/// <summary>
/// 检测两个矩阵的矩阵乘法后得到的新矩阵在row和col
/// 列的算式。
/// </summary>
/// <param name="matrix1"></param>
/// <param name="matrix2"></param>
/// <param name="row"></param>
/// <param name="col"></param>
/// <returns></returns>
public static string TestMatrixMultiMatrix(SparseMatrix matrix1, SparseMatrix matrix2, int row, int col)
{
decimal sumVal = 0;
SparseMatrixCell rowHead = matrix1._rowHead[row];
SparseMatrixCell colHead = matrix2._colHead[col];
StringBuilder sb = new StringBuilder();
string connChar = "";
while (rowHead != null && colHead != null)
{
if (rowHead.ColIndex == colHead.RowIndex)
{
sb.Append(connChar).Append(rowHead.Val).Append("*").Append(colHead.Val);
connChar = "+";
sumVal += rowHead.Val * colHead.Val;
colHead = colHead.Down;
rowHead = rowHead.Right;
}
else if (rowHead.ColIndex > colHead.RowIndex)
{
colHead = colHead.Down;
}
else if (rowHead.ColIndex < colHead.RowIndex)
{
rowHead = rowHead.Right;
}
}
sb.Append("=").Append(sumVal);
return(sb.ToString());
}
/// <summary>
/// 把数据追加到结尾
/// </summary>
/// <param name="rowIndex"></param>
/// <param name="colIndex"></param>
/// <param name="val"></param>
void AppendToTail(int rowIndex, int colIndex, decimal val)
{
SparseMatrixCell cell = new SparseMatrixCell
{
ColIndex = colIndex,
RowIndex = rowIndex,
Val = val
};
SparseMatrixCell tempColTail = _colTail[colIndex];
if (tempColTail == null)
{
_colHead[colIndex] = cell;
}
else
{
(cell.Up = tempColTail).Down = cell;
}
_colTail[colIndex] = cell;
SparseMatrixCell tempRowTail = _rowTail[rowIndex];
if (tempRowTail == null)
{
_rowHead[rowIndex] = cell;
}
else
{
(cell.Left = tempRowTail).Right = cell;
}
_rowTail[rowIndex] = cell;
}
/// <summary>
/// 矩阵向量化
/// </summary>
public SparseMatrix Vec()
{
if (ColCount == 1)
{
return((SparseMatrix)Clone());
}
SparseMatrix newMatrix = new SparseMatrix(ColCount * RowCount, 1);
//find=true（寻找头部）、find=false（寻找尾部）
SparseMatrixCell newHead = null;
SparseMatrixCell tempTail = null;
IEnumerator ie = _colHead.GetEnumerator();
for (; ie.MoveNext();)
{
newHead = (SparseMatrixCell)ie.Current;
if (newHead != null)
{
tempTail = _colTail[newHead.ColIndex];
break;
}
}
if (newHead != null)
{
SparseMatrixCell tempHead = null;
for (; ie.MoveNext();)
{
tempHead = (SparseMatrixCell)ie.Current;
if (tempHead != null)
{
tempTail.Down = tempHead;
tempHead.Up = tempTail;
tempTail = _colTail[tempHead.ColIndex];
}
}
}
newMatrix._colHead[0] = newHead;
SparseMatrixCell newTail = newHead;
while (true)
{
newTail.RowIndex = RowCount * newTail.ColIndex + newTail.RowIndex;
newTail.ColIndex = 0;
newTail.Right = newTail.Left = null;
newMatrix._rowTail.AppendToTail(newTail, newTail.RowIndex);
newMatrix._rowHead.AppendToTail(newTail, newTail.RowIndex);
if (newTail.Down == null)
{
break;
}
else
{
newTail = newTail.Down;
}
}
newMatrix._colTail[0] = newTail;
return(newMatrix);
}
