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Python Articles
Page 225 of 855
Evaluate a 2-D Hermite series at points (x,y) with 3D array of coefficient in Python
To evaluate a 2D Hermite series at points (x, y), use the hermite.hermval2d() method in NumPy. This method returns the values of the two-dimensional polynomial at points formed with pairs of corresponding values from x and y. The first parameter consists of x and y coordinates. 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 and if it isn't an ndarray it is treated as a scalar. ...
Read MoreIntegrate a Hermite series and set the Integration constant in Python
To integrate a Hermite series, use the hermite.hermint() method in Python. This method integrates a Hermite series and allows you to set integration constants. Syntax numpy.polynomial.hermite.hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters The method accepts the following parameters − c − Array of Hermite series coefficients. For multidimensional arrays, different axes correspond to different variables m − Order of integration (must be positive, default: 1) k − Integration constant(s). If empty list (default), all constants are zero. For m=1, can be a scalar lbnd − Lower bound of the integral (default: 0) ...
Read MoreEvaluate a 2-D Laguerre series on the Cartesian product of x and y in Python
To evaluate a 2-D Laguerre series on the Cartesian product of x and y, use the polynomial.laguerre.laggrid2d() method in Python. The method returns the values of the two dimensional Laguerre series at points in the Cartesian product of x and y. If c has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape + y.shape. Syntax numpy.polynomial.laguerre.laggrid2d(x, y, c) Parameters x, y: The two dimensional series is evaluated at the points in the Cartesian product of x ...
Read MoreEvaluate a 3D Laguerre series at points (x,y,z) with 2D array of coefficient in Python
To evaluate a 3D Laguerre series at points (x, y, z), use the polynomial.laguerre.lagval3d() 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. If c has fewer than 3 dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape. The 1st parameter is 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. Syntax ...
Read MoreEvaluate a 2D Laguerre series at points (x,y) with 3D array of coefficients in Python
To evaluate a 2D Laguerre series at points (x, y), use the polynomial.laguerre.lagval2d() method in NumPy. This method returns values of the two-dimensional polynomial at points formed with pairs of corresponding values from x and y coordinates. Syntax numpy.polynomial.laguerre.lagval2d(x, y, c) Parameters x, y: The two-dimensional series is evaluated at 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. c: Array of coefficients ordered so that the coefficient of the term of multi-degree i, ...
Read MoreGenerate a Vandermonde matrix of the Hermite polynomial with float array of points in Python
To generate a Vandermonde matrix of the Hermite polynomial, use the hermvander() function from NumPy's polynomial module. The method returns the pseudo-Vandermonde matrix where each row contains the Hermite polynomial basis functions evaluated at the corresponding point. The shape of the returned matrix is x.shape + (deg + 1, ), where the last index corresponds to the degree of the Hermite polynomial. The x parameter is an array of points (converted to float64 or complex128), and deg is the degree of the resulting matrix. Syntax numpy.polynomial.hermite.hermvander(x, deg) Parameters x: Array of points. If ...
Read MoreGenerate a Vandermonde matrix of the Hermite polynomial in Python
To generate a Vandermonde matrix of the Hermite polynomial, use the hermite.hermvander() function in Python NumPy. This method returns a pseudo-Vandermonde matrix where each row corresponds to a point and each column represents increasing degrees of Hermite polynomials. The shape of the returned matrix is x.shape + (deg + 1, ), where the last index represents the degree of the corresponding Hermite polynomial. The dtype matches the converted input array x. Parameters x: Array of points where the dtype is converted to float64 or complex128 depending on whether any elements are complex. Scalar values are converted to ...
Read MoreCompute the roots of a Hermite series with given complex roots in Python
To compute the roots of a Hermite series, use the hermite.hermroots() 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 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 the value of the series near such points is ...
Read MoreCompute the roots of a Hermite series in Python
To compute the roots of a Hermite series, use the hermite.hermroots() 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 MoreEvaluate a Laguerre series at multidimensional array of points x in Python
To evaluate a Laguerre series at multi-dimensional array of points x, use the polynomial.laguerre.lagval() method in Python NumPy. This function allows you to evaluate Laguerre polynomials efficiently across multiple dimensions. Function Parameters The lagval() function accepts three parameters: x: The evaluation points. If x is a list or tuple, it is converted to an ndarray. The elements must support addition and multiplication operations. c: Array of coefficients where c[n] contains coefficients for terms of degree n. For multidimensional arrays, remaining indices enumerate multiple polynomials. tensor: Boolean parameter (default True). When True, evaluates every column of coefficients ...
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