/// <summary>
/// Check if a matrix is multiplication compatible with the instance.
/// </summary>
/// <param name="m">Matrix to check.</param>
/// <exception cref="DimensionMismatchException"> if the matrix is not
/// multiplication-compatible with instance.</exception>
protected void checkMultiplicationCompatible(FieldMatrix <T> m)
{
if (getColumnDimension() != m.getRowDimension())
{
throw new DimensionMismatchException(m.getRowDimension(), getColumnDimension());
}
}
/// <summary>
/// Check if a matrix is subtraction compatible with the instance.
/// </summary>
/// <param name="m">Matrix to check.</param>
/// <exception cref="MatrixDimensionMismatchExceptio">n if the matrix is not
/// subtraction-compatible with instance.</exception>
protected void checkSubtractionCompatible(FieldMatrix <T> m)
{
if ((getRowDimension() != m.getRowDimension()) ||
(getColumnDimension() != m.getColumnDimension()))
{
throw new MatrixDimensionMismatchException(m.getRowDimension(), m.getColumnDimension(),
getRowDimension(), getColumnDimension());
}
}
/// <summary>
/// Returns true iff <c>object</c> is a
/// <c>FieldMatrix</c> instance with the same dimensions as this
/// and all corresponding matrix entries are equal.
/// </summary>
/// <param name="obj">the object to test equality against.</param>
/// <returns>true if object equals this</returns>
public override Boolean Equals(Object obj)
{
if (obj == this)
{
return(true);
}
if (obj is FieldMatrix <T> )
{
return(false);
}
FieldMatrix <T> m = (FieldMatrix <T>)obj;
int nRows = getRowDimension();
int nCols = getColumnDimension();
if (m.getColumnDimension() != nCols || m.getRowDimension() != nRows)
{
return(false);
}
for (int row = 0; row < nRows; ++row)
{
for (int col = 0; col < nCols; ++col)
{
if (!getEntry(row, col).Equals(m.getEntry(row, col)))
{
return(false);
}
}
}
return(true);
}
/// <inheritdoc/>
public void setColumnMatrix(int column, FieldMatrix <T> matrix)
{
checkColumnIndex(column);
int nRows = getRowDimension();
if ((matrix.getRowDimension() != nRows) ||
(matrix.getColumnDimension() != 1))
{
throw new MatrixDimensionMismatchException(matrix.getRowDimension(),
matrix.getColumnDimension(),
nRows, 1);
}
for (int i = 0; i < nRows; ++i)
{
setEntry(i, column, matrix.getEntry(i, 0));
}
}
/// <inheritdoc/>
public void setRowMatrix(int row, FieldMatrix <T> matrix)
{
checkRowIndex(row);
int nCols = getColumnDimension();
if ((matrix.getRowDimension() != 1) ||
(matrix.getColumnDimension() != nCols))
{
throw new MatrixDimensionMismatchException(matrix.getRowDimension(),
matrix.getColumnDimension(),
1, nCols);
}
for (int i = 0; i < nCols; ++i)
{
setEntry(row, i, matrix.getEntry(0, i));
}
}
/// <summary>
/// Calculates the LU-decomposition of the given matrix.
/// </summary>
/// <param name="matrix">The matrix to decompose.</param>
/// <exception cref="NonSquareMatrixException"> if matrix is not square</exception>
public FieldLUDecomposition(FieldMatrix <T> matrix)
{
if (!matrix.isSquare())
{
throw new NonSquareMatrixException(matrix.getRowDimension(), matrix.getColumnDimension());
}
int m = matrix.getColumnDimension();
field = matrix.getField();
lu = matrix.getData();
pivot = new int[m];
cachedL = null;
cachedU = null;
cachedP = null;
// Initialize permutation array and parity
for (int row = 0; row < m; row++)
{
pivot[row] = row;
}
even = true;
singular = false;
// Loop over columns
for (int col = 0; col < m; col++)
{
T sum = field.getZero();
// upper
for (int row = 0; row < col; row++)
{
T[] luRow = lu[row];
sum = luRow[col];
for (int i = 0; i < row; i++)
{
sum = sum.subtract(luRow[i].multiply(lu[i][col]));
}
luRow[col] = sum;
}
// lower
int nonZero = col; // permutation row
for (int row = col; row < m; row++)
{
T[] luRow = lu[row];
sum = luRow[col];
for (int i = 0; i < col; i++)
{
sum = sum.subtract(luRow[i].multiply(lu[i][col]));
}
luRow[col] = sum;
if (lu[nonZero][col].Equals(field.getZero()))
{
// try to select a better permutation choice
++nonZero;
}
}
// Singularity check
if (nonZero >= m)
{
singular = true;
return;
}
// Pivot if necessary
if (nonZero != col)
{
T tmp = field.getZero();
for (int i = 0; i < m; i++)
{
tmp = lu[nonZero][i];
lu[nonZero][i] = lu[col][i];
lu[col][i] = tmp;
}
int temp = pivot[nonZero];
pivot[nonZero] = pivot[col];
pivot[col] = temp;
even = !even;
}
// Divide the lower elements by the "winning" diagonal elt.
T luDiag = lu[col][col];
for (int row = col + 1; row < m; row++)
{
T[] luRow = lu[row];
luRow[col] = luRow[col].divide(luDiag);
}
}
}
/// <inheritdoc/>
public FieldMatrix <U> solve(FieldMatrix <U> b)
{
int m = pivot.Length;
if (b.getRowDimension() != m)
{
throw new DimensionMismatchException(b.getRowDimension(), m);
}
if (singular)
{
throw new SingularMatrixException();
}
int nColB = b.getColumnDimension();
// Apply permutations to b
U[][] bp = MathArrays.buildArray(field, m, nColB);
for (int row = 0; row < m; row++)
{
U[] bpRow = bp[row];
int pRow = pivot[row];
for (int col = 0; col < nColB; col++)
{
bpRow[col] = b.getEntry(pRow, col);
}
}
// Solve LY = b
for (int col = 0; col < m; col++)
{
U[] bpCol = bp[col];
for (int i = col + 1; i < m; i++)
{
U[] bpI = bp[i];
U luICol = lu[i][col];
for (int j = 0; j < nColB; j++)
{
bpI[j] = bpI[j].subtract(bpCol[j].multiply(luICol));
}
}
}
// Solve UX = Y
for (int col = m - 1; col >= 0; col--)
{
U[] bpCol = bp[col];
U luDiag = lu[col][col];
for (int j = 0; j < nColB; j++)
{
bpCol[j] = bpCol[j].divide(luDiag);
}
for (int i = 0; i < col; i++)
{
U[] bpI = bp[i];
U luICol = lu[i][col];
for (int j = 0; j < nColB; j++)
{
bpI[j] = bpI[j].subtract(bpCol[j].multiply(luICol));
}
}
}
return(new Array2DRowFieldMatrix <U>(field, bp, false));
}