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numpy.polynomial.laguerre.lagadd polynomial.laguerre.lagadd(c1, c2)[source]
Add one Laguerre series to another. Returns the sum of two Laguerre series c1 + c2. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2. Parameters ... | numpy.reference.generated.numpy.polynomial.laguerre.lagadd |
numpy.polynomial.laguerre.lagcompanion polynomial.laguerre.lagcompanion(c)[source]
Return the companion matrix of c. The usual companion matrix of the Laguerre polynomials is already symmetric when c is a basis Laguerre polynomial, so no scaling is applied. Parameters
carray_like
1-D array of Laguerre series ... | numpy.reference.generated.numpy.polynomial.laguerre.lagcompanion |
numpy.polynomial.laguerre.lagder polynomial.laguerre.lagder(c, m=1, scl=1, axis=0)[source]
Differentiate a Laguerre series. Returns the Laguerre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). ... | numpy.reference.generated.numpy.polynomial.laguerre.lagder |
numpy.polynomial.laguerre.lagdiv polynomial.laguerre.lagdiv(c1, c2)[source]
Divide one Laguerre series by another. Returns the quotient-with-remainder of two Laguerre series c1 / c2. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1,2,3] represents the series P_0 + 2*P_1 + 3*... | numpy.reference.generated.numpy.polynomial.laguerre.lagdiv |
numpy.polynomial.laguerre.lagdomain polynomial.laguerre.lagdomain = array([0, 1])
An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it i... | numpy.reference.generated.numpy.polynomial.laguerre.lagdomain |
numpy.polynomial.laguerre.lagfit polynomial.laguerre.lagfit(x, y, deg, rcond=None, full=False, w=None)[source]
Least squares fit of Laguerre series to data. Return the coefficients of a Laguerre series of degree deg that is the least squares fit to the data values y given at points x. If y is 1-D the returned coeff... | numpy.reference.generated.numpy.polynomial.laguerre.lagfit |
numpy.polynomial.laguerre.lagfromroots polynomial.laguerre.lagfromroots(roots)[source]
Generate a Laguerre series with given roots. The function returns the coefficients of the polynomial \[p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),\] in Laguerre form, where the r_n are the roots specified in roots. If a zero... | numpy.reference.generated.numpy.polynomial.laguerre.lagfromroots |
numpy.polynomial.laguerre.laggauss polynomial.laguerre.laggauss(deg)[source]
Gauss-Laguerre quadrature. Computes the sample points and weights for Gauss-Laguerre quadrature. These sample points and weights will correctly integrate polynomials of degree \(2*deg - 1\) or less over the interval \([0, \inf]\) with the ... | numpy.reference.generated.numpy.polynomial.laguerre.laggauss |
numpy.polynomial.laguerre.laggrid2d polynomial.laguerre.laggrid2d(x, y, c)[source]
Evaluate a 2-D Laguerre series on the Cartesian product of x and y. This function returns the values: \[p(a,b) = \sum_{i,j} c_{i,j} * L_i(a) * L_j(b)\] where the points (a, b) consist of all pairs formed by taking a from x and b fro... | numpy.reference.generated.numpy.polynomial.laguerre.laggrid2d |
numpy.polynomial.laguerre.laggrid3d polynomial.laguerre.laggrid3d(x, y, z, c)[source]
Evaluate a 3-D Laguerre series on the Cartesian product of x, y, and z. This function returns the values: \[p(a,b,c) = \sum_{i,j,k} c_{i,j,k} * L_i(a) * L_j(b) * L_k(c)\] where the points (a, b, c) consist of all triples formed b... | numpy.reference.generated.numpy.polynomial.laguerre.laggrid3d |
numpy.polynomial.laguerre.lagint polynomial.laguerre.lagint(c, m=1, k=[], lbnd=0, scl=1, axis=0)[source]
Integrate a Laguerre series. Returns the Laguerre series coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is add... | numpy.reference.generated.numpy.polynomial.laguerre.lagint |
numpy.polynomial.laguerre.lagline polynomial.laguerre.lagline(off, scl)[source]
Laguerre series whose graph is a straight line. Parameters
off, sclscalars
The specified line is given by off + scl*x. Returns
yndarray
