std.algorithm, std.traits,
std.typecons, std.numeric, std.range, std.conv;
T[][] elementwiseMat(string op, T, U)(in T[][] A, in U B)
pure /*nothrow*/ if (is(U == T) || is(U == T[][])) {
static if (is(U == T[][]))
assert(A.length == B.length);
if (A.empty)
return null;
auto R = new typeof(return)(A.length, A[0].length);
template elementwiseMat(string op) {
T[][] elementwiseMat(T, U)(in T[][] A, in U B)
pure nothrow if (is(U == T) || is(U == T[][])) {
static if (is(U == T[][]))
assert(A.length == B.length);
if (A.empty)
return null;
auto R = new typeof(return)(A.length, A[0].length);
foreach (immutable r, const row; A)
static if (is(U == T)) {
R[r][] = mixin("row[] " ~ op ~ "B");
} else {
assert(row.length == B[r].length);
R[r][] = mixin("row[] " ~ op ~ "B[r][]");
}
foreach (immutable r, const row; A)
static if (is(U == T)) {
R[r][] = mixin("row[] " ~ op ~ "B");
} else {
assert(row.length == B[r].length);
R[r][] = mixin("row[] " ~ op ~ "B[r][]");
}
return R;
return R;
}
}
T[][] msum(T)(in T[][] A, in T[][] B) pure /*nothrow*/ {
return elementwiseMat!(q{ + }, T, T[][])(A, B);
}
T[][] msub(T)(in T[][] A, in T[][] B) pure /*nothrow*/ {
return elementwiseMat!(q{ - }, T, T[][])(A, B);
}
T[][] pmul(T)(in T[][] A, in T x) pure /*nothrow*/ {
return elementwiseMat!(q{ * }, T, T)(A, x);
}
T[][] pdiv(T)(in T[][] A, in T x) pure /*nothrow*/ {
return elementwiseMat!(q{ / }, T, T)(A, x);
}
alias msum = elementwiseMat!q{ + },
msub = elementwiseMat!q{ - },
pmul = elementwiseMat!q{ * },
pdiv = elementwiseMat!q{ / };
bool isRectangular(T)(in T[][] mat) /*pure nothrow*/ {
bool isRectangular(T)(in T[][] mat) pure nothrow {
return mat.all!(r => r.length == mat[0].length);
}
T[][] matMul(T)(in T[][] a, in T[][] b) /*pure nothrow*/
T[][] matMul(T)(in T[][] a, in T[][] b) pure nothrow
in {
assert(a.isRectangular && b.isRectangular &&
a[0].length == b.length);
@ -106,7 +100,7 @@ T[][] matEmbed(T)(in T[][] A, in T[][] B,
in size_t row, in size_t col) pure nothrow {
auto C = new T[][](rows(A), cols(A));
foreach (immutable i, const arow; A)
C[i][] = arow[]; // some wasted copies
C[i][] = arow[]; // Some wasted copies.
foreach (immutable i, const brow; B)
C[row + i][col .. col + brow.length] = brow[];
return C;
@ -125,8 +119,8 @@ T[][] makeHouseholder(T)(in T[][] a) {
}
Tuple!(T[][],"Q", T[][],"R") QRdecomposition(T)(T[][] A) {
immutable m = rows(A);
immutable n = cols(A);
immutable m = A.rows;
immutable n = A.cols;
auto Q = matId!T(m);
// Work on n columns of A.
@ -173,7 +167,7 @@ T[][] solveUpperTriangular(T)(in T[][] R, in T[][] b) pure nothrow {
}
/// Solve a linear least squares problem by QR decomposition.
T[][] lsqr(T)(T[][] A, in T[][] b) {
T[][] lsqr(T)(T[][] A, in T[][] b) pure nothrow {
const qr = QRdecomposition(A);
immutable size_t n = cols(qr.R);
return solveUpperTriangular(
@ -181,7 +175,8 @@ T[][] lsqr(T)(T[][] A, in T[][] b) {
slice2D(matMul(transpose(qr.Q), b), 0, n-1, 0, 0));
}
Unqual!T[][] polyFit(T)(in T[][] x, in T[][] y, in size_t n) {
Unqual!T[][] polyFit(T)(in T[][] x, in T[][] y, in size_t n)
pure nothrow {
immutable size_t m = cols(x);
auto A = new Unqual!T[][](m, n + 1);
foreach (immutable i, row; A)