Kernels

Kern_Linear

class Kern_Linear : public virtual Kern_Base 

Linear kernel also knows as dot product kernel

Defined for two vectors x and y:

\[ K(\mathbf{x}, \mathbf{y}) = \mathbf{x}^T \mathbf{y} = \sum_i x^{(i)} y^{(i)} \]

See also

Kern_Base BF_Linear

Subclassed by DM_Kern_Linear

Public Functions

virtual std::string get_label() const override: Return label of this object.

virtual double prime(const aed_type &b, const aed_type &af, const aed_type &ff) const override

Calculate inner product of the kernel derivative wrt to the second argument (b wrt af) with the force descriptor

b = basis vector
af = atomic energy descriptor
ff = force descriptor (TODO i-th dir component of it) TODO consider calculating all 3-directions at once

inline virtual void set_basis(const Matrix) override: Set basis for calculations.

Public Members

std::string label = "Kern_Linear": Label used for this class

Kern_Quadratic

class Kern_Quadratic : public virtual Kern_Base 

Quadratic kernel - special case of 2nd order polynomial kernel

Defined for two vectors x and y:

\[ K(\mathbf{x}, \mathbf{y}) = \Big( \mathbf{x}^T \mathbf{y} \Big)^2 = \Big( \sum_i x^{(i)} y^{(i)} \Big)^2 \]

See also

Kern_Base

Subclassed by DM_Kern_Quadratic

Public Functions

virtual double prime(const aed_type &b, const aed_type &af, const aed_type &ff) const override

Calculate inner product of the kernel derivative wrt to the second argument (b wrt af) with the force descriptor

b = basis vector
af = atomic energy descriptor
ff = force descriptor (TODO i-th dir component of it) TODO consider calculating all 3-directions at once

virtual std::string get_label() const override: Return label of this object.

Public Members

std::string label = "Kern_Quadratic": Label used for this class

Kern_LQ

class Kern_LQ : public virtual Kern_Base 

Linear + Quadratic kernel

Defined for two vectors x and y:

\[ K(\mathbf{x}, \mathbf{y}) = \mathbf{x}^T \mathbf{y} + \Big(\mathbf{x}^T \mathbf{y} \Big)^2 = \sum_i x^{(i)} y^{(i)} + \Big(\sum_i x^{(i)} y^{(i)} \Big)^2 \]

See also

Kern_Base Kern_Linear Kern_Quadratic

Subclassed by DM_Kern_LQ

Public Functions

virtual double prime(const aed_type &b, const aed_type &af, const aed_type &ff) const override

Calculate inner product of the kernel derivative wrt to the second argument (b wrt af) with the force descriptor

b = basis vector
af = atomic energy descriptor
ff = force descriptor (TODO i-th dir component of it) TODO consider calculating all 3-directions at once

virtual std::string get_label() const override: Return label of this object.

Public Members

std::string label = "Kern_LQ": Label used for this class

Kern_RBF

class Kern_RBF : public virtual Kern_Base 

Radial Basis Function kernel.

Defined for two vectors x and y:

\[ K(\mathbf{x}, \mathbf{y}) = \exp\Big( -\frac{||\mathbf{x}-\mathbf{y}||^2} {2\sigma^2} \Big) \]

Required Config key: MPARAMS <double> \( \sigma \)

See also

Kern_Base Kern_Linear Kern_Quadratic

Subclassed by DM_Kern_RBF

Public Functions

Kern_RBF(): Label used for this class

virtual double prime(const aed_type &b, const aed_type &af, const aed_type &ff) const override

Calculate inner product of the kernel derivative wrt to the second argument (b wrt af) with the force descriptor

b = basis vector
af = atomic energy descriptor
ff = force descriptor (TODO i-th dir component of it) TODO consider calculating all 3-directions at once

virtual std::string get_label() const override: Return label of this object.

Kern_Polynomial

class Kern_Polynomial : public virtual Kern_Base 

Polynomial kernel.

Defined for two vectors x and y:

\[ K(\mathbf{x}, \mathbf{y}) = \big( \gamma*\mathbf{x}^T \mathbf{y} + \mathrm{c} \big)^{\mathrm{d}} \]

Required Config key: MPARAMS <int> d <double> \( \gamma \) c

See also

Kern_Base

Subclassed by DM_Kern_Polynomial

Public Functions

virtual std::string get_label() const override: Return label of this object.

virtual double prime(const aed_type &b, const aed_type &af, const aed_type &ff) const override

Calculate inner product of the kernel derivative wrt to the second argument (b wrt af) with the force descriptor

b = basis vector
af = atomic energy descriptor
ff = force descriptor (TODO i-th dir component of it) TODO consider calculating all 3-directions at once

Public Members

std::string label = "Kern_Polynomial": Label used for this class

Kern_Sigmoid

class Kern_Sigmoid : public virtual Kern_Base 

Sigmoid kernel.

Defined for two vectors x and y:

\[ K(\mathbf{x}, \mathbf{y}) = \tanh\big( \gamma*\mathbf{x}^T \mathbf{y} + \mathrm{c} \big) \]

Required Config key: MPARAMS <double> \( \gamma \) c

See also

Kern_Base

Subclassed by DM_Kern_Sigmoid

Public Functions

Kern_Sigmoid(): Label used for this class

virtual double prime(const aed_type &b, const aed_type &af, const aed_type &ff) const override

Calculate inner product of the kernel derivative wrt to the second argument (b wrt af) with the force descriptor

b = basis vector
af = atomic energy descriptor
ff = force descriptor (TODO i-th dir component of it) TODO consider calculating all 3-directions at once

virtual std::string get_label() const override: Return label of this object.

Kernel

class Kern_Base : public virtual Function_Base 

Abstract class to be used as a base for all kernels.

b = basis vector
af = atomic energy descriptor
ff = force descriptor
all derivatives are defined wrt to the second argument

Subclassed by DM_Kern_Base, Kern_LQ, Kern_Linear, Kern_Polynomial, Kern_Quadratic, Kern_RBF, Kern_Sigmoid

Public Functions

virtual double prime(const aed_type &b, const aed_type &af, const aed_type &ff) const = 0

Calculate inner product of the kernel derivative wrt to the second argument (b wrt af) with the force descriptor

b = basis vector
af = atomic energy descriptor
ff = force descriptor (TODO i-th dir component of it) TODO consider calculating all 3-directions at once

virtual void set_basis(const Matrix b): Set basis for calculations.

virtual const Matrix &get_basis() const: Return basis stored by this object.

virtual Matrix get_basis(): Return basis stored by this object.