This module’s representation of the Laguerre series for off + scl*x. See also nu... | numpy.reference.generated.numpy.polynomial.laguerre.lagline |
numpy.polynomial.laguerre.lagmul polynomial.laguerre.lagmul(c1, c2)[source]
Multiply one Laguerre series by another. Returns the product of two Laguerre series c1 * c2. The arguments are sequences of coefficients, from lowest order “term” to highest, e.g., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2. Paramet... | numpy.reference.generated.numpy.polynomial.laguerre.lagmul |
numpy.polynomial.laguerre.lagmulx polynomial.laguerre.lagmulx(c)[source]
Multiply a Laguerre series by x. Multiply the Laguerre series c by x, where x is the independent variable. Parameters
carray_like
1-D array of Laguerre series coefficients ordered from low to high. Returns
outndarray
Array repres... | numpy.reference.generated.numpy.polynomial.laguerre.lagmulx |
numpy.polynomial.laguerre.lagone polynomial.laguerre.lagone = array([1])
An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an inte... | numpy.reference.generated.numpy.polynomial.laguerre.lagone |
numpy.polynomial.laguerre.lagpow polynomial.laguerre.lagpow(c, pow, maxpower=16)[source]
Raise a Laguerre series to a power. Returns the Laguerre series c raised to the power pow. The argument c is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series P_0 + 2*P_1 + 3*P_2. Parameters
c... | numpy.reference.generated.numpy.polynomial.laguerre.lagpow |
numpy.polynomial.laguerre.lagroots polynomial.laguerre.lagroots(c)[source]
Compute the roots of a Laguerre series. Return the roots (a.k.a. “zeros”) of the polynomial \[p(x) = \sum_i c[i] * L_i(x).\] Parameters
c1-D array_like
1-D array of coefficients. Returns
outndarray
Array of the roots of the se... | numpy.reference.generated.numpy.polynomial.laguerre.lagroots |
numpy.polynomial.laguerre.lagsub polynomial.laguerre.lagsub(c1, c2)[source]
Subtract one Laguerre series from another. Returns the difference of two Laguerre series c1 - c2. The sequences of coefficients are from lowest order term to highest, i.e., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2. Parameters
c... | numpy.reference.generated.numpy.polynomial.laguerre.lagsub |
numpy.polynomial.laguerre.lagtrim polynomial.laguerre.lagtrim(c, tol=0)[source]
Remove “small” “trailing” coefficients from a polynomial. “Small” means “small in absolute value” and is controlled by the parameter tol; “trailing” means highest order coefficient(s), e.g., in [0, 1, 1, 0, 0] (which represents 0 + x + ... | numpy.reference.generated.numpy.polynomial.laguerre.lagtrim |
numpy.polynomial.laguerre.Laguerre.__call__ method polynomial.laguerre.Laguerre.__call__(arg)[source]
Call self as a function. | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.__call__ |
numpy.polynomial.laguerre.Laguerre.basis method classmethod polynomial.laguerre.Laguerre.basis(deg, domain=None, window=None)[source]
Series basis polynomial of degree deg. Returns the series representing the basis polynomial of degree deg. New in version 1.7.0. Parameters
degint
Degree of the basis polynom... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.basis |
numpy.polynomial.laguerre.Laguerre.cast method classmethod polynomial.laguerre.Laguerre.cast(series, domain=None, window=None)[source]
Convert series to series of this class. The series is expected to be an instance of some polynomial series of one of the types supported by by the numpy.polynomial module, but could... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.cast |
numpy.polynomial.laguerre.Laguerre.convert method polynomial.laguerre.Laguerre.convert(domain=None, kind=None, window=None)[source]
Convert series to a different kind and/or domain and/or window. Parameters
domainarray_like, optional
The domain of the converted series. If the value is None, the default domain... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.convert |
numpy.polynomial.laguerre.Laguerre.copy method polynomial.laguerre.Laguerre.copy()[source]
Return a copy. Returns
new_seriesseries
Copy of self. | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.copy |
