Fix comment typos, doubled words, grammar errors, and copy-paste mistakes

libeigen/eigen!2173

Closes #3034

Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>

Eigen/src/Core/Array.h

@@ -141,7 +141,7 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
    * This constructor is for 1D array or vectors with more than 4 coefficients.
    *
    * \warning To construct a column (resp. row) vector of fixed length, the number of values passed to this
-   * constructor must match the the fixed number of rows (resp. columns) of \c *this.
+   * constructor must match the fixed number of rows (resp. columns) of \c *this.
    *
    *
    * Example: \include Array_variadic_ctor_cxx11.cpp

Eigen/src/Core/ArrayWrapper.h

@@ -21,7 +21,7 @@ namespace Eigen {
  * \brief Expression of a mathematical vector or matrix as an array object
  *
  * This class is the return type of MatrixBase::array(), and most of the time
- * this is the only way it is use.
+ * this is the only way it is used.
  *
  * \sa MatrixBase::array(), class MatrixWrapper
  */
@@ -96,7 +96,7 @@ class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> > {
  * \brief Expression of an array as a mathematical vector or matrix
  *
  * This class is the return type of ArrayBase::matrix(), and most of the time
- * this is the only way it is use.
+ * this is the only way it is used.
  *
  * \sa MatrixBase::matrix(), class ArrayWrapper
  */

Eigen/src/Core/DiagonalMatrix.h

@@ -61,7 +61,7 @@ class DiagonalBase : public EigenBase<Derived> {
   /**
    * Constructs a dense matrix from \c *this. Note, this directly returns a dense matrix type,
    * not an expression.
-   * \returns A dense matrix, with its diagonal entries set from the the derived object. */
+   * \returns A dense matrix, with its diagonal entries set from the derived object. */
   EIGEN_DEVICE_FUNC DenseMatrixType toDenseMatrix() const { return derived(); }
 
   /** \returns a reference to the derived object's vector of diagonal coefficients. */

Eigen/src/Core/Dot.h

@@ -54,7 +54,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
 
 /** \returns, for vectors, the squared \em l2 norm of \c *this, and for matrices the squared Frobenius norm.
  * In both cases, it consists in the sum of the square of all the matrix entries.
- * For vectors, this is also equals to the dot product of \c *this with itself.
+ * For vectors, this is also equal to the dot product of \c *this with itself.
  *
  * \sa dot(), norm(), lpNorm()
  */
@@ -66,7 +66,7 @@ MatrixBase<Derived>::squaredNorm() const {
 
 /** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm.
  * In both cases, it consists in the square root of the sum of the square of all the matrix entries.
- * For vectors, this is also equals to the square root of the dot product of \c *this with itself.
+ * For vectors, this is also equal to the square root of the dot product of \c *this with itself.
  *
  * \sa lpNorm(), dot(), squaredNorm()
  */

Eigen/src/Core/GenericPacketMath.h

@@ -610,7 +610,7 @@ EIGEN_DEVICE_FUNC inline bool pselect<bool>(const bool& cond, const bool& a, con
   return cond ? a : b;
 }
 
-/** \internal \returns the min or of \a a and \a b (coeff-wise)
+/** \internal \returns the min or max of \a a and \a b (coeff-wise)
     If either \a a or \a b are NaN, the result is implementation defined. */
 template <int NaNPropagation, bool IsInteger>
 struct pminmax_impl {
@@ -648,7 +648,7 @@ struct pminmax_impl<PropagateNumbers, false> {
 #define EIGEN_BINARY_OP_NAN_PROPAGATION(Type, Func) [](const Type& aa, const Type& bb) { return Func(aa, bb); }
 
