Generic Solvers Module

class NTPolySwig.ChebyshevPolynomial(degree)

A Class For Computing Matrix functions based on Chebyshev polynomials.

Compute(InputMat, OutputMat, solver_parameters)

Compute A Matrix Chebyshev Polynomial.:type InputMat: Matrix_ps

Parameters:

• InputMat – input matrix.:type OutputMat: Matrix_ps

• OutputMat – = p(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

ComputeFactorized(InputMat, OutputMat, solver_parameters)

Compute A Matrix Chebyshev Polynomial Recursively.:type InputMat: Matrix_ps

Parameters:

• InputMat – input matrix.:type OutputMat: Matrix_ps

• OutputMat – = p(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

SetCoefficient(degree, coefficient)

Set a polynomial coefficient.:type degree: int

Parameters:

• degree – for which to set the coefficient.:type coefficient: float

• coefficient – value.

property thisown

The membership flag

class NTPolySwig.ExponentialSolvers

A Module For Computing General Matrix Exponentials.

static ComputeDenseExponential(InputMat, OutputMat, solver_parameters)

Compute the matrix exponential (dense version).:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the exponential of.:type OutputMat: Matrix_ps

• OutputMat – = exp(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static ComputeDenseLogarithm(InputMat, OutputMat, solver_parameters)

Compute the matrix logarithm (dense version).:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the exponential of.:type OutputMat: Matrix_ps

• OutputMat – = log(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static ComputeExponential(InputMat, OutputMat, solver_parameters)

Compute the matrix exponential.:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the exponential of.:type OutputMat: Matrix_ps

• OutputMat – = exp(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static ComputeExponentialPade(InputMat, OutputMat, solver_parameters)

Compute the matrix exponential using the Pade method.:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the exponential of.:type OutputMat: Matrix_ps

• OutputMat – = exp(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static ComputeLogarithm(InputMat, OutputMat, solver_parameters)

Compute the matrix logarithm.:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the exponential of.:type OutputMat: Matrix_ps

• OutputMat – = log(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

property thisown

The membership flag

class NTPolySwig.HermitePolynomial(degree)

A Class For Computing Matrix functions based on Hermite polynomials.

Compute(InputMat, OutputMat, solver_parameters)

Compute A Matrix Hermite Polynomial.:type InputMat: Matrix_ps

Parameters:

• InputMat – input matrix.:type OutputMat: Matrix_ps

• OutputMat – = p(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

SetCoefficient(degree, coefficient)

Set a polynomial coefficient.:type degree: int

Parameters:

• degree – for which to set the coefficient.:type coefficient: float

• coefficient – value.

property thisown

The membership flag

class NTPolySwig.InverseSolvers

A class for inverting matrices.

static DenseInvert(Overlap, InverseMat, solver_parameters)

Compute the inverse of a matrix (dense version).:type Overlap: Matrix_ps

Parameters:

• Overlap – the matrix to invert.:type InverseMat: Matrix_ps

• InverseMat – = Overlap^-1.:type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static Invert(Overlap, InverseMat, solver_parameters)

Compute the inverse of a matrix. An implementation of Hotelling’s method.:type Overlap: Matrix_ps

Parameters:

• Overlap – the matrix to invert.:type InverseMat: Matrix_ps

• InverseMat – = Overlap^-1.:type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static PseudoInverse(Overlap, InverseMat, solver_parameters)

Compute the pseudoinverse of a matrix. An implementation of Hotelling’s method, with a different convergence criteria.:type Overlap: Matrix_ps

Parameters:

• Overlap – the matrix to invert.:type InverseMat: Matrix_ps

• InverseMat – = Overlap^-1.:type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

property thisown

The membership flag

class NTPolySwig.LinearSolvers

A class for solving matrix equations.

static CGSolver(AMat, XMat, BMat, solver_parameters)

Solve the matrix equation AX = B using conjugate gradient method.:type AMat: Matrix_ps

Parameters:

• AMat – the matrix A, must be symmetric, positive definite.:type XMat: Matrix_ps

• XMat – the solved for matrix X.:type BMat: Matrix_ps

• BMat – the right hand side.:type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static CholeskyDecomposition(AMat, LMat, solver_parameters)

Compute The Cholesky Decomposition of a Symmetric Positive Definite matrix.:type AMat: Matrix_ps

Parameters:

• AMat – the matrix A, must be symmetric, positive definite.:type LMat: Matrix_ps

• LMat – the matrix computed.:type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

property thisown

The membership flag

class NTPolySwig.Polynomial(degree)

A Class For Computing General Matrix Polynomials.