numpy.polynomial.laguerre.Laguerre.cutdeg method polynomial.laguerre.Laguerre.cutdeg(deg)[source]
Truncate series to the given degree. Reduce the degree of the series to deg by discarding the high order terms. If deg is greater than the current degree a copy of the current series is returned. This can be useful in ... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.cutdeg |
numpy.polynomial.laguerre.Laguerre.degree method polynomial.laguerre.Laguerre.degree()[source]
The degree of the series. New in version 1.5.0. Returns
degreeint
Degree of the series, one less than the number of coefficients. | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.degree |
numpy.polynomial.laguerre.Laguerre.deriv method polynomial.laguerre.Laguerre.deriv(m=1)[source]
Differentiate. Return a series instance of that is the derivative of the current series. Parameters
mnon-negative int
Find the derivative of order m. Returns
new_seriesseries
A new series representing the d... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.deriv |
numpy.polynomial.laguerre.Laguerre.domain attribute polynomial.laguerre.Laguerre.domain = array([0, 1]) | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.domain |
numpy.polynomial.laguerre.Laguerre.fit method classmethod polynomial.laguerre.Laguerre.fit(x, y, deg, domain=None, rcond=None, full=False, w=None, window=None)[source]
Least squares fit to data. Return a series instance that is the least squares fit to the data y sampled at x. The domain of the returned instance ca... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.fit |
numpy.polynomial.laguerre.Laguerre.fromroots method classmethod polynomial.laguerre.Laguerre.fromroots(roots, domain=[], window=None)[source]
Return series instance that has the specified roots. Returns a series representing the product (x - r[0])*(x - r[1])*...*(x - r[n-1]), where r is a list of roots. Parameters... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.fromroots |
numpy.polynomial.laguerre.Laguerre.has_samecoef method polynomial.laguerre.Laguerre.has_samecoef(other)[source]
Check if coefficients match. New in version 1.6.0. Parameters
otherclass instance
The other class must have the coef attribute. Returns
boolboolean
True if the coefficients are the same, F... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.has_samecoef |
numpy.polynomial.laguerre.Laguerre.has_samedomain method polynomial.laguerre.Laguerre.has_samedomain(other)[source]
Check if domains match. New in version 1.6.0. Parameters
otherclass instance
The other class must have the domain attribute. Returns
boolboolean
True if the domains are the same, False... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.has_samedomain |
numpy.polynomial.laguerre.Laguerre.has_sametype method polynomial.laguerre.Laguerre.has_sametype(other)[source]
Check if types match. New in version 1.7.0. Parameters
otherobject
Class instance. Returns
boolboolean
True if other is same class as self | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.has_sametype |
numpy.polynomial.laguerre.Laguerre.has_samewindow method polynomial.laguerre.Laguerre.has_samewindow(other)[source]
Check if windows match. New in version 1.6.0. Parameters
otherclass instance
The other class must have the window attribute. Returns
boolboolean
True if the windows are the same, False... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.has_samewindow |
numpy.polynomial.laguerre.Laguerre.identity method classmethod polynomial.laguerre.Laguerre.identity(domain=None, window=None)[source]
Identity function. If p is the returned series, then p(x) == x for all values of x. Parameters
domain{None, array_like}, optional
If given, the array must be of the form [beg,... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.identity |
numpy.polynomial.laguerre.Laguerre.integ method polynomial.laguerre.Laguerre.integ(m=1, k=[], lbnd=None)[source]
Integrate. Return a series instance that is the definite integral of the current series. Parameters
mnon-negative int
The number of integrations to perform.
