Matrix Chain Multiplication With Example
For example if we had four matrices A B C and D we would have. Matrix Multiplication Let A be an n x m matrix B an m x p matrix The product of A and B is n x p matrix AB whose ij-th entry is k1 m a ik b kj In other words we multiply the entries of the i-th row of A with the entries of the j-th column of B and add them up.
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Initialize for k i to j 1 do try all possible splits costRec-Matrix-Chainp i k Rec-Matrix-Chainp k 1 j pi 1pkpj.
Matrix chain multiplication with example. Recursion tree for Matrix-chain14 22 34 23 44 11 22 14 11 24 12 34 44 33 44 11 12 3323 13. In other words no matter how we parenthesize the product the result will be the same. The multiplication sequence is recovered as follows.
Matrix Chain Multiplication Using Dynamic Programming. Do q m i k m k 1 j p i-1 p k p j 10. END Matrix-chain Return Matrix-chain1n Running time.
In other words no matter how the product is parenthesized the result obtained will remain the same. We have many options to multiply a chain of matrices because matrix multiplication is associative. 2n Exponential is.
Do j i l -1 7. Do for i 1 to n-l 1 6. ABCD AB CD A BCD.
1 1. We are given the sequence 4 10 3 12 20 and 7. We multiply the individual elements along the first row of matrix A with the corresponding elements down the first column of matrix B and add the results.
Algorithm of Matrix Chain Multiplication MATRIX-CHAIN-ORDER p 1. A BC 40 x 2 x 60 20 x 40 x 60 48 000 operations. We have many options to multiply a chain of matrices because matrix multiplication is associative.
This gives us the number we need to put in the first row first column position in the answer matrix. For l 2 to n l is the chain length 5. Matrix Chain Multiplication Consider the case multiplying these 4 matrices.
ABCD A BCD AB CD A BCD A B CD. Tn nX 1 k1 Tk Tn k O1 2 nX 1 k1 Tk On 2 Tn 1 2 2 Tn 2 2 2 2. We have many options to multiply a chain of matrices because matrix multiplication is associative.
For i 1 to n 3. Here are many options because matrix multiplication is associative. Let we have n number of matrices A1 A2 A3 An and dimensions are d0 x d1 d1 x d2 d2 x d3.
ABCD - This is a 2x4 multiplied by a 4x1 so 2x4x1 8 multiplications plus whatever work it will take to multiply BCD. ABCD - This is a 2x2 multiplied. ABCD AB CD A BCD.
C is a 2 60 matrix then. Solving a chain of matrix that A i A i1 A i2 A i3. We compute the optimal solution for the product of 2 matrices.
Step2 for i in range 1 to N-1. Problem is that we compute the same result over and over again. Algorithm For Matrix Chain Multiplication Step1 Create a dp matrix and set all values with a big valueINFINITY.
211 -4-2 -16 18 32. Assume that the array 5 has been computed. A is a 20 40 matrix B is a 40 2 matrix and.
A j A i A i1 A i2 A i3. For k i to j-1 9. In the Chain Matrix Multiplication Problem the fundamental choice is which smaller parts of the chain to calculate first before combining them together.
Please like and subscribe. We know M i i 0 for all i. Matrix Chain Multiplication Problem Prachi Joshi Example.
D n-1 x d n ie Dimension of Matrix A i is d i-1 x d i. For example if we had four matrices A B C and D we would have. In other words no matter how we parenthesize the product the result will be the same.
Basic case else mi j infinity. Do m i i 0 4. The matrices have size 4 x 10 10 x 3 3 x 12 12 x 20 20 x 7.
We are given the sequence 4 10 3 12 20 and 7. ABC 20 x 40 x 2 20 x 2 x 60 2 400. Mij 8.
We need to compute M ij 0 i j 5. ABCD AB CD A BCD. In other words no matter how we parenthesize the product the result will be the same.
The matrices have size 4 x 10 10 x 3 3 x 12 12 x 20 20 x 7. Rec-Matrix-Chainarray p int i int j if i j mi i 0. For example for four matrices A B C and D we would have.
For example if we had four matrices A B C and D we would have. Let us proceed with working away from the diagonal. The Chain Matrix Multiplication Problem Given dimensions corresponding to matr 5 5 5 ix sequence 5 5 5.
Example of Finding the Multiplication Sequence. Example of Matrix Chain Multiplication.
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