added headers for monomial basis and abstract base class

code/include/toolboxes/sphericalbasisbase.h

+/*!
+ * @file sphericalbasisbase.h
+ * @brief Base Class to handle basis classes on the unit sphere
+ * @author S. Schotthöfer
+ *
+ */
+
+#ifndef SPHERICALBASISBASE_H
+#define SPHERICALBASISBASE_H
+
+#include "common/typedef.h"
+class Config;
+
+class SphericalBasisBase
+{
+  public:
+    SphericalBasisBase() {}
+    ~SphericalBasisBase() {}
+
+    /*! @brief: Create a set of basis functions on the unit sphere defined in settings
+     *  @param: Pointer to the config file
+     *  @returns: Pointer to the createt basis class */
+    static SphericalBasisBase* Create( Config* settings );
+
+    /*! @brief  : Computes all N basis functions at point (my, phi)
+     *  @param  : my = cos(theta) - spherical coordinate, -1 <= x <= 1
+     *  @param  : phi - spherical coordinate, 0 <= phi <= 2*pi
+     *  @return : vector of basis functions at point (my, phi) with size N
+     */
+    virtual Vector ComputeSphericalBasis( double my, double phi ) = 0;
+
+    /*! @brief  : Computes all basis functions at point (x, y, z) on the unit sphere
+     *  @param  : x,y,z = coordinates on unit sphere
+     *  @return : vector of basis functions at point (x,y,z) with size N
+     */
+    virtual Vector ComputeSphericalBasis( double x, double y, double z ) = 0;
+};
+
+#endif    // SPHERICALBASISBASE_H

code/include/toolboxes/sphericalmonomials.h

+/*!
+ * @file sphericalmonomials.h
+ * @brief Class for efficient computation of a spherical monomial basis
+ * @author S. Schotthöfer
+ */
+
+#ifndef SPHERICALMONOMIALS_H
+#define SPHERICALMONOMIALS_H
+
+#include "common/typedef.h"
+#include "toolboxes/sphericalbasisbase.h"
+#include <vector>
+
+class SphericalMonomials : public SphericalBasisBase
+{
+  public:
+    /*! @brief : Sets up class for monomial basis on sphere up to degree L.
+     *           The basis then consists of N = L.
+     *  @param : L_degree - maximum degree of spherical harmonics basis, 0 <= L <= 1000 (upper bound
+     *                      due to numerical stability)
+     * */
+    SphericalMonomials( unsigned L_degree );
+
+    /*! @brief  : Computes all N = L² +2L basis functions at point (my, phi)
+     *  @param  : my = cos(theta) - spherical coordinate, -1 <= x <= 1
+     *  @param  : phi - spherical coordinate, 0 <= phi <= 2*pi
+     *  @return : vector of basis functions at point (my, phi) with size N = L² +2L
+     */
+    Vector ComputeSphericalBasis( double my, double phi ) override;
+
+    /*! @brief  : Computes all N = L² +2L basis functions at point (x, y, z) on the unit sphere
+     *  @param  : x,y,z = coordinates on unit sphere
+     *  @return : vector of basis functions at point (x,y,z) with size N = L² +2L
+     */
+    Vector ComputeSphericalBasis( double x, double y, double z ) override;
+
+  private:
+    /*! @brief: maximal degree of the spherical monomial basis (this is "L" in the comments)*/
+    unsigned _LMaxDegree;
+
+    /*! @brief: Spatial dimension of the unit sphere (1,2,3) */
+    unsigned _spatialDim;
+
+    /*! @brief: spherical monomial basis function vector of
+     *         degree  0 <= l <= L
+     *         length : COmputed with ComputeBasisSize
+     */
+    Vector _YBasis;
+
+    /*! @brief: Computes the amount of lin. independent monomials of degree degree and
+     *          spatial dimension dim. len of a single oder: (degree + _spatialDim -1) over (degree)
+     *  @return: lenght of a single dimension */
+    unsigned ComputeDimensionSize( unsigned degree );
+
+    /*! @brief: Computes the length of the basis vector for a given max degree and
+     *          spatial dimension dim. len of a single oder: (degree + _spatialDim -1) over (degree)
+     *  @return: lenght of whole basis */
+    unsigned ComputeBasisSize( unsigned degree );
+
+    /*! @brief: Function to compute factorial of n (n!) in recursive manner */
+    unsigned Factorial( unsigned n );
+
+    /*! @brief: Function to compute first component of spherical unit vector
+     *          Omega_x = sqrt(1-my*my)*cos(phi)
+     *  @return: first component of spherical unit vector */
+    double Omega_x( double my, double phi );
+
+    /*! @brief: Function to compute first component of spherical unit vector
+     *          Omega_x = sqrt(1-my*my)*sin(phi)
+     *  @return: first component of spherical unit vector */
+    double Omega_y( double my, double phi );
+
+    /*! @brief: Function to compute first component of spherical unit vector
+     *          Omega_z = my
+     *  @return: first component of spherical unit vector */
+    double Omega_z( double my );
+
+    /*! @brief: Helper Function to compute basis^exponent. */
+    double Power( double basis, unsigned exponent );
+};
+#endif    // SPHERICALMONOMIALS_H