Given two vectors, a = [a0, a1, ..., aM] and b = [b0, b1, ..., bN], the outer product [1] is −[[a0*b0 a0*b1 ... a0*bN ] [a1*b0 . [ ... . [aM*b0 aM*bN ]]To get the Outer product of two arrays, use the numpy.outer() method in Python. The numpy.ones() return a new array of given shape and type, filled with ones. The numpy.linspace() returns evenly spaced numbers over a specified interval.StepsAt first, import the required libraries −import numpy as np The real part −rl = np.outer(np.ones((5, )), np.linspace(-2, 2, 5)) print("The real part of the complex number...", ... Read More

To get the Outer product of two One-Dimensional arrays, use the numpy.outer() method in Python. The 1st parameter a is the first input vector. Input is flattened if not already 1-dimensional. The 2nd parameter b is the second input vector. Input is flattened if not already 1-dimensional. The 3rd parameter out is a location where the result is stored.Given two vectors, a = [a0, a1, ..., aM] and b = [b0, b1, ..., bN], the outer product [1] is −[[a0*b0 a0*b1 ... a0*bN ] [a1*b0 . [ ... . [aM*b0 aM*bN ]]StepsAt first, import the required libraries ... Read More

To get the Outer product of two multi-dimensional arrays, use the numpy.outer() method in Python. The 1st parameter a is the first input vector. Input is flattened if not already 1-dimensional. The 2nd parameter b is the second input vector. Input is flattened if not already 1-dimensional. The 3rd parameter out is a location where the result is stored.Given two vectors, a = [a0, a1, ..., aM] and b = [b0, b1, ..., bN], the outer product [1] is −[[a0*b0 a0*b1 ... a0*bN ] [a1*b0 . [ ... . [aM*b0 aM*bN ]]StepsAt first, import the required libraries ... Read More

To Compute the sign and natural logarithm of the determinant of an array, use the numpy.linalg.slogdet() method in Python. The 1st parameter, s is an input array, has to be a square 2-D array.The method, with sign returns a number representing the sign of the determinant. For a real matrix, this is 1, 0, or -1. For a complex matrix, this is a complex number with absolute value 1, or else 0. The method, with logdet returns the natural log of the absolute value of the determinant. If the determinant is zero, then sign will be 0 and logdet will ... Read More

To return the cumulative product of array elements over a given axis treating NaNs as one, use the nancumprod() method. The cumulative product does not change when NaNs are encountered and leading NaNs are replaced by ones. Ones are returned for slices that are all-NaN or empty.The method returns a new array holding the result is returned unless out is specified, in which case it is returned. Cumulative works like, 5, 5*10, 5*10*15, 5*10*15*20. The 1st parameter is the input array. The 2nd parameter is the Axis along which the cumulative product is computed. By default the input is flattened.The ... Read More

To return the cumulative product of array elements over a given axis treating NaNs as one, use the nancumprod() method. The cumulative product does not change when NaNs are encountered and leading NaNs are replaced by ones. Ones are returned for slices that are all-NaN or empty. The method returns a new array holding the result is returned unless out is specified, in which case it is returned.Cumulative works like, 5, 5*10, 5*10*15, 5*10*15*20. The 1st parameter is the input array. The 2nd parameter is the Axis along which the cumulative product is computed. By default the input is flattened. ... Read More

Suppose, we have n integers in an array nums. We have to find out if the numbers in the array are pairwise coprime, setwise coprime, or not coprime.Two numbers nums[i] and nums[j] are said to be pairwise coprime if gcd(nums[i], nums[j]) = 1. This should hold for every number pair in the array and i < j.The numbers are said to be setwise coprime if gcd(nums[i]) = 1.If they are neither, we say that they are not coprime.So, if the input is like n = 4, nums = {7, 11, 13, 17}, then the output will be the numbers are ... Read More

To integrate a Laguerre series, use the laguerre.lagint() method in Python. The method returns the Laguerre series 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 1st parameter, c is an array of Laguerre 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 an order of integration, must be positive. (Default: ... Read More

To generate a Chebyshev series with given roots, use the chebyshev.chebfromroots() method in Python Numpy. The method returns 1-D array of coefficients. If all roots are real then out is a real array, if some of the roots are complex, then out is complex even if all the coefficients in the result are real. The parameter roots are the sequence containing the roots.StepsAt first, import the required library −import numpy as np from numpy.polynomial import chebyshev as CTo generate a Chebyshev series with given roots, use the chebyshev.chebfromroots() method in Python Numpy −print("Result...", C.chebfromroots((-1, 0, 1)))Get the datatype −print("Type...", C.chebfromroots((-1, ... Read More

To Integrate a Chebyshev series, use the chebyshev.chebint() method in Python. Returns the Chebyshev series 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 1st parameter, c is an array of Chebyshev 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 an order of integration, must be positive. (Default: 1). The 3rd parameter, k is an Integration constant(s). The value of the first ... Read More