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docs: Improve comments and documentation in Strassen algorithm #792

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73ffe16
Improve comments and documentation in Strassen algorithm
ITZ-NIHALPATEL Oct 17, 2025
e1c9e73
Merge pull request #1 from ITZ-NIHALPATEL/ITZ-NIHALPATEL-patch-1
ITZ-NIHALPATEL Oct 17, 2025
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85 changes: 65 additions & 20 deletions math/matrix/strassenmatrixmultiply.go
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Original file line number Diff line number Diff line change
Expand Up @@ -4,16 +4,30 @@
// This program takes two matrices as input and performs matrix multiplication
// using the Strassen algorithm, which is an optimized divide-and-conquer
// approach. It allows for efficient multiplication of large matrices.
// time complexity: O(n^2.81)
// space complexity: O(n^2)
//
// Example:
// | 1 2 | * | 5 6 | = | (1*5 + 2*7) (1*6 + 2*8) | = | 19 22 |
// | 3 4 | | 7 8 | | (3*5 + 4*7) (3*6 + 4*8) | | 43 50 |
//
// Strassen's algorithm achieves a better time complexity by using
// 7 recursive multiplications instead of the 8 used in a standard
// divide-and-conquer approach.
//
// time complexity: O(n^log2(7)) ≈ O(n^2.81)
// space complexity: O(n^2) for storing submatrices
// author(s): Mohit Raghav(https://github.com/mohit07raghav19)
// See strassenmatrixmultiply_test.go for test cases
package matrix

// Perform matrix multiplication using Strassen's algorithm
// StrassenMatrixMultiply performs matrix multiplication using Strassen's
// divide-and-conquer algorithm.
//
// NOTE: This implementation expects the matrices to be square (n x n).
// The base case for the recursion is a 1x1 matrix.
func (A Matrix[T]) StrassenMatrixMultiply(B Matrix[T]) (Matrix[T], error) {
n := A.rows
// Check if matrices are 2x2 or smaller
// Base case for the recursion:
// If the matrix is 1x1, perform a single multiplication.
if n == 1 {
a1, err := A.Get(0, 0)
if err != nil {
Expand All @@ -26,10 +40,15 @@ func (A Matrix[T]) StrassenMatrixMultiply(B Matrix[T]) (Matrix[T], error) {
result := New(1, 1, a1*b1)
return result, nil
} else {
// Calculate the size of submatrices
// --- 1. DIVIDE ---
// Calculate the size of submatrices (quadrants)
mid := n / 2

// Create submatrices
// Create submatrices (A11, A12, A21, A22 and B11, B12, B21, B22)
// A = | A11 A12 |
// | A21 A22 |
// B = | B11 B12 |
// | B21 B22 |
A11, err := A.SubMatrix(0, 0, mid, mid)
if err != nil {
return Matrix[T]{}, err
Expand Down Expand Up @@ -64,83 +83,95 @@ func (A Matrix[T]) StrassenMatrixMultiply(B Matrix[T]) (Matrix[T], error) {
return Matrix[T]{}, err
}

// Calculate result submatrices
A1, err := A11.Add(A22)
// --- 2. CALCULATE INTERMEDIATE TERMS ---
// These are the 10 additions/subtractions required to
// set up the 7 recursive multiplication steps.
A1, err := A11.Add(A22) // A1 = A11 + A22
if err != nil {
return Matrix[T]{}, err
}

A2, err := B11.Add(B22)
A2, err := B11.Add(B22) // A2 = B11 + B22
if err != nil {
return Matrix[T]{}, err
}

A3, err := A21.Add(A22)
A3, err := A21.Add(A22) // A3 = A21 + A22
if err != nil {
return Matrix[T]{}, err
}

A4, err := A11.Add(A12)
A4, err := A11.Add(A12) // A4 = A11 + A12
if err != nil {
return Matrix[T]{}, err
}

A5, err := B11.Add(B12)
A5, err := B11.Add(B12) // A5 = B11 + B12
if err != nil {
return Matrix[T]{}, err
}

A6, err := B21.Add(B22)
A6, err := B21.Add(B22) // A6 = B21 + B22
if err != nil {
return Matrix[T]{}, err
}
//
S1, err := B12.Subtract(B22)
S1, err := B12.Subtract(B22) // S1 = B12 - B22
if err != nil {
return Matrix[T]{}, err
}
S2, err := B21.Subtract(B11)
S2, err := B21.Subtract(B11) // S2 = B21 - B11
if err != nil {
return Matrix[T]{}, err
}
S3, err := A21.Subtract(A11)
S3, err := A21.Subtract(A11) // S3 = A21 - A11
if err != nil {
return Matrix[T]{}, err
}
S4, err := A12.Subtract(A22)
S4, err := A12.Subtract(A22) // S4 = A12 - A22
if err != nil {
return Matrix[T]{}, err
}
// Recursive steps

// --- 3. CONQUER ---
// Recursive steps: Calculate the 7 Strassen products (M1 to M7).
// M1 = (A11 + A22) * (B11 + B22)
M1, err := A1.StrassenMatrixMultiply(A2)
if err != nil {
return Matrix[T]{}, err
}
// M2 = (A21 + A22) * B11
M2, err := A3.StrassenMatrixMultiply(B11)
if err != nil {
return Matrix[T]{}, err
}
// M3 = A11 * (B12 - B22)
M3, err := A11.StrassenMatrixMultiply(S1)
if err != nil {
return Matrix[T]{}, err
}
// M4 = A22 * (B21 - B11)
M4, err := A22.StrassenMatrixMultiply(S2)
if err != nil {
return Matrix[T]{}, err
}
// M5 = (A11 + A12) * B22
M5, err := A4.StrassenMatrixMultiply(B22)
if err != nil {
return Matrix[T]{}, err
}
// M6 = (A21 - A11) * (B11 + B12)
M6, err := S3.StrassenMatrixMultiply(A5)
if err != nil {
return Matrix[T]{}, err
}
// M7 = (A12 - A22) * (B21 + B22)
M7, err := S4.StrassenMatrixMultiply(A6)

if err != nil {
return Matrix[T]{}, err
} //
// (Temporary combinations for calculating C submatrices)
A7, err := M1.Add(M4)

if err != nil {
Expand All @@ -161,30 +192,39 @@ func (A Matrix[T]) StrassenMatrixMultiply(B Matrix[T]