JordanAlgebra.h¶

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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.

Parameters

vec – pointer to the vector data.
vecSize – the length of the vector.
varsCount – the count of variables (subvectors) in vec.

Returns

a pointer to a NumericsMatrix

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

Returns reflection matrix.

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

Parameters: size – is the size of rectangular metrix
Returns: reflection matrix.

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.

Parameters

vec – pointer to the vector data.
vecSize – the length of the vector.
varsCount – the count of variables (subvectors) in vec.

Returns

a pointer to a NumericsMatrix

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

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

Create the Arrow representation matrix from vector.

Parameters

vecSize – the length of the vector.
varsCount – the count of variables (subvectors) in vec.

Returns

a pointer to the identity element of the Jordan algebra

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_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\in\mathbb{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\in\mathbb{R}^{vecSize\times 2*varsCount}).

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 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_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_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