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Numpy Articles
Page 22 of 81
Raise a Laguerre series to a power in Python
To raise a Laguerre series to a power, use the polynomial.laguerre.lagpow() method in NumPy. The method returns the Laguerre series c raised to the power pow. The argument c is a sequence of coefficients ordered from low to high. For example, [1, 2, 3] represents the series P₀ + 2*P₁ + 3*P₂. Syntax numpy.polynomial.laguerre.lagpow(c, pow, maxpower=16) Parameters The function accepts the following parameters ? c − 1-D array of Laguerre series coefficients ordered from low to high pow − Power to which the series will be raised maxpower − Maximum power allowed ...
Read MoreDivide one Laguerre series by another in Python
To divide one Laguerre series by another, use the polynomial.laguerre.lagdiv() method in Python NumPy. The method returns a [quo, rem] array of Laguerre series coefficients representing the quotient and remainder. The function performs polynomial division where the arguments are sequences of coefficients from lowest order "term" to highest. For example, [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters c1 and c2 are 1-D arrays of Laguerre series coefficients ordered from low to high. Syntax numpy.polynomial.laguerre.lagdiv(c1, c2) Parameters: c1, c2 − 1-D arrays of Laguerre series coefficients ordered from ...
Read MoreMultiply one Laguerre series to another in Python
To multiply one Laguerre series to another, use the polynomial.laguerre.lagmul() method in Python NumPy. This function returns the multiplication of two Laguerre series 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.lagmul(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 multiply two Laguerre series step by step ? import numpy as np from numpy.polynomial import laguerre ...
Read MoreMultiply a Laguerre series by an independent variable in Python
To multiply a Laguerre series by an independent variable, use the polynomial.laguerre.lagmulx() method in Python. This function multiplies the Laguerre series c by x, where x is the independent variable. The parameter c is a 1-D array of Laguerre series coefficients ordered from low to high. Syntax numpy.polynomial.laguerre.lagmulx(c) Parameters: c - 1-D array of Laguerre series coefficients ordered from low to high Returns: Array representing the Laguerre series multiplied by x Example Let's create a Laguerre series with coefficients [1, 2, 3] and multiply it by the independent variable ? ...
Read MoreSubtract 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 ...
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