Computer Systems: A Programmer's Perspective (3rd Edition)
3rd Edition
ISBN: 9780134092669
Author: Bryant, Randal E. Bryant, David R. O'Hallaron, David R., Randal E.; O'Hallaron, Bryant/O'hallaron
Publisher: PEARSON
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Question
Chapter 6.2, Problem 6.7PP
Program Plan Intro
Given Information:
The sample program for sum of a 3-D array is given below:
// Sum of a 3-dimensional array
int sumarray3d(int a[N] [N] [N])
{
//variable declaration
int i,j,k, sum=0;
//Traverse the array
for(i=0;i<n;i++)
{
for(j=0;j>N;j++)
{
for(k=0;k<N;k++)
{
//sum of all the array elements
sum = sum+ a[k][i][j];
}
}
}
return sum;
}
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(Sparse matrix–vector product) Recall from Section 3.4.2 that a matrix is said to be sparse if most of its entries are zero. More formally, assume a m × n matrix A has sparsity coefficient γ(A) ≪ 1, where γ(A) ≐ d(A)/s(A), d(A) is the number of nonzero elements in A, and s(A) is the size of A (in this case, s(A) = mn). 1. Evaluate the number of operations (multiplications and additions) that are required to form the matrix– vector product Ax, for any given vector x ∈ Rn and generic, non-sparse A. Show that this number is reduced by a factor γ(A), if A is sparse. 2. Now assume that A is not sparse, but is a rank-one modification of a sparse matrix. That is, A is of the form à + uv⊤, where à ∈ Rm,n is sparse, and u ∈ Rm, v ∈ Rm are given. Devise a method to compute the matrix–vector product Ax that exploits sparsity.
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Chapter 6 Solutions
Computer Systems: A Programmer's Perspective (3rd Edition)
Ch. 6.1 - Prob. 6.1PPCh. 6.1 - Prob. 6.2PPCh. 6.1 - Prob. 6.3PPCh. 6.1 - Prob. 6.4PPCh. 6.1 - Prob. 6.5PPCh. 6.1 - Prob. 6.6PPCh. 6.2 - Prob. 6.7PPCh. 6.2 - Prob. 6.8PPCh. 6.4 - Prob. 6.9PPCh. 6.4 - Prob. 6.10PP
Ch. 6.4 - Prob. 6.11PPCh. 6.4 - Prob. 6.12PPCh. 6.4 - Prob. 6.13PPCh. 6.4 - Prob. 6.14PPCh. 6.4 - Prob. 6.15PPCh. 6.4 - Prob. 6.16PPCh. 6.5 - Prob. 6.17PPCh. 6.5 - Prob. 6.18PPCh. 6.5 - Prob. 6.19PPCh. 6.5 - Prob. 6.20PPCh. 6.6 - Prob. 6.21PPCh. 6 - Prob. 6.22HWCh. 6 - Prob. 6.23HWCh. 6 - Suppose that a 2 MB file consisting of 512-byte...Ch. 6 - The following table gives the parameters for a...Ch. 6 - The following table gives the parameters for a...Ch. 6 - Prob. 6.27HWCh. 6 - This problem concerns the cache in Practice...Ch. 6 - Suppose we have a system with the following...Ch. 6 - Suppose we have a system with following...Ch. 6 - Suppose that a program using the cache in Problem...Ch. 6 - Repeat Problem 6.31 for memory address0x16E8 A....Ch. 6 - Prob. 6.33HWCh. 6 - Prob. 6.34HWCh. 6 - Prob. 6.35HWCh. 6 - Prob. 6.36HWCh. 6 - Prob. 6.37HWCh. 6 - Prob. 6.38HWCh. 6 - Prob. 6.39HWCh. 6 - Given the assumptions in Problem 6.38, determine...Ch. 6 - You are writing a new 3D game that you hope will...Ch. 6 - Prob. 6.42HWCh. 6 - Prob. 6.43HWCh. 6 - Prob. 6.45HWCh. 6 - Prob. 6.46HW
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