tensap.functions.polynomials package¶

Submodules¶

tensap.functions.polynomials.orthonormal_polynomials module¶

Module orthonormal_polynomials.

class tensap.functions.polynomials.orthonormal_polynomials.DiscretePolynomials(measure=None)¶

Bases: tensap.functions.polynomials.orthonormal_polynomials.OrthonormalPolynomials

Class DiscretePolynomials.

Polynomials orthonormal with respect to a discrete measure.

Methods

`d_poly_coef`(ind)	Return the coefficients of the first order derivative of the polynomials of degrees contained in ind.
`d_polyval`(ind, x)	Evaluate the first order derivative of the polynomials of degrees contained in ind at the points x.
`dn_poly_coeff`(n, ind)	Return the coefficients of the n-th order derivative of the polynomials of degrees contained in ind.
`dn_polyval`(n, ind, x)	Evaluate the n-th order derivative of the polynomials of degrees contained in ind at the points x.
`domain`()	Return the support of the associated measure.
`is_orthonormal`()	Check the orthonormality of the basis created by the functions of self.
`mean`(ind[, measure])	Return the mean of the polynomials of degrees contained in ind, with a Measure given by measure if provided, or to self.measure otherwise.
`moment`(ind[, measure])	Return the integral of products of polynomials p_i, i in ind, using a gauss integration rule.
`ndim`()	Return the dimension of the output of the polynomials.
`one`()	Coefficients and corresponding indices for the decomposition of the constant function 1.
`poly_coeff`(ind)	Compute the coefficients of the monomials used to create the polynomials of degree specified in ind.
`polyval`(ind, x)	Evaluate the polynomials of degrees contained in ind at the points x.
`random`(ind[, n, measure])	Return an array of size n of random evaluations of the polynomials for which the degree is in ind.
`roots`(deg)	Return the roots of the polynomial of degree deg.
`truncated_domain`()	Return the truncated support of the associated measure.

class tensap.functions.polynomials.orthonormal_polynomials.EmpiricalPolynomials(sample, n=None)¶

Bases: tensap.functions.polynomials.orthonormal_polynomials.OrthonormalPolynomials

Class EmpiricalPolynomials.

Polynomials defined on R and orthonormal with respect to the gaussian kernel smoothed distribution based on a sample x, which was centered and normalized (unit variance).

Methods

`d_poly_coef`(ind)	Return the coefficients of the first order derivative of the polynomials of degrees contained in ind.
`d_polyval`(ind, x)	Evaluate the first order derivative of the polynomials of degrees contained in ind at the points x.
`dn_poly_coeff`(n, ind)	Return the coefficients of the n-th order derivative of the polynomials of degrees contained in ind.
`dn_polyval`(n, ind, x)	Evaluate the n-th order derivative of the polynomials of degrees contained in ind at the points x.
`domain`()	Return the support of the associated measure.
`is_orthonormal`()	Check the orthonormality of the basis created by the functions of self.
`mean`(ind[, measure])	Return the mean of the polynomials of degrees contained in ind, with a Measure given by measure if provided, or to self.measure otherwise.
`moment`(ind[, measure])	Return the integral of products of polynomials p_i, i in ind, using a gauss integration rule.
`ndim`()	Return the dimension of the output of the polynomials.
`one`()	Coefficients and corresponding indices for the decomposition of the constant function 1.
`poly_coeff`(ind)	Compute the coefficients of the monomials used to create the polynomials of degree specified in ind.
`polyval`(ind, x)	Evaluate the polynomials of degrees contained in ind at the points x.
`random`(ind[, n, measure])	Return an array of size n of random evaluations of the polynomials for which the degree is in ind.
`roots`(deg)	Return the roots of the polynomial of degree deg.
`truncated_domain`()	Return the truncated support of the associated measure.

class tensap.functions.polynomials.orthonormal_polynomials.HermitePolynomials(n=50)¶

Bases: tensap.functions.polynomials.orthonormal_polynomials.OrthonormalPolynomials

Class HermitePolynomials.

Polynomials defined on R and orthonormal with respect to the standard gaussian measure 1/sqrt(2*pi)*exp(-x^2/2).

