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 generate a monic polynomial with given roots, use the polynomial.polyfromroots() method in Python Numpy. The method returns the 1-D array of the polynomial’s coefficients If all the roots are real, then out is also real, otherwise it is complex. The parameter roots are the sequence containing the roots.StepsAt first, import the required library −from numpy.polynomial import polynomial as PGenerating a monic polynomial −print("Result...", P.polyfromroots((-1, 0, 1))) Get the datatype −print("Type...", P.polyfromroots((-1, 0, 1)).dtype)Get the shape −print("Shape...", P.polyfromroots((-1, 0, 1)).shape) Examplefrom numpy.polynomial import polynomial as P # To generate a monic polynomial with given roots, use the polynomial.polyfromroots() method ... 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 generate a pseudo Vandermonde matrix of the Chebyshev polynomial, use the chebyshev.chebvander() in Python Numpy. The method returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y).The parameter x, y are the arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. The parameter, deg is the list of maximum degrees of the form [x_deg, y_deg].StepsAt first, import the required library −import numpy as np from numpy.polynomial import chebyshev as CCreate arrays of ... Read More

To generate a Vandermonde matrix of the Chebyshev polynomial, use the chebyshev.chebvander() 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 degree of the corresponding Chebyshev polynomial. 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 ... Read More

To generate a Vandermonde matrix of the Chebyshev polynomial, use the chebyshev.chebvander() 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 degree of the corresponding Chebyshev polynomial. 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 ... Read More

The arctanh is a multivalued function: for each x there are infinitely many numbers z such that tanh(z) = x. The convention is to return the z whose imaginary part lies in [-pi/2, pi/2]. The inverse hyperbolic tangent is also known as atanh or tanh^-1.To compute the inverse Hyperbolic tangent of array elements, use the numpy.arctanh() method in Python Numpy. The method returns the array of the same shape as x. This is a scalar if x is a scalar. The 1st parameter, x is input array. The 2nd and 3rd parameters are optional.The 2nd parameter is an ndarray, A ... Read More

To calculate the n-th discrete difference, use the numpy.diff() method. The first difference is given by out[i] = a[i+1] - a[i] along the given axis, higher differences are calculated by using diff recursively. The diff() method returns the n-th differences. The shape of the output is the same as a except along axis where the dimension is smaller by n. The type of the output is the same as the type of the difference between any two elements of a. This is the same as the type of a in most cases. A notable exception is datetime64, which results in ... Read More

To return the cumulative sum of array elements over a given axis treating NaNs as zero, use the nancumprod() method. The cumulative sum does not change when NaNs are encountered and leading NaNs are replaced by zeros. Zeros are returned for slices that are all-NaN or empty.The 1st parameter is the input array. The 2nd parameter is the axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array. The 3rd parameter is the type of the returned array and of the accumulator in which the elements are summed. If dtype ... Read More

The numpy.can_cast() method returns True if scalar and data type can occur according to the casting rule. The 1st parameter is the scalar or data type or array to cast from. The 2nd parameter is the data type to cast to.StepsAt first, import the required library −import numpy as npChecking if scalar and data type can occur according to the casting rule. −print("Checking with can_cast() method in Numpy") print("Result...", np.can_cast(20, 'i1')) print("Result...", np.can_cast(280, 'i1')) print("Result...", np.can_cast(80, 'u1')) print("Result...", np.can_cast(300.7, np.float32)) print("Result...", np.can_cast(120.6, np.float64)) print("Result...", np.can_cast(7.2e100, np.float32)) print("Result...", np.can_cast(6.5e100, np.float64))Exampleimport numpy as np # The numpy.can_cast() method returns True if ... Read More