 /** \internal \returns the min of \a a and \a b  (coeff-wise).
-    If \a a or \b b is NaN, the return value is implementation defined. */
+    If \a a or \a b is NaN, the return value is implementation defined. */
 template <typename Packet>
 EIGEN_DEVICE_FUNC inline Packet pmin(const Packet& a, const Packet& b) {
   return numext::mini(a, b);
@@ -663,7 +663,7 @@ EIGEN_DEVICE_FUNC inline Packet pmin(const Packet& a, const Packet& b) {
 }
 
 /** \internal \returns the max of \a a and \a b  (coeff-wise)
-    If \a a or \b b is NaN, the return value is implementation defined. */
+    If \a a or \a b is NaN, the return value is implementation defined. */
 template <typename Packet>
 EIGEN_DEVICE_FUNC inline Packet pmax(const Packet& a, const Packet& b) {
   return numext::maxi(a, b);

Eigen/src/Core/Matrix.h

@@ -271,7 +271,7 @@ class Matrix : public PlainObjectBase<Matrix<Scalar_, Rows_, Cols_, Options_, Ma
    * This constructor is for 1D array or vectors with more than 4 coefficients.
    *
    * \warning To construct a column (resp. row) vector of fixed length, the number of values passed to this
-   * constructor must match the the fixed number of rows (resp. columns) of \c *this.
+   * constructor must match the fixed number of rows (resp. columns) of \c *this.
    *
    *
    * Example: \include Matrix_variadic_ctor_cxx11.cpp

Eigen/src/Core/PlainObjectBase.h

@@ -461,7 +461,7 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type {
    * This constructor is for 1D array or vectors with more than 4 coefficients.
    *
    * \warning To construct a column (resp. row) vector of fixed length, the number of values passed to this
-   * constructor must match the the fixed number of rows (resp. columns) of \c *this.
+   * constructor must match the fixed number of rows (resp. columns) of \c *this.
    */
   template <typename... ArgTypes>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PlainObjectBase(const Scalar& a0, const Scalar& a1, const Scalar& a2,

Eigen/src/Core/SkewSymmetricMatrix3.h

@@ -62,7 +62,7 @@ class SkewSymmetricBase : public EigenBase<Derived> {
   /**
    * Constructs a dense matrix from \c *this. Note, this directly returns a dense matrix type,
    * not an expression.
-   * \returns A dense matrix, with its entries set from the the derived object. */
+   * \returns A dense matrix, with its entries set from the derived object. */
   EIGEN_DEVICE_FUNC DenseMatrixType toDenseMatrix() const { return derived(); }
 
   /** Determinant vanishes */

Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h

@@ -1753,7 +1753,7 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psqrt_complex(const P
   const RealPacket cst_imag_sign_mask = pset1<Packet>(Scalar(RealScalar(0.0), RealScalar(-0.0))).v;
   RealPacket imag_signs = pand(a.v, cst_imag_sign_mask);
   Packet negative_real_result;
-  // Notice that rho is positive, so taking it's absolute value is a noop.
+  // Notice that rho is positive, so taking its absolute value is a noop.
   negative_real_result.v = por(pabs(pcplxflip(positive_real_result).v), imag_signs);
 
   // Step 5. Select solution branch based on the sign of the real parts.
@@ -1877,7 +1877,7 @@ struct psign_impl<Packet, std::enable_if_t<!is_scalar<Packet>::value &&
   }
 };
 
-// \internal \returns the the sign of a complex number z, defined as z / abs(z).
+// \internal \returns the sign of a complex number z, defined as z / abs(z).
 template <typename Packet>
 struct psign_impl<Packet, std::enable_if_t<!is_scalar<Packet>::value &&
                                            NumTraits<typename unpacket_traits<Packet>::type>::IsComplex &&

Eigen/src/Core/util/Macros.h

@@ -595,7 +595,7 @@
 // without an explicit launch_bounds attribute is called with a threads_per_block value
 // greater than 256.
 //
-// This is a regression in functioanlity and is expected to be fixed within the next
+// This is a regression in functionality and is expected to be fixed within the next
 // couple of ROCm releases (compiler will go back to using 1024 value as the default)
 //
 // In the meantime, we will use a "only enabled for HIP" macro to set the launch_bounds