Methods

`d_poly_coef`(ind)	Return the coefficients of the first order derivative of the polynomials of degrees contained in ind.
`d_polyval`(ind, x)	Evaluate the first order derivative of the polynomials of degrees contained in ind at the points x.
`dn_poly_coeff`(n, ind)	Return the coefficients of the n-th order derivative of the polynomials of degrees contained in ind.
`dn_polyval`(n, ind, x)	Evaluate the n-th order derivative of the polynomials of degrees contained in ind at the points x.
`domain`()	Return the support of the associated measure.
`is_orthonormal`()	Check the orthonormality of the basis created by the functions of self.
`mean`(ind[, measure])	Return the mean of the polynomials of degrees contained in ind, with a Measure given by measure if provided, or to self.measure otherwise.
`moment`(ind[, measure])	Return the integral of products of polynomials p_i, i in ind, using a gauss integration rule.
`ndim`()	Return the dimension of the output of the polynomials.
`one`()	Coefficients and corresponding indices for the decomposition of the constant function 1.
`poly_coeff`(ind)	Compute the coefficients of the monomials used to create the polynomials of degree specified in ind.
`polyval`(ind, x)	Evaluate the polynomials of degrees contained in ind at the points x.
`random`(ind[, n, measure])	Return an array of size n of random evaluations of the polynomials for which the degree is in ind.
`roots`(deg)	Return the roots of the polynomial of degree deg.
`truncated_domain`()	Return the truncated support of the associated measure.

class tensap.functions.polynomials.orthonormal_polynomials.LegendrePolynomials(n=50)¶

Bases: tensap.functions.polynomials.orthonormal_polynomials.OrthonormalPolynomials

Class LegendrePolynomials.

Polynomials defined on [-1,1], orthonormal with respect to the standard uniform measure 1/2.

Methods

`d_poly_coef`(ind)	Return the coefficients of the first order derivative of the polynomials of degrees contained in ind.
`d_polyval`(ind, x)	Evaluate the first order derivative of the polynomials of degrees contained in ind at the points x.
`dn_poly_coeff`(n, ind)	Return the coefficients of the n-th order derivative of the polynomials of degrees contained in ind.
`dn_polyval`(n, ind, x)	Evaluate the n-th order derivative of the polynomials of degrees contained in ind at the points x.
`domain`()	Return the support of the associated measure.
`is_orthonormal`()	Check the orthonormality of the basis created by the functions of self.
`mean`(ind[, measure])	Return the mean of the polynomials of degrees contained in ind, with a Measure given by measure if provided, or to self.measure otherwise.
`moment`(ind[, measure])	Return the integral of products of polynomials p_i, i in ind, using a gauss integration rule.
`ndim`()	Return the dimension of the output of the polynomials.
`one`()	Coefficients and corresponding indices for the decomposition of the constant function 1.
`poly_coeff`(ind)	Compute the coefficients of the monomials used to create the polynomials of degree specified in ind.
`polyval`(ind, x)	Evaluate the polynomials of degrees contained in ind at the points x.
`random`(ind[, n, measure])	Return an array of size n of random evaluations of the polynomials for which the degree is in ind.
`roots`(deg)	Return the roots of the polynomial of degree deg.
`truncated_domain`()	Return the truncated support of the associated measure.

class tensap.functions.polynomials.orthonormal_polynomials.OrthonormalPolynomials¶

Bases: tensap.functions.polynomials.polynomials.UnivariatePolynomials

Class OrthonormalPolynomials.

Attributes

measuretensap.Measure: The measure associated with the orthonormal polynomials.

Methods

`d_poly_coef`(ind)	Return the coefficients of the first order derivative of the polynomials of degrees contained in ind.
`d_polyval`(ind, x)	Evaluate the first order derivative of the polynomials of degrees contained in ind at the points x.
`dn_poly_coeff`(n, ind)	Return the coefficients of the n-th order derivative of the polynomials of degrees contained in ind.
`dn_polyval`(n, ind, x)	Evaluate the n-th order derivative of the polynomials of degrees contained in ind at the points x.
`domain`()	Return the support of the associated measure.
`is_orthonormal`()	Check the orthonormality of the basis created by the functions of self.
`mean`(ind[, measure])	Return the mean of the polynomials of degrees contained in ind, with a Measure given by measure if provided, or to self.measure otherwise.
`moment`(ind[, measure])	Return the integral of products of polynomials p_i, i in ind, using a gauss integration rule.
`ndim`()	Return the dimension of the output of the polynomials.
`one`()	Coefficients and corresponding indices for the decomposition of the constant function 1.
`poly_coeff`(ind)	Compute the coefficients of the monomials used to create the polynomials of degree specified in ind.
`polyval`(ind, x)	Evaluate the polynomials of degrees contained in ind at the points x.
`random`(ind[, n, measure])	Return an array of size n of random evaluations of the polynomials for which the degree is in ind.
`roots`(deg)	Return the roots of the polynomial of degree deg.
`truncated_domain`()	Return the truncated support of the associated measure.