/// <summary>
/// 矩阵对角化
/// </summary>
public SparseMatrix Diag()
{
if (ColCount != 1)
{
throw new Exception("只有向量才能对角化！");
}
SparseMatrix newMatrix = new SparseMatrix(RowCount, RowCount);
SparseMatrixCell current = _colHead[0], temp;
for (int i; current != null;)
{
i = current.RowIndex;
newMatrix._colTail.AppendToTail(current, i);
newMatrix._rowTail.AppendToTail(current, i);
newMatrix._colHead.AppendToTail(current, i);
newMatrix._rowHead.AppendToTail(current, i);
current.ColIndex = i;
temp = current;
current = current.Down;
temp.Down = temp.Up = temp.Left = temp.Right = null;
}
return(newMatrix);
}
/// <summary>
/// 读取/写入稀疏矩阵指定行列的元素
/// </summary>
/// <param name="rowIndex"></param>
/// <param name="colIndex"></param>
/// <returns></returns>
public decimal this[int rowIndex, int colIndex]
{
set
{
if (value == 0)
{
return;
}
if (colIndex < -1 || rowIndex < -1 || colIndex >= ColCount || rowIndex >= RowCount)
{
throw new Exception($"索引错误，矩阵的大小是：{RowCount}x{ColCount}");
}
SparseMatrixCell setVal = new SparseMatrixCell
{
Val = value,
ColIndex = colIndex,
RowIndex = rowIndex
};
SparseMatrixCell tempHead = _colHead[colIndex];
SparseMatrixCell tempTail;
if (tempHead == null)
{
_colHead[colIndex] = setVal;
_colTail[colIndex] = setVal;
}
else
{
tempTail = _colTail[colIndex];
}
while (tempHead != null)
{
if (tempHead.RowIndex == rowIndex)
{
tempHead.Val = value;
return;
}
else if (tempHead.RowIndex < rowIndex)
{
if (tempHead.Down == null)
{
tempHead.Down = setVal;
setVal.Up = tempHead;
_colTail[colIndex] = setVal;
break;
}
else
{
tempHead = tempHead.Down;
}
}
else if (tempHead.RowIndex > rowIndex)
{
if (tempHead.Up == null)
{
tempHead.Up = setVal;
setVal.Down = tempHead;
_colHead[colIndex] = setVal;
}
else
{
tempHead.Up.Down = setVal;
setVal.Up = tempHead.Up;
setVal.Down = tempHead;
tempHead.Up = setVal;
}
break;
}
}
tempHead = _rowHead[rowIndex];
if (tempHead == null)
{
_rowHead[rowIndex] = setVal;
_rowTail[rowIndex] = setVal;
return;
}
while (tempHead != null)
{
if (tempHead.ColIndex == colIndex)
{
tempHead.Val = value;
return;
}
else if (tempHead.ColIndex < colIndex)
{
if (tempHead.Right == null)
{
tempHead.Right = setVal;
setVal.Left = tempHead;
_rowTail[rowIndex] = setVal;
return;
}
else
{
tempHead = tempHead.Right;
}
}
else if (tempHead.ColIndex > colIndex)
{
if (tempHead.Left == null)
{
tempHead.Left = setVal;
setVal.Right = tempHead;
_rowHead[rowIndex] = setVal;
}
else
{
tempHead.Left.Right = setVal;
setVal.Left = tempHead.Left;
setVal.Right = tempHead;
tempHead.Left = setVal;
}
return;
}
}
}
get
{
if (colIndex < -1 || rowIndex < -1 || colIndex >= ColCount || rowIndex >= RowCount)
{
throw new Exception($"索引错误，矩阵的大小是：{RowCount}x{ColCount}");
}
SparseMatrixCell lastHead;
SparseMatrixCell lastTail;
if (rowIndex > colIndex)
{
lastHead = _rowHead[rowIndex];
if (lastHead == null)
{
return(0);
}
