| public SetRow ( int passedrowIndex, double passedRow ) : void | ||
| passedrowIndex | int | |
| passedRow | double | |
| 리턴 | void | |
public void Matrix_GetRowStandardTest()
{
Matrix testMatrix = new Matrix(2, 3);
double[] rowTwoOfTestMatrix = { 7, 8, 9 };
testMatrix.SetRow(1, rowTwoOfTestMatrix);
testMatrix.GetRow(1).ShouldBeEquivalentTo(rowTwoOfTestMatrix);
}
public void Matrix_DecomposeTest3_DifferentSigns()
{
Matrix matrixA = new Matrix(9,9);
//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.SetRow(0, row1OfMatrixA);
matrixA.SetRow(1, row2OfMatrixA);
matrixA.SetRow(2, row3OfMatrixA);
matrixA.SetRow(3, row4OfMatrixA);
matrixA.SetRow(4, row5OfMatrixA);
matrixA.SetRow(5, row6OfMatrixA);
matrixA.SetRow(6, row7OfMatrixA);
matrixA.SetRow(7, row8OfMatrixA);
matrixA.SetRow(8, row9OfMatrixA);
//The LUP Decomposition
//Correct L Part
Matrix correctLPartOfLUPDecomposition = new Matrix(9,9);
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.SetRow(0, row1OfLMatrix);
correctLPartOfLUPDecomposition.SetRow(1, row2OfLMatrix);
correctLPartOfLUPDecomposition.SetRow(2, row3OfLMatrix);
correctLPartOfLUPDecomposition.SetRow(3, row4OfLMatrix);
correctLPartOfLUPDecomposition.SetRow(4, row5OfLMatrix);
correctLPartOfLUPDecomposition.SetRow(5, row6OfLMatrix);
correctLPartOfLUPDecomposition.SetRow(6, row7OfLMatrix);
correctLPartOfLUPDecomposition.SetRow(7, row8OfLMatrix);
correctLPartOfLUPDecomposition.SetRow(8, row9OfLMatrix);
//Correct U Part
Matrix correctUPartOfLUPDecomposition = new Matrix(9,9);
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.SetRow(0, row1OfUMatrix);
correctUPartOfLUPDecomposition.SetRow(1, row2OfUMatrix);
correctUPartOfLUPDecomposition.SetRow(2, row3OfUMatrix);
correctUPartOfLUPDecomposition.SetRow(3, row4OfUMatrix);
correctUPartOfLUPDecomposition.SetRow(4, row5OfUMatrix);
correctUPartOfLUPDecomposition.SetRow(5, row6OfUMatrix);
correctUPartOfLUPDecomposition.SetRow(6, row7OfUMatrix);
correctUPartOfLUPDecomposition.SetRow(7, row8OfUMatrix);
correctUPartOfLUPDecomposition.SetRow(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();
}
}
}
public void Matrix_InsertMatrixTest()
{
Matrix originalMatrix = new Matrix(3,3);
double[] matrix1Row1 = { 1, 5, 6 };
double[] matrix1Row2 = { 2, 4, 7 };
double[] matrix1Row3 = { 3, 6, 8 };
originalMatrix.SetRow(0, matrix1Row1);
originalMatrix.SetRow(1, matrix1Row2);
originalMatrix.SetRow(2, matrix1Row3);
Matrix matrixToInsert = Matrix.IdentityMatrix(2);
Matrix expectedResult = new Matrix(3,3);
double[] expectedResultRow1 = { 1, 5, 6 };
double[] expectedResultRow2 = { 1, 0, 7 };
double[] expectedResultRow3 = { 0, 1, 8 };
expectedResult.SetRow(0, expectedResultRow1);
expectedResult.SetRow(1, expectedResultRow2);
expectedResult.SetRow(2, expectedResultRow3);
Matrix actualResult = originalMatrix.InsertMatrixAt(matrixToInsert, 1, 0);
bool equalityResult = (actualResult == expectedResult);
equalityResult.Should().BeTrue();
}
public void Matrix_RemoveColumnsTest()
{
Matrix testMatrix = new Matrix(2,5);
double[] row1 = { 1, 2, 3, 4, 5 };
double[] row2 = { 1, 2, 3, 4, 5 };
testMatrix.SetRow(0, row1);
testMatrix.SetRow(1, row2);
int[] columnsToRemove = { 1, 3, 4 };
Matrix actualMatrix = testMatrix.RemoveColumns(columnsToRemove);
Matrix expectedMatrix = new Matrix(2);
double[] expectedRow1 = { 1, 3};
double[] expectedRow2 = { 1, 3};
expectedMatrix.SetRow(0, expectedRow1);
expectedMatrix.SetRow(1, expectedRow2);
(actualMatrix == expectedMatrix).Should().BeTrue();
}
public void MatricesMatrix_ConvertToMatrixTest_VariedDistances()
{
Matrix m1 = new Matrix(1,1);
Matrix m2 = new Matrix(2,2);
Matrix m3 = new Matrix(3,3);
Matrix m4 = new Matrix(4,4);
double[] m1Row1 = { 1};