d_polyval(ind, x)¶

Evaluate the first order derivative of the polynomials of degrees contained in ind at the points x.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials to be evaluated.
xlist or numpy.ndarray: The points at which the derivatives of the polynomials are to be evaluated.

Returns

numpy.ndarray: The evaluation of the first order derivatives of the selected polynomials at the points x.

dn_polyval(n, ind, x)¶

Evaluate the n-th order derivative of the polynomials of degrees contained in ind at the points x.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials to be evaluated.
xlist or numpy.ndarray: The points at which the derivatives of the polynomials are to be evaluated.

Returns

numpy.ndarray: The evaluation of the n-th order derivatives of the selected polynomials at the points x.

domain()¶

Return the support of the associated measure.

Returns

numpy.ndarray: The support of the associated measure.

static is_orthonormal()¶

Check the orthonormality of the basis created by the functions of self.

Returns

bool: Indicates if the polynomials are orthonormal.

moment(ind, measure=None)¶

Return the integral of products of polynomials p_i, i in ind, using a gauss integration rule.

The integral is with respect to a measure mu which is taken as the measure to the polynomials if not provided in input

Assuming ind is a numpy.ndarray:

if ind.ndim == 1, and ind is of length N, return the float
m = int p_ind[0](x)…p_ind[N-1](x) dmu(x),
else if ind.ndim == 2, and ind is N-by-M,
return the vector m of length N such that m[j] = int p_ind[j, 0](x)…p_ind[j, M-1](x) dmu(x)

Parameters

indlist or numpy.ndarray: Contains the degrees of the considered polynomials.
measuretensap.Measure, optional: The measure used for the computation of the moments. The default is None, indicating to use self.measure.

Returns

numpy.ndarray: Contains the integrals of products of polynomials.

static one()¶: Coefficients and corresponding indices for the decomposition of the constant function 1.

poly_coeff(ind)¶

Compute the coefficients of the monomials used to create the polynomials of degree specified in ind.

Parameters

indind or numpy.ndarray: The orders of the polynomials to be evaluated.

polyval(ind, x)¶

Evaluate the polynomials of degrees contained in ind at the points x.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials to be evaluated.
xlist or numpy.ndarray: The points at which the polynomials are to be evaluated.

Returns

numpy.ndarray: The evaluation of the selected polynomials at the points x.

random(ind, n=1, measure=None)¶

Return an array of size n of random evaluations of the polynomials for which the degree is in ind. If measure is not provided, the random generation is performed using self.measure.

Parameters

indlist or numpy.ndarray: The indices of the polynomials to be evaluated.
nint, optional: The number of random evaluations. The default is 1.
measuretensap.ProbabilityMeasure, optional: The probability measure used for the generation of the input points. The default is None, indicating to use self.measure.

Returns

outnumpy.ndarray: The random evaluations of the polynomials.
xnumpy.ndarray: The randomly drawn input points.

roots(deg)¶

Return the roots of the polynomial of degree deg.

Parameters

degint: The degree of the polynomial for which the roots are to be computed.

Returns

numpy.ndarray: The roots of the polynomial of degree deg.

truncated_domain()¶

Return the truncated support of the associated measure.

Returns

numpy.ndarray: The truncated support of the associated measure.

class tensap.functions.polynomials.orthonormal_polynomials.ShiftedOrthonormalPolynomials(polynomials, shift, scaling)¶

Bases: tensap.functions.polynomials.polynomials.UnivariatePolynomials

Class ShiftedOrthonormalPolynomials.

