/// <summary>
/// 2つの行列を左側右側として連結した1個の行列を戻す。
/// </summary>
/// <param name="left">左側の行列</param>
/// <param name="right">右側の行列</param>
/// <returns>[left right]</returns>
public static WWMatrix JoinH(WWMatrix left, WWMatrix right)
{
if (left.Row != right.Row)
{
throw new ArgumentException("left.Row != right.Row");
}
var r = new WWMatrix(left.Row, left.Column + right.Column);
for (int y = 0; y < left.Row; ++y)
{
for (int x = 0; x < left.Column; ++x)
{
r.Set(y, x, left.At(y, x));
}
}
for (int y = 0; y < right.Row; ++y)
{
for (int x = 0; x < right.Column; ++x)
{
r.Set(y, left.Column + x, right.At(y, x));
}
}
return(r);
}
/// <summary>
/// 2つの行列を上側、下側として連結した1個の行列を戻す。
/// </summary>
/// <param name="top">上側の行列</param>
/// <param name="bottom">下側の行列</param>
/// <returns>[top;bottom]</returns>
public static WWMatrix JoinV(WWMatrix top, WWMatrix bottom)
{
if (top.Column != bottom.Column)
{
throw new ArgumentException("top.column != bottom.column");
}
var r = new WWMatrix(top.Row + bottom.Row, top.Column);
for (int y = 0; y < top.Row; ++y)
{
for (int x = 0; x < top.Column; ++x)
{
r.Set(y, x, top.At(y, x));
}
}
for (int y = 0; y < bottom.Row; ++y)
{
for (int x = 0; x < bottom.Column; ++x)
{
r.Set(top.Row + y, x, bottom.At(y, x));
}
}
return(r);
}
public static WWMatrix Mul(WWMatrix lhs, WWMatrix rhs)
{
if (lhs.Column != rhs.Row)
{
throw new ArgumentException("lhs.Column != rhs.Row");
}
int loopCount = lhs.Column;
var rv = new WWMatrix(lhs.Row, rhs.Column);
for (int r = 0; r < rv.Row; ++r)
{
for (int c = 0; c < rv.Column; ++c)
{
double v = 0;
for (int i = 0; i < loopCount; ++i)
{
v += lhs.At(r, i) * rhs.At(i, c);
}
rv.Set(r, c, v);
}
}
return(rv);
}
/// <summary>
/// aを縦行列と見做して後から掛ける
/// rv := M x aT
/// 自分自身を変更しない。
/// </summary>
/// <returns>乗算結果の行列を転置したもの</returns>
public double[] Mul(double[] a)
{
if (mCol != a.Length)
{
throw new ArgumentException("a.Length != mat.Col");
}
var aT = new WWMatrix(a.Length, 1, a);
var rv = Mul(aT);
return(rv.ToArray());
}
public WWMatrix ToMatrix()
{
WWMatrix rv = new WWMatrix(mRow, mCol);
for (int r = 0; r < mRow; ++r)
{
for (int c = 0; c < mCol; ++c)
{
rv.Set(r, c, At(r, c).Val);
}
}
return(rv);
}
/// <summary>
/// 転置した行列を作って戻す。
/// 自分自身を変更しない。
/// </summary>
/// <returns>転置した行列。</returns>
public WWMatrix Transpose()
{
var t = new WWMatrix(mCol, mRow);
for (int y = 0; y < mRow; ++y)
{
for (int x = 0; x < mCol; ++x)
{
t.Set(x, y, At(y, x));
}
}
return(t);
}
/// <summary>
/// https://en.wikipedia.org/wiki/Crout_matrix_decomposition
/// </summary>
public static ResultEnum LUdecompose(WWMatrix inA, out WWMatrix outL, out WWMatrix outU, double epsilon = 1.0e-7)
{
if (inA.Row < 2 || inA.Row != inA.Column)
{
outL = new WWMatrix(0, 0);
outU = new WWMatrix(0, 0);
return(ResultEnum.UnsupportedMatrixShape);
}
int N = inA.Row;
outL = new WWMatrix(N, N);
outU = new WWMatrix(N, N);
outU.SetIdentity();
for (int x = 0; x < N; ++x)
{
for (int y = x; y < N; ++y)
{
double sum = 0;
for (int k = 0; k < x; ++k)
{
sum += outL.At(y, k) * outU.At(k, x);
}
outL.Set(y, x, inA.At(y, x) - sum);
}
for (int y = x; y < N; ++y)
{
double sum = 0;
for (int k = 0; k < x; ++k)
{
sum += outL.At(x, k) * outU.At(k, y);
}
if (WWMathUtil.IsAlmostZero(outL.At(x, x), epsilon))
{
return(ResultEnum.FailedToChoosePivot);
}
outU.Set(x, y, (inA.At(x, y) - sum) / outL.At(x, x));
}
}
return(ResultEnum.Success);
}
public static double[] Transform(double[] from)
{
if (!IsPowerOf2(from.Length))
{
throw new ArgumentException("from length is not power of 2");
}
int L = from.Length;
// Lは2のN乗。
int N = 0;
for (int i = L; 1 < i; i /= 2)
{
++N;
}
var m = new WWMatrix(L, N + 1);
for (int r = 0; r < L; ++r)
