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To get the Least squares fit of Laguerre series to data, use the laguerre.lagfit() method in Python numpy. The method returns the Laguerre coefficients ordered from low to high. If y was 2-D, the coefficients for the data in column k of y are in column k.The parameter, x are the x-coordinates of the M sample (data) points (x[i], y[i]). The parameter, y are the y-coordinates of the sample points. Several sets of sample points sharing the same xcoordinates can be (independently) fit with one call to polyfit by passing in for y a 2-D array that contains one data ... Read More
To return the scaled companion matrix of a 1-D array of Laguerre polynomial coefficients, use the laguerre.lagvander3d() in Python Numpy. The usual companion matrix of the Laguerre polynomials is already symmetric when c is a basis Laguerre polynomial, so no scaling is applied.Returns the Companion matrix of dimensions (deg, deg). The parameter, c is a 1-D array of Laguerre series coefficients ordered from low to high degree.StepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate a 1D array of coefficients −c = np.array([1, 2, 3])Display the array −print("Our Array...", c)Check the Dimensions −print("Dimensions ... Read More
To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander2d() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Laguerre polynomial. The dtype will be the same as the converted x.The parameter, x, y returns an 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 a list of ... Read More
To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander2d() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Laguerre polynomial. The dtype will be the same as the converted x.The parameter, x, y returns an 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 a list of ... Read More
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.The 1st parameter, c is an array of Laguerre series coefficients. If c is multidimensional the different axis correspond ... Read More
Splitting a string means being able to get a part of a string, and that part can either be based on a position or a character in the string.In Go, if we want to split a string on the basis of positions, we can make use of the [ ] (square brackets) and then pass the indices in them separated by a colon.SyntaxConsider the syntax shown below.sl[startingIndex : EndingIndex]It should be noted that the element at the EndingIndex in the slice won't be considered, as the range is from startingIndex to (EndingIndex−1).Example 1Now, let's consider an example where we will ... Read More
Suppose we have a string S of length n, with only two types of characters, 'A' or 'P'. There are n students in a row, the ith student is angry if S[i] = 'A', if it is 'P' it says S[i] is patient. An angry student at index i will hit patient student in index i+1 in every minute, and for the last student even it he is angry, he cannot hit anyone. After hitting a patient student, that student also gets angry. We have to find the minimum minutes for after that no new students get angry.So, if the ... Read More
Suppose we have two numbers n and k. We have unlimited number of coins worth values 1 to n. We want to take some values whose sum is k. We can select multiple same valued coins to get total sum k. We have to count the minimum number of coins needed to get the sum k.So, if the input is like n = 6; k = 16, then the output will be 3, because (2 * 6) + 4.StepsTo solve this, we will follow these steps −c := (n + k - 1) / n return cExampleLet us see the ... Read More
Suppose we have two numbers n and k. We have to choose the maximum number of distinct elements from 1 to n, so that no subset whose sum is equal to k. If we can find then return the chosen numbers.So, if the input is like n = 5; k = 3, then the output will be [4, 5, 2]StepsTo solve this, we will follow these steps −for initialize i := (k + 1) / 2, when i
Suppose we have five numbers s, v1, v2, t1 and t2. Amal and Bimal are playing a typing game, they are playing their game online. In this game they will type a string whose length is s. Amal types one character in v1 milliseconds and Bimal types one character in v2 milliseconds. Amal's network delay is t1 milliseconds, and Bimal's network delay is t2 milliseconds.If the connection delay is t milliseconds, the competition passes for a participant as follows −Exactly after t milliseconds after the game start the participant receives the text to be entered.Right after that he starts to ... Read More