karray_like
Integration constants. T... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.integ |
numpy.polynomial.laguerre.Laguerre.linspace method polynomial.laguerre.Laguerre.linspace(n=100, domain=None)[source]
Return x, y values at equally spaced points in domain. Returns the x, y values at n linearly spaced points across the domain. Here y is the value of the polynomial at the points x. By default the dom... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.linspace |
numpy.polynomial.laguerre.Laguerre.mapparms method polynomial.laguerre.Laguerre.mapparms()[source]
Return the mapping parameters. The returned values define a linear map off + scl*x that is applied to the input arguments before the series is evaluated. The map depends on the domain and window; if the current domain... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.mapparms |
numpy.polynomial.laguerre.Laguerre.roots method polynomial.laguerre.Laguerre.roots()[source]
Return the roots of the series polynomial. Compute the roots for the series. Note that the accuracy of the roots decrease the further outside the domain they lie. Returns
rootsndarray
Array containing the roots of the... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.roots |
numpy.polynomial.laguerre.Laguerre.trim method polynomial.laguerre.Laguerre.trim(tol=0)[source]
Remove trailing coefficients Remove trailing coefficients until a coefficient is reached whose absolute value greater than tol or the beginning of the series is reached. If all the coefficients would be removed the serie... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.trim |
numpy.polynomial.laguerre.Laguerre.truncate method polynomial.laguerre.Laguerre.truncate(size)[source]
Truncate series to length size. Reduce the series to length size by discarding the high degree terms. The value of size must be a positive integer. This can be useful in least squares where the coefficients of the... | numpy.reference.generated.numpy.polynomial.laguerre.laguerre.truncate |
numpy.polynomial.laguerre.lagval polynomial.laguerre.lagval(x, c, tensor=True)[source]
Evaluate a Laguerre series at points x. If c is of length n + 1, this function returns the value: \[p(x) = c_0 * L_0(x) + c_1 * L_1(x) + ... + c_n * L_n(x)\] The parameter x is converted to an array only if it is a tuple or a li... | numpy.reference.generated.numpy.polynomial.laguerre.lagval |
numpy.polynomial.laguerre.lagval2d polynomial.laguerre.lagval2d(x, y, c)[source]
Evaluate a 2-D Laguerre series at points (x, y). This function returns the values: \[p(x,y) = \sum_{i,j} c_{i,j} * L_i(x) * L_j(y)\] The parameters x and y are converted to arrays only if they are tuples or a lists, otherwise they are... | numpy.reference.generated.numpy.polynomial.laguerre.lagval2d |
numpy.polynomial.laguerre.lagval3d polynomial.laguerre.lagval3d(x, y, z, c)[source]
Evaluate a 3-D Laguerre series at points (x, y, z). This function returns the values: \[p(x,y,z) = \sum_{i,j,k} c_{i,j,k} * L_i(x) * L_j(y) * L_k(z)\] The parameters x, y, and z are converted to arrays only if they are tuples or a ... | numpy.reference.generated.numpy.polynomial.laguerre.lagval3d |
numpy.polynomial.laguerre.lagvander polynomial.laguerre.lagvander(x, deg)[source]
Pseudo-Vandermonde matrix of given degree. Returns the pseudo-Vandermonde matrix of degree deg and sample points x. The pseudo-Vandermonde matrix is defined by \[V[..., i] = L_i(x)\] where 0 <= i <= deg. The leading indices of V inde... | numpy.reference.generated.numpy.polynomial.laguerre.lagvander |
numpy.polynomial.laguerre.lagvander2d polynomial.laguerre.lagvander2d(x, y, deg)[source]
Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y). The pseudo-Vandermonde matrix is defined by \[V[..., (deg[1] + 1)*i + j] = L_i(x) * L_j(y),\] where 0 <... | numpy.reference.generated.numpy.polynomial.laguerre.lagvander2d |
numpy.polynomial.laguerre.lagvander3d polynomial.laguerre.lagvander3d(x, y, z, deg)[source]
Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y, z). If l, m, n are the given degrees in x, y, z, then The pseudo-Vandermonde matrix is defined by \[V... | numpy.reference.generated.numpy.polynomial.laguerre.lagvander3d |
numpy.polynomial.laguerre.lagweight polynomial.laguerre.lagweight(x)[source]