double[] m2Row1 = { 2, 2 };
double[] m2Row2 = { 2, 2 };
double[] m3Row1 = { 3, 3, 3 };
double[] m3Row2 = { 3, 3, 3 };
double[] m3Row3 = { 3, 3, 3 };
double[] m4Row1 = { 4, 4, 4, 4 };
double[] m4Row2 = { 4, 4, 4, 4 };
double[] m4Row3 = { 4, 4, 4, 4 };
double[] m4Row4 = { 4, 4, 4, 4 };
m1.SetRow(0, m1Row1);
m2.SetRow(0, m2Row1);
m2.SetRow(1, m2Row2);
m3.SetRow(0, m3Row1);
m3.SetRow(1, m3Row2);
m3.SetRow(2, m3Row3);
m4.SetRow(0, m4Row1);
m4.SetRow(1, m4Row2);
m4.SetRow(2, m4Row3);
m4.SetRow(3, m4Row4);
MatricesMatrix testMatricesMatrix = new MatricesMatrix(2, 2);
testMatricesMatrix.SetElement(0, 0, m1);
testMatricesMatrix.SetElement(0, 1, m3);
testMatricesMatrix.SetElement(1, 0, m2);
testMatricesMatrix.SetElement(1, 1, m4);
Matrix expectedResult = new Matrix(7, 6);
double[] expectedRow1 = { 1, 0, 3, 3, 3, 0 };
double[] expectedRow2 = { 0, 0, 3, 3, 3, 0 };
double[] expectedRow3 = { 0, 0, 3, 3, 3, 0 };
double[] expectedRow4 = { 2, 2, 4, 4, 4, 4 };
double[] expectedRow5 = { 2, 2, 4, 4, 4, 4 };
double[] expectedRow6 = { 0, 0, 4, 4, 4, 4 };
double[] expectedRow7 = { 0, 0, 4, 4, 4, 4 };
expectedResult.SetRow(0, expectedRow1);
expectedResult.SetRow(1, expectedRow2);
expectedResult.SetRow(2, expectedRow3);
expectedResult.SetRow(3, expectedRow4);
expectedResult.SetRow(4, expectedRow5);
expectedResult.SetRow(5, expectedRow6);
expectedResult.SetRow(6, expectedRow7);
Matrix actualResult = testMatricesMatrix.ConvertToMatrix();
(actualResult == expectedResult).Should().BeTrue();
}
public void MatricesMatrix_ConvertToMatrixTest()
{
Matrix m1 = new Matrix(2);
Matrix m2 = new Matrix(2, 3);
Matrix m3 = new Matrix(2);
Matrix m4 = new Matrix(2, 3);
double[] m1Row1 = { 1, 1 };
double[] m1Row2 = { 1, 1 };
double[] m2Row1 = { 2, 2, 2 };
double[] m2Row2 = { 2, 2, 2 };
double[] m3Row1 = { 3, 3 };
double[] m3Row2 = { 3, 3 };
double[] m4Row1 = { 4, 4, 4 };
double[] m4Row2 = { 4, 4, 4 };
m1.SetRow(0, m1Row1);
m1.SetRow(1, m1Row2);
m2.SetRow(0, m2Row1);
m2.SetRow(1, m2Row2);
m3.SetRow(0, m3Row1);
m3.SetRow(1, m3Row2);
m4.SetRow(0, m4Row1);
m4.SetRow(1, m4Row2);
MatricesMatrix testMatricesMatrix = new MatricesMatrix(2, 2);
testMatricesMatrix.SetElement(0, 0, m1);
testMatricesMatrix.SetElement(0, 1, m2);
testMatricesMatrix.SetElement(1, 0, m3);
testMatricesMatrix.SetElement(1, 1, m4);
Matrix expectedResult = new Matrix(4, 5);
double[] expectedRow1 = { 1, 1, 2, 2, 2 };
double[] expectedRow2 = { 1, 1, 2, 2, 2 };
double[] expectedRow3 = { 3, 3, 4, 4, 4 };
double[] expectedRow4 = { 3, 3, 4, 4, 4 };
expectedResult.SetRow(0, expectedRow1);
expectedResult.SetRow(1, expectedRow2);
expectedResult.SetRow(2, expectedRow3);
expectedResult.SetRow(3, expectedRow4);
Matrix actualResult = testMatricesMatrix.ConvertToMatrix();
(actualResult == expectedResult).Should().BeTrue();
}
// --------------------------------------------------------------------------------------------------------------
/// <summary>
/// Performs Doolittle decomposition with partial pivoting and returns a combined LU matrix
/// </summary>
/// <param name="permutationArray">Keeps track of how the matrices have been rearranged during the calculation</param>
/// <param name="toggle">is +1 or -1 (even or odd)</param>
/// <returns></returns>
public Matrix Decompose(out int[] permutationArray, out int toggle)
{
if (!this.IsSquare())
{
throw new Exception("LU-Decomposition can only be found for a square matrix");
}
Matrix decomposedMatrix = new Matrix(_matrix); // 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
//Loop through the columns
for (int columnIndex = 0; columnIndex < NumberOfRows - 1; columnIndex++)
{
//Find largest value in the current column
double maxOfColumn = Math.Abs(decomposedMatrix.GetElement(columnIndex, columnIndex));
