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Technical articles with clear explanations and examples
Evaluate a 3-D polynomial on the Cartesian product of x, y and z in Python
To evaluate a 3-D polynomial on the Cartesian product of x, y, z coordinates, use the numpy.polynomial.polynomial.polygrid3d() method in Python. This method evaluates a three-dimensional polynomial at points in the Cartesian product of the input arrays. Syntax numpy.polynomial.polynomial.polygrid3d(x, y, z, c) Parameters The function accepts the following parameters − x, y, z − The three-dimensional series is evaluated at points in the Cartesian product of x, y, and z. If any parameter is a list or tuple, it is converted to an ndarray first. c − Array of coefficients ordered so that ...
Read MoreEvaluate a 2-D Chebyshev series at points (x, y) 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 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. The parameter c is an array of coefficients ordered so that the coefficient of the term of multidegree i, j ...
Read MoreEvaluate a Chebyshev series at points x broadcast over the columns of the coefficient in Python
To evaluate a Chebyshev series at points x, use the chebyshev.chebval() method in Python NumPy. This function allows you to evaluate Chebyshev polynomials with given coefficients at specific points, with control over how broadcasting is handled. Syntax numpy.polynomial.chebyshev.chebval(x, c, tensor=True) Parameters x: If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. The elements must support addition and multiplication with themselves and with the elements of c. c: An array of coefficients ordered so that the coefficients for terms of ...
Read MoreEvaluate a Chebyshev series at points x and the shape of the coefficient array extended for each dimension of x in Python
To evaluate a Chebyshev series at points x, use the chebyshev.chebval() method in Python NumPy. This function evaluates Chebyshev polynomials at specified points and handles multidimensional coefficient arrays efficiently. Parameters The chebval() method takes three main parameters: x: The points where the series is evaluated. Can be a scalar, list, tuple, or ndarray c: Array of coefficients where c[n] contains coefficients for terms of degree n tensor: Boolean flag controlling shape extension behavior (default: True) Understanding the Tensor Parameter When tensor=True, the coefficient array shape is extended with ones on the right for ...
Read MoreEvaluate a 3-D polynomial at points (x, y, z) with 2D array of coefficient in Python
To evaluate a 3-D polynomial at points (x, y, z), use the polynomial.polyval3d() 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.polynomial.polyval3d(x, y, z, c) 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 is first converted to an ndarray, ...
Read MoreEvaluate a 3-D Hermite_e series on the Cartesian product of x, y and z with 4d array of coefficient in Python
To evaluate a 3-D Hermite_e series on the Cartesian product of x, y and z, use the hermite_e.hermegrid3d(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. Parameters The method accepts the following parameters: 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 it is left unchanged. c: A 4D array ...
Read MoreEvaluate a 3-D Hermite_e series on the Cartesian product of x, y and z in Python
To evaluate a 3-D Hermite_e series on the Cartesian product of x, y and z, use the hermite_e.hermegrid3d(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. Syntax numpy.polynomial.hermite_e.hermegrid3d(x, y, z, c) Parameters The parameters are 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 ...
Read MoreEvaluate a 2-D Hermite_e series on the Cartesian product of x and y with 1d array of coefficient in Python
To evaluate a 2-D Hermite_e series on the Cartesian product of x and y, use the hermite_e.hermegrid2d() method in Python. This method evaluates a two-dimensional Hermite_e polynomial at points formed by the Cartesian product of two arrays. Syntax numpy.polynomial.hermite_e.hermegrid2d(x, y, c) Parameters x, y − Arrays representing the coordinates. The series is evaluated at points in the Cartesian product of x and y c − Array of coefficients ordered so that coefficients for terms of degree i, j are in c[i, j] Basic Example Let's start with a simple example ...
Read MoreDifferentiate a Hermite_e series with multidimensional coefficients over axis 1 in Python
To differentiate a Hermite_e series with multidimensional coefficients, use the hermite_e.hermeder() method in Python. This method allows you to compute derivatives across specific axes of multidimensional coefficient arrays. Parameters The hermite_e.hermeder() method accepts the following parameters: c: Array of Hermite_e series coefficients. For multidimensional arrays, different axes correspond to different variables m: Number of derivatives (default: 1). Must be non-negative scl: Scalar multiplier applied to each differentiation (default: 1) axis: Axis over which the derivative is taken (default: 0) Example: Differentiating Along Axis 1 Let's create a multidimensional coefficient array and differentiate along ...
Read MoreDifferentiate a Hermite_e series with multidimensional coefficients over specific axis in Python
To differentiate a Hermite_e series with multidimensional coefficients, use the hermite_e.hermeder() method in Python. This method allows you to compute derivatives along specific axes of multidimensional coefficient arrays. Syntax numpy.polynomial.hermite_e.hermeder(c, m=1, scl=1, axis=0) Parameters The method accepts the following parameters ? c − Array of Hermite_e series coefficients. For multidimensional arrays, 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 ...
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