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28  * LU decompostion</a> to support linear system
31 * The LU decompostion is performed as needed, to support the following operations: <ul>
39 * The LU decomposition is stored and reused on subsequent calls. If matrix
43 * LU decomposition will not be discarded. In this case, you need to
64 /** Bound to determine effective singularity in LU decomposition */
73 /** Entries of cached LU decomposition.
76 protected BigDecimal lu[][] = null;
78 /** Permutation associated with LU decomposition */
81 /** Parity of the permutation associated with the LU decomposition */
114 lu = null;
131 lu = null;
174 lu = null;
206 lu = null;
236 lu = null;
744 lu = null;
946 if (isSingular()) { // note: this has side effect of attempting LU decomp if lu == null
951 det = det.multiply(lu[i][i]);
970 if (lu == null) {
977 } else { // LU decomp must have been successfully performed
1152 if (this.isSingular()) { // side effect: compute LU decomp
1173 final BigDecimal[] luI = lu[i];
1183 final BigDecimal luDiag = lu[col][col];
1189 final BigDecimal[] luI = lu[i];
1203 * LU decompostion</a> for this matrix, storing the result for use by other methods.
1211 * to force recomputation of the LU decomposition when changes have been
1225 lu = this.getData();
1241 final BigDecimal[] luRow = lu[row];
1244 sum = sum.subtract(luRow[i].multiply(lu[i][col]));
1253 final BigDecimal[] luRow = lu[row];
1256 sum = sum.subtract(luRow[i].multiply(lu[i][col]));
1268 if (lu[max][col].abs().compareTo(TOO_SMALL) <= 0) {
1269 lu = null;
1277 tmp = lu[max][i];
1278 lu[max][i] = lu[col][i];
1279 lu[col][i] = tmp;
1288 final BigDecimal luDiag = lu[col][col];
1290 final BigDecimal[] luRow = lu[row];
1384 * Returns the LU decomposition as a BigMatrix.
1385 * Returns a fresh copy of the cached LU matrix if this has been computed;
1388 * affect the LU decomposition property.
1390 * The matrix returned is a compact representation of the LU decomposition.
1403 * The L and U matrices satisfy the matrix equation LU = permuteRows(this), <br>
1407 * @return LU decomposition matrix
1411 if (lu == null) {
1414 return new BigMatrixImpl(lu);
1418 * Returns the permutation associated with the lu decomposition.
1482 lu = null;
1502 lu = null;