int pivotRowIndex = columnIndex;
// loop through all of the rows in this column
for (int rowIndex = columnIndex + 1; rowIndex < NumberOfRows; rowIndex++)
{
if (Math.Abs(decomposedMatrix.GetElement(rowIndex, columnIndex)) > maxOfColumn)
{
maxOfColumn = Math.Abs(decomposedMatrix.GetElement(rowIndex, columnIndex));
pivotRowIndex = rowIndex;
}
}
if (pivotRowIndex != columnIndex) // if largest value not on pivot, swap rows
{
double[] rowPtr = decomposedMatrix.GetRow(pivotRowIndex);
decomposedMatrix.SetRow(pivotRowIndex, decomposedMatrix.GetRow(columnIndex));
decomposedMatrix.SetRow(columnIndex, rowPtr);
int tmp = permutationArray[pivotRowIndex]; // and swap permutation info
permutationArray[pivotRowIndex] = permutationArray[columnIndex];
permutationArray[columnIndex] = tmp;
toggle = -toggle; // adjust the row-swap toggle
}
//Check to see if there is a zero on the diagonal. If so, try to get rid of it by swapping with a row that is beneath the row with a zero on the diagonal
// double elementOnDiagonal = decomposedMatrix.GetElement(columnIndex, columnIndex);
//if (Math.Round(elementOnDiagonal, 6) == 0.0)
//{
// // find a good row to swap
// int goodRow = -1;
// for (int row = columnIndex + 1; row < decomposedMatrix.NumberOfRows; row++)
// {
// double element = decomposedMatrix.GetElement(row, columnIndex);
// if (Math.Round(element, 6) != 0.0)
// {
// goodRow = row;
// }
// }
// if (goodRow != -1)
// {
// // swap rows so 0.0 no longer on diagonal
// double[] rowPtr = decomposedMatrix.GetRow(goodRow);
// decomposedMatrix.SetRow(goodRow, decomposedMatrix.GetRow(columnIndex));
// decomposedMatrix.SetRow(columnIndex, rowPtr);
// int tmp = permutationArray[goodRow]; // and swap perm info
// permutationArray[goodRow] = permutationArray[columnIndex];
// permutationArray[columnIndex] = tmp;
// toggle = -toggle; // adjust the row-swap toggle
// }
// else
// {
// // throw new Exception("Cannot use Doolittle's method on this matrix");
// }
//}
//Find the next value to insert into the decomposed matrix
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 column loop
return decomposedMatrix;
} // MatrixDecompose
/// <summary>
/// Returns a matrix that can be multiplied by another matrix to represent a rotation of that matrix about the Z axis by the specified angle
/// </summary>
public static Matrix RotationMatrixAboutZ(Angle rotationAngle)
{
Matrix rotationMatrix = new Matrix(3);
double[] row1 = {Math.Cos(rotationAngle.InRadians.Value), -Math.Sin(rotationAngle.InRadians.Value), 0};
double[] row2 = {Math.Sin(rotationAngle.InRadians.Value), Math.Cos(rotationAngle.InRadians.Value), 0};
double[] row3 = {0, 0, 1};
rotationMatrix.SetRow(0, row1);
rotationMatrix.SetRow(1, row2);
rotationMatrix.SetRow(2, row3);
return rotationMatrix;
}
/// <summary>
/// Takes values from a matrix and determines a cofactor by removing a certain row and column from the matrix.
/// Logic developed with help from Andrew Morton on stackoverflow:
/// http://stackoverflow.com/questions/24416946/next-step-in-calculating-a-matrix-determinant
/// </summary>
public Matrix GetSubMatrix(int[] indicesOfRowsToKeep, int[] indicesOfColumnsToKeep)
{
Matrix subMatrix = new Matrix(indicesOfRowsToKeep.Length, indicesOfColumnsToKeep.Length);
Matrix tempMatrix = new Matrix(indicesOfRowsToKeep.Length, this.NumberOfColumns);
int insertRowAt = 0;
foreach (int rowToKeep in indicesOfRowsToKeep)
{
tempMatrix.SetRow(insertRowAt, this.GetRow(rowToKeep));
insertRowAt++;
}
int insertColumnAt = 0;
foreach (int columnToKeep in indicesOfColumnsToKeep)
{
subMatrix.SetColumn(insertColumnAt, tempMatrix.GetColumn(columnToKeep));
insertColumnAt++;
}
return subMatrix;
}
