我正在编写自己的矩阵类，其中包含矩阵类所需的方法。
代码的内容取自here
除了我的Decompose方法之外，一切似乎都很完美（有关LU分解矩阵的含义的更多信息，请查看here）：
public Matrix Decompose(out int[] permutationArray, out int toggle)
{
// Doolittle LUP decomposition with partial pivoting.
// rerturns: result is L (with 1s on diagonal) and U; perm holds row permutations; toggle is +1 or -1 (even or odd)
if (!this.IsSquare())
{
throw new Exception("LU-Decomposition can only be found for a square matrix");
}
Matrix decomposedMatrix = new Matrix(this); // copy this matrix before messing with it
permutationArray = new int[NumberOfRows]; // set up row permutation result
for (int i = 0; i < NumberOfRows; ++i)
{
permutationArray[i] = i;
}
toggle = 1; // toggle tracks row swaps. +1 -> even, -1 -> odd. used by MatrixDeterminant
for (int columnIndex = 0; columnIndex < NumberOfRows - 1; columnIndex++) // each column
{
// find largest value in col j
double maxOfColumn = Math.Abs(decomposedMatrix.GetElement(columnIndex, columnIndex));
int pivotRowIndex = columnIndex;
for (int rowIndex = columnIndex + 1; rowIndex < NumberOfRows; rowIndex++)
{
if (Math.Abs(decomposedMatrix.GetElement(rowIndex,columnIndex)) > maxOfColumn)
{
maxOfColumn = decomposedMatrix.GetElement(rowIndex, columnIndex);
pivotRowIndex = rowIndex;
}
}
if (pivotRowIndex != columnIndex) // if largest value not on pivot, swap rows
{
double[] rowPtr = decomposedMatrix.GetRow(pivotRowIndex);
decomposedMatrix.SetRowOfMatrix(pivotRowIndex, decomposedMatrix.GetRow(columnIndex));
decomposedMatrix.SetRowOfMatrix(columnIndex, rowPtr);
int tmp = permutationArray[pivotRowIndex]; // and swap permutation info
permutationArray[pivotRowIndex] = permutationArray[columnIndex];
permutationArray[columnIndex] = tmp;
toggle = -toggle; // adjust the row-swap toggle
}
if (decomposedMatrix.GetElement(columnIndex, columnIndex) == 0.0)
{
// find a good row to swap
int goodRow = -1;
for (int row = columnIndex + 1; row < decomposedMatrix.NumberOfRows; row++)
{
if (decomposedMatrix.GetElement(row, columnIndex) != 0.0)
{
goodRow = row;
}
}
if (goodRow == -1)
{
throw new Exception("Cannot use Doolittle's method on this matrix");
}
// swap rows so 0.0 no longer on diagonal
double[] rowPtr = decomposedMatrix.GetRow(goodRow);
decomposedMatrix.SetRowOfMatrix(goodRow, decomposedMatrix.GetRow(columnIndex));
decomposedMatrix.SetRowOfMatrix(columnIndex, rowPtr);
int tmp = permutationArray[goodRow]; // and swap perm info
permutationArray[goodRow] = permutationArray[columnIndex];
permutationArray[columnIndex] = tmp;
toggle = -toggle; // adjust the row-swap toggle
}
for (int rowIndex = columnIndex + 1; rowIndex < this.NumberOfRows; ++rowIndex)
{
double valueToStore = decomposedMatrix.GetElement(rowIndex, columnIndex) / decomposedMatrix.GetElement(columnIndex, columnIndex);
decomposedMatrix.SetElement(rowIndex, columnIndex, valueToStore);
for (int nextColumnIndex = columnIndex + 1; nextColumnIndex < NumberOfRows; ++nextColumnIndex)
{
