|
| auto | bilinearInterpolation (const auto &tx, const auto &ty, const auto &c00, const auto &c10, const auto &c01, const auto &c11) |
| | Bilinear interpolation.
|
| double | calcEllipticalIntegral (double phi, double m) |
| | Calculates the incomplete elliptical integral of the second kind.
|
| template<std::floating_point T> |
| T | csc (const T &x) |
| | Calculates the cosecant of a value (csc(x) = sec(pi/2 - x) = 1 / sin(x))
|
| template<typename Derived> |
| Derived::PlainObject | expm (const Eigen::MatrixBase< Derived > &X, size_t order) |
| | Calculates the state transition matrix 𝚽 limited to specified order in 𝐅𝜏ₛ
|
| template<typename Derived> |
| Eigen::Matrix< typename Derived::Scalar, 3, 3 > | expMapMatrix (const Eigen::MatrixBase< Derived > &v) |
| | Calculates the matrix exponential map of the given vector.
|
| template<typename Derived> |
| Eigen::Quaternion< typename Derived::Scalar > | expMapQuat (const Eigen::MatrixBase< Derived > &v) |
| | Calculates the quaternionic exponential map of the given vector.
|
| uint64_t | factorial (uint64_t n) |
| | Calculates the factorial of an unsigned integer.
|
| template<std::integral Out, size_t Bits, std::integral In> |
| constexpr Out | interpretAs (In in) |
| | Interprets the input integer with certain amount of Bits as Output type. Takes care of sign extension.
|
| template<typename Derived> |
| Derived::PlainObject | inverseSqrt (const Eigen::MatrixBase< Derived > &matrix) |
| | Returns the inverse square root of a matrix.
|
| template<typename Derived> |
| Eigen::Matrix3< typename Derived::Scalar > | J_r (const Eigen::MatrixBase< Derived > &phi) |
| | Calculates the right Jacobian of SO(3) which relates additive increments in the tangent space to multiplicative increments applied on the right-hand side.
|
| template<typename Derived> |
| Derived::PlainObject | lerp (const Eigen::MatrixBase< Derived > &a, const Eigen::MatrixBase< Derived > &b, auto t) |
| | Linear interpolation between vectors.
|
| LerpSearchResult | lerpSearch (const auto &data, const auto &value) |
| | Searches the value in the data container.
|
| template<typename Derived> |
| std::optional< std::pair< Eigen::Matrix< typename Derived::Scalar, Derived::RowsAtCompileTime, Derived::ColsAtCompileTime >, Eigen::Vector< typename Derived::Scalar, Derived::RowsAtCompileTime > > > | LtDLdecomp_choleskyFact (const Eigen::MatrixBase< Derived > &Q) |
| | Find (L^T D L)-decomposition of Q-matrix via a backward Cholesky factorization in a bordering method formulation.
|
| template<typename Derived> |
| std::optional< std::pair< Eigen::Matrix< typename Derived::Scalar, Derived::RowsAtCompileTime, Derived::ColsAtCompileTime >, Eigen::Vector< typename Derived::Scalar, Derived::RowsAtCompileTime > > > | LtDLdecomp_outerProduct (const Eigen::MatrixBase< Derived > &Qmatrix) |
| | Find (L^T D L)-decomposition of Q-matrix via outer product method.
|
| double | normalCDF (double value) |
| | Calculates the cumulative distribution function (CDF) of the standard normal distribution.
|
| template<std::floating_point T> |
| constexpr T | round (const T &value, size_t digits) |
| | Round the number to the specified amount of digits.
|
| template<std::floating_point T> |
| constexpr T | roundSignificantDigits (T value, size_t digits) |
| | Round the number to the specified amount of significant digits.
|
| template<std::floating_point T> |
| T | sec (const T &x) |
| | Calculates the secant of a value (sec(x) = csc(pi/2 - x) = 1 / cos(x))
|
| template<typename T> |
| int | sgn (const T &val) |
| | Returns the sign of the given value.
|
| template<typename T> |
| T | sign (const T &x, const T &y) |
| | Change the sign of x according to the value of y.
|
| template<typename Derived> |
| Eigen::Matrix< typename Derived::Scalar, 3, 3 > | skewSymmetricMatrix (const Eigen::MatrixBase< Derived > &a) |
| | Calculates the skew symmetric matrix of the given vector. This is needed to perform the cross product with a scalar product operation.
|
| template<typename Derived> |
| Eigen::Matrix< typename Derived::Scalar, 3, 3 > | skewSymmetricMatrixSquared (const Eigen::MatrixBase< Derived > &a) |
| | Calculates the square of a skew symmetric matrix of the given vector.
|
| template<typename DerivedA, typename DerivedQ> |
| DerivedA::Scalar | squaredNormVectorMatrix (const Eigen::MatrixBase< DerivedA > &a, const Eigen::MatrixBase< DerivedQ > &Q) |
| | Calculates the squared norm of the vector and matrix.
|
1.14.0 
![\begin{equation} \label{eq:eq-normalDistCDF-erf}
\Phi(x) = \frac{1}{2} \left[ 1 + \text{erf}{\left(\frac{x}{\sqrt{2}}\right)} \right]
\end{equation}](form_88.svg)
![\begin{equation} \label{eq:eq-normalDistCDF-erfc}
\begin{aligned}
\Phi(x) &= \frac{1}{2} \left[ 1 - \text{erf}{\left(-\frac{x}{\sqrt{2}}\right)} \right] \\
&= \frac{1}{2} \text{erfc}{\left(-\frac{x}{\sqrt{2}}\right)}
\end{aligned}
\end{equation}](form_92.svg)
