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Page 201 of 2547
Differentiate a Laguerre series with multidimensional coefficients over axis 1 in Python
To differentiate a Laguerre series with multidimensional coefficients, use the laguerre.lagder() method in Python NumPy. This method returns the Laguerre series coefficients differentiated m times along a specified axis. The coefficient array c represents Laguerre series from low to high degree. For example, [1, 2, 3] represents 1*L_0 + 2*L_1 + 3*L_2, while [[1, 2], [1, 2]] represents a 2D series if axis=0 is x and axis=1 is y. Syntax numpy.polynomial.laguerre.lagder(c, m=1, scl=1, axis=0) Parameters c − Array of Laguerre series coefficients. For multidimensional arrays, different axes correspond to different variables. m ...
Read MoreDifferentiate a Laguerre series with multidimensional coefficients over specific axis in Python
To differentiate a Laguerre series with multidimensional coefficients, use the laguerre.lagder() method in Python. This method returns the Laguerre series coefficients differentiated m times along a specified axis. At each iteration, the result is multiplied by a scalar value. The coefficient array represents Laguerre polynomials where [1, 2, 3] represents the series 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. Syntax laguerre.lagder(c, m=1, scl=1, axis=0) Parameters c: Array of Laguerre series ...
Read MoreDifferentiate a Laguerre series and multiply each differentiation by a scalar 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 axis. At each iteration, the result is multiplied by a scalar value scl. The coefficient array c represents coefficients from low to high degree. For example, [1, 2, 3] represents the series 1*L_0 + 2*L_1 + 3*L_2, where L_n are Laguerre polynomials. Syntax numpy.polynomial.laguerre.lagder(c, m=1, scl=1, axis=0) Parameters c − Array of Laguerre series coefficients m − Number of derivatives taken (default: 1) scl − Scalar multiplier applied to each ...
Read MoreGet the Least squares fit of Laguerre series to data in Python
The Laguerre series is a set of orthogonal polynomials useful for data fitting. NumPy's laguerre.lagfit() method performs least squares fitting of Laguerre series to data points. Syntax laguerre.lagfit(x, y, deg, rcond=None, full=False, w=None) Parameters x − x-coordinates of the sample points y − y-coordinates of the sample points deg − degree of the fitting polynomial rcond − relative condition number (optional) full − if True, returns diagnostic information (default: False) w − weights for each data point (optional) Return Value Returns Laguerre coefficients ordered from low to high. When full=True, ...
Read MoreGenerate a Pseudo Vandermonde matrix of the Laguerre polynomial and x, y floating array of points in Python
To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander2d() function in NumPy. This method returns a pseudo-Vandermonde matrix where each element corresponds to a Laguerre polynomial evaluated at the given points. The pseudo-Vandermonde matrix has shape x.shape + (deg + 1, ), where the last index represents the degree of the corresponding Laguerre polynomial. The dtype matches the converted input arrays. Syntax numpy.polynomial.laguerre.lagvander2d(x, y, deg) Parameters x, y − Array of points with coordinates. Converted to float64 or complex128 depending on element types deg − List of maximum ...
Read MoreGenerate 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 ...
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