double valueToStore2 = decomposedMatrix.GetElement(rowIndex, nextColumnIndex) -
decomposedMatrix.GetElement(rowIndex, columnIndex) * decomposedMatrix.GetElement(columnIndex, nextColumnIndex);
decomposedMatrix.SetElement(rowIndex, nextColumnIndex, valueToStore2);
}
}
} // main j column loop
return decomposedMatrix;
} // MatrixDecompose
这是失败的单元测试：（请注意！如果开始矩阵使用正数而不是负数，则完全相同的单位测试通过）
[TestMethod()]
public void Matrix_DecomposeTest3_DifferentSigns()
{
Matrix matrixA = new Matrix(9);
//Set up matrix A
double[] row1OfMatrixA = { 3, 0, 0, -7, 0, 0, 0, 0, 0 };
double[] row2OfMatrixA = { 0, 1, 8, 0, -4, 2, 0, 0, 0 };
double[] row3OfMatrixA = { 0, 2, 8, 0, -9, 3, 0, 0, 0 };
double[] row4OfMatrixA = { -5, 0, 0, 4, 0, 7, -1, 0, 3 };
double[] row5OfMatrixA = { 0, -3, -7, 0, 7, -8, 0, -3, 0 };
double[] row6OfMatrixA = { 0, 7, 2, 5, -3, 7, -2, 0, 4 };
double[] row7OfMatrixA = { 0, 0, 0, -2, 0, -8, 4, 0, 7 };
double[] row8OfMatrixA = { 0, 0, 0, 0, -9, 0, 0, 3, 0 };
double[] row9OfMatrixA = { 0, 0, 0, 1, 0, 4, 7, 0, 6 };
matrixA.SetRowOfMatrix(0, row1OfMatrixA);
matrixA.SetRowOfMatrix(1, row2OfMatrixA);
matrixA.SetRowOfMatrix(2, row3OfMatrixA);
matrixA.SetRowOfMatrix(3, row4OfMatrixA);
matrixA.SetRowOfMatrix(4, row5OfMatrixA);
matrixA.SetRowOfMatrix(5, row6OfMatrixA);
matrixA.SetRowOfMatrix(6, row7OfMatrixA);
matrixA.SetRowOfMatrix(7, row8OfMatrixA);
matrixA.SetRowOfMatrix(8, row9OfMatrixA);
Console.Out.Write(matrixA);
//The LUP Decomposition
//Correct L Part
Matrix correctLPartOfLUPDecomposition = new Matrix(9);
double[] row1OfLMatrix = { 1, 0, 0, 0, 0, 0, 0, 0, 0 };
double[] row2OfLMatrix = { 0, 1, 0, 0, 0, 0, 0, 0, 0 };
double[] row3OfLMatrix = { 0, .143, 1, 0, 0, 0, 0, 0, 0 };
double[] row4OfLMatrix = { -.6, 0, 0, 1, 0, 0, 0, 0, 0 };
double[] row5OfLMatrix = { 0, 0, 0, 0, 1, 0, 0, 0, 0 };
double[] row6OfLMatrix = { 0, 0, 0, .435, 0, 1, 0, 0, 0 };
double[] row7OfLMatrix = { 0, 0, 0, -.217, 0, -.5, 1, 0, 0 };
double[] row8OfLMatrix = { 0, -.429, -.796, -.342, -.319, .282, -.226, 1, 0 };
double[] row9OfLMatrix = { 0.000, 0.286, 0.963, 0.161, 0.523, 0.065, 0.013, 0.767, 1.000 };
correctLPartOfLUPDecomposition.SetRowOfMatrix(0, row1OfLMatrix);
correctLPartOfLUPDecomposition.SetRowOfMatrix(1, row2OfLMatrix);
correctLPartOfLUPDecomposition.SetRowOfMatrix(2, row3OfLMatrix);
correctLPartOfLUPDecomposition.SetRowOfMatrix(3, row4OfLMatrix);
correctLPartOfLUPDecomposition.SetRowOfMatrix(4, row5OfLMatrix);
correctLPartOfLUPDecomposition.SetRowOfMatrix(5, row6OfLMatrix);
correctLPartOfLUPDecomposition.SetRowOfMatrix(6, row7OfLMatrix);
correctLPartOfLUPDecomposition.SetRowOfMatrix(7, row8OfLMatrix);
correctLPartOfLUPDecomposition.SetRowOfMatrix(8, row9OfLMatrix);
//Correct U Part
Matrix correctUPartOfLUPDecomposition = new Matrix(9);
double[] row1OfUMatrix = { -5.000, 0.000, 0.000, 4.000, 0.000, 7.000, -1.000, 0.000, 3.000 };
double[] row2OfUMatrix = { 0.000, 7.000, 2.000, 5.000, -3.000, 7.000, -2.000, 0.000, 4.000 };
double[] row3OfUMatrix = { 0.000, 0.000, 7.714, -0.714, -3.571, 1.000, 0.286, 0.000, -0.571 };
