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Eigen/src/Core/CwiseNullaryOp.h

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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_CWISE_NULLARY_OP_H
+#define EIGEN_CWISE_NULLARY_OP_H
+
+/** \class CwiseNullaryOp
+  *
+  * \brief Generic expression of a matrix where all coefficients are defined by a functor
+  *
+  * \param NullaryOp template functor implementing the operator
+  *
+  * This class represents an expression of a generic zeroary operator.
+  * It is the return type of the ones(), zero(), constant() and random() functions,
+  * and most of the time this is the only way it is used.
+  *
+  * However, if you want to write a function returning such an expression, you
+  * will need to use this class.
+  *
+  */
+template<typename NullaryOp, typename MatrixType>
+struct ei_traits<CwiseNullaryOp<NullaryOp, MatrixType> >
+{
+  typedef typename MatrixType::Scalar Scalar;
+  enum {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+    Flags = (MatrixType::Flags & ~VectorizableBit)
+      | ei_functor_traits<NullaryOp>::IsVectorizable
+      | (ei_functor_traits<NullaryOp>::IsRepeatable ? 0 : EvalBeforeNestingBit),
+    CoeffReadCost = ei_functor_traits<NullaryOp>::Cost
+  };
+};
+
+template<typename NullaryOp, typename MatrixType>
+class CwiseNullaryOp : ei_no_assignment_operator,
+  public MatrixBase<CwiseNullaryOp<NullaryOp, MatrixType> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseNullaryOp)
+
+    CwiseNullaryOp(int rows, int cols, const NullaryOp& func = NullaryOp())
+      : m_rows(rows), m_cols(cols), m_functor(func)
+    {
+      ei_assert(rows > 0
+          && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
+          && cols > 0
+          && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
+    }
+
+  private:
+
+    int _rows() const { return m_rows.value(); }
+    int _cols() const { return m_cols.value(); }
+
+    const Scalar _coeff(int rows, int cols) const
+    {
+      return m_functor(rows, cols);
+    }
+
+    PacketScalar _packetCoeff(int, int) const
+    {
+      return m_functor.packetOp();
+    }
+
+  protected:
+    const ei_int_if_dynamic<RowsAtCompileTime> m_rows;
+    const ei_int_if_dynamic<ColsAtCompileTime> m_cols;
+    const NullaryOp m_functor;
+};
+
+
+/* \returns an expression of a custom coefficient-wise operator \a func of *this and \a other
+  *
+  * The template parameter \a CustomNullaryOp is the type of the functor
+  * of the custom operator (see class CwiseNullaryOp for an example)
+  *
+  * \sa class CwiseNullaryOp, MatrixBase::operator+, MatrixBase::operator-, MatrixBase::cwiseProduct, MatrixBase::cwiseQuotient
+  */
+template<typename Derived>
+template<typename CustomNullaryOp>
+const CwiseNullaryOp<CustomNullaryOp, Derived>
+MatrixBase<Derived>::cwiseCreate(int rows, int cols, const CustomNullaryOp& func)
+{
+  return CwiseNullaryOp<CustomNullaryOp, Derived>(rows, cols, func);
+}
+
+template<typename Derived>
+template<typename CustomNullaryOp>
+const CwiseNullaryOp<CustomNullaryOp, Derived>
+MatrixBase<Derived>::cwiseCreate(int size, const CustomNullaryOp& func)
+{
+  ei_assert(IsVectorAtCompileTime);
+  if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, Derived>(1, size, func);
+  else return CwiseNullaryOp<CustomNullaryOp, Derived>(size, 1, func);
+}
+
+template<typename Derived>
+template<typename CustomNullaryOp>
+const CwiseNullaryOp<CustomNullaryOp, Derived>
+MatrixBase<Derived>::cwiseCreate(const CustomNullaryOp& func)
+{
+  return CwiseNullaryOp<CustomNullaryOp, Derived>(rows(), cols(), func);
+}
+
+/* \returns an expression of the coefficient-wise \< operator of *this and \a other
+  *
+  * \sa class CwiseNullaryOp
+  */
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_constant_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::constant(int rows, int cols, const Scalar& value)
+{
+  return cwiseCreate(rows, cols, ei_scalar_constant_op<Scalar>(value));
+}
+
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_constant_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::constant(int size, const Scalar& value)
+{
+  return cwiseCreate(size, ei_scalar_constant_op<Scalar>(value));
+}
+
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_constant_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::constant(const Scalar& value)
+{
+  return cwiseCreate(RowsAtCompileTime, ColsAtCompileTime, ei_scalar_constant_op<Scalar>(value));
+}
+
+template<typename Derived>
+bool MatrixBase<Derived>::isEqualToConstant
+(const Scalar& value, typename NumTraits<Scalar>::Real prec) const
+{
+  for(int j = 0; j < cols(); j++)
+    for(int i = 0; i < rows(); i++)
+      if(!ei_isApprox(coeff(i, j), value, prec))
+        return false;
+  return true;
+}
+
+template<typename Derived>
+Derived& MatrixBase<Derived>::setConstant(const Scalar& value)
+{
+  return *this = constant(rows(), cols(), value);
+}
+
+// zero:
+
+/** \returns an expression of a zero matrix.
