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Python Articles
Page 238 of 855
Evaluate a Hermite series at points x in Python
To evaluate a Hermite series at points x, use the hermite.hermval() method in Python NumPy. This function evaluates a Hermite polynomial series at given points using the coefficients provided. Syntax numpy.polynomial.hermite.hermval(x, c, tensor=True) Parameters The function accepts three parameters ? x: Points at which to evaluate the Hermite series. Can be a scalar, list, or array. c: Array of coefficients ordered so that coefficients for terms of degree n are in c[n]. tensor: If True (default), evaluates each coefficient column for every element of x. If False, broadcasts x over coefficient columns. ...
Read MoreRaise a Hermite series to a power in Python
To raise a Hermite series to a power, use the polynomial.hermite.hermpow() method in NumPy. This method returns a Hermite series raised to the specified power. The argument c is a sequence of coefficients ordered from low to high, where [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. Syntax numpy.polynomial.hermite.hermpow(c, pow, maxpower=16) Parameters The function accepts the following parameters: c: 1-D array of Hermite series coefficients ordered from low to high pow: Power to which the series will be raised maxpower: Maximum power allowed (default is 16) to limit series ...
Read MoreDivide one Hermite series by another in Python
To divide one Hermite series by another, use the polynomial.hermite.hermdiv() method in Python NumPy. The method returns a tuple containing two arrays: the quotient and remainder of the division. The arguments are sequences of coefficients from lowest order "term" to highest, e.g., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. Syntax numpy.polynomial.hermite.hermdiv(c1, c2) Parameters: c1, c2: 1-D arrays of Hermite series coefficients ordered from low to high degree Returns: A tuple (quotient, remainder) where both are arrays of Hermite series coefficients. Example Let's divide two Hermite series ...
Read MoreMultiply one Hermite series to another in Python
To multiply one Hermite series to another, use the polynomial.hermite.hermmul() method in Python NumPy. This method returns an array representing the Hermite series of their product. The arguments are sequences of coefficients ordered from lowest to highest degree, e.g., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. Syntax numpy.polynomial.hermite.hermmul(c1, c2) Parameters c1, c2: 1-D arrays of Hermite series coefficients ordered from low to high degree. Return Value Returns a 1-D array representing the coefficients of the product Hermite series. Example Let's multiply two Hermite series using coefficient ...
Read MoreMultiply a Hermite series by an independent variable in Python
To multiply the Hermite series by x, where x is the independent variable, use the polynomial.hermite.hermmulx() method in Python NumPy. The method returns an array representing the result of the multiplication. The parameter c is a 1-D array of Hermite series coefficients ordered from low to high. Syntax numpy.polynomial.hermite.hermmulx(c) Parameters c: A 1-D array of Hermite series coefficients ordered from low to high degree. Example Let's create a simple example to demonstrate the multiplication of a Hermite series by the independent variable ? import numpy as np from numpy.polynomial import ...
Read MoreGet the Least squares fit of Chebyshev series to data in Python
To get the least-squares fit of Chebyshev series to data, use the chebyshev.chebfit() function in NumPy. This method returns Chebyshev coefficients ordered from low to high, allowing you to fit polynomial approximations to your data using Chebyshev polynomials. Syntax numpy.polynomial.chebyshev.chebfit(x, y, deg, rcond=None, full=False, w=None) Parameters The function accepts the following parameters: x − The x-coordinates of the M sample points (x[i], y[i]) y − The y-coordinates of the sample points. Can be 2-D array for multiple data sets deg − Degree(s) of the fitting polynomials. If integer, includes all terms up ...
Read MoreDifferentiate a polynomial with multidimensional coefficients in Python
To differentiate a polynomial with multidimensional coefficients, use the polynomial.polyder() method in NumPy. This function differentiates polynomial coefficients c along a specified axis, returning the derivative coefficients. The coefficient array represents polynomials where [1, 2, 3] means 1 + 2*x + 3*x², while [[1, 2], [1, 2]] represents 1 + 1*x + 2*y + 2*x*y if axis=0 is x and axis=1 is y. Syntax numpy.polynomial.polynomial.polyder(c, m=1, scl=1, axis=0) Parameters The function accepts the following parameters ? c − Array of polynomial coefficients (multidimensional arrays correspond to different variables) m − Number ...
Read MoreGenerate a Pseudo-Vandermonde matrix of given degree with complex array of points coordinates in Python
To generate a Pseudo-Vandermonde matrix of given degree with complex coordinates, use the polyvander2d() function from NumPy's polynomial module. This function creates a 2D Vandermonde matrix from arrays of point coordinates with specified maximum degrees for each dimension. Syntax numpy.polynomial.polynomial.polyvander2d(x, y, deg) Parameters x, y: Arrays of point coordinates with the same shape. Complex values are supported. deg: List of maximum degrees in the form [x_deg, y_deg]. Example Let's create a Pseudo-Vandermonde matrix using complex coordinate arrays ? import numpy as np from numpy.polynomial.polynomial import polyvander2d # Create arrays ...
Read MoreGenerate a Pseudo-Vandermonde matrix of given degree with float array of points coordinates in Python
To generate a Pseudo-Vandermonde matrix of given degree, use the polynomial.polyvander2d() in Python NumPy. The method returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y). The parameters x and y are arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. The parameter deg is a list of maximum degrees of the form [x_deg, y_deg]. Syntax numpy.polynomial.polynomial.polyvander2d(x, y, deg) Parameters x, y − Arrays of point coordinates, all of the same shape ...
Read MoreEvaluate a Hermite series at points x and the shape of coefficient array extended for each dimension of x in Python
The Hermite series evaluation in Python NumPy allows you to compute polynomial values at specific points using the hermite.hermval() method. This function is particularly useful when working with multidimensional coefficient arrays and controlling how the evaluation is broadcast across dimensions. Syntax hermite.hermval(x, c, tensor=True) Parameters The hermval() method accepts three parameters: x: Points at which to evaluate the series. Can be a scalar, list, or array c: Coefficient array where c[n] contains coefficients for degree n terms tensor: Controls broadcasting behavior (default: True) Understanding the tensor Parameter When tensor=True, ...
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