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Programming Articles
Page 203 of 2547
Subtract one Laguerre series from another in Python
To subtract one Laguerre series from another, use the polynomial.laguerre.lagsub() method in Python NumPy. The method returns an array of Laguerre series coefficients representing their difference c1 - c2. The sequences of coefficients are ordered from lowest order term to highest, i.e., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. Syntax numpy.polynomial.laguerre.lagsub(c1, c2) Parameters The parameters c1 and c2 are 1-D arrays of Laguerre series coefficients ordered from low to high degree. Example Let's create two Laguerre series and subtract one from another ? import numpy as ...
Read MoreGenerate a Pseudo Vandermonde matrix of the Hermite polynomial with complex array of points coordinates in Python
To generate a pseudo Vandermonde matrix of the Hermite polynomial with complex coordinates, use the hermite.hermvander2d() function in NumPy. This function creates a 2D Vandermonde matrix where each row corresponds to a point and columns represent different polynomial terms. Syntax numpy.polynomial.hermite.hermvander2d(x, y, deg) Parameters The function accepts the following parameters: x, y − Arrays of point coordinates with the same shape. Complex values are automatically handled. deg − List of maximum degrees in the form [x_deg, y_deg]. Example Let's create a pseudo Vandermonde matrix using complex coordinate arrays: ...
Read MoreGenerate a Hermite series with given roots in Python
To generate a Hermite series with given roots, use the hermite.hermfromroots() method in Python NumPy. The method returns a 1-D array of coefficients. If all roots are real then out is a real array, if some of the roots are complex, then out is complex even if all the coefficients in the result are real. Syntax numpy.polynomial.hermite.hermfromroots(roots) Parameters The parameter roots is the sequence containing the roots of the Hermite polynomial. Example Let's generate a Hermite series with roots (-1, 0, 1) − import numpy as np from numpy.polynomial import ...
Read MoreIntegrate a Chebyshev series over specific axis in Python
To integrate a Chebyshev series over a specific axis in Python, use the numpy.polynomial.chebyshev.chebint() method. This function returns the Chebyshev series coefficients integrated m times from a lower bound along the specified axis. Syntax numpy.polynomial.chebyshev.chebint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters The chebint() method accepts the following parameters ? c − Array of Chebyshev series coefficients. For multidimensional arrays, different axes correspond to different variables m − Order of integration (must be positive). Default is 1 k − Integration constants. If empty list (default), all constants are set to zero lbnd − ...
Read MoreIntegrate a Hermite series over axis 0 in Python
To integrate a Hermite series over a specific axis, use the hermite.hermint() method in Python. This function performs integration along the specified axis of a multidimensional array of Hermite series coefficients. Parameters The hermint() method accepts several parameters ? c ? Array of Hermite series coefficients. For multidimensional arrays, different axes correspond to different variables m ? Order of integration (must be positive, default: 1) k ? Integration constant(s). Default is empty list (all constants set to zero) lbnd ? Lower bound of the integral (default: 0) scl ? Scaling factor applied after each integration (default: ...
Read MoreEvaluate a 2-D Laguerre series on the Cartesian product of x and y with 1d array of coefficient in Python
To evaluate a 2-D Laguerre series on the Cartesian product of x and y, use the polynomial.laguerre.laggrid2d() method in Python. The method returns the values of the two dimensional Laguerre series at points in the Cartesian product of x and y. If c has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape + y.shape. The 1st parameter, x and y, defines where the two dimensional series is evaluated at the points in the Cartesian product. If x or y is a list ...
Read MoreIntegrate a Hermite series and multiply the result by a scalar before the integration constant is added in Python
To integrate a Hermite series and multiply the result by a scalar before adding the integration constant, use the hermite.hermint() method in Python. This function provides control over the integration process through several parameters including the scalar multiplier. Syntax hermite.hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters The key parameters for scalar multiplication during integration are ? c ? Array of Hermite series coefficients m ? Order of integration (default: 1) k ? Integration constant(s) (default: []) lbnd ? Lower bound of integral (default: 0) scl ? Scalar multiplier applied before adding integration ...
Read MoreIntegrate a Hermite series and set the lower bound of the integral in Python
To integrate a Hermite series, use the hermite.hermint() method in Python. This function integrates Hermite polynomials represented as coefficient arrays and allows you to set a custom lower bound for the integral. Syntax The syntax of hermite.hermint() is ? hermite.hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters The function accepts the following parameters ? Parameter Description Default c Array of Hermite series coefficients Required m Order of integration (must be positive) 1 k Integration constant(s) [] (zeros) lbnd Lower bound of the integral ...
Read MoreEvaluate a 3-D Hermite series at points (x,y,z) with 2D array of coefficient in Python
To evaluate a 3D Hermite series at points (x, y, z), use the hermite.hermval3d() 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 series at points (x,y) with 1D array of coefficient in Python
To evaluate a 2D Hermite series at points (x, y), use the hermite.hermval2d() method in Python NumPy. The method returns the values of the two dimensional polynomial at points formed with pairs of corresponding values from x and y. The first parameter contains x and y coordinates. The two dimensional series is evaluated at the points (x, y), where x and y must have the same shape. If x or y is a list or tuple, it is first converted to an ndarray. The second parameter, c, is an array of coefficients ordered so that the coefficient of the ...
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