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so zero() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_zero_int_int.cpp
+  * Output: \verbinclude MatrixBase_zero_int_int.out
+  *
+  * \sa zero(), zero(int)
+  */
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_constant_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::zero(int rows, int cols)
+{
+  return constant(rows, cols, Scalar(0));
+}
+
+/** \returns an expression of a zero vector.
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this MatrixBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so zero() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_zero_int.cpp
+  * Output: \verbinclude MatrixBase_zero_int.out
+  *
+  * \sa zero(), zero(int,int)
+  */
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_constant_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::zero(int size)
+{
+  return constant(size, Scalar(0));
+}
+
+/** \returns an expression of a fixed-size zero matrix or vector.
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * Example: \include MatrixBase_zero.cpp
+  * Output: \verbinclude MatrixBase_zero.out
+  *
+  * \sa zero(int), zero(int,int)
+  */
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_constant_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::zero()
+{
+  return constant(Scalar(0));
+}
+
+/** \returns true if *this is approximately equal to the zero matrix,
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isZero.cpp
+  * Output: \verbinclude MatrixBase_isZero.out
+  *
+  * \sa class Zero, zero()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isZero
+(typename NumTraits<Scalar>::Real prec) const
+{
+  for(int j = 0; j < cols(); j++)
+    for(int i = 0; i < rows(); i++)
+      if(!ei_isMuchSmallerThan(coeff(i, j), static_cast<Scalar>(1), prec))
+        return false;
+  return true;
+}
+
+/** Sets all coefficients in this expression to zero.
+  *
+  * Example: \include MatrixBase_setZero.cpp
+  * Output: \verbinclude MatrixBase_setZero.out
+  *
+  * \sa class Zero, zero()
+  */
+template<typename Derived>
+Derived& MatrixBase<Derived>::setZero()
+{
+  return setConstant(Scalar(0));
+}
+
+// ones:
+
+/** \returns an expression of a matrix where all coefficients equal one.
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so ones() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_ones_int_int.cpp
+  * Output: \verbinclude MatrixBase_ones_int_int.out
+  *
+  * \sa ones(), ones(int), isOnes(), class Ones
+  */
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_constant_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::ones(int rows, int cols)
+{
+  return constant(rows, cols, Scalar(1));
+}
+
+/** \returns an expression of a vector where all coefficients equal one.
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this MatrixBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so ones() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_ones_int.cpp
+  * Output: \verbinclude MatrixBase_ones_int.out
+  *
+  * \sa ones(), ones(int,int), isOnes(), class Ones
+  */
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_constant_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::ones(int size)
+{
+  return constant(size, Scalar(1));
+}
+
+/** \returns an expression of a fixed-size matrix or vector where all coefficients equal one.
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * Example: \include MatrixBase_ones.cpp
+  * Output: \verbinclude MatrixBase_ones.out
+  *
+  * \sa ones(int), ones(int,int), isOnes(), class Ones
+  */
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_constant_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::ones()
+{
+  return constant(Scalar(1));
+}
+
+/** \returns true if *this is approximately equal to the matrix where all coefficients
+  *          are equal to 1, within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isOnes.cpp
+  * Output: \verbinclude MatrixBase_isOnes.out
+  *
+  * \sa class Ones, ones()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isOnes
+(typename NumTraits<Scalar>::Real prec) const
+{
+  return isEqualToConstant(Scalar(1));
+}
+
+/** Sets all coefficients in this expression to one.
+  *
+  * Example: \include MatrixBase_setOnes.cpp
+  * Output: \verbinclude MatrixBase_setOnes.out
+  *
+  * \sa class Ones, ones()
+  */
+template<typename Derived>
+Derived& MatrixBase<Derived>::setOnes()
+{
+  return setConstant(Scalar(1));
+}
+
+// random:
+
+/** \returns a random matrix (not an expression, the matrix is immediately evaluated).