Weight function of the Laguerre polynomials. The weight function is \(exp(-x)\) and the interval of integration is \([0, \inf]\). The Laguerre polynomials are orthogonal, but not normalized, with respect to this weight function. Parameter... | numpy.reference.generated.numpy.polynomial.laguerre.lagweight |
numpy.polynomial.laguerre.lagx polynomial.laguerre.lagx = array([ 1, -1])
An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an int... | numpy.reference.generated.numpy.polynomial.laguerre.lagx |
numpy.polynomial.laguerre.lagzero polynomial.laguerre.lagzero = array([0])
An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an in... | numpy.reference.generated.numpy.polynomial.laguerre.lagzero |
numpy.polynomial.laguerre.poly2lag polynomial.laguerre.poly2lag(pol)[source]
Convert a polynomial to a Laguerre series. Convert an array representing the coefficients of a polynomial (relative to the “standard” basis) ordered from lowest degree to highest, to an array of the coefficients of the equivalent Laguerre ... | numpy.reference.generated.numpy.polynomial.laguerre.poly2lag |
numpy.polynomial.legendre.leg2poly polynomial.legendre.leg2poly(c)[source]
Convert a Legendre series to a polynomial. Convert an array representing the coefficients of a Legendre series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the “standard” b... | numpy.reference.generated.numpy.polynomial.legendre.leg2poly |
numpy.polynomial.legendre.legadd polynomial.legendre.legadd(c1, c2)[source]
Add one Legendre series to another. Returns the sum of two Legendre series c1 + c2. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2. Parameters ... | numpy.reference.generated.numpy.polynomial.legendre.legadd |
numpy.polynomial.legendre.legcompanion polynomial.legendre.legcompanion(c)[source]
Return the scaled companion matrix of c. The basis polynomials are scaled so that the companion matrix is symmetric when c is an Legendre basis polynomial. This provides better eigenvalue estimates than the unscaled case and for basi... | numpy.reference.generated.numpy.polynomial.legendre.legcompanion |
numpy.polynomial.legendre.legder polynomial.legendre.legder(c, m=1, scl=1, axis=0)[source]
Differentiate a Legendre series. Returns the Legendre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). ... | numpy.reference.generated.numpy.polynomial.legendre.legder |
numpy.polynomial.legendre.legdiv polynomial.legendre.legdiv(c1, c2)[source]
Divide one Legendre series by another. Returns the quotient-with-remainder of two Legendre series c1 / c2. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1,2,3] represents the series P_0 + 2*P_1 + 3*... | numpy.reference.generated.numpy.polynomial.legendre.legdiv |
numpy.polynomial.legendre.legdomain polynomial.legendre.legdomain = array([-1, 1])
An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it ... | numpy.reference.generated.numpy.polynomial.legendre.legdomain |
numpy.polynomial.legendre.Legendre.__call__ method polynomial.legendre.Legendre.__call__(arg)[source]
Call self as a function. | numpy.reference.generated.numpy.polynomial.legendre.legendre.__call__ |
numpy.polynomial.legendre.Legendre.basis method classmethod polynomial.legendre.Legendre.basis(deg, domain=None, window=None)[source]
Series basis polynomial of degree deg. Returns the series representing the basis polynomial of degree deg. New in version 1.7.0. Parameters
degint
Degree of the basis polynom... | numpy.reference.generated.numpy.polynomial.legendre.legendre.basis |
numpy.polynomial.legendre.Legendre.cast method classmethod polynomial.legendre.Legendre.cast(series, domain=None, window=None)[source]
Convert series to series of this class. The series is expected to be an instance of some polynomial series of one of the types supported by by the numpy.polynomial module, but could... | numpy.reference.generated.numpy.polynomial.legendre.legendre.cast |
numpy.polynomial.legendre.Legendre.convert method polynomial.legendre.Legendre.convert(domain=None, kind=None, window=None)[source]
Convert series to a different kind and/or domain and/or window. Parameters
domainarray_like, optional
The domain of the converted series. If the value is None, the default domain... | numpy.reference.generated.numpy.polynomial.legendre.legendre.convert |
numpy.polynomial.legendre.Legendre.copy method polynomial.legendre.Legendre.copy()[source]