HornerCompute(InputMat, OutputMat, solver_parameters)

Compute A Matrix Polynomial Using Horner’s Method.:type InputMat: Matrix_ps

Parameters:

• InputMat – input matrix.:type OutputMat: Matrix_ps

• OutputMat – = p(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

PatersonStockmeyerCompute(InputMat, OutputMat, solver_parameters)

Compute A Matrix Polynomial Using Paterson and Stockmeyer’s Method.:type InputMat: Matrix_ps

Parameters:

• InputMat – input matrix.:type OutputMat: Matrix_ps

• OutputMat – = p(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

SetCoefficient(degree, coefficient)

Set a polynomial coefficient.:type degree: int

Parameters:

• degree – for which to set the coefficient.:type coefficient: float

• coefficient – value.

property thisown

The membership flag

class NTPolySwig.RootSolvers

A Class For Computing General Matrix Roots.

static ComputeInverseRoot(InputMat, OutputMat, root, solver_parameters)

Compute the general matrix inverse root.:type InputMat: Matrix_ps

Parameters:

• InputMat – input matrix.:type OutputMat: Matrix_ps

• OutputMat – = InputMat^(-1/root):type root: int

• root – = which root:type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static ComputeRoot(InputMat, OutputMat, root, solver_parameters)

Compute a general matrix root.:type InputMat: Matrix_ps

Parameters:

• InputMat – input matrix.:type OutputMat: Matrix_ps

• OutputMat – = InputMat^(1/root):type root: int

• root – = which root:type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

property thisown

The membership flag

class NTPolySwig.SignSolvers

A Class For Computing The Matrix Sign Function.

static ComputeDenseSign(Mat1, SignMat, solver_parameters)

Compute the matrix sign function (dense version).:type Mat1: Matrix_ps

Parameters:

• Mat1 – input matrix.:type SignMat: Matrix_ps

• SignMat – = Sign(Mat1):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static ComputePolarDecomposition(Mat1, Umat, Hmat, solver_parameters)

Computes the polar decomposition of a matrix Mat1 = U*H.:type Mat1: Matrix_ps

Parameters:

• Mat1 – input matrix.:type Umat: Matrix_ps

• Umat – the unitary polar factor.:type Hmat: Matrix_ps

• Hmat – the hermitian matrix factor.:type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static ComputeSign(Mat1, SignMat, solver_parameters)

Compute the matrix sign function.:type Mat1: Matrix_ps

Parameters:

• Mat1 – input matrix.:type SignMat: Matrix_ps

• SignMat – = Sign(Mat1):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

property thisown

The membership flag

class NTPolySwig.SquareRootSolvers

A Class For Computing The Square Root of a Matrix.

static DenseInverseSquareRoot(InputMat, OutputMat, solver_parameters)

Compute the inverse square root of a matrix (dense version).:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the inversesquareroot of.:type OutputMat: Matrix_ps

• OutputMat – = InputMat^-1/2.:type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static DenseSquareRoot(InputMat, OutputMat, solver_parameters)

Compute the square root of a matrix (dense version).:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the inversesquareroot of.:type OutputMat: Matrix_ps

• OutputMat – = InputMat^1/2.:type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static InverseSquareRoot(InputMat, OutputMat, solver_parameters)

Compute the inverse square root of a matrix.:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the inversesquareroot of.:type OutputMat: Matrix_ps

• OutputMat – = InputMat^-1/2.:type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static SquareRoot(InputMat, OutputMat, solver_parameters)

Compute the square root of a matrix.:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the inversesquareroot of.:type OutputMat: Matrix_ps

• OutputMat – = InputMat^1/2.:type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

property thisown

The membership flag

class NTPolySwig.TrigonometrySolvers

A Module For Computing Trigonometric functions of a Matrix.

static Cosine(InputMat, OutputMat, solver_parameters)

Compute the cosine of a matrix.:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the cosine of.:type OutputMat: Matrix_ps

• OutputMat – = cos(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static DenseCosine(InputMat, OutputMat, solver_parameters)

Compute the cosine of a matrix (dense version).:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the cosine of.:type OutputMat: Matrix_ps

• OutputMat – = cos(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static DenseSine(InputMat, OutputMat, solver_parameters)

Compute the sine of a matrix (dense version).:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the sine of.:type OutputMat: Matrix_ps

• OutputMat – = sin(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

static Sine(InputMat, OutputMat, solver_parameters)

Compute the sine of a matrix.:type InputMat: Matrix_ps

Parameters:

• InputMat – matrix to compute the sine of.:type OutputMat: Matrix_ps

• OutputMat – = sin(InputMat):type solver_parameters: SolverParameters

• solver_parameters – parameters for the solver

property thisown

The membership flag