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.
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
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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
![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 \( B \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F430bfeaa-46a3-49aa-aa65-0ce9c05d75e6%2Fa749c463-2c49-4e03-84c9-73275dca1ff3%2Ff7sdvmb_processed.jpeg&w=3840&q=75)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F430bfeaa-46a3-49aa-aa65-0ce9c05d75e6%2Fa749c463-2c49-4e03-84c9-73275dca1ff3%2Fpj9a2fl_processed.jpeg&w=3840&q=75)
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.
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