Return a copy. Returns
new_seriesseries
Copy of self. | numpy.reference.generated.numpy.polynomial.legendre.legendre.copy |
numpy.polynomial.legendre.Legendre.cutdeg method polynomial.legendre.Legendre.cutdeg(deg)[source]
Truncate series to the given degree. Reduce the degree of the series to deg by discarding the high order terms. If deg is greater than the current degree a copy of the current series is returned. This can be useful in ... | numpy.reference.generated.numpy.polynomial.legendre.legendre.cutdeg |
numpy.polynomial.legendre.Legendre.degree method polynomial.legendre.Legendre.degree()[source]
The degree of the series. New in version 1.5.0. Returns
degreeint
Degree of the series, one less than the number of coefficients. | numpy.reference.generated.numpy.polynomial.legendre.legendre.degree |
numpy.polynomial.legendre.Legendre.deriv method polynomial.legendre.Legendre.deriv(m=1)[source]
Differentiate. Return a series instance of that is the derivative of the current series. Parameters
mnon-negative int
Find the derivative of order m. Returns
new_seriesseries
A new series representing the d... | numpy.reference.generated.numpy.polynomial.legendre.legendre.deriv |
numpy.polynomial.legendre.Legendre.domain attribute polynomial.legendre.Legendre.domain = array([-1, 1]) | numpy.reference.generated.numpy.polynomial.legendre.legendre.domain |
numpy.polynomial.legendre.Legendre.fit method classmethod polynomial.legendre.Legendre.fit(x, y, deg, domain=None, rcond=None, full=False, w=None, window=None)[source]
Least squares fit to data. Return a series instance that is the least squares fit to the data y sampled at x. The domain of the returned instance ca... | numpy.reference.generated.numpy.polynomial.legendre.legendre.fit |
numpy.polynomial.legendre.Legendre.fromroots method classmethod polynomial.legendre.Legendre.fromroots(roots, domain=[], window=None)[source]
Return series instance that has the specified roots. Returns a series representing the product (x - r[0])*(x - r[1])*...*(x - r[n-1]), where r is a list of roots. Parameters... | numpy.reference.generated.numpy.polynomial.legendre.legendre.fromroots |
numpy.polynomial.legendre.Legendre.has_samecoef method polynomial.legendre.Legendre.has_samecoef(other)[source]
Check if coefficients match. New in version 1.6.0. Parameters
otherclass instance
The other class must have the coef attribute. Returns
boolboolean
True if the coefficients are the same, F... | numpy.reference.generated.numpy.polynomial.legendre.legendre.has_samecoef |
numpy.polynomial.legendre.Legendre.has_samedomain method polynomial.legendre.Legendre.has_samedomain(other)[source]
Check if domains match. New in version 1.6.0. Parameters
otherclass instance
The other class must have the domain attribute. Returns
boolboolean
True if the domains are the same, False... | numpy.reference.generated.numpy.polynomial.legendre.legendre.has_samedomain |
numpy.polynomial.legendre.Legendre.has_sametype method polynomial.legendre.Legendre.has_sametype(other)[source]
Check if types match. New in version 1.7.0. Parameters
otherobject
Class instance. Returns
boolboolean
True if other is same class as self | numpy.reference.generated.numpy.polynomial.legendre.legendre.has_sametype |
numpy.polynomial.legendre.Legendre.has_samewindow method polynomial.legendre.Legendre.has_samewindow(other)[source]
Check if windows match. New in version 1.6.0. Parameters
otherclass instance
The other class must have the window attribute. Returns
boolboolean
True if the windows are the same, False... | numpy.reference.generated.numpy.polynomial.legendre.legendre.has_samewindow |
numpy.polynomial.legendre.Legendre.identity method classmethod polynomial.legendre.Legendre.identity(domain=None, window=None)[source]
Identity function. If p is the returned series, then p(x) == x for all values of x. Parameters
domain{None, array_like}, optional
If given, the array must be of the form [beg,... | numpy.reference.generated.numpy.polynomial.legendre.legendre.identity |
numpy.polynomial.legendre.Legendre.integ method polynomial.legendre.Legendre.integ(m=1, k=[], lbnd=None)[source]
Integrate. Return a series instance that is the definite integral of the current series. Parameters
mnon-negative int
The number of integrations to perform.