Attributes

measuretensap.Measure: The measure associated with the ShiftedOrthonormalPolynomials.
polynomialstensap.OrthonormalPolynomials: The OrthonormalPolynomials which are shifted.
shiftfloat: The shifting parameter.
scalingfloat: The scaling parameter.

Methods

`d_poly_coef`(ind)	Return the coefficients of the first order derivative of the polynomials of degrees contained in ind.
`d_polyval`(ind, x)	Evaluate the first order derivative of the polynomials of degrees contained in ind at the points x.
`dn_poly_coeff`(n, ind)	Return the coefficients of the n-th order derivative of the polynomials of degrees contained in ind.
`dn_polyval`(n, ind, x)	Evaluate the n-th order derivative of the polynomials of degrees contained in ind at the points x.
`domain`()	Return the support of the associated shifted measure.
`is_orthonormal`()	Check the orthonormality of the basis created by the functions of self.
`mean`(ind, *measure)	Return the mean of the polynomials of degrees contained in ind, with a Measure given by measure if provided, or to self.measure otherwise.
`moment`(ind, *measure)	Return the integral of products of polynomials p_i, i in ind, using a gauss integration rule.
`ndim`()	Return the dimension of the output of the polynomials.
`one`()	Coefficients and corresponding indices for the decomposition of the constant function 1.
`poly_coeff`()	Compute the coefficients of the monomials used to create the polynomials of degree specified in ind.
`polyval`(ind, x)	Evaluate the polynomials of degrees contained in ind at the points x.
`random`(ind[, n, measure])	Return an array of size n of random evaluations of the shifted polynomials for which the degree is in ind.
`roots`(n)	Return the roots of the shifted polynomial of degree deg.
`truncated_domain`()	Return the truncated support of the associated shifted measure.

d_polyval(ind, x)¶

Evaluate the first order derivative of the polynomials of degrees contained in ind at the points x.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials to be evaluated.
xlist or numpy.ndarray: The points at which the derivatives of the polynomials are to be evaluated.

Returns

numpy.ndarray: The evaluation of the first order derivatives of the selected polynomials at the points x.

dn_polyval(n, ind, x)¶

Evaluate the n-th order derivative of the polynomials of degrees contained in ind at the points x.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials to be evaluated.
xlist or numpy.ndarray: The points at which the derivatives of the polynomials are to be evaluated.

Returns

numpy.ndarray: The evaluation of the n-th order derivatives of the selected polynomials at the points x.

domain()¶

Return the support of the associated shifted measure.

Returns

numpy.ndarray: The support of the associated measure.

static is_orthonormal()¶

Check the orthonormality of the basis created by the functions of self.

Returns

bool: Indicates if the polynomials are orthonormal.

mean(ind, *measure)¶

Return the mean of the polynomials of degrees contained in ind, with a Measure given by measure if provided, or to self.measure otherwise.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials for which the mean is to be computed.
measuretensap.Measure, optional: The measure used for the computation of the mean. The default is None, indicating to use self.measure.

Returns

numpy.ndarray: The mean of the selected polynomials.

moment(ind, *measure)¶

Return the integral of products of polynomials p_i, i in ind, using a gauss integration rule.

The integral is with respect to a measure mu which is taken as the measure to the polynomials if not provided in input

Assuming ind is a numpy.ndarray:

if ind.ndim == 1, and ind is of length N, return the float
m = int p_ind[0](x)…p_ind[N-1](x) dmu(x),
else if ind.ndim == 2, and ind is N-by-M,
return the vector m of length N such that m[j] = int p_ind[j, 0](x)…p_ind[j, M-1](x) dmu(x)

Parameters

indlist or numpy.ndarray: Contains the degrees of the considered polynomials.
measuretensap.Measure, optional: The measure used for the computation of the moments. The default is None, indicating to use self.measure.

Returns

numpy.ndarray: Contains the integrals of products of polynomials.

static ndim()¶

Return the dimension of the output of the polynomials.

Returns

int: The dimension of the output of the polynomials.

static one()¶: Coefficients and corresponding indices for the decomposition of the constant function 1.

static poly_coeff()¶

Compute the coefficients of the monomials used to create the polynomials of degree specified in ind.

Parameters

indind or numpy.ndarray: The orders of the polynomials to be evaluated.

polyval(ind, x)¶

Evaluate the polynomials of degrees contained in ind at the points x.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials to be evaluated.
xlist or numpy.ndarray: The points at which the polynomials are to be evaluated.

