File numerics/src/tools/JordanAlgebra.h

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Functions of the Jordan algebra.

Typedefs

typedef long double float_type

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

float_type dnrm2l(const unsigned int n, const double *x)

float_type dnrm2sqrl(const unsigned int n, const double *x)

void Qx05y(const double *const x, const double *const y, const unsigned int vecSize, const size_t varsCount, double *out)

void Qx50y(const double *const x, const double *const y, const unsigned int vecSize, const size_t varsCount, double *out)

void Jinv(const double *const x, const unsigned int vecSize, const size_t varsCount, double *out)

void Jsqrt(const double *const x, const unsigned int vecSize, const size_t varsCount, double *out)

void Jsqrtinv(const double *const x, const unsigned int vecSize, const size_t varsCount, double *out)

void Nesterov_Todd_vector(short T, const double *const x, const double *const y, const unsigned int vecSize, const size_t varsCount, double *p)

void Nesterov_Todd_vector_b(const double *const x, const double *const y, const unsigned int vecSize, const size_t varsCount, double *p)

void Qxy(const double *const x, const double *const y, const unsigned int vecSize, const size_t varsCount, double *z)

void QNTpz(const double *const x, const double *const y, const double *const z, const unsigned int vecSize, const size_t varsCount, double *out)

void QNTpinvz(const double *const x, const double *const y, const double *const z, const unsigned int vecSize, const size_t varsCount, double *out)

void QNTpinv2z(const double *const x, const double *const y, const double *const z, const unsigned int vecSize, const size_t varsCount, double *out)

void Jxinvprody(const double *const x, const double *const y, const unsigned int vecSize, const size_t varsCount, double *out)

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

float_type ld_gammal(const double *const x, const size_t dimension)

NumericsMatrix *NTmat(const double *const x, const double *const z, const unsigned int vecSize, const size_t varsCount)

NumericsMatrix *NTmatinv(const double *const x, const double *const z, const unsigned int vecSize, const size_t varsCount)

NumericsMatrix *NTmatsqr(const double *const x, const double *const z, const unsigned int vecSize, const size_t varsCount)