karray_like
Integration constants. T... | numpy.reference.generated.numpy.polynomial.legendre.legendre.integ |
numpy.polynomial.legendre.Legendre.linspace method polynomial.legendre.Legendre.linspace(n=100, domain=None)[source]
Return x, y values at equally spaced points in domain. Returns the x, y values at n linearly spaced points across the domain. Here y is the value of the polynomial at the points x. By default the dom... | numpy.reference.generated.numpy.polynomial.legendre.legendre.linspace |
numpy.polynomial.legendre.Legendre.mapparms method polynomial.legendre.Legendre.mapparms()[source]
Return the mapping parameters. The returned values define a linear map off + scl*x that is applied to the input arguments before the series is evaluated. The map depends on the domain and window; if the current domain... | numpy.reference.generated.numpy.polynomial.legendre.legendre.mapparms |
numpy.polynomial.legendre.Legendre.roots method polynomial.legendre.Legendre.roots()[source]
Return the roots of the series polynomial. Compute the roots for the series. Note that the accuracy of the roots decrease the further outside the domain they lie. Returns
rootsndarray
Array containing the roots of the... | numpy.reference.generated.numpy.polynomial.legendre.legendre.roots |
numpy.polynomial.legendre.Legendre.trim method polynomial.legendre.Legendre.trim(tol=0)[source]
Remove trailing coefficients Remove trailing coefficients until a coefficient is reached whose absolute value greater than tol or the beginning of the series is reached. If all the coefficients would be removed the serie... | numpy.reference.generated.numpy.polynomial.legendre.legendre.trim |
numpy.polynomial.legendre.Legendre.truncate method polynomial.legendre.Legendre.truncate(size)[source]
Truncate series to length size. Reduce the series to length size by discarding the high degree terms. The value of size must be a positive integer. This can be useful in least squares where the coefficients of the... | numpy.reference.generated.numpy.polynomial.legendre.legendre.truncate |
numpy.polynomial.legendre.legfit polynomial.legendre.legfit(x, y, deg, rcond=None, full=False, w=None)[source]
Least squares fit of Legendre series to data. Return the coefficients of a Legendre series of degree deg that is the least squares fit to the data values y given at points x. If y is 1-D the returned coeff... | numpy.reference.generated.numpy.polynomial.legendre.legfit |
numpy.polynomial.legendre.legfromroots polynomial.legendre.legfromroots(roots)[source]
Generate a Legendre series with given roots. The function returns the coefficients of the polynomial \[p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),\] in Legendre form, where the r_n are the roots specified in roots. If a zero... | numpy.reference.generated.numpy.polynomial.legendre.legfromroots |
numpy.polynomial.legendre.leggauss polynomial.legendre.leggauss(deg)[source]
Gauss-Legendre quadrature. Computes the sample points and weights for Gauss-Legendre quadrature. These sample points and weights will correctly integrate polynomials of degree \(2*deg - 1\) or less over the interval \([-1, 1]\) with the we... | numpy.reference.generated.numpy.polynomial.legendre.leggauss |
numpy.polynomial.legendre.leggrid2d polynomial.legendre.leggrid2d(x, y, c)[source]
Evaluate a 2-D Legendre series on the Cartesian product of x and y. This function returns the values: \[p(a,b) = \sum_{i,j} c_{i,j} * L_i(a) * L_j(b)\] where the points (a, b) consist of all pairs formed by taking a from x and b fro... | numpy.reference.generated.numpy.polynomial.legendre.leggrid2d |
numpy.polynomial.legendre.leggrid3d polynomial.legendre.leggrid3d(x, y, z, c)[source]
Evaluate a 3-D Legendre series on the Cartesian product of x, y, and z. This function returns the values: \[p(a,b,c) = \sum_{i,j,k} c_{i,j,k} * L_i(a) * L_j(b) * L_k(c)\] where the points (a, b, c) consist of all triples formed b... | numpy.reference.generated.numpy.polynomial.legendre.leggrid3d |
numpy.polynomial.legendre.legint polynomial.legendre.legint(c, m=1, k=[], lbnd=0, scl=1, axis=0)[source]
Integrate a Legendre series. Returns the Legendre series coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is add... | numpy.reference.generated.numpy.polynomial.legendre.legint |
numpy.polynomial.legendre.legline polynomial.legendre.legline(off, scl)[source]
Legendre series whose graph is a straight line. Parameters
off, sclscalars
The specified line is given by off + scl*x. Returns
yndarray
This module’s representation of the Legendre series for off + scl*x. See also nu... | numpy.reference.generated.numpy.polynomial.legendre.legline |
numpy.polynomial.legendre.legmul polynomial.legendre.legmul(c1, c2)[source]
