sync the documentation examples

Eigen/src/LU/Inverse.h

@@ -351,6 +351,9 @@ inline const ei_inverse_impl<Derived> MatrixBase<Derived>::inverse() const
   *                                The matrix will be declared invertible if the absolute value of its
   *                                determinant is greater than this threshold.
   *
+  * Example: \include MatrixBase_computeInverseAndDetWithCheck.cpp
+  * Output: \verbinclude MatrixBase_computeInverseAndDetWithCheck.out
+  *
   * \sa inverse(), computeInverseWithCheck()
   */
 template<typename Derived>
@@ -387,6 +390,9 @@ inline void MatrixBase<Derived>::computeInverseAndDetWithCheck(
   *                                The matrix will be declared invertible if the absolute value of its
   *                                determinant is greater than this threshold.
   *
+  * Example: \include MatrixBase_computeInverseWithCheck.cpp
+  * Output: \verbinclude MatrixBase_computeInverseWithCheck.out
+  *
   * \sa inverse(), computeInverseAndDetWithCheck()
   */
 template<typename Derived>

doc/examples/Tutorial_PartialLU_solve.cpp

@@ -12,7 +12,6 @@ int main(int, char *[])
    b << 3, 3, 4;
    cout << "Here is the matrix A:" << endl << A << endl;
    cout << "Here is the vector b:" << endl << b << endl;
-   Vector3f x;
-   A.partialLu().solve(b, &x);
+   Vector3f x = A.partialLu().solve(b);
    cout << "The solution is:" << endl << x << endl;
 }

doc/snippets/MatrixBase_computeInverse.cpp

@@ -1,5 +0,0 @@
-Matrix3d m = Matrix3d::Random();
-cout << "Here is the matrix m:" << endl << m << endl;
-Matrix3d inv;
-m.computeInverse(&inv);
-cout << "Its inverse is:" << endl << inv << endl;

doc/snippets/MatrixBase_computeInverseAndDetWithCheck.cpp

@@ -0,0 +1,13 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+Matrix3d inverse;
+bool invertible;
+double determinant;
+m.computeInverseAndDetWithCheck(inverse,determinant,invertible);
+cout << "Its determinant is " << determinant << endl;
+if(invertible) {
+  cout << "It is invertible, and its inverse is:" << endl << inverse << endl;
+}
+else {
+  cout << "It is not invertible." << endl;
+}

doc/snippets/MatrixBase_computeInverseWithCheck.cpp

@@ -1,8 +1,10 @@
 Matrix3d m = Matrix3d::Random();
 cout << "Here is the matrix m:" << endl << m << endl;
-Matrix3d inv;
-if(m.computeInverseWithCheck(&inv)) {
-  cout << "It is invertible, and its inverse is:" << endl << inv << endl;
+Matrix3d inverse;
+bool invertible;
+m.computeInverseWithCheck(inverse,invertible);
+if(invertible) {
+  cout << "It is invertible, and its inverse is:" << endl << inverse << endl;
 }
 else {
   cout << "It is not invertible." << endl;

doc/snippets/PartialLU_solve.cpp

@@ -2,7 +2,6 @@ MatrixXd A = MatrixXd::Random(3,3);
 MatrixXd B = MatrixXd::Random(3,2);
 cout << "Here is the invertible matrix A:" << endl << A << endl;
 cout << "Here is the matrix B:" << endl << B << endl;
-MatrixXd X;
-A.partialLu().solve(B, &X);
+MatrixXd X = A.partialLu().solve(B);
 cout << "Here is the (unique) solution X to the equation AX=B:" << endl << X << endl;
 cout << "Relative error: " << (A*X-B).norm() / B.norm() << endl;

doc/snippets/Tutorial_solve_multiple_rhs.cpp

@@ -3,7 +3,7 @@ A << 1,2,3,  4,5,6,  7,8,10;
 Matrix<float,3,2> B;
 B << 3,1, 3,1, 4,1;
 Matrix<float,3,2> X;
-A.partialLu().solve(B, &X);
+X = A.partialLu().solve(B);
 cout << "The solution with right-hand side (3,3,4) is:" << endl;
 cout << X.col(0) << endl;
 cout << "The solution with right-hand side (1,1,1) is:" << endl;

doc/snippets/Tutorial_solve_reuse_decomposition.cpp

@@ -4,10 +4,10 @@ PartialLU<Matrix3f> luOfA(A); // compute LU decomposition of A
 Vector3f b;
 b << 3,3,4;
 Vector3f x;
-luOfA.solve(b, &x);
+x = luOfA.solve(b);
 cout << "The solution with right-hand side (3,3,4) is:" << endl;
 cout << x << endl;
 b << 1,1,1;
-luOfA.solve(b, &x);
+x = luOfA.solve(b);
 cout << "The solution with right-hand side (1,1,1) is:" << endl;
 cout << x << endl;

doc/snippets/Tutorial_solve_singular.cpp

@@ -5,5 +5,5 @@ b << 3, 3, 4;
 cout << "Here is the matrix A:" << endl << A << endl;
 cout << "Here is the vector b:" << endl << b << endl;
 Vector3f x;
-A.partialLu().solve(b, &x);
+x = A.partialLu().solve(b);
 cout << "The solution is:" << endl << x << endl;