# File numerics/src/tools/JordanAlgebra.h¶

Go to the source code of this file

Functions of the Jordan algebra.

Functions

NumericsMatrix *Arrow_repr(const double *const vec, const unsigned int vecSize, const size_t varsCount)

Create the Arrow representation matrix from vector.

Return

a pointer to a NumericsMatrix

Parameters
• vec: pointer to the vector data.

• vecSize: the length of the vector.

• varsCount: the count of variables (subvectors) in vec.

void JA_det(const double *const vec, const unsigned int vecSize, const size_t varsCount, double *out)

Compute element by element square root.

Parameters
• vec: is the vector

• vecSize: is the size of the vector vec

• varsCount: is the count of variables (subvectors) in vec.

• out: is the vector of determinants

void JA_eigenvals(const double *const vec, const unsigned int vecSize, const size_t varsCount, double *out)

Returns the eigenvalues of each element in the vector.

Parameters
• vec: is the pointer to the vector data.

• vecSize: is the length of the vector.

• varsCount: is the count of variables (subvectors) in vec.

• out: is the result vector of eigenvalues (out{R}^{2*varsCount})..

void JA_eigenvecs(const double *const vec, const unsigned int vecSize, const size_t varsCount, double **out)

Returns the eigenvectors of each element in the vector.

Parameters
• vec: is the pointer to the vector data.

• vecSize: is the length of the vector.

• varsCount: is the count of variables (subvectors) in vec.

• out: is the result matrix of eigenvactors (out{R}^{vecSize 2*varsCount}).

double *JA_iden(const unsigned int vecSize, const size_t varsCount)

Create the Arrow representation matrix from vector.

Return

a pointer to the identity element of the Jordan algebra

Parameters
• vecSize: the length of the vector.

• varsCount: the count of variables (subvectors) in vec.

void JA_inv(const double *const vec, const unsigned int vecSize, const size_t varsCount, double *out)

Compute element by element the inverse of the vector.

Parameters
• vec: is the vector

• vecSize: is the size of the vector vec

• varsCount: is the count of variables (subvectors) in vec.

• out: is the inverse of the vector

void JA_power2(const double *const vec, const unsigned int vecSize, const size_t varsCount, double *out)

Compute element by element the square of the vector.

Parameters
• vec: is the vector

• vecSize: is the size of the vector vec

• varsCount: is the count of variables (subvectors) in vec.

• out: is the square of the vector

void JA_prod(const double *const vec1, const double *const vec2, const unsigned int vecSize, const int varsCount, double *out)

Jordan product of two vectors.

Parameters
• vec1: is a vector;

• vec2: is a vector;

• vecSize: is the length of the vectors;

• varsCount: is the count of variables (subvectors) in x and y.

• out: is the result vector of the Jordan product.

void JA_sqrt(const double *const vec, const unsigned int vecSize, const size_t varsCount, double *out)

Compute element by element square root.

Parameters
• vec: is the vector

• vecSize: is the size of the vector vec

• varsCount: is the count of variables (subvectors) in vec.

• out: is the sqrt vector

void JA_sqrt_inv(const double *const vec, const unsigned int vecSize, const size_t varsCount, double *out)

Compute element by element inverse of square root.

Parameters
• vec: is the vector

• vecSize: is the size of the vector vec

• varsCount: is the count of variables (subvectors) in vec.

• out: is the inverse of sqrt vector

void NesterovToddVector(const double *const vec1, const double *const vec2, const unsigned int vecSize, const size_t varsCount, double *out)
NumericsMatrix *Quad_repr(const double *const vec, const unsigned int vecSize, const size_t varsCount)

Returns quadratic representation of the vector x by formula 2*xx^T - det(x)R.

Return

a pointer to a NumericsMatrix

Parameters
• vec: pointer to the vector data.

• vecSize: the length of the vector.

• varsCount: the count of variables (subvectors) in vec.

NumericsMatrix *Reflect_mat(const unsigned int size, NM_types type)

Returns reflection matrix.

|1 0 … 0| R = |0 -1 … 0| | …….. 0| |0 0 … -1|

Return

reflection matrix.

Parameters
• size: is the size of rectangular metrix