C++  Write a multithreaded program using only Pthreads that uses several threads to multiply two matrices. The multiplication of matrix A with M rows and L columns, and a matrix B with L rows and N columns gives a resulting matrix C with M rows and N columns, and is given by the formula,   In matrix multiplication, each element Cij is the dot product of the ith row vector of A with the jth column vector of B. The program uses one thread to calculate a dot product. Exact result please.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
icon
Related questions
Question

C++ 

Write a multithreaded program using only Pthreads that uses several threads to multiply two matrices. The multiplication of matrix A with M rows and L columns, and a matrix B with L rows and N columns gives a resulting matrix C with M rows and N columns, and is given by the formula,

 

In matrix multiplication, each element Cij is the dot product of the ith row vector of A with the jth column vector of B. The program uses one thread to calculate a dot product. Exact result please. 

 

The image contains a mathematical formula typically used in matrix multiplication:

\[ C_{ij} = \sum_{k=0}^{L-1} A_{ik} B_{kj} \]

This equation represents the computation of the element \( C_{ij} \) in the resulting matrix \( C \), obtained by multiplying matrices \( A \) and \( B \). The formula sums the product of elements from the \( i \)-th row of matrix \( A \) and the \( j \)-th column of matrix \( B \).

- \( 0 \leq i < M \) and \( 0 \leq j < N \) define the dimensions of the resulting matrix \( C \), where \( M \) is the number of rows and \( N \) is the number of columns.
- \( L \) represents the shared dimension between matrices \( A \) and \( B \), indicating the number of columns in \( A \) and the number of rows in \( B \).
Transcribed Image Text:The image contains a mathematical formula typically used in matrix multiplication: \[ C_{ij} = \sum_{k=0}^{L-1} A_{ik} B_{kj} \] This equation represents the computation of the element \( C_{ij} \) in the resulting matrix \( C \), obtained by multiplying matrices \( A \) and \( B \). The formula sums the product of elements from the \( i \)-th row of matrix \( A \) and the \( j \)-th column of matrix \( B \). - \( 0 \leq i < M \) and \( 0 \leq j < N \) define the dimensions of the resulting matrix \( C \), where \( M \) is the number of rows and \( N \) is the number of columns. - \( L \) represents the shared dimension between matrices \( A \) and \( B \), indicating the number of columns in \( A \) and the number of rows in \( B \).
### Matrix Multiplication Example

In this example, we demonstrate the multiplication of two matrices, \( \Lambda \) and \( B \), resulting in the matrix labeled as "Result."

#### Matrix Definitions:

- **Matrix \( \Lambda \):**
  \[
  \Lambda = \begin{bmatrix}
  5 & 2 & 3 \\
  4 & 5 & 7 \\
  6 & 3 & 7 \\
  1 & 3 & 4 \\
  \end{bmatrix}
  \]

- **Matrix \( B \):**
  \[
  B = \begin{bmatrix}
  4 & 5 & 6 & 1 \\
  3 & 2 & 3 & 5 \\
  2 & 8 & 7 & 7 \\
  \end{bmatrix}
  \]

#### Resulting Matrix:

The product of \( \Lambda \) and \( B \) is the resulting matrix:

\[
Result = \begin{bmatrix}
32 & 53 & 57 & 36 \\
45 & 86 & 88 & 78 \\
47 & 92 & 94 & 70 \\
21 & 43 & 43 & 44 \\
\end{bmatrix}
\]

#### Explanation of the Multiplication Process:

**Step-by-Step Calculation:**

For each element in the resulting matrix, take the corresponding row from \( \Lambda \) and the column from \( B \), multiply their respective components, and sum up the products.

For example, the element in the first row, first column of the Result matrix is calculated as follows:

- \((5 \times 4) + (2 \times 3) + (3 \times 2) = 20 + 6 + 6 = 32\)

Follow this method for each element in the Result matrix to complete the matrix multiplication.
Transcribed Image Text:### Matrix Multiplication Example In this example, we demonstrate the multiplication of two matrices, \( \Lambda \) and \( B \), resulting in the matrix labeled as "Result." #### Matrix Definitions: - **Matrix \( \Lambda \):** \[ \Lambda = \begin{bmatrix} 5 & 2 & 3 \\ 4 & 5 & 7 \\ 6 & 3 & 7 \\ 1 & 3 & 4 \\ \end{bmatrix} \] - **Matrix \( B \):** \[ B = \begin{bmatrix} 4 & 5 & 6 & 1 \\ 3 & 2 & 3 & 5 \\ 2 & 8 & 7 & 7 \\ \end{bmatrix} \] #### Resulting Matrix: The product of \( \Lambda \) and \( B \) is the resulting matrix: \[ Result = \begin{bmatrix} 32 & 53 & 57 & 36 \\ 45 & 86 & 88 & 78 \\ 47 & 92 & 94 & 70 \\ 21 & 43 & 43 & 44 \\ \end{bmatrix} \] #### Explanation of the Multiplication Process: **Step-by-Step Calculation:** For each element in the resulting matrix, take the corresponding row from \( \Lambda \) and the column from \( B \), multiply their respective components, and sum up the products. For example, the element in the first row, first column of the Result matrix is calculated as follows: - \((5 \times 4) + (2 \times 3) + (3 \times 2) = 20 + 6 + 6 = 32\) Follow this method for each element in the Result matrix to complete the matrix multiplication.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Array
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education