Programming Articles - Page 716 of 3366

To generate a Vandermonde matrix of given degree, use the polynomial.polyvander() in Python Numpy. The method returns the Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where the last index is the power of x. The dtype will be the same as the converted x.The parameter, a is Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. The parameter, deg is the degree of the resulting matrix.StepsAt first, import the required ... Read More

To generate a Vandermonde matrix of given degree, use the polynomial.polyvander() in Python Numpy. The method returns rhe Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where the last index is the power of x. The dtype will be the same as the converted x.The parameter, a is Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. The parameter, deg is the degree of the resulting matrix.StepsAt first, import the required ... Read More

To generate a Vandermonde matrix of given degree, use the polynomial.polyvander() in Python Numpy. The method returns rhe Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where the last index is the power of x. The dtype will be the same as the converted x. The parameter, a is Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. The parameter, deg is the degree of the resulting matrix.StepsAt first, import the ... Read More

To evaluate a polynomial specified by its roots at points x, use the polynomial.polyvalfromroots() method in Python Numpy. The 1st parameter is x. If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of r.The 2nd parameter, r is an array of roots. If r is multidimensional the first index is the root index, while the remaining indices enumerate multiple polynomials. For instance, in the two dimensional case the ... Read More

To evaluate a polynomial specified by its roots at points x, use the polynomial.polyvalfromroots() method in Python Numpy. The 1st parameter is x. If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of r.The 2nd parameter, r is an array of roots. If r is multidimensional the first index is the root index, while the remaining indices enumerate multiple polynomials. For instance, in the two dimensional case the ... Read More

To evaluate a polynomial specified by its roots at points x, use the polynomial.polyvalfromroots() method in Python Numpy. The 1st parameter is x. If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of r.The 2nd parameter, r is an array of roots. If r is multidimensional the first index is the root index, while the remaining indices enumerate multiple polynomials. For instance, in the two dimensional case the ... Read More

To Integrate a polynomial, use the polynomial.polyint() method in Python. Returns the polynomial coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The scaling factor is for use in a linear change of variable. The argument c is an array of coefficients, from low to high degree along each axis, e.g., [1, 2, 3] represents the polynomial 1 + 2*x + 3*x**2 while [[1, 2], [1, 2]] represents 1 + 1*x + 2*y + 2*x*y if axis=0 is x and axis=1 is y.The ... Read More

To Integrate a polynomial, use the polynomial.polyint() method in Python. Returns the polynomial coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The scaling factor is for use in a linear change of variable. The argument c is an array of coefficients, from low to high degree along each axis, e.g., [1, 2, 3] represents the polynomial 1 + 2*x + 3*x**2 while [[1, 2], [1, 2]] represents 1 + 1*x + 2*y + 2*x*y if axis=0 is x and axis=1 is y.The ... Read More

Hermite_e series is also known as probabilist's Hermite polynomial or the physicist's Hermite polynomial the available in mathematics which is used to sum of the weighted hermites polynomials. In some particular cases of the quantum mechanics, the Hermite_e series the weight function is given as e^(−x^2). The following is the formula for Hermite_e series. H_n(x) = (-1)^n e^(x^2/2) d^n/dx^n(e^(-x^2/2)) Where, H_n(x) is the nth Hermite polynomial of degree n x is the independent variable d^n/dx^n denotes the nth derivative with respect to x. Defining the coefficients To perform differentiation of the Hermite_e series first we have ... Read More

To differentiate a Hermite_e series, use the hermite_e.hermeder() method in Python. The 1st parameter, c is an array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.The 2nd parameter, m is the number of derivatives taken, must be non-negative. (Default: 1). The 3rd parameter, scl is a scalar. Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1). The 4th parameter, axis is an Axis over which the ... Read More