Eigen/src/Eigenvalues/ComplexQZ.h

@@ -203,7 +203,7 @@ class ComplexQZ {
 
   inline Mat2 computeZk2(const Row2& b);
 
-  // This is basically taken from from Eigen3::RealQZ
+  // This is basically taken from Eigen3::RealQZ
   void hessenbergTriangular(const MatrixType& A, const MatrixType& B);
 
   // This function can be called when m_Q and m_Z are initialized and m_S, m_T
@@ -243,7 +243,7 @@ void ComplexQZ<MatrixType_>::compute(const MatrixType& A, const MatrixType& B, b
   reduceHessenbergTriangular();
 }
 
-// This is basically taken from from Eigen3::RealQZ
+// This is basically taken from Eigen3::RealQZ
 template <typename MatrixType_>
 void ComplexQZ<MatrixType_>::hessenbergTriangular(const MatrixType& A, const MatrixType& B) {
   // Copy A and B, these will be the matrices on which we operate later

Eigen/src/Geometry/OrthoMethods.h

@@ -200,7 +200,7 @@ struct unitOrthogonal_selector<Derived, 3> {
   EIGEN_DEVICE_FUNC static inline VectorType run(const Derived& src) {
     VectorType perp;
     /* Let us compute the crossed product of *this with a vector
-     * that is not too close to being colinear to *this.
+     * that is not too close to being collinear to *this.
      */
 
     /* unless the x and y coords are both close to zero, we can
@@ -213,7 +213,7 @@ struct unitOrthogonal_selector<Derived, 3> {
       perp.coeffRef(2) = 0;
     }
     /* if both x and y are close to zero, then the vector is close
-     * to the z-axis, so it's far from colinear to the x-axis for instance.
+     * to the z-axis, so it's far from collinear to the x-axis for instance.
      * So we take the crossed product with (1,0,0) and normalize it.
      */
     else {
@@ -242,7 +242,7 @@ struct unitOrthogonal_selector<Derived, 2> {
  * \returns a unit vector which is orthogonal to \c *this
  *
  * The size of \c *this must be at least 2. If the size is exactly 2,
- * then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
+ * then the returned vector is a counter-clockwise rotation of \c *this, i.e., (-y,x).normalized().
  *
  * \sa cross()
  */

Eigen/src/Geometry/Rotation2D.h

@@ -23,7 +23,7 @@ namespace Eigen {
  *
  * \tparam Scalar_ the scalar type, i.e., the type of the coefficients
  *
- * This class is equivalent to a single scalar representing a counter clock wise rotation
+ * This class is equivalent to a single scalar representing a counter-clockwise rotation
  * as a single angle in radian. It provides some additional features such as the automatic
  * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar
  * interface to Quaternion in order to facilitate the writing of generic algorithms
@@ -57,7 +57,7 @@ class Rotation2D : public RotationBase<Rotation2D<Scalar_>, 2> {
   Scalar m_angle;
 
  public:
-  /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
+  /** Construct a 2D counter-clockwise rotation from the angle \a a in radian. */
   EIGEN_DEVICE_FUNC explicit inline Rotation2D(const Scalar& a) : m_angle(a) {}
 
   /** Default constructor without initialization. The represented rotation is undefined. */

Eigen/src/Geometry/Transform.h

@@ -745,7 +745,7 @@ Transform<Scalar, Dim, Mode, Options>& Transform<Scalar, Dim, Mode, Options>::op
 
 /** \returns a QMatrix from \c *this assuming the dimension is 2.
  *
- * \warning this conversion might loss data if \c *this is not affine
+ * \warning this conversion might lose data if \c *this is not affine
  *
  * This function is available only if the token EIGEN_QT_SUPPORT is defined.
  */