Returns

numpy.ndarray: The evaluation of the selected polynomials at the points x.

random(ind, n=1, measure=None)¶

Return an array of size n of random evaluations of the shifted polynomials for which the degree is in ind. If measure is not provided, the random generation is performed using self.measure.

Parameters

indlist or numpy.ndarray: The indices of the polynomials to be evaluated.
nint, optional: The number of random evaluations. The default is 1.
measuretensap.ProbabilityMeasure, optional: The probability measure used for the generation of the input points. The default is None, indicating to use self.measure.

Returns

fxnumpy.ndarray: The random evaluations of the polynomials.
xnumpy.ndarray: The randomly drawn input points.

roots(n)¶

Return the roots of the shifted polynomial of degree deg.

Parameters

degint: The degree of the polynomial for which the roots are to be computed.

Returns

numpy.ndarray: The roots of the polynomial of degree deg.

truncated_domain()¶

Return the truncated support of the associated shifted measure.

Returns

numpy.ndarray: The truncated support of the associated measure.

tensap.functions.polynomials.polynomials module¶

Module polynomials.

class tensap.functions.polynomials.polynomials.CanonicalPolynomials(measure=None)¶

Bases: tensap.functions.polynomials.polynomials.UnivariatePolynomials

Class CanonicalPolynomials.

Attributes

measureNone or tensap.Measure: The measure associated with the canonical polynomials.

Methods

`d_poly_coef`(ind)	Return the coefficients of the first order derivative of the polynomials of degrees contained in ind.
`d_polyval`(ind, x)	Evaluate the first order derivative of the polynomials of degrees contained in ind at the points x.
`dn_poly_coeff`(n, ind)	Return the coefficients of the n-th order derivative of the polynomials of degrees contained in ind.
`dn_polyval`(n, ind, x)	Evaluate the n-th order derivative of the polynomials of degrees contained in ind at the points x.
`domain`()	Return the domain of the canonical polynomials.
`is_orthonormal`()	Check the orthonormality of the basis created by the functions of self.
`mean`(ind[, measure])	Return the mean of the polynomials of degrees contained in ind, with a Measure given by measure if provided, or to self.measure otherwise.
`moment`(ind[, measure])	Return the integral of products of polynomials p_i, i in ind, using a gauss integration rule.
`ndim`()	Return the dimension of the output of the polynomials.
`one`()	Coefficients and corresponding indices for the decomposition of the constant function 1.
`poly_coeff`(ind)	Compute the coefficients of the monomials used to create the polynomials of degree specified in ind.
`polyval`(ind, x)	Evaluate the polynomials of degrees contained in ind at the points x.

d_polyval(ind, x)¶

Evaluate the first order derivative of the polynomials of degrees contained in ind at the points x.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials to be evaluated.
xlist or numpy.ndarray: The points at which the derivatives of the polynomials are to be evaluated.

Returns

numpy.ndarray: The evaluation of the first order derivatives of the selected polynomials at the points x.

static domain()¶

Return the domain of the canonical polynomials.

Returns

list: The domain of the canonical polynomials.

static is_orthonormal()¶

Check the orthonormality of the basis created by the functions of self.

Returns

bool: Indicates if the polynomials are orthonormal.

static one()¶: Coefficients and corresponding indices for the decomposition of the constant function 1.

poly_coeff(ind)¶

Compute the coefficients of the monomials used to create the polynomials of degree specified in ind.

Parameters

indind or numpy.ndarray: The orders of the polynomials to be evaluated.

class tensap.functions.polynomials.polynomials.UnivariatePolynomials¶

Bases: abc.ABC

Class UnivariatePolynomials.

