math/include/mrpt/math/utils.h

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          http://www.mrpt.org/                          |
   |                                                                        |
   | Copyright (c) 2005-2018, Individual contributors, see AUTHORS file     |
   | See: http://www.mrpt.org/Authors - All rights reserved.                |
   | Released under BSD License. See details in http://www.mrpt.org/License |
   +------------------------------------------------------------------------+ */
#pragma once
 
#include <cstdarg>
#include <cstdio>
#include <cmath>
#include <iosfwd>
#include <vector>
#include <limits>  // numeric_limits
#include <mrpt/core/exceptions.h>
#include <mrpt/math/eigen_frwds.h>
 
namespace mrpt
{
/** This base provides a set of functions for maths stuff.
 * \ingroup mrpt_math_grp
 */
namespace math
{
/**\brief Compare 2 floats and determine whether they are equal
 * \return True if equal, false otherwise
 * \param a Fist num
 * \param b Second num
 * \param epsilon Difference below which a, b are considered equal
 */
template <class T1, class T2>
bool approximatelyEqual(T1 a, T1 b, T2 epsilon)
{
    return fabs(a - b) <= ((fabs(a) > fabs(b) ? fabs(b) : fabs(a)) * epsilon);
}
 
/**\brief Compare 2 floats and determine whether they are equal
 * \return True if equal, false otherwise
 * \param a Fist num
 * \param b Second num
 */
template <class T>
bool approximatelyEqual(T a, T b)
{
    return approximatelyEqual(a, b, std::numeric_limits<T>::epsilon());
}
 
/**\brief Absolute difference between two numbers.
 *
 */
template <class T>
T absDiff(const T& lhs, const T& rhs)
{
    return lhs > rhs ? lhs - rhs : rhs - lhs;
}
 
/** \addtogroup container_ops_grp
 * @{ */
 
/** Loads one row of a text file as a numerical std::vector.
 * \return false on EOF or invalid format.
 * The body of the function is implemented in MATH.cpp
 */
bool loadVector(std::istream& f, std::vector<int>& d);
 
/** Loads one row of a text file as a numerical std::vector.
 * \return false on EOF or invalid format.
 * The body of the function is implemented in MATH.cpp
 */
bool loadVector(std::istream& f, std::vector<double>& d);
 
void medianFilter(
    const std::vector<double>& inV, std::vector<double>& outV,
    const int& winSize, const int& numberOfSigmas = 2);
 
/** Generates an equidistant sequence of numbers given the first one, the last
  one and the desired number of points.
  \sa sequence */
template <typename T, typename VECTOR>
void linspace(T first, T last, size_t count, VECTOR& out_vector)
{
    if (count < 2)
    {
        out_vector.assign(count, last);
        return;
    }
    else
    {
        out_vector.resize(count);
        const T incr = (last - first) / T(count - 1);
        T c = first;
        for (size_t i = 0; i < count; i++, c += incr) out_vector[i] = c;
    }
}
 
/** Generates a sequence of values [first,first+STEP,first+2*STEP,...]   \sa
 * linspace, sequence */
template <class T, T STEP>
inline std::vector<T> sequenceStdVec(T first, size_t length)
{
    std::vector<T> ret(length);
    if (!length) return ret;
    size_t i = 0;
    while (length--)
    {
        ret[i++] = first;
        first += STEP;
    }
    return ret;
}
 
/** Normalize a vector, such as its norm is the unity.
 *  If the vector has a null norm, the output is a null vector.
 */
template <class VEC1, class VEC2>
void normalize(const VEC1& v, VEC2& out_v)
{
    typename VEC1::Scalar total = 0;
    const size_t N = v.size();
    for (size_t i = 0; i < N; i++) total += square(v[i]);
    total = std::sqrt(total);
    if (total)
    {
        out_v = v * (1.0 / total);
    }
    else
        out_v.assign(v.size(), 0);
}
 
/** Extract a column from a vector of vectors, and store it in another vector.
 *  - Input data can be: std::vector<mrpt::math::CVectorDouble>,
 * std::deque<std::list<double> >, std::list<CArrayDouble<5> >, etc. etc.
 *  - Output is the sequence:  data[0][idx],data[1][idx],data[2][idx], etc..
 *
 *  For the sake of generality, this function does NOT check the limits in
 * the number of column, unless it's implemented in the [] operator of each of
 * the "rows".
 */
template <class VECTOR_OF_VECTORS, class VECTORLIKE>
inline void extractColumnFromVectorOfVectors(
    const size_t colIndex, const VECTOR_OF_VECTORS& data,
    VECTORLIKE& out_column)
{
    const size_t N = data.size();
    out_column.resize(N);
    for (size_t i = 0; i < N; i++) out_column[i] = data[i][colIndex];
}
 
