Phil Steitz a écrit :
> Any ideas on where this stuff can go???
I am beginning to think we should have a few different matrices shapes:
upper triangular, lower triangular, diagonal, tri-diagonal and perhaps
sparse.
In this case, this could be put as an specialized implementation of
solve in a triangular matrix class.
Luc
>> -
>> + + /** TODO: Find a home for the following methods in the
>> linear package */ + + /**
>> + * <p>Uses back substitution to solve the system</p>
>> + * + * <p>coefficients X = constants</p>
>> + * + * <p>coefficients must upper-triangular and constants
>> must be a column + * matrix. The solution is returned as a column
>> matrix.</p>
>> + * + * <p>The number of columns in coefficients determines
>> the length
>> + * of the returned solution vector (column matrix). If constants
>> + * has more rows than coefficients has columns, excess rows are
>> ignored.
>> + * Similarly, extra (zero) rows in coefficients are ignored</p>
>> + * + * @param coefficients upper-triangular coefficients matrix
>> + * @param constants column RHS constants matrix
>> + * @return solution matrix as a column matrix
>> + * + */
>> + private static RealMatrix solveUpperTriangular(RealMatrixImpl
>> coefficients,
>> + RealMatrixImpl constants) {
>> + if (!isUpperTriangular(coefficients, 1E-12)) {
>> + throw new IllegalArgumentException(
>> + "Coefficients is not upper-triangular");
>> + }
>> + if (constants.getColumnDimension() != 1) {
>> + throw new IllegalArgumentException(
>> + "Constants not a column matrix.");
>> + }
>> + int length = coefficients.getColumnDimension();
>> + double[][] cons = constants.getDataRef();
>> + double[][] coef = coefficients.getDataRef();
>> + double x[] = new double[length];
>> + for (int i = 0; i < length; i++) {
>> + int index = length - 1 - i;
>> + double sum = 0;
>> + for (int j = index + 1; j < length; j++) {
>> + sum += coef[index][j] * x[j];
>> + }
>> + x[index] = (cons[index][0] - sum) / coef[index][index];
>> + } + return new RealMatrixImpl(x);
>> + }
>> + + /**
>> + * <p>Returns true iff m is an upper-triangular matrix.</p>
>> + * + * <p>Makes sure all below-diagonal elements are within
>> epsilon of 0.</p>
>> + * + * @param m matrix to check
>> + * @param epsilon maximum allowable absolute value for elements
>> below
>> + * the main diagonal
>> + * + * @return true if m is upper-triangular; false otherwise
>> + * @throws NullPointerException if m is null
>> + */
>> + private static boolean isUpperTriangular(RealMatrixImpl m, double
>> epsilon) {
>> + double[][] data = m.getDataRef();
>> + int nCols = m.getColumnDimension();
>> + int nRows = m.getRowDimension();
>> + for (int r = 0; r < nRows; r++) {
>> + int bound = Math.min(r, nCols);
>> + for (int c = 0; c < bound; c++) {
>> + if (Math.abs(data[r][c]) > epsilon) {
>> + return false;
>> + }
>> + }
>> + }
>> + return true;
>> + }
>> }
>>
>>
>
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