Used specific properties of dense matrices in applyKnownSolution().

MathLib/LinAlg/Dense/DenseTools.cpp

@@ -17,41 +17,41 @@
 namespace MathLib
 {
 
-void applyKnownSolution(DenseMatrix<double> &eqsA, DenseVector<double> &eqsRHS, std::size_t k, double x)
+void applyKnownSolution(DenseMatrix<double> &eqsA, DenseVector<double> &eqsRHS, std::size_t k,
+		double val)
 {
-    const size_t n_rows = eqsA.getNRows();
-    const size_t n_cols = eqsA.getNCols();
-    //A(k, j) = 0.
-    for (size_t j=0; j<n_cols; j++)
+    const std::size_t n_rows = eqsA.getNRows();
+    const std::size_t n_cols = eqsA.getNCols();
+
+    // set all entries of the k-th row of the matrix to zero
+    // except the diagonal entry that is set to one
+    for (std::size_t j=0; j<n_cols; j++)
         eqsA(k, j) = .0;
-    //A(k, k) = 1,
     eqsA(k,k) = 1.0;
-    //b_i -= A(i,k)*val, i!=k
-    for (size_t i=0; i<n_rows; ++i)
-    {
-      if (i==k) continue;
-      double v_i_k = .0;
-      for (size_t j=0; j<n_cols; ++j)
-      {
-        if (j==k) {
-          v_i_k = eqsA(i, k);
-          eqsA(i, k) = .0;
-          break;
-        } else if (j>k) {
-          break;
-        }
-      }
-      eqsRHS[i] -= v_i_k*x;
-    }
-    //b_k = val
-    eqsRHS[k] = x;
+
+    // b_i -= A(i,k)*val, i!=k and
+    // set the entries of the k-th column of the matrix to zero
+    // except the diagonal entry A(k,k)
+	for (std::size_t i = 0; i < k; ++i)
+	{
+		eqsRHS[i] -= eqsA(i, k) * val;
+		eqsA(i, k) = 0.0;
+	}
+	for (std::size_t i = k+1; i < n_rows; ++i)
+	{
+		eqsRHS[i] -= eqsA(i, k) * val;
+		eqsA(i, k) = 0.0;
+	}
+
+    // b_k = val
+    eqsRHS[k] = val;
 }
 
-void applyKnownSolution(DenseMatrix<double> &A, DenseVector<double> &b, const std::vector<std::size_t> &_vec_knownX_id, const std::vector<double> &_vec_knownX_x)
+void applyKnownSolution(DenseMatrix<double> &A, DenseVector<double> &b, const std::vector<std::size_t> &vec_knownX_id, const std::vector<double> &vec_knownX_x)
 {
-    const std::size_t n_bc = _vec_knownX_id.size();
+    const std::size_t n_bc = vec_knownX_id.size();
     for (std::size_t i_bc=0; i_bc<n_bc; i_bc++) {
-        applyKnownSolution(A, b, _vec_knownX_id[i_bc], _vec_knownX_x[i_bc]);
+        applyKnownSolution(A, b, vec_knownX_id[i_bc], vec_knownX_x[i_bc]);
     }
 }
 

MathLib/LinAlg/Dense/DenseTools.h

@@ -23,30 +23,35 @@ namespace MathLib
 {
 
 /**
- * apply known solutions to a system of linear equations
+ * Apply known solutions to a system of linear equations.
  *
- * This function introduces the given constrain by diagonalizing a coefficient matrix.
- * Symmetricity of the matrix is preserved.
+ * This function introduces the given constrains by diagonalizing a coefficient matrix.
+ * Symmetry of the matrix is preserved.
  *
- * @param A                 Coefficient matrix
- * @param b                 RHS vector
- * @param _vec_knownX_id    a vector of known solution entry IDs
- * @param _vec_knownX_x     a vector of known solutions
+ * @param A                Coefficient matrix
+ * @param b                RHS vector
+ * @param vec_knownX_id    a vector of known solution entry IDs
+ * @param vec_knownX_x     a vector of known solutions
  */
-void applyKnownSolution(DenseMatrix<double> &A, DenseVector<double> &b, const std::vector<std::size_t> &_vec_knownX_id, const std::vector<double> &_vec_knownX_x);
+void applyKnownSolution(DenseMatrix<double> &A, DenseVector<double> &b,
+		const std::vector<std::size_t> &vec_knownX_id, const std::vector<double> &vec_knownX_x);
 
 /**
- * apply known solutions to a system of linear equations
+ * Apply known solutions to a system of linear equations \f$A x = b\f$.
  *
- * This function introduces the given constrain by diagonalizing a coefficient matrix.
- * Symmetricity of the matrix is preserved.
+ * This function introduces the given constrain into the system of linear
+ * equations. For this purpose it modifies the entries of \f$A\f$ in the
+ * \f$k\f$-th row and column, i.e. all those entries are set to zero except
+ * the diagonal entry that is set to one. The right
+ * hand side \f$b\f$ is modified, too. The symmetry of \f$A\f$ is preserved.
  *
  * @param A         Coefficient matrix
  * @param b         RHS vector
  * @param row_id    a known solution entry ID
- * @param x         a known solution
+ * @param val       a known solution
  */
-void applyKnownSolution(DenseMatrix<double> &A, DenseVector<double> &b, std::size_t row_id, double x);
+void applyKnownSolution(DenseMatrix<double> &A, DenseVector<double> &b, std::size_t row_id,
+		double val);
 
 } // MathLib