{
m.Set(r, 0, from[r]);
}
for (int c = 0; c < N; ++c)
{
for (int r = 0; r < L / 2; ++r)
{
m.Set(r, c + 1, m.At(r * 2, c) + m.At(r * 2 + 1, c));
}
for (int r = 0; r < L / 2; ++r)
{
m.Set(r + L / 2, c + 1, m.At(r * 2, c) - m.At(r * 2 + 1, c));
}
}
var rv = new double[L];
for (int r = 0; r < L; ++r)
{
rv[r] = m.At(r, N);
}
return(rv);
}
/// <summary>
/// aとbが大体同じ時true。異なるときfalse。
/// </summary>
public static bool IsSame(WWMatrix a, WWMatrix b, double epsilon = 1.0e-7)
{
if (a.Column != b.Column ||
a.Row != b.Row)
{
return(false);
}
for (int y = 0; y < a.Row; ++y)
{
for (int x = 0; x < a.Column; ++x)
{
if (!WWMathUtil.IsAlmostZero(a.At(y, x) - b.At(y, x), epsilon))
{
return(false);
}
}
}
return(true);
}
/// <summary>
/// Solve and find f for Ku = f
/// </summary>
/// <param name="K">N * N matrix</param>
/// <param name="f">N elem vertical vector</param>
/// <returns>u : N elem vertical vector. zero elem vector returns when failed.</returns>
public static double[] SolveKu_eq_f(WWMatrix K, double[] f)
{
int N = K.Row;
if (K.Column != N)
{
throw new ArgumentException("K.col != K.row");
}
if (f.Length != N)
{
throw new ArgumentException("f.Length != K.row");
}
var u = new double[N];
WWMatrix L;
WWMatrix P;
WWMatrix U;
var r = WWMatrix.LUdecompose2(K, out L, out P, out U);
if (r != WWMatrix.ResultEnum.Success)
{
return(new double[0]);
}
// Reorder f
var fr = P.Mul(f);
var c = new double[N];
// 前進消去 Lc=fによりcを求める。
// L c = f
// L → L (既知)
// c → c (既知)
// f → fr (既知)
for (int i = 0; i < N; ++i)
{
double t = fr[i];
for (int j = 0; j < i; ++j)
{
// i: row番号、j:col番号。
t -= L.At(i, j) * c[j];
}
c[i] = t / L.At(i, i);
}
// cが求まった。
// U u = c
// U → U (既知)
// u → u (解)
// c → c (既知)
// 後退代入で解uを得る。
for (int i = N - 1; 0 <= i; --i)
{
double t = c[i];
// j=i+1行目より下のu_jは求まっている。
for (int j = i + 1; j < N; ++j)
{
t -= U.At(i, j) * u[j];
}
u[i] = t / U.At(i, i);
}
return(u);
}
/// <summary>
/// https://www.student.cs.uwaterloo.ca/~cs370/notes/LUExample2.pdf
/// </summary>
public static ResultEnum LUdecompose2(WWMatrix inA, out WWMatrix outL, out WWMatrix outP, out WWMatrix outU, double epsilon = 1.0e-7)
{
if (inA.Row < 2 || inA.Row != inA.Column)
{
outP = new WWMatrix(0, 0);
outL = new WWMatrix(0, 0);
outU = new WWMatrix(0, 0);
return(ResultEnum.UnsupportedMatrixShape);
}
int N = inA.Row;
outP = new WWMatrix(N, N).SetIdentity();
outL = new WWMatrix(N, N).SetIdentity();
outU = new WWMatrix(N, N);
outU = inA.DeepCopy();
var PA = new WWMatrix(N, N);
// Lの0行目は [1 0 0 ... 0]
for (int c = 0; c < N - 1; ++c)
{
// c個目のピボットを選択する。
// Uのc列を比較し、絶対値が最大のものを選ぶ。
// Pのc行目が決定する。
int maxRow = c;
{
double maxAbs = 0;
for (int y = c; y < N; ++y)
{
if (maxAbs < Math.Abs(outU.At(y, c)))
{
maxAbs = Math.Abs(outU.At(y, c));
maxRow = y;
}
}
}
// ピボットは、maxRow行c列。
outU.ExchangeRows(c, maxRow);
outP.ExchangeRows(c, maxRow);
outL.ExchangeRows(c, maxRow);
outL.ExchangeCols(c, maxRow);
// 並び替えによりuccがピボットになった。
double ucc = outU.At(c, c);
if (WWMathUtil.IsAlmostZero(ucc, epsilon))
{
return(ResultEnum.FailedToChoosePivot);
}
for (int k = c + 1; k < N; ++k)
{
// Uのk列目の計算。
// Uのk列目を0にするために、1列目を何倍して足すか。
double ukc = outU.At(k, c);
double ratio = ukc / ucc;
for (int x = 0; x < N; ++x)
{
double ucx = outU.At(c, x);
double ukx = outU.At(k, x);
outU.Set(k, x, ukx - ratio * ucx);
}
// Lのk行c列 = ratio。
outL.Set(k, c, ratio);
}
}
return(ResultEnum.Success);
}
/// <summary>
/// rv := this x a
/// 自分自身を変更しない。
/// </summary>
/// <returns>乗算結果。</returns>
public WWMatrix Mul(WWMatrix a)
{
return(Mul(this, a));
}
/// <summary>
/// コピーを作って戻す。
/// mの実体も複製される。
/// </summary>
public WWMatrix DeepCopy()
{
var r = new WWMatrix(mRow, mCol, m);
return(r);
}
