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Technical articles with clear explanations and examples
Evaluate a Legendre series at points x and the shape of the coefficient array extended for each dimension of x in Python
To evaluate a Legendre series at points x, use the polynomial.legendre.legval() method in NumPy. This function allows you to evaluate Legendre polynomials with specified coefficients at given points, with control over how multidimensional coefficient arrays are handled. Syntax numpy.polynomial.legendre.legval(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 terms of degree n tensor: Boolean controlling shape behavior for multidimensional arrays (default: True) Understanding the Tensor Parameter ...
Read MoreEvaluate a Legendre series at points x when coefficients are multi-dimensional in Python
To evaluate a Legendre series at points x with multi-dimensional coefficients, use the polynomial.legendre.legval() method in Python NumPy. This method handles arrays of coefficients where each column represents a separate polynomial. Syntax numpy.polynomial.legendre.legval(x, c, tensor=True) Parameters The method accepts three parameters ? x − Points at which to evaluate the series. Can be scalar, list, or array c − Array of coefficients. For multi-dimensional arrays, columns represent different polynomials tensor − If True (default), evaluates every column for every point in x Example Let's create a multi-dimensional coefficient array ...
Read MoreDifferentiate a Hermite series and set the derivatives in Python
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 MoreDifferentiate a Hermite series with multidimensional coefficients in Python
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 MoreDifferentiate 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 ...
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