Eigen/src/KLUSupport/KLUSupport.h

@@ -112,7 +112,7 @@ class KLU : public SparseSolverBase<KLU<MatrixType_> > {
     eigen_assert(m_isInitialized && "Decomposition is not initialized.");
     return m_info;
   }
-  /** Computes the sparse Cholesky decomposition of \a matrix
+  /** Computes the sparse LU factorization of \a matrix
    *  Note that the matrix should be column-major, and in compressed format for best performance.
    *  \sa SparseMatrix::makeCompressed().
    */
@@ -147,7 +147,7 @@ class KLU : public SparseSolverBase<KLU<MatrixType_> > {
    */
   inline const klu_common &kluCommon() const { return m_common; }
 
-  /** Provides access to the control settings array used by UmfPack.
+  /** Provides access to the control settings array used by KLU.
    *
    * If this array contains NaN's, the default values are used.
    *
@@ -157,7 +157,7 @@ class KLU : public SparseSolverBase<KLU<MatrixType_> > {
 
   /** Performs a numeric decomposition of \a matrix
    *
-   * The given matrix must have the same sparsity than the matrix on which the pattern anylysis has been performed.
+   * The given matrix must have the same sparsity as the matrix on which the pattern analysis has been performed.
    *
    * \sa analyzePattern(), compute()
    */

Eigen/src/MetisSupport/MetisSupport.h

@@ -38,7 +38,7 @@ class MetisOrdering {
     IndexVector visited(m);
     visited.setConstant(-1);
     for (StorageIndex j = 0; j < m; j++) {
-      // Compute the union structure of of A(j,:) and At(j,:)
+      // Compute the union structure of A(j,:) and At(j,:)
       visited(j) = j;  // Do not include the diagonal element
       // Get the nonzeros in row/column j of A
       for (typename MatrixType::InnerIterator it(A, j); it; ++it) {

Eigen/src/OrderingMethods/Eigen_Colamd.h

@@ -713,7 +713,7 @@ static void init_scoring(
   for (c = n_col - 1; c >= 0; c--) {
     deg = Col[c].length;
     if (deg == 0) {
-      /* this is a empty column, kill and order it last */
+      /* this is an empty column, kill and order it last */
       Col[c].shared2.order = --n_col2;
       Col[c].kill_principal();
     }

Eigen/src/PardisoSupport/PardisoSupport.h

@@ -157,7 +157,7 @@ class PardisoImpl : public SparseSolverBase<Derived> {
 
   /** Performs a numeric decomposition of \a matrix
    *
-   * The given matrix must have the same sparsity than the matrix on which the symbolic decomposition has been
+   * The given matrix must have the same sparsity as the matrix on which the symbolic decomposition has been
    * performed.
    *
    * \sa analyzePattern()

Eigen/src/SVD/BDCSVD.h

@@ -453,7 +453,7 @@ void BDCSVD<MatrixType, Options>::copyUV(const HouseholderU& householderU, const
  *  A = [A1]
  *      [A2]
  * such that A1.rows()==n1, then we assume that at least half of the columns of A1 and A2 are zeros.
- * We can thus pack them prior to the the matrix product. However, this is only worth the effort if the matrix is large
+ * We can thus pack them prior to the matrix product. However, this is only worth the effort if the matrix is large
  * enough.
  */
 template <typename MatrixType, int Options>

Eigen/src/SVD/UpperBidiagonalization.h

@@ -330,7 +330,7 @@ UpperBidiagonalization<MatrixType_>& UpperBidiagonalization<MatrixType_>::comput
   Index cols = matrix.cols();
   EIGEN_ONLY_USED_FOR_DEBUG(cols);
 
-  eigen_assert(rows >= cols && "UpperBidiagonalization is only for Arices satisfying rows>=cols.");
+  eigen_assert(rows >= cols && "UpperBidiagonalization is only for matrices satisfying rows>=cols.");
 
   m_householder = matrix;
 