Multiply one Legendre series by another. Returns the product of two Legendre series c1 * c2. The arguments are sequences of coefficients, from lowest order “term” to highest, e.g., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2. Paramet... | numpy.reference.generated.numpy.polynomial.legendre.legmul |
numpy.polynomial.legendre.legmulx polynomial.legendre.legmulx(c)[source]
Multiply a Legendre series by x. Multiply the Legendre series c by x, where x is the independent variable. Parameters
carray_like
1-D array of Legendre series coefficients ordered from low to high. Returns
outndarray
Array repres... | numpy.reference.generated.numpy.polynomial.legendre.legmulx |
numpy.polynomial.legendre.legone polynomial.legendre.legone = array([1])
An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an inte... | numpy.reference.generated.numpy.polynomial.legendre.legone |
numpy.polynomial.legendre.legpow polynomial.legendre.legpow(c, pow, maxpower=16)[source]
Raise a Legendre series to a power. Returns the Legendre series c raised to the power pow. The argument c is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series P_0 + 2*P_1 + 3*P_2. Parameters
c... | numpy.reference.generated.numpy.polynomial.legendre.legpow |
numpy.polynomial.legendre.legroots polynomial.legendre.legroots(c)[source]
Compute the roots of a Legendre series. Return the roots (a.k.a. “zeros”) of the polynomial \[p(x) = \sum_i c[i] * L_i(x).\] Parameters
c1-D array_like
1-D array of coefficients. Returns
outndarray
Array of the roots of the se... | numpy.reference.generated.numpy.polynomial.legendre.legroots |
numpy.polynomial.legendre.legsub polynomial.legendre.legsub(c1, c2)[source]
Subtract one Legendre series from another. Returns the difference of two Legendre series c1 - c2. The sequences of coefficients are from lowest order term to highest, i.e., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2. Parameters
c... | numpy.reference.generated.numpy.polynomial.legendre.legsub |
numpy.polynomial.legendre.legtrim polynomial.legendre.legtrim(c, tol=0)[source]
Remove “small” “trailing” coefficients from a polynomial. “Small” means “small in absolute value” and is controlled by the parameter tol; “trailing” means highest order coefficient(s), e.g., in [0, 1, 1, 0, 0] (which represents 0 + x + ... | numpy.reference.generated.numpy.polynomial.legendre.legtrim |
numpy.polynomial.legendre.legval polynomial.legendre.legval(x, c, tensor=True)[source]
Evaluate a Legendre series at points x. If c is of length n + 1, this function returns the value: \[p(x) = c_0 * L_0(x) + c_1 * L_1(x) + ... + c_n * L_n(x)\] The parameter x is converted to an array only if it is a tuple or a li... | numpy.reference.generated.numpy.polynomial.legendre.legval |
numpy.polynomial.legendre.legval2d polynomial.legendre.legval2d(x, y, c)[source]
Evaluate a 2-D Legendre series at points (x, y). This function returns the values: \[p(x,y) = \sum_{i,j} c_{i,j} * L_i(x) * L_j(y)\] The parameters x and y are converted to arrays only if they are tuples or a lists, otherwise they are... | numpy.reference.generated.numpy.polynomial.legendre.legval2d |
numpy.polynomial.legendre.legval3d polynomial.legendre.legval3d(x, y, z, c)[source]
Evaluate a 3-D Legendre series at points (x, y, z). This function returns the values: \[p(x,y,z) = \sum_{i,j,k} c_{i,j,k} * L_i(x) * L_j(y) * L_k(z)\] The parameters x, y, and z are converted to arrays only if they are tuples or a ... | numpy.reference.generated.numpy.polynomial.legendre.legval3d |
numpy.polynomial.legendre.legvander polynomial.legendre.legvander(x, deg)[source]
Pseudo-Vandermonde matrix of given degree. Returns the pseudo-Vandermonde matrix of degree deg and sample points x. The pseudo-Vandermonde matrix is defined by \[V[..., i] = L_i(x)\] where 0 <= i <= deg. The leading indices of V inde... | numpy.reference.generated.numpy.polynomial.legendre.legvander |
numpy.polynomial.legendre.legvander2d polynomial.legendre.legvander2d(x, y, deg)[source]
Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y). The pseudo-Vandermonde matrix is defined by \[V[..., (deg[1] + 1)*i + j] = L_i(x) * L_j(y),\] where 0 <... | numpy.reference.generated.numpy.polynomial.legendre.legvander2d |
numpy.polynomial.legendre.legvander3d polynomial.legendre.legvander3d(x, y, z, deg)[source]
Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y, z). If l, m, n are the given degrees in x, y, z, then The pseudo-Vandermonde matrix is defined by \[V... | numpy.reference.generated.numpy.polynomial.legendre.legvander3d |
numpy.polynomial.legendre.legweight polynomial.legendre.legweight(x)[source]
Weight function of the Legendre polynomials. The weight function is \(1\) and the interval of integration is \([-1, 1]\). The Legendre polynomials are orthogonal, but not normalized, with respect to this weight function. Parameters
xar... | numpy.reference.generated.numpy.polynomial.legendre.legweight |
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