lastTail = _rowTail[rowIndex];
bool nearHead = (colIndex << 1) < lastTail.ColIndex + lastHead.ColIndex;
if (nearHead)
{
while (true)
{
if (lastHead.ColIndex == colIndex)
{
return(lastHead.Val);
}
else if (lastHead.ColIndex < colIndex)
{
if (lastHead.Right == null)
{
return(0);
}
else
{
lastHead = lastHead.Right;
}
}
else if (lastHead.ColIndex > colIndex)
{
return(0);
}
}
}
else
{
while (true)
{
if (lastTail.ColIndex == colIndex)
{
return(lastTail.Val);
}
else if (lastTail.ColIndex > colIndex)
{
if (lastTail.Left == null)
{
return(0);
}
else
{
lastTail = lastTail.Left;
}
}
else if (lastTail.ColIndex < colIndex)
{
return(0);
}
}
}
}
else
{
lastHead = _colHead[colIndex];
if (lastHead == null)
{
return(0);
}
lastTail = _colTail[colIndex];
bool nearHead = (rowIndex << 1) < lastHead.RowIndex + lastTail.RowIndex;
if (nearHead)
{
while (true)
{
if (lastHead.RowIndex == rowIndex)
{
return(lastHead.Val);
}
else if (lastHead.RowIndex < rowIndex)
{
if (lastHead.Down == null)
{
return(0);
}
else
{
lastHead = lastHead.Down;
}
}
else if (lastHead.RowIndex > rowIndex)
{
return(0);
}
}
}
else
{
while (true)
{
if (lastTail.RowIndex == rowIndex)
{
return(lastTail.Val);
}
else if (lastTail.RowIndex > rowIndex)
{
if (lastTail.Up == null)
{
return(0);
}
else
{
lastTail = lastTail.Up;
}
}
else if (lastTail.RowIndex < rowIndex)
{
return(0);
}
}
}
}
}
}
/// <summary>
/// 把值追加到指定位置上。
/// </summary>
/// <param name="rowIndex"></param>
/// <param name="colIndex"></param>
/// <param name="val"></param>
private void AddTo(int rowIndex, int colIndex, decimal val)
{
if (val == 0)
{
return;
}
if (colIndex < -1 || rowIndex < -1 || colIndex >= ColCount || rowIndex >= RowCount)
{
throw new Exception($"索引错误，矩阵的大小是：{RowCount}x{ColCount}");
}
SparseMatrixCell setVal = new SparseMatrixCell
{
Val = val,
ColIndex = colIndex,
RowIndex = rowIndex
};
SparseMatrixCell temp = _colHead[colIndex];
while (true)
{
if (temp == null)
{
_colHead[colIndex] = setVal;
}
else if (temp.RowIndex == rowIndex)
{
temp.Val += val;
return;
}
else if (temp.RowIndex < rowIndex)
{
if (temp.Down == null)
{
temp.Down = setVal;
setVal.Up = temp;
}
else
{
temp = temp.Down;
continue;
}
}
else if (temp.RowIndex < rowIndex && temp.Down.RowIndex > rowIndex)
{
temp.Down.Up = setVal;
setVal.Down = temp.Down;
temp.Down = setVal;
setVal.Up = temp;
}
else
{
continue;
}
break;
}
temp = _rowHead[rowIndex];
while (true)
{
if (temp == null)
{
_rowHead[rowIndex] = setVal;
}
else if (temp.ColIndex == colIndex)
{
temp.Val += val;
return;
}
else if (temp.ColIndex < colIndex)
{
if (temp.Right == null)
{
temp.Right = setVal;
setVal.Left = temp;
}
else
{
temp = temp.Right;
continue;
}
}
else if (temp.ColIndex < colIndex && temp.Right.ColIndex > colIndex)
{
temp.Right.Left = setVal;
setVal.Right = temp.Right;
temp.Right = setVal;
setVal.Left = temp;
}
else
{
continue;
}
break;
}
}