@@ -350,7 +350,7 @@ UpperBidiagonalization<MatrixType_>& UpperBidiagonalization<MatrixType_>::comput
   EIGEN_ONLY_USED_FOR_DEBUG(rows);
   EIGEN_ONLY_USED_FOR_DEBUG(cols);
 
-  eigen_assert(rows >= cols && "UpperBidiagonalization is only for Arices satisfying rows>=cols.");
+  eigen_assert(rows >= cols && "UpperBidiagonalization is only for matrices satisfying rows>=cols.");
 
   m_householder = matrix;
   upperbidiagonalization_inplace_blocked(m_householder, m_bidiagonal);

Eigen/src/SparseCholesky/SimplicialCholesky.h

@@ -416,7 +416,7 @@ class SimplicialLLT : public SimplicialCholeskyBase<SimplicialLLT<MatrixType_, U
 
   /** Performs a numeric decomposition of \a matrix
    *
-   * The given matrix must have the same sparsity than the matrix on which the symbolic decomposition has been
+   * The given matrix must have the same sparsity as the matrix on which the symbolic decomposition has been
    * performed.
    *
    * \sa analyzePattern()
@@ -505,7 +505,7 @@ class SimplicialLDLT : public SimplicialCholeskyBase<SimplicialLDLT<MatrixType_,
 
   /** Performs a numeric decomposition of \a matrix
    *
-   * The given matrix must have the same sparsity than the matrix on which the symbolic decomposition has been
+   * The given matrix must have the same sparsity as the matrix on which the symbolic decomposition has been
    * performed.
    *
    * \sa analyzePattern()
@@ -587,7 +587,7 @@ class SimplicialNonHermitianLLT
 
   /** Performs a numeric decomposition of \a matrix
    *
-   * The given matrix must have the same sparsity than the matrix on which the symbolic decomposition has been
+   * The given matrix must have the same sparsity as the matrix on which the symbolic decomposition has been
    * performed.
    *
    * \sa analyzePattern()
@@ -677,7 +677,7 @@ class SimplicialNonHermitianLDLT
 
   /** Performs a numeric decomposition of \a matrix
    *
-   * The given matrix must have the same sparsity than the matrix on which the symbolic decomposition has been
+   * The given matrix must have the same sparsity as the matrix on which the symbolic decomposition has been
    * performed.
    *
    * \sa analyzePattern()
@@ -761,7 +761,7 @@ class SimplicialCholesky : public SimplicialCholeskyBase<SimplicialCholesky<Matr
 
   /** Performs a numeric decomposition of \a matrix
    *
-   * The given matrix must have the same sparsity than the matrix on which the symbolic decomposition has been
+   * The given matrix must have the same sparsity as the matrix on which the symbolic decomposition has been
    * performed.
    *
    * \sa analyzePattern()

Eigen/src/SparseLU/SparseLU.h

@@ -360,7 +360,7 @@ class SparseLU : public SparseSolverBase<SparseLU<MatrixType_, OrderingType_>>,
   /** \brief Give the absolute value of the determinant.
    *
    * \returns the absolute value of the determinant of the matrix of which
-   * *this is the QR decomposition.
+   * *this is the LU factorization.
    *
    * \warning a determinant can be very big or small, so for matrices
    * of large enough dimension, there is a risk of overflow/underflow.
@@ -389,7 +389,7 @@ class SparseLU : public SparseSolverBase<SparseLU<MatrixType_, OrderingType_>>,
   /** \brief Give the natural log of the absolute determinant.
    *
    * \returns the natural log of the absolute value of the determinant of the matrix
-   * of which **this is the QR decomposition
+   * of which *this is the LU factorization
    *
    * \note This method is useful to work around the risk of overflow/underflow that's
    * inherent to the determinant computation.

Eigen/src/SuperLUSupport/SuperLUSupport.h

@@ -487,7 +487,7 @@ class SuperLU : public SuperLUBase<MatrixType_, SuperLU<MatrixType_> > {
 
   /** Performs a numeric decomposition of \a matrix
    *
-   * The given matrix must have the same sparsity than the matrix on which the symbolic decomposition has been
+   * The given matrix must have the same sparsity as the matrix on which the symbolic decomposition has been
    * performed.
    *
    * \sa analyzePattern()
@@ -792,7 +792,7 @@ class SuperILU : public SuperLUBase<MatrixType_, SuperILU<MatrixType_> > {
 
   /** Performs a numeric decomposition of \a matrix
    *
-   * The given matrix must have the same sparsity than the matrix on which the symbolic decomposition has been
+   * The given matrix must have the same sparsity as the matrix on which the symbolic decomposition has been
    * performed.
    *
    * \sa analyzePattern()

Eigen/src/ThreadPool/ThreadLocal.h

@@ -90,7 +90,7 @@ struct ThreadLocalNoOpRelease {
 //
 //   Eigen::ThreadLocal<Counter> counter(10);
 //
-//   // Each thread will have access to it's own counter object.
+//   // Each thread will have access to its own counter object.
 //   Counter& cnt = counter.local();
 //   cnt++;
 //

Eigen/src/UmfPackSupport/UmfPackSupport.h

@@ -425,7 +425,7 @@ class UmfPackLU : public SparseSolverBase<UmfPackLU<MatrixType_> > {
 
   /** Performs a numeric decomposition of \a matrix
    *
-   * The given matrix must have the same sparsity than the matrix on which the pattern anylysis has been performed.
+   * The given matrix must have the same sparsity as the matrix on which the pattern analysis has been performed.
    *
    * \sa analyzePattern(), compute()
    */

Eigen/src/plugins/BlockMethods.inc

@@ -990,7 +990,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename ConstNColsBlockXpr<N>::Type middl
 /// Example: \include MatrixBase_block_int_int.cpp
 /// Output: \verbinclude MatrixBase_block_int_int.out
 ///
-/// \note The usage of of this overload is discouraged from %Eigen 3.4, better used the generic
+/// \note The usage of this overload is discouraged from %Eigen 3.4, better use the generic
 /// block(Index,Index,NRowsType,NColsType), here is the one-to-one equivalence:
 /// \code
 /// mat.template block<NRows,NCols>(i,j)  <-->  mat.block(i,j,fix<NRows>,fix<NCols>)
@@ -1032,7 +1032,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename ConstFixedBlockXpr<NRows, N
 /// Example: \include MatrixBase_template_int_int_block_int_int_int_int.cpp
 /// Output: \verbinclude MatrixBase_template_int_int_block_int_int_int_int.out
 ///
-/// \note The usage of of this overload is discouraged from %Eigen 3.4, better used the generic
+/// \note The usage of this overload is discouraged from %Eigen 3.4, better use the generic
 /// block(Index,Index,NRowsType,NColsType), here is the one-to-one complete equivalence:
 /// \code
 /// mat.template block<NRows,NCols>(i,j,rows,cols)     <-->  mat.block(i,j,fix<NRows>(rows),fix<NCols>(cols))

unsupported/Eigen/CXX11/src/Tensor/TensorReduction.h

@@ -835,7 +835,7 @@ struct TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, M
     } else if (PreservingInnerMostDims) {
       const Index firstIndex = firstInput(index);
       const int innermost_dim = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? 0 : NumOutputDims - 1;
-      // TBD: extend this the the n innermost dimensions that we preserve.
+      // TBD: extend this to the n innermost dimensions that we preserve.
       if (((firstIndex % m_dimensions[innermost_dim]) + PacketSize - 1) < m_dimensions[innermost_dim]) {
         Op reducer(m_reducer);
         typename Self::PacketReturnType accum = reducer.template initializePacket<typename Self::PacketReturnType>();