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Articles by AmitDiwan
Page 23 of 840
Generate a Laguerre series with given complex roots in Python
To generate a Laguerre series with given complex roots, use the laguerre.lagfromroots() method in Python NumPy. This method returns a 1-D array of coefficients representing the Laguerre polynomial. If all roots are real, the output is a real array. If some roots are complex, the output is complex even if all coefficients in the result are real. Syntax numpy.polynomial.laguerre.lagfromroots(roots) Parameters roots: A sequence containing the roots of the polynomial. Example with Complex Roots Let's generate a Laguerre series with complex conjugate roots − from numpy.polynomial import laguerre as L ...
Read MoreGenerate a Laguerre series with given roots in Python
To generate a Laguerre series with given roots in Python NumPy, use the laguerre.lagfromroots() method. This function returns a 1-D array of coefficients representing the polynomial. If all roots are real, the output is a real array; if some roots are complex, the output is complex even if all resulting coefficients are real. Syntax numpy.polynomial.laguerre.lagfromroots(roots) Parameters: roots − Sequence containing the roots of the polynomial Returns: 1-D array of Laguerre series coefficients ordered from lowest to highest degree. Example with Real Roots Let's generate a Laguerre series with roots at ...
Read MoreIntegrate a Laguerre series over axis 0 in Python
To integrate a Laguerre series over a specific axis in Python, use the numpy.polynomial.laguerre.lagint() method. This function integrates a Laguerre series along a specified axis, returning the integrated coefficients. Syntax numpy.polynomial.laguerre.lagint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters c − Array of Laguerre 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 ...
Read MoreDifferentiate 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 ...
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