Methods

`d_poly_coef`(ind)	Return the coefficients of the first order derivative of the polynomials of degrees contained in ind.
`d_polyval`(ind, x)	Evaluate the first order derivative of the polynomials of degrees contained in ind at the points x.
`dn_poly_coeff`(n, ind)	Return the coefficients of the n-th order derivative of the polynomials of degrees contained in ind.
`dn_polyval`(n, ind, x)	Evaluate the n-th order derivative of the polynomials of degrees contained in ind at the points x.
`is_orthonormal`()	Check the orthonormality of the basis created by the functions of self.
`mean`(ind[, measure])	Return the mean of the polynomials of degrees contained in ind, with a Measure given by measure if provided, or to self.measure otherwise.
`moment`(ind[, measure])	Return the integral of products of polynomials p_i, i in ind, using a gauss integration rule.
`ndim`()	Return the dimension of the output of the polynomials.
`one`()	Coefficients and corresponding indices for the decomposition of the constant function 1.
`poly_coeff`(ind)	Compute the coefficients of the monomials used to create the polynomials of degree specified in ind.
`polyval`(ind, x)	Evaluate the polynomials of degrees contained in ind at the points x.

d_poly_coef(ind)¶

Return the coefficients of the first order derivative of the polynomials of degrees contained in ind.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials to be evaluated.

Returns

numpy.ndarray: The coefficients of the first order derivative of the polynomials of order contained in ind.

d_polyval(ind, x)¶

Evaluate the first order derivative of the polynomials of degrees contained in ind at the points x.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials to be evaluated.
xlist or numpy.ndarray: The points at which the derivatives of the polynomials are to be evaluated.

Returns

numpy.ndarray: The evaluation of the first order derivatives of the selected polynomials at the points x.

dn_poly_coeff(n, ind)¶

Return the coefficients of the n-th order derivative of the polynomials of degrees contained in ind.

Parameters

nint: The degrees of derivation of the polynomials.
indlist or numpy.ndarray: The orders of the polynomials to be evaluated.

Returns

numpy.ndarray: The coefficients of the n-th order derivative of the polynomials of order contained in ind.

dn_polyval(n, ind, x)¶

Evaluate the n-th order derivative of the polynomials of degrees contained in ind at the points x.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials to be evaluated.
xlist or numpy.ndarray: The points at which the derivatives of the polynomials are to be evaluated.

Returns

numpy.ndarray: The evaluation of the n-th order derivatives of the selected polynomials at the points x.

abstract is_orthonormal()¶

Check the orthonormality of the basis created by the functions of self.

Returns

bool: Indicates if the polynomials are orthonormal.

mean(ind, measure=None)¶

Return the mean of the polynomials of degrees contained in ind, with a Measure given by measure if provided, or to self.measure otherwise.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials for which the mean is to be computed.
measuretensap.Measure, optional: The measure used for the computation of the mean. The default is None, indicating to use self.measure.

Returns

numpy.ndarray: The mean of the selected polynomials.

moment(ind, measure=None)¶

Return the integral of products of polynomials p_i, i in ind, using a gauss integration rule.

The integral is with respect to a measure mu which is taken as the measure to the polynomials if not provided in input

Assuming ind is a numpy.ndarray:

if ind.ndim == 1, and ind is of length N, return the float
m = int p_ind[0](x)…p_ind[N-1](x) dmu(x),
else if ind.ndim == 2, and ind is N-by-M,
return the vector m of length N such that m[j] = int p_ind[j, 0](x)…p_ind[j, M-1](x) dmu(x)

Parameters

indlist or numpy.ndarray: Contains the degrees of the considered polynomials.
measuretensap.Measure, optional: The measure used for the computation of the moments. The default is None, indicating to use self.measure.

Returns

numpy.ndarray: Contains the integrals of products of polynomials.

static ndim()¶

Return the dimension of the output of the polynomials.

Returns

int: The dimension of the output of the polynomials.

abstract one()¶: Coefficients and corresponding indices for the decomposition of the constant function 1.

abstract poly_coeff(ind)¶

Compute the coefficients of the monomials used to create the polynomials of degree specified in ind.

Parameters

indind or numpy.ndarray: The orders of the polynomials to be evaluated.

polyval(ind, x)¶

Evaluate the polynomials of degrees contained in ind at the points x.

Parameters

indlist or numpy.ndarray: The degrees of the polynomials to be evaluated.
xlist or numpy.ndarray: The points at which the polynomials are to be evaluated.

Returns

numpy.ndarray: The evaluation of the selected polynomials at the points x.

tensap.functions.polynomials package¶

Submodules¶

tensap.functions.polynomials.orthonormal_polynomials module¶

tensap.functions.polynomials.polynomials module¶

Module contents¶

tensap

Navigation

Related Topics