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To differentiate a Hermite series, use the hermite.hermder() method in Python. This function computes the derivative of a Hermite series representation of a polynomial. 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) Basic ... Read More
To differentiate a Hermite series with multidimensional coefficients, use the hermite.hermder() method in Python. This function handles multidimensional arrays where different axes correspond to different variables. 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 (default: 1). Must be non-negative scl: Scalar multiplier for each differentiation (default: 1). Final result is multiplied by scl**m axis: Axis over which the derivative is taken (default: 0) Example Let's ... Read More
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 More
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 More
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 More
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 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. Parameters The lagder() method accepts the following parameters ? c − An array of ... Read More
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 More
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 More
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 More