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The hessian() function computes the Hessian of a given function. The hessian() function can be accessed from the torch.autograd.functional module. The function whose Hessian is being computed takes a tensor as the input and returns a tuple of tensors or a tensor. The hessian() function returns a tensor with the Hessian values computed for a function with the given input.Syntaxtorch.autograd.functional.hessian(func, input)Parametersfunc − It's a Python function for which the Hessian is computed.input − It’s input to the function, func.StepsWe could use the following steps to compute the Hessian of a given function −Import the required library. In all the following ... Read More
The jacobian() function computes the Jacobian of a given function. The jacobian() function can be accessed from the torch.autograd.functional module. The function whose Jacobian is being computed takes a tensor as the input and returns a tuple of tensors or a tensor. The jacobian() function returns a tensor with Jacobian values computed for a function with the given input.Syntaxtorch.autograd.functional.jacobian(func, input)Parametersfunc − It's a Python function for which the Jacobian is computed.input − It’s the input to the function, func.StepsWe could use the following steps to compute the Jacobian of a given function −Import the required library. In all the following ... Read More
In this problem, we are given an array arr[] consisting of n integer values. Our task is to find the sum of all unique subarray sum for a given array. Subarray sum is the sum of elements of the given subarray.Let's take an example to understand the problem, Input : arr[] = {1, 2, 4} Output : 23Explanation −All subarrays of the given array are : (1), (2), (4), (1, 2), (2, 4), (1, 2, 4) Sum of subarrays = 1 + 2 + 4 + (1+2) + (2+4) + (1+2+4) = 23Solution ApproachA solution to the problem is by ... Read More
In this problem, we are given a binary tree. Our task is to find the sum of all left right in a given Binary Tree.Let's take an example to understand the problem, Input :Output : 8Explanation −All leaf nodes of the tree are : 1, 8 Sum = 1 + 8 = 9Solution ApproachA simple solution to the problem is traversing the tree from root to leaf. If a node is a left leaf node, add it to sum. When the whole tree is traversed. Print Sum.ExampleProgram to illustrate the working of our solution#include using namespace std; struct Node{ ... Read More
In this problem, we are given a binary tree. Our task is to find the sum of all left leaves in a given Binary Tree.Let's take an example to understand the problem, Input : Output : 11Explanation −All leaf nodes of the tree are : 2, 9 Sum = 2 + 9 = 11Solution ApproachA simple solution to the problem is traversing the tree from root to leaf. If a node is a left leaf node, add it to sum. When the whole tree is traversed. Print Sum.ExampleProgram to illustrate the working of our solution#include using namespace std; struct Node{ ... Read More
In this problem, we are given an array arr[] consisting of N integers stored in unsorted order. Our task is to find a subarray with a given sum.Let's take an example to understand the problem, Input : arr[] = {2, 5, -1, 4, 6, -9, 5} sum = 14 Output : subarray = {5, -1, 4, 6}Explanation −Subarray sum = 5 - 1 + 4 + 6 = 14Solution ApproachA simple solution to the problem is using nested loops. We will loop through the array and using an inner loop, we will find subarray. For each subarray we will find ... Read More
In this problem, we are given an array arr[] consisting of N positive integers stored in unsorted order. Our task is to find a subarray with a given sum.Let's take an example to understand the problem, Input : arr[] = {2, 5, 1, 4, 6, 9, 5} sum = 11 Output : subarray = {1, 4, 6}Explanation −Subarray sum = 1 + 4 + 6 = 11Solution ApproachA simple solution to the problem is using nested loops. We will loop through the array and using an inner loop, we will find subarray. For each subarray we will find the sum ... Read More
In this problem, we are given a string str and an integer pow. Our task is to find a sub-string with given power.We need to return the substring whose power is equal to pow.Power of string is the sum of powers of its characters.Power of character : a -> 1, b -> 2, c -> 3, ...Let's take an example to understand the problem, Input : string = "programming" power = 49 Output : 'pro'Explanation −Power of matrix : pro, power(p) = 16 power(p) = 18 power(p) = 15 Total = 16 + 18 + 15 = 49Solution ApproachA simple ... Read More
In Ruby, we can take the help of lambda functions when we want to use anonymous functions. They are also treated like objects in Ruby, as everything in Ruby is treated as objects.SyntaxThe syntax of declaring a lambda function is shown below.lambda = lambda {}Or, we can also make use of lambda literal.lambda = ->() {} Let's first check the type of the lambda functions in Ruby with the help of a program.Example 1Consider the code shown belowsome_lambda_function = lambda { puts "Welcome to TutorialsPoint!"} puts some_lambda_function.classOutputProc Example 2Now let's create another program where we will use our own ... Read More
In Ruby, the class whose objects can be ordered uses the Comparable mixin. Class definitions need to include an operator to compare receivers with each other. The operator will return either -1, 0, or 1.It returns -1 if the receiver is less than another object.If it is greater than another object, then it returns 1.It returns 0 if the receiver is equal to another object.In the Comparable module, the operator is used to implement the conventional comparison operators (*, =, and >) and sometimes also between? method as well.Now that we know a little about the comparable module in ... Read More