/** Computes the factorial of an integer number and returns it as a 64-bit
 * integer number.
 */
uint64_t factorial64(unsigned int n);
 
/** Computes the factorial of an integer number and returns it as a double value
 * (internally it uses logarithms for avoiding overflow).
 */
double factorial(unsigned int n);
 
/** Generates a string with the MATLAB commands required to plot an confidence
 * interval (ellipse) for a 2D Gaussian ('float' version)..
 *  \param cov22 The 2x2 covariance matrix
 *  \param mean  The 2-length vector with the mean
 *  \param stdCount How many "quantiles" to get into the area of the ellipse:
 * 2: 95%, 3:99.97%,...
 *  \param style A matlab style string, for colors, line styles,...
 *  \param nEllipsePoints The number of points in the ellipse to generate
 * \ingroup stats_grp
 */
std::string MATLAB_plotCovariance2D(
    const CMatrixFloat& cov22, const CVectorFloat& mean, const float& stdCount,
    const std::string& style = std::string("b"),
    const size_t& nEllipsePoints = 30);
 
/** Generates a string with the MATLAB commands required to plot an confidence
 * interval (ellipse) for a 2D Gaussian ('double' version).
 *  \param cov22 The 2x2 covariance matrix
 *  \param mean  The 2-length vector with the mean
 *  \param stdCount How many "quantiles" to get into the area of the ellipse:
 * 2: 95%, 3:99.97%,...
 *  \param style A matlab style string, for colors, line styles,...
 *  \param nEllipsePoints The number of points in the ellipse to generate
 * \ingroup stats_grp
 */
std::string MATLAB_plotCovariance2D(
    const CMatrixDouble& cov22, const CVectorDouble& mean,
    const float& stdCount, const std::string& style = std::string("b"),
    const size_t& nEllipsePoints = 30);
 
/** Assignment operator for initializing a std::vector from a C array (The
 *vector will be automatically set to the correct size).
 * \code
 *   CVectorDouble  v;
 *  const double numbers[] = { 1,2,3,5,6,7,8,9,10 };
 *  loadVector( v, numbers );
 * \endcode
 * \note This operator performs the appropiate type castings, if required.
 */
template <typename EIGEN_VECTOR, typename At, size_t N>
EIGEN_VECTOR& loadVector(EIGEN_VECTOR& v, At (&theArray)[N])
{
    MRPT_COMPILE_TIME_ASSERT(N != 0);
    v.derived().resize(N);
    for (size_t i = 0; i < N; i++)
        (v.derived())[i] =
            static_cast<typename EIGEN_VECTOR::Scalar>(theArray[i]);
    return v;
}
//! \overload
template <typename T, typename At, size_t N>
std::vector<T>& loadVector(std::vector<T>& v, At (&theArray)[N])
{
    MRPT_COMPILE_TIME_ASSERT(N != 0);
    v.resize(N);
    for (size_t i = 0; i < N; i++) v[i] = static_cast<T>(theArray[i]);
    return v;
}
 
/**  @} */  // end of grouping container_ops_grp
 
/** \defgroup mrpt_math_io Custom I/O for math containers
 * \ingroup mrpt_math_grp */
/** \addtogroup mrpt_math_io
 * @{ */
 
/** Saves to a plain-text file the nonzero entries of a Eigen sparse matrix,
 * represented as a vector of triplets.
 *  Output format is one line per entry with the format: "i j val", i:row,
 * j:col, val:value.
 * \tparam TRIPLET should be Eigen::Triplet<T>
 */
template <class TRIPLET>
bool saveEigenSparseTripletsToFile(
    const std::string& sFile, std::vector<TRIPLET>& tri)
{
#if defined(_MSC_VER) && \
    (_MSC_VER >= 1400)  // Use a secure version in Visual Studio 2005+
    FILE* f;
    if (0 != ::fopen_s(&f, sFile.c_str(), "wt")) f = nullptr;
#else
    FILE* f = ::fopen(sFile.c_str(), "wt");
#endif
 
    if (!f) return false;
 
    for (size_t i = 0; i < tri.size(); i++)
        fprintf(
            f, "%u %u %e\n", 1 + tri[i].row(), 1 + tri[i].col(),
            tri[i].value());
 
    fclose(f);
    return true;
}
 
/** @} */  // End of mrpt_math_io
 
}  // namespace math
 
}  // namespace mrpt