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Generate a Pseudo Vandermonde matrix of the Laguerre polynomial and x, y array of points in Python
To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander2d() in Python NumPy. The method returns the pseudo-Vandermonde matrix where each element corresponds to the evaluation of Laguerre polynomials at given points. The parameter x, y are arrays of points with the same shape. The dtype is converted to float64 or complex128 depending on whether any elements are complex. The parameter deg is a list of maximum degrees of the form [x_deg, y_deg]. Syntax numpy.polynomial.laguerre.lagvander2d(x, y, deg) Example Let's create a pseudo Vandermonde matrix using coordinate points and specified polynomial ...
Read MoreDifferentiate a Laguerre series and set the derivatives in Python
To differentiate a Laguerre series, use the laguerre.lagder() method in Python. The method returns the Laguerre series coefficients differentiated m times along the specified axis. At each iteration, the result is multiplied by a scaling factor. The argument c is an array of coefficients from low to high degree along each axis. For example, [1, 2, 3] represents the series 1*L₀ + 2*L₁ + 3*L₂, while [[1, 2], [1, 2]] represents a two-dimensional series if axis=0 is x and axis=1 is y. Syntax numpy.polynomial.laguerre.lagder(c, m=1, scl=1, axis=0) Parameters Parameter Description Default ...
Read MorePython – numpy.meshgrid
numpy.meshgrid() is used to create coordinate matrices from coordinate vectors. It's particularly useful for creating grids for plotting, evaluating functions over 2D domains, and mathematical computations that require coordinate pairs. Syntax numpy.meshgrid(*xi, **kwargs) Parameters Meshgrid can accept the following parameters − x1, x2, …, xn − It represents the coordinates of a grid. indexing − It is an optional parameter which defines the Cartesian 'xy' by default and matrix 'ij' index of output. sparse − It is an optional parameter. If we like ...
Read MorePython – numpy.geomspace
numpy.geomspace() returns a set of numbers spaced evenly on a log scale (a geometric progression). This function is useful for creating exponentially spaced arrays where each element is a constant multiple of the previous one. Key differences from similar functions ? Linspace − Creates linearly spaced numbers between two endpoints Logspace − Creates logarithmically spaced numbers using base and power endpoints Geomspace − Creates geometrically spaced numbers using actual start and stop values Syntax numpy.geomspace(start, stop, num=50, endpoint=True, dtype=None) Parameters The above function accepts the following parameters ? ...
Read MoreDifferentiate a Laguerre series with multidimensional coefficients in Python
To differentiate a Laguerre series with multidimensional coefficients, use the laguerre.lagder() method in Python. The method returns the Laguerre series coefficients differentiated m times along a specified axis. At each iteration, the result is multiplied by a scaling factor. The coefficient array c represents Laguerre polynomial terms where [1, 2, 3] represents 1*L_0 + 2*L_1 + 3*L_2. For multidimensional arrays like [[1, 2], [1, 2]], it represents 1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y) if axis=0 is x and axis=1 is y. Parameters The lagder() method accepts the following parameters ? c − Array of ...
Read MoreDifferentiate a Laguerre series in Python
To differentiate a Laguerre series, use the laguerre.lagder() method in Python. The method returns the Laguerre series coefficients differentiated m times along the specified axis. At each iteration, the result is multiplied by scl. The argument c is an array of coefficients from low to high degree along each axis. For example, [1, 2, 3] represents the series 1*L_0 + 2*L_1 + 3*L_2, while [[1, 2], [1, 2]] represents 1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y) if axis=0 is x and axis=1 is y. Syntax laguerre.lagder(c, m=1, scl=1, axis=0) Parameters c: Array ...
Read MoreEvaluate a 3-D Laguerre series on the Cartesian product of x, y and z with 2d array of coefficient in Python
To evaluate a 3-D Laguerre series on the Cartesian product of x, y and z, use the polynomial.laguerre.laggrid3d() method in Python. The method returns the values of the three-dimensional Laguerre series at points in the Cartesian product of x, y and z. If the coefficient array c has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape. Parameters The method accepts the following parameters: x, y, z − Three-dimensional series is evaluated at the points ...
Read MoreEvaluate a 2-D Laguerre series on the Cartesian product of x and y with 3d array of coefficient in Python
To evaluate a 2-D Laguerre series on the Cartesian product of x and y with a 3D array of coefficients, use the numpy.polynomial.laguerre.laggrid2d() method in Python. This method returns the values of the two-dimensional Laguerre series at points in the Cartesian product of x and y. The coefficient array c should be ordered so that the coefficient of the term of multi-degree i, j is contained in c[i, j]. When c has more than two dimensions, the additional indices enumerate multiple sets of coefficients, allowing for batch evaluation. Syntax numpy.polynomial.laguerre.laggrid2d(x, y, c) Parameters ...
Read MoreEvaluate a Laguerre series at points x and the shape of the coefficient array extended for each dimension of x in Python
To evaluate a Laguerre series at points x, use the polynomial.laguerre.lagval() method in Python NumPy. This function allows you to evaluate Laguerre polynomials with given coefficients at specified points, with control over how multidimensional coefficient arrays are handled. Syntax numpy.polynomial.laguerre.lagval(x, c, tensor=True) Parameters The function accepts three parameters: x: Points at which to evaluate the series. Can be scalar, list, or array c: Array of coefficients ordered so that coefficients for terms of degree n are in c[n] tensor: Boolean controlling evaluation behavior for multidimensional arrays (default: True) Understanding the ...
Read MoreEvaluate a Laguerre series at points x when coefficients are multi-dimensional in Python
To evaluate a Laguerre series at points x with multi-dimensional coefficients, use the polynomial.laguerre.lagval() method in Python NumPy. This method allows evaluation of multiple polynomials simultaneously when coefficients are arranged in a multi-dimensional array. Parameters The lagval() method takes three main parameters: x: The evaluation points. Can be a scalar, list, or array c: Array of coefficients where coefficients for degree n are in c[n]. For multi-dimensional arrays, additional indices represent multiple polynomials tensor: Boolean parameter (default True) controlling how x and c interact during evaluation Basic Example with Multi-dimensional Coefficients Let's create ...
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