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Page 187 of 2547
Differentiate a Legendre series with multidimensional coefficients over axis 1 in Python
To differentiate a Legendre series with multidimensional coefficients, use the polynomial.legendre.legder() method in Python. This method returns the Legendre series coefficients differentiated m times along the specified axis. Syntax numpy.polynomial.legendre.legder(c, m=1, scl=1, axis=0) Parameters The function accepts the following parameters: c: Array of Legendre series coefficients. For multidimensional arrays, different axes correspond to different variables m: Number of derivatives taken, must be non-negative (Default: 1) scl: Scalar multiplier for each differentiation. Final result is multiplied by scl**m (Default: 1) axis: Axis over which the derivative is taken (Default: 0) Example: ...
Read MoreDifferentiate a Legendre series with multidimensional coefficients over specific axis in Python
To differentiate a Legendre series with multidimensional coefficients, use the numpy.polynomial.legendre.legder() method. This function returns the Legendre series coefficients differentiated m times along a specified axis. Syntax numpy.polynomial.legendre.legder(c, m=1, scl=1, axis=0) Parameters The function accepts the following parameters − c − Array of Legendre series coefficients. For multidimensional arrays, different axes correspond to different variables m − Number of derivatives taken (default: 1). Must be non-negative scl − Scalar multiplier for each differentiation (default: 1). Final result is multiplied by scl**m axis − Axis over which the derivative is taken (default: 0) ...
Read MoreEvaluate a 2-D Hermite_e series on the Cartesian product of x and y with 3d array of coefficient in Python
To evaluate a 2-D Hermite_e series on the Cartesian product of x and y, use the hermite_e.hermegrid2d() method in Python. This method returns the values of the two-dimensional polynomial at points in the Cartesian product of x and y coordinates. Syntax numpy.polynomial.hermite_e.hermegrid2d(x, y, c) Parameters The parameters are: x, y: The two dimensional series is evaluated at points in the Cartesian product of x and y. If x or y is a list or tuple, it is first converted to an ndarray c: Array of coefficients ordered so that coefficients for terms ...
Read MoreEvaluate a 2-D Hermite_e series on the Cartesian product of x and y in Python
To evaluate a 2-D Hermite_e series on the Cartesian product of x and y, use the hermite_e.hermegrid2d() method in Python. This method returns the values of the two-dimensional polynomial at points in the Cartesian product of x and y. Syntax numpy.polynomial.hermite_e.hermegrid2d(x, y, c) Parameters The method accepts the following parameters ? x, y ? The two-dimensional series is evaluated at the points in the Cartesian product of x and y. If x or y is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, ...
Read MoreGenerate a Pseudo Vandermonde matrix of the Legendre polynomial and x, y, z complex array of points in Python
To generate a pseudo Vandermonde matrix of the Legendre polynomial with x, y, z sample points, use the legendre.legvander3d() method in NumPy. This function returns a 3D pseudo-Vandermonde matrix of degrees deg and sample points (x, y, z). The parameters x, y, z are arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. The parameter deg is a list of maximum degrees of the form [x_deg, y_deg, z_deg]. Syntax legendre.legvander3d(x, y, ...
Read MoreGenerate a Pseudo Vandermonde matrix of the Legendre polynomial and x, y, z floating array of points in Python
The pseudo-Vandermonde matrix of Legendre polynomials is a mathematical construct used in polynomial interpolation and approximation. In NumPy, the legendre.legvander3d() function generates this matrix for three-dimensional sample points (x, y, z). Syntax numpy.polynomial.legendre.legvander3d(x, y, z, deg) Parameters The function accepts the following parameters ? x, y, z ? Arrays of point coordinates with the same shape deg ? List of maximum degrees [x_deg, y_deg, z_deg] Example Here's how to generate a pseudo-Vandermonde matrix using three-dimensional sample points ? import numpy as np from numpy.polynomial import legendre as ...
Read MoreEvaluate a 3-D Hermite_e series at points (x,y,z) with 2D array of coefficient in Python
To evaluate a 3D Hermite_e series at points (x, y, z), use the hermite_e.hermeval3d() method in NumPy. The method returns the values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z. The first parameter consists of x, y, z coordinates. The three dimensional series is evaluated at the points (x, y, z), where x, y, and z must have the same shape. If any of x, y, or z is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn't an ...
Read MoreEvaluate a 2-D Hermite_e series at points (x,y) with 1D array of coefficient in Python
To evaluate a 2D Hermite_e series at points (x, y), use the hermeval2d() method from NumPy's polynomial module. This function evaluates a two-dimensional Hermite_e polynomial at specified coordinate pairs and returns the corresponding values. Syntax numpy.polynomial.hermite_e.hermeval2d(x, y, c) Parameters The function accepts three parameters: x, y: The coordinate arrays where the polynomial is evaluated. They must have the same shape. c: Array of coefficients ordered so that the coefficient of term with multi-degree i, j is in c[i, j]. Example Let's create a 1D coefficient array and evaluate the ...
Read MoreDivide one Hermite_e series by another in Python
To divide one Hermite_e series by another, use the polynomial.hermite_e.hermediv() method in Python NumPy. The method returns a tuple containing the quotient and remainder as arrays of Hermite_e series coefficients. The method performs polynomial long division on two Hermite_e series c1 / c2, where the arguments are sequences of coefficients from lowest order "term" to highest. For example, [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. Syntax numpy.polynomial.hermite_e.hermediv(c1, c2) Parameters c1, c2: 1-D arrays of Hermite_e series coefficients ordered from low to high degree. Return Value Returns a ...
Read MoreMultiply one Hermite_e series to another in Python
To multiply one Hermite_e series to another, use the polynomial.hermite_e.hermemul() method in Python NumPy. The method returns an array representing the Hermite_e series of their product. 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. Syntax numpy.polynomial.hermite_e.hermemul(c1, c2) Parameters The parameters are 1-D arrays of Hermite_e series coefficients ordered from low to high ? c1, c2 − 1-D arrays of Hermite_e polynomial coefficients Example Let's multiply two Hermite_e series using coefficient arrays ? ...
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