C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN: 9781337102087
Author: D. S. Malik
Publisher: Cengage Learning
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IN PYTHON:
import numpy as npimport numpy.linalg as la
def smallest_eig(A):"""Given a positive definite symmetric matrix A,calculates the smallest eigenvalue of A andthe corresponding eigevector by using the inverseiteration.
You are not allowed to use numpy.linalg functionsfor calculating the eigenvalues. However, you can usenumpy linalg functions for solving linear equations andfor calculating norms.
Output: a tuple (lam, x), where lam is the smallesteigenvalue and x is the corresponding eigenvector
"""n = A.shape[0]lam = 0x = np.random.randn(n)passreturn (lam, x)
Develop a solution that will calculate the average temperature, given a set of temperatures. The number of temperatures may differ from time to time. (Use a trip values to stop the processing of the loop.) Test the solution with the following 10 temperatures.
78 90
85 80
87 83
75 90
86 70
As the algorithm performs division of numbers with high precision, it is very common to see really big numbers after the period (for example: 1200.2300001), which is not desirable because of several reasons:
may cause confusion to some users when they see such big numbers;
uses more memory to store a bigger number;
it just does not make sense to display currency number in this format.
For this reason, you are going to implement a utility function to format any number into the appropriate currency format, using 2 decimal places.
For example: The number 1200.2300001 would be became: 1200.23
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- Create a function that returns the nth catalan number. In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects. They are named after the Belgian mathematician Eugène Charles Catalan (1814-1894). For more info, check out the resource tab. Examples getCatalanNumber (0) → 1 getCatalanNumber (6) → 132 getCatalanNumber (8) 1430 Notes Inputs are zero and positive integers.arrow_forwardAssuming that you have the functions "drawPolygon(int[] x, int[] y, int n)" for drawing polygon, "drawRectangle(int x, int y, int width, int height)" for drawing rectangle and "drawCircle(int xc, intyc, int radius)" for drawing circle; draw the given shape. Where: R(300,250), T1(325,275), T2(475,275), T3(400,400), Pı(285.250), P2(225.275), P3(200,450), P4(285, 300), Q1(515,250), Q2(575,275), Q3(600,450), Q4(515,300) C6: (300,75), R=50 C7: (500,75), R=50 C1: (400,150), R=100 С4: (350,150), R-10 C5: (450,150), R=10 C2: (400,195), R=50 C3: (400,175), R=30 C8: (400,225), R=15 P1 R P2, T2 P4 Q2 Q4 T3 Pa 200arrow_forwardThe Fibonacci sequence is a famous sequence in mathematics. The first element in the sequence is 0 and the second element is 1. The nth element is defined as Fn = Fn-1 + Fn-2- Implement the fib function, which takes an integer n and returns the n th Fibonacci number. Use a while loop in your solution. def fib(n): """Returns the nth Fibonacci number. >>> fib (0) 0 >>> fib (1) 1 >>> fib(2) 1 >>> fib(3) 2 >>> fib(4) 3 >>> fib(5) 5 >>> fib(6) 8 >>> fib (100) 354224848179261915075 "*** YOUR CODE HERE ***"arrow_forward
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