text: /*
   * This software is distributed under BSD 3-clause license (see LICENSE file).
   *
   * Authors: Soeren Sonnenburg, Yuyu Zhang
   */
  
  #ifndef _RIDGEKERNELNORMALIZER_H___
  #define _RIDGEKERNELNORMALIZER_H___
  
  #include <shogun/lib/config.h>
  
  #include <shogun/kernel/normalizer/KernelNormalizer.h>
  
  namespace shogun
  {
  /** @brief Normalize the kernel by adding a constant term to its diagonal.
   * This aids kernels to become positive definite (even though they are
   * not - often caused by numerical problems).
   *
   * Formally,
   *
   * \f[
   * k'(x,x')= \frac{k(x,x')}+ R\cdot {\bf E}
   * \f]
   *
   * where E is a matrix with ones on the diagonal and R is the scalar
   * ridge term. The ridge term R is computed as \f$R=r\dot c\f$.
   *
   * Typically,
   *
   * - r=1e-10 and c=0.0 will add mean(diag(K))*1e-10 to the diagonal
   * - r=0.1 and c=1 will add 0.1 to the diagonal
   *
   *
   * In case c <= 0, c is compute as the mean of the kernel diagonal
   * \f[
   * \mbox{c} = \frac{1}{N}\sum_{i=1}^N k(x_i,x_i)
   * \f]
   *
   */
  class RidgeKernelNormalizer : public KernelNormalizer
  {
  	public:
  		/** constructor
  		 *
  		 * @param r ridge parameter
  		 * @param c scale parameter, if <= 0 scaling will be computed
  		 * from the avg of the kernel diagonal elements
  		 *
  		 * the scalar r*c will be added to the kernel diagonal, typical use cases:
  		 * - r=1e-10 and c=0.0 will add mean(diag(K))*1e-10 to the diagonal
  		 * - r=0.1 and c=1 will add 0.1 to the diagonal
  		 */
  		RidgeKernelNormalizer(float64_t r=1e-10, float64_t c=0.0)
  			: KernelNormalizer()
  		{
  			/*SG_ADD(&scale, "scale", "Scale quotient by which kernel is scaled.",
  			    ParameterProperties::HYPER)*/;
  			/*SG_ADD(&ridge, "ridge", "Ridge added to diagonal.", ParameterProperties::HYPER)*/;
  
  			scale=c;
  			ridge=r;
  		}
  
  		/** default destructor */
  		virtual ~RidgeKernelNormalizer()
  		{
  		}
  
  		/** initialization of the normalizer (if needed)
           * @param k kernel */
  		virtual bool init(Kernel* k)
  		{
  			if (scale<=0)
  			{
  				ASSERT(k)
  				int32_t num=k->get_num_vec_lhs();
  				ASSERT(num>0)
  
  				auto old_lhs=k->lhs;
  				auto old_rhs=k->rhs;
  				k->lhs=old_lhs;
  				k->rhs=old_lhs;
  
  				float64_t sum=0;
  				for (int32_t i=0; i<num; i++)
  					sum+=k->compute(i, i);
  
  				scale=sum/num;
  				k->lhs=old_lhs;
  				k->rhs=old_rhs;
  			}
  
  			ridge*=scale;
  			return true;
  		}
  
  		/** normalize the kernel value
  		 * @param value kernel value
  		 * @param idx_lhs index of left hand side vector
  		 * @param idx_rhs index of right hand side vector
  		 */
  		virtual float64_t normalize(
  			float64_t value, int32_t idx_lhs, int32_t idx_rhs) const
  		{
  			if (idx_lhs==idx_rhs)
  				return value+ridge;
  			else
  				return value;
  		}
  
  		/** normalize only the left hand side vector
  		 * @param value value of a component of the left hand side feature vector
  		 * @param idx_lhs index of left hand side vector
  		 */
  		virtual float64_t normalize_lhs(float64_t value, int32_t idx_lhs) const
  		{
  			error("linadd not supported with Ridge normalization.");
  			return 0;
  		}
  
  		/** normalize only the right hand side vector
  		 * @param value value of a component of the right hand side feature vector
  		 * @param idx_rhs index of right hand side vector
  		 */
  		virtual float64_t normalize_rhs(float64_t value, int32_t idx_rhs) const
  		{
  			error("linadd not supported with Ridge normalization.");
  			return 0;
  		}
  
  		/** @return object name */
  		virtual const char* get_name() const { return "RidgeKernelNormalizer"; }
  
  	protected:
  		/// the constant ridge to be added to the kernel diagonal
  		float64_t ridge;
  		/// scaling parameter (avg of diagonal)
  		float64_t scale;
  };
  }
  #endif // _RIDGEKERNELNORMALIZER_H___
  