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Python Articles
Page 234 of 855
Differentiate a Hermite series in Python
To differentiate a Hermite series, use the hermite.hermder() method in Python. This function computes the derivative of a Hermite series represented by its coefficients. Syntax numpy.polynomial.hermite.hermder(c, m=1, scl=1, axis=0) Parameters The hermder() method accepts the following parameters ? c ? Array of Hermite series coefficients. If multidimensional, different axes correspond to different variables. m ? Number of derivatives taken, must be non-negative (Default: 1). scl ? Scalar multiplier for each differentiation. Final result is multiplied by scl**m (Default: 1). axis ? Axis over which the derivative is taken (Default: 0). ...
Read MoreEvaluate a 3-D Hermite series on the Cartesian product of x, y and z with 2d array of coefficient in Python
To evaluate a 3-D Hermite series on the Cartesian product of x, y and z, use the hermite.hermgrid3d(x, y, z, c) method in Python. The method returns the values of the three-dimensional polynomial at points in the Cartesian product of x, y and z. Understanding the Parameters The hermgrid3d() method accepts four parameters: x, y, z − The three dimensional series is evaluated at the points in the Cartesian product of x, y, and z. If x, y, or z is a list or tuple, it is first converted to an ndarray, otherwise it is left ...
Read MoreEvaluate a 3-D Hermite series on the Cartesian product of x, y and z with 4d array of coefficient in Python
To evaluate a 3-D Hermite series on the Cartesian product of x, y and z, use the hermite.hermgrid3d(x, y, z, c) method in Python. This method evaluates a three-dimensional Hermite polynomial at all combinations of points from the input arrays. Parameters The method takes four parameters: x, y, z − The three coordinate arrays. The series is evaluated at points in the Cartesian product of x, y, and z. If any parameter is a list or tuple, it's converted to an ndarray. c − A 4D array of coefficients where c[i, j, k, :] contains coefficients ...
Read MoreEvaluate a 3-D Hermite series on the Cartesian product of x, y and z in Python
To evaluate a 3-D Hermite series on the Cartesian product of x, y and z, use the hermite.hermgrid3d(x, y, z, c) method in Python. This method returns the values of the three-dimensional polynomial at points in the Cartesian product of x, y, and z coordinates. Syntax numpy.polynomial.hermite.hermgrid3d(x, y, z, c) Parameters The parameters are: x, y, z − The three-dimensional series is evaluated at points in the Cartesian product of x, y, and z. If x, y, or z is a list or tuple, it is first converted to an ndarray, otherwise ...
Read MoreDifferentiate a Laguerre series, set the derivatives 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 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. Parameters The lagder() method accepts the following parameters ? c − An array of ...
Read MoreDifferentiate a Hermite series and multiply each differentiation by a scalar in Python
To differentiate a Hermite series, use the hermite.hermder() method in Python. The method allows you to differentiate Hermite series coefficients and multiply each differentiation by a scalar value. Syntax hermite.hermder(c, m=1, scl=1, axis=0) Parameters The hermder() method accepts the following parameters ? c − Array of Hermite series coefficients. For multidimensional arrays, different axes correspond to different variables m − Number of derivatives taken, must be non-negative (Default: 1) scl − Scalar multiplier. Each differentiation is multiplied by this value, resulting in multiplication by scl**m (Default: 1) axis − Axis over which ...
Read MoreEvaluate a 2D Laguerre series at points (x,y) in Python
To evaluate a 2D Laguerre series at points (x, y), use the polynomial.laguerre.lagval2d() method in Python NumPy. The method returns the values of the two-dimensional polynomial at points formed with pairs of corresponding values from x and y. Syntax numpy.polynomial.laguerre.lagval2d(x, y, c) Parameters The function takes three parameters: x, y − The two dimensional series is evaluated at the points (x, y), where x and y must have the same shape. If x or y is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged ...
Read MoreGenerate a Vandermonde matrix of the Chebyshev polynomial in Python
To generate a Vandermonde matrix of the Chebyshev polynomial, use the chebyshev.chebvander() function in NumPy. The method returns the Vandermonde matrix where each column represents a different degree of the Chebyshev polynomial. The shape of the returned matrix is x.shape + (deg + 1, ), where the last index corresponds to the degree of the Chebyshev polynomial. The function takes two parameters: x is an array of points (converted to float64 or complex128), and deg is the degree of the resulting matrix. Syntax numpy.polynomial.chebyshev.chebvander(x, deg) Parameters x: Array of points. The dtype is ...
Read MoreCompute the roots of a Chebyshev series with given complex roots in Python
To compute the roots of a Chebyshev series, use the chebyshev.chebroots() method in Python NumPy. The method returns an array of the roots of the series. If all the roots are real, then the output is also real, otherwise it is complex. The parameter c is a 1-D array of coefficients. The root estimates are obtained as the eigenvalues of the companion matrix. Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as ...
Read MoreGenerate a Chebyshev series with given complex roots in Python
To generate a Chebyshev series with given complex roots, use the chebyshev.chebfromroots() method in NumPy. The method returns a 1-D array of coefficients. If all roots are real then the output is a real array; if some of the roots are complex, then the output is complex even if all coefficients in the result are real. Syntax numpy.polynomial.chebyshev.chebfromroots(roots) Parameters roots − A sequence containing the roots from which to generate the Chebyshev series. Example with Complex Roots Let's generate a Chebyshev series using complex roots -j and j where j is the ...
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