double[] row4OfUMatrix = { 0.000, 0.000, 0.000, -4.600, 0.000, 4.200, -0.600, 0.000, 1.800 };
double[] row5OfUMatrix = { 0.000, 0.000, 0.000, 0.000, -9.000, 0.000, 0.000, 3.000, 0.000 };
double[] row6OfUMatrix = { 0.000, 0.000, 0.000, 0.000, 0.000, -9.826, 4.261, 0.000, 6.217 };
double[] row7OfUMatrix = { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 9.000, 0.000, 9.500 };
double[] row8OfUMatrix = { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, -2.043, 2.272 };
double[] row9OfUMatrix = { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, -3.153 };
correctUPartOfLUPDecomposition.SetRowOfMatrix(0, row1OfUMatrix);
correctUPartOfLUPDecomposition.SetRowOfMatrix(1, row2OfUMatrix);
correctUPartOfLUPDecomposition.SetRowOfMatrix(2, row3OfUMatrix);
correctUPartOfLUPDecomposition.SetRowOfMatrix(3, row4OfUMatrix);
correctUPartOfLUPDecomposition.SetRowOfMatrix(4, row5OfUMatrix);
correctUPartOfLUPDecomposition.SetRowOfMatrix(5, row6OfUMatrix);
correctUPartOfLUPDecomposition.SetRowOfMatrix(6, row7OfUMatrix);
correctUPartOfLUPDecomposition.SetRowOfMatrix(7, row8OfUMatrix);
correctUPartOfLUPDecomposition.SetRowOfMatrix(8, row9OfUMatrix);
//Calculate values for the above
int[] permutationArray;
int toggleValue;
Matrix decomposeResult = matrixA.Decompose(out permutationArray, out toggleValue);
Matrix calculatedLPartOfLUPDecomposition = decomposeResult.ExtractLower();
Matrix calculatedUPartOfLUPDecomposition = decomposeResult.ExtractUpper();
//Compare the two matrices
double tolerance = .001;
Matrix LDifferenceMatrix = calculatedLPartOfLUPDecomposition - correctLPartOfLUPDecomposition;
Matrix UDifferenceMatrix = calculatedUPartOfLUPDecomposition - correctUPartOfLUPDecomposition;
for (int i = 0; i < LDifferenceMatrix.NumberOfRows; i++)
{
for (int j = 0; j < LDifferenceMatrix.NumberOfColumns; j++)
{
(Math.Abs(LDifferenceMatrix.GetElement(i, j)) < tolerance).Should().BeTrue();
}
}
for (int i = 0; i < UDifferenceMatrix.NumberOfRows; i++)
{
for (int j = 0; j < UDifferenceMatrix.NumberOfColumns; j++)
{
(Math.Abs(UDifferenceMatrix.GetElement(i, j)) < tolerance).Should().BeTrue();
}
}
}
我使用找到的here工具获得了单元测试的数字。
我有单元测试了Matrix的所有其他方法，它们都通过了。
我对分解方法有什么看法？
答案 0 :(得分：1)
在哪里选择结果列的最大值：
maxOfColumn = decomposedMatrix.GetElement(rowIndex, columnIndex);
你应该真正选择那里找到的最大绝对值（你在if语句中做到这一点，之后似乎已经忘记了）。我会通过添加评论来明确指出，以便下一个阅读此代码的人可以更清楚地看到它
//if a value with a larger absolute value has been found replace the currently selectedmax
if (Math.Abs(decomposedMatrix.GetElement(rowIndex,columnIndex)) > maxOfColumn)
{
maxOfColumn = Math.Abs(decomposedMatrix.GetElement(rowIndex, columnIndex));
答案 1 :(得分：0)
此
if (Math.Abs(decomposedMatrix.GetElement(rowIndex,columnIndex)) > maxOfColumn)
{
maxOfColumn = decomposedMatrix.GetElement(rowIndex, columnIndex);
应该是：
if (Math.Abs(decomposedMatrix.GetElement(rowIndex,columnIndex)) > maxOfColumn)
{
maxOfColumn = Math.Abs(decomposedMatrix.GetElement(rowIndex, columnIndex));