To get the Least squares fit of Laguerre series to data, use the laguerre.lagfit() method in Python numpy. The method returns the Laguerre coefficients ordered from low to high. If y was 2-D, the coefficients for the data in column k of y are in column k.The parameter, x are the x-coordinates of the M sample (data) points (x[i], y[i]). The parameter, y are the y-coordinates of the sample points. Several sets of sample points sharing the same xcoordinates can be (independently) fit with one call to polyfit by passing in for y a 2-D array that contains one data ... Read More

To return the scaled companion matrix of a 1-D array of Laguerre polynomial coefficients, use the laguerre.lagvander3d() in Python Numpy. The usual companion matrix of the Laguerre polynomials is already symmetric when c is a basis Laguerre polynomial, so no scaling is applied.Returns the Companion matrix of dimensions (deg, deg). The parameter, c is a 1-D array of Laguerre series coefficients ordered from low to high degree.StepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate a 1D array of coefficients −c = np.array([1, 2, 3])Display the array −print("Our Array...", c)Check the Dimensions −print("Dimensions ... Read More

To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander2d() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Laguerre polynomial. The dtype will be the same as the converted x.The parameter, x, y returns an Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. The parameter, deg is a list of ... Read More

To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander2d() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Laguerre polynomial. The dtype will be the same as the converted x.The parameter, x, y returns an Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. The parameter, deg is a list of ... Read More

To differentiate a Laguerre series, use the laguerre.lagder() method in Python. The method returns the Laguerre series coefficients c differentiated m times along 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, e.g., [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.The 1st parameter, c is an array of Laguerre series coefficients. If c is multidimensional the different axis correspond ... Read More

numpy.meshgrid() is used to return coordinate matrices from coordinate vectors. Its syntax is as follows −numpy.meshgrid(*xi, **kwargs)ParametersMeshgrid 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 to use sparse grid for conserving memory, then we have to set this parameter to True. By default, it is False.copy − It returns a copy of the original array for conversing memory when the parameter is True. ... Read More

numpy.reshape() gives a new shape to an array without changing its data. Its syntax is as follows −numpy.reshape(arr, newshape, order='C')Parametersnumpy.reshape() can accept the following parameters −arr − Input array.shape − endpoint of the sequencenewshape − If an integer, then the result it will be a 1-D array of that length, and one dimension can be -1.order − It defines the order in which the input array elements should be read.If the order is ‘C’, then it reads and writes the elements which are using a C-like index order where the last index changes the fastest and the first axis index ... Read More

numpy.geomspace() returns a set of numbers spaced evenly on a log scale (a geometric progression).Linspace − It is similar to geomspace, but endpoints specified using the log and base.Logspace − It is similar to geomspace, but endpoints specified with arithmetic instead of geometric progression.Syntaxnumpy.goemspace(start, stop, num = 50, endpoint = True/False, dtype = None)ParametersThe above function can accept the following parameters −start − Start of the sequence; default is zero.stop − Endpoint of the sequence.num − Number of elements which are generated between the start and stop sequence.endpoint − It controls whether the stop value is included in the output ... Read More

numpy.logspace returns a set of numbers spaced evenly on a log scale. Its syntax is as follows −numpy.logspace(start, stop, num = 50, endpoint = True/False, base = 10.0, dtype = None)ParametersThe logspace function can accept the following parameters −start − Start of the sequence; default is zero.stop − Endpoint of the sequence.num − Number of elements to be generated between the start and stop sequence.endpoint − It controls whether the stop value is included in the output array or not. If the endpoint is True, then the stop parameter is included as the last item in the nd.array. If endpoint=false, ... Read More

The numpy.linspace function is used to create a set of evenly spaced numbers within a defined interval.Syntaxnumpy.linspace(start, stop, num = 50, endpoint = True/False, retstep = False/True, dtype = None)ParametersThe function can accept the following parameters −start − Start of the sequence; by default, it is considered as zero.stop − Endpoint of the sequence.num − Number of elements to be generated between start and stop.endpoint − It controls whether the stop value is included in the output array or not. If the endpoint is True, then the stop parameter is included as the the last item in the nd.array. If ... Read More