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so ei_random() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_random_int_int.cpp
+  * Output: \verbinclude MatrixBase_random_int_int.out
+  *
+  * \sa ei_random(), ei_random(int)
+  */
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_random_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::random(int rows, int cols)
+{
+  return cwiseCreate(rows, cols, ei_scalar_random_op<Scalar>());
+}
+
+/** \returns a random vector (not an expression, the vector is immediately evaluated).
+  *
+  * The parameter \a size is the size of the returned vector.
+  * Must be compatible with this MatrixBase type.
+  *
+  * \only_for_vectors
+  *
+  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+  * it is redundant to pass \a size as argument, so ei_random() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_random_int.cpp
+  * Output: \verbinclude MatrixBase_random_int.out
+  *
+  * \sa ei_random(), ei_random(int,int)
+  */
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_random_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::random(int size)
+{
+  return cwiseCreate(size, ei_scalar_random_op<Scalar>());
+}
+
+/** \returns a fixed-size random matrix or vector
+  * (not an expression, the matrix is immediately evaluated).
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variants taking size arguments.
+  *
+  * Example: \include MatrixBase_random.cpp
+  * Output: \verbinclude MatrixBase_random.out
+  *
+  * \sa ei_random(int), ei_random(int,int)
+  */
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_random_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::random()
+{
+  return cwiseCreate(RowsAtCompileTime, ColsAtCompileTime, ei_scalar_random_op<Scalar>());
+}
+
+/** Sets all coefficients in this expression to random values.
+  *
+  * Example: \include MatrixBase_setRandom.cpp
+  * Output: \verbinclude MatrixBase_setRandom.out
+  *
+  * \sa class Random, ei_random()
+  */
+template<typename Derived>
+Derived& MatrixBase<Derived>::setRandom()
+{
+  return *this = random(rows(), cols());
+}
+
+// Identity:
+
+/** \returns an expression of the identity matrix (not necessarily square).
+  *
+  * The parameters \a rows and \a cols are the number of rows and of columns of
+  * the returned matrix. Must be compatible with this MatrixBase type.
+  *
+  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+  * it is redundant to pass \a rows and \a cols as arguments, so identity() should be used
+  * instead.
+  *
+  * Example: \include MatrixBase_identity_int_int.cpp
+  * Output: \verbinclude MatrixBase_identity_int_int.out
+  *
+  * \sa identity(), setIdentity(), isIdentity()
+  */
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_identity_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::identity(int rows, int cols)
+{
+  return cwiseCreate(rows, cols, ei_scalar_identity_op<Scalar>());
+}
+
+/** \returns an expression of the identity matrix (not necessarily square).
+  *
+  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+  * need to use the variant taking size arguments.
+  *
+  * Example: \include MatrixBase_identity.cpp
+  * Output: \verbinclude MatrixBase_identity.out
+  *
+  * \sa identity(int,int), setIdentity(), isIdentity()
+  */
+template<typename Derived>
+const CwiseNullaryOp<ei_scalar_identity_op<typename ei_traits<Derived>::Scalar>, Derived>
+MatrixBase<Derived>::identity()
+{
+  return cwiseCreate(RowsAtCompileTime, ColsAtCompileTime, ei_scalar_identity_op<Scalar>());
+}
+
+/** \returns true if *this is approximately equal to the identity matrix
+  *          (not necessarily square),
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isIdentity.cpp
+  * Output: \verbinclude MatrixBase_isIdentity.out
+  *
+  * \sa class Identity, identity(), identity(int,int), setIdentity()
+  */
+template<typename Derived>
+bool MatrixBase<Derived>::isIdentity
+(typename NumTraits<Scalar>::Real prec) const
+{
+  for(int j = 0; j < cols(); j++)
+  {
+    for(int i = 0; i < rows(); i++)
+    {
+      if(i == j)
+      {
+        if(!ei_isApprox(coeff(i, j), static_cast<Scalar>(1), prec))
+          return false;
+      }
+      else
+      {
+        if(!ei_isMuchSmallerThan(coeff(i, j), static_cast<RealScalar>(1), prec))
+          return false;
+      }
+    }
+  }
+  return true;
+}
+
+/** Writes the identity expression (not necessarily square) into *this.
+  *
+  * Example: \include MatrixBase_setIdentity.cpp
+  * Output: \verbinclude MatrixBase_setIdentity.out
+  *
+  * \sa class Identity, identity(), identity(int,int), isIdentity()
+  */
+template<typename Derived>
+Derived& MatrixBase<Derived>::setIdentity()
+{
+  return *this = identity(rows(), cols());
+}
+
+#endif // EIGEN_CWISE_NULLARY_OP_H