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Technical articles with clear explanations and examples
Generate a monic polynomial with given complex roots in Python
To generate a monic polynomial with given complex roots, use the polynomial.polyfromroots() method in Python NumPy. The method returns a 1-D array of the polynomial's coefficients. If all the roots are real, then the output is also real, otherwise it is complex. The parameter roots is the sequence containing the roots. Syntax numpy.polynomial.polynomial.polyfromroots(roots) Parameters roots − Sequence containing the roots of the polynomial Return Value Returns a 1-D array of polynomial coefficients ordered from low to high degree. Example with Complex Roots Let's generate a monic polynomial with ...
Read MoreEvaluate a 3-D Chebyshev series at points (x, y, z) with 4D array of coefficient in Python
To evaluate a 3-D Chebyshev series at points (x, y, z), use the polynomial.chebval3d() method in Python NumPy. The method returns the values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z. Syntax numpy.polynomial.chebyshev.chebval3d(x, y, z, c) Parameters The function accepts the following parameters − x, y, z − The three dimensional series is evaluated at the points (x, y, z), where x, y, and z must have the same shape. If any of x, y, or z is a list or tuple, it ...
Read MoreEvaluate a 3-D Chebyshev series at points (x, y, z) in Python
To evaluate a 3-D Chebyshev series at points (x, y, z), use the polynomial.chebval3d() method in NumPy. The method returns the values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z. Syntax numpy.polynomial.chebyshev.chebval3d(x, y, z, c) Parameters The parameters are: x, y, z − The three dimensional series is evaluated at the points (x, y, z), where x, y, and z must have the same shape. If any of x, y, or z is a list or tuple, it is ...
Read MoreEvaluate a 2-D Chebyshev series at points (x, y) with 3D array of coefficient in Python
To evaluate a 2-D Chebyshev series at points (x, y), use the polynomial.chebval2d() method in Python NumPy. The method returns the values of the two dimensional Chebyshev series at points formed from pairs of corresponding values from x and y. The parameter c is an array of coefficients ordered so that the coefficient of the term of multidegree i, j is contained in c[i, j]. If c has dimension greater than 2, the remaining indices enumerate multiple sets of coefficients. Syntax numpy.polynomial.chebyshev.chebval2d(x, y, c) Parameters The parameters x and y represent evaluation points ...
Read MoreEvaluate a Chebyshev series at points x when coefficients are multi-dimensional in Python
To evaluate a Chebyshev series at points x with multi-dimensional coefficients, use the chebyshev.chebval() method in NumPy. This method handles coefficient arrays where each column represents a different polynomial series. Syntax numpy.polynomial.chebyshev.chebval(x, c, tensor=True) Parameters x: Points at which to evaluate the series. Can be scalar, list, or array. c: Array of coefficients. For multi-dimensional arrays, each column represents a separate polynomial. tensor: If True (default), evaluates every column of coefficients for every element of x. If False, broadcasts x over the columns. Example Let's create a 2D coefficient array ...
Read MoreEvaluate a Chebyshev series at points x in Python
To evaluate a Chebyshev series at points x, use the chebyshev.chebval() method in Python NumPy. This function computes the value of a Chebyshev polynomial at specified points using the coefficients provided. Syntax numpy.polynomial.chebyshev.chebval(x, c, tensor=True) Parameters The function accepts three parameters: x − Points at which to evaluate the series. Can be a scalar, list, or array c − Array of coefficients where c[n] contains coefficients for degree n terms tensor − If True (default), evaluates every column of c for every element of x Basic Example Let's evaluate ...
Read MoreRaise a Chebyshev series to a power in Python
To raise a Chebyshev series to a power, use the chebyshev.chebpow() method in Python NumPy. This function returns the Chebyshev series c 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 T_0 + 2*T_1 + 3*T_2. Syntax numpy.polynomial.chebyshev.chebpow(c, pow, maxpower=16) Parameters c − 1-D array of Chebyshev 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 growth ...
Read MoreDivide one Chebyshev series by another in Python
To divide one Chebyshev series by another, use the polynomial.chebyshev.chebdiv() method in Python NumPy. The method returns arrays of Chebyshev series coefficients representing the quotient and remainder. The method returns the quotient-with-remainder of two Chebyshev series c1 / c2. The arguments are sequences of coefficients from lowest order "term" to highest, e.g., [1, 2, 3] represents the series T_0 + 2*T_1 + 3*T_2. The parameters c1 and c2 are 1-D arrays of Chebyshev series coefficients ordered from low to high. Syntax numpy.polynomial.chebyshev.chebdiv(c1, c2) Parameters c1 − 1-D array of Chebyshev series coefficients ...
Read MoreEvaluate a Hermite_e series at array of points x in Python
To evaluate a Hermite_e series at points x, use the hermite_e.hermeval() method in Python NumPy. This function computes the value of a Hermite_e polynomial series at given points using the provided coefficients. Syntax numpy.polynomial.hermite_e.hermeval(x, c, tensor=True) Parameters The function accepts the following parameters ? x − Array of points where the series is evaluated. Can be scalar, list, or ndarray c − Array of coefficients ordered so that coefficients for degree n are in c[n] tensor − If True (default), evaluates every column of coefficients for every element of x ...
Read MoreMultiply one Chebyshev series to another in Python
To multiply one Chebyshev series to another, use the polynomial.chebyshev.chebmul() method in Python. This method returns an array of Chebyshev series coefficients representing their product. The arguments are sequences of coefficients, from lowest order "term" to highest, e.g., [1, 2, 3] represents the series T_0 + 2*T_1 + 3*T_2. Syntax numpy.polynomial.chebyshev.chebmul(c1, c2) Parameters The parameters are: c1, c2 − 1-D arrays of Chebyshev series coefficients ordered from low to high degree Example Let's multiply two Chebyshev series using chebmul() ? import numpy as np from numpy.polynomial import chebyshev ...
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