Matrix Multiplication Algorithm In C

10 Apr, 2021

Before jumping to Strassens algorithm it is necessary that you should be familiar with matrix multiplication using the Divide and Conquer method. Use the following func- tion signature and implement the naive matrix multiplication algorithm with three nested loops.

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Next we display the final matrix.

Matrix multiplication algorithm in c. Enter the row and column of the second b matrix. K suma 0. Refer to this blog ideaAdd a link description.

After learning Data Structure and Algorithm Analysis C Version Third Edition 1633 STRASSEN matrix multiplied algorithm flow use C to implement STRASSEN method to seek matrix multiplication. I for j 0. Scalar multiplication is compatible with multiplication of matrix.

C Programming Matrix Multiplication Step 1. Let A 1 x 2 B 2 x 3 C 3 x 2. If 3 matrices A B C we can find the final result in two ways ABC or A BC.

Then ABC 10305 10560 1500 3000 4500 operations A BC 30560 103060 9000 18000 27000 operations. Consider naive square matrix multiplication. If c1 r2 cout.

Declare variables and initialize necessary variables. To calculate AB we need 123 6 multiplications. Record algorithm analysis homework.

For example suppose A is a 10 30 matrix B is a 30 5 matrix and C is a 5 60 matrix. J Cij 0. K0 AF All matrix entries are single precision floating point numbers.

To do so we are taking input from the user for row number column number first matrix elements and second matrix elements. Co MatrixB f co MatrixB co f. Then we are performing multiplication on the matrices.

We use pointers in C to multiply to matrices. Enter the row and column of the first a matrix. K Cij AikBkj How fast can this run.

For f 0. Using the Master Theorem with T n 8T n2 O n2 we still get a runtime of O n3. Partition b into four sub matrices b11 b12 b21 b22.

λ AB λA B and A Bλ Matrix Multiplication Algorithm. We can add subtract multiply and divide 2 matrices. MatrixR j k suma.

Enter the elements of the second b matrix. For k 0. The second one consist of transposing the matrix B first and then do the multiplication by rows.

Strassens insight was that we dont actually need 8 recursive calls to complete this process. Clearly the first parenthesization requires less number of. Do for j 0.

Void MADD1 float A float B float C int n. F for co 0. That is n1 Cij Cij AikBkj.

Check if the number of columns of first matrix is same as the rows of second matrixcondition for matrix multiplication Applying proper loops use the formula C ij A ik B ik where ijk are positive integers and ijk. If we follow first way ie. Algorithm for Strassens matrix multiplication.

Matrix multiplication follows distributive rule over matrix addition. Enter the elements of the first a matrix. Both the matrices a and b are displayed using a nested for.

A - matrix of dimensions nxm B - matrix of dimensions mxn C - resultant matrix C A x B for i 1 to n for j1 to m for k1 to n C ijC ij A ik B kj First let us see if we can do any SIMD Single Instruction Multiple Data type operations. Please refer to the following post as a prerequisite of the code. Algorithm Strassenn a b d begin If n threshold then compute C a b is a conventional matrix.

We get same result in any way since matrix multiplication satisfies associativity property. Of rows and columns of both the elements. Naive Matrix Multiplication Algorithm.

Then we are performing multiplication on the matrices entered by the user. L suma MatrixA j lMatrixB l k. Define Aij AAjni define Bij BBjni define Cij CCjni for i 0.

Matrix Multiplication in C Matrix multiplication is another important program that makes use of the two-dimensional arrays to multiply the cluster of values in the form of matrices and with the rules of matrices of mathematics. To do so we are taking input from the user for row number column number first matrix elements and second matrix elements. In this C program the user will insert the order for a matrix followed by that specific number of elements.

The first one is normal method. Multiplication of Rectangular Matrices. C.

MatrixMultiply P Q. Matrix multiplication in C We can add subtract multiply and divide 2 matrices. Assume dimension of P is a x b dimension of Q is z x y Begin if b is not same as z then exit otherwise define R matrix as a x y for i in range 0 to a - 1 do for j in range 0 to y 1 do for k in range 0 to z do R i j R i j P i k Q k j done done done End.

Else Partition a into four sub matrices a11 a12 a21 a22. For l 0. The above strategy is the basic O N3 strategy.

J for k 0. Matrix multiplication in C Matrix multiplication in C. A B C AB AC Right Distribution A B C AC AC.

Divide and Conquer Method Consider two matrices A and B with 4x4 dimension each as shown below The matrix multiplication of the above two matrices A and B is Matrix C. Matrix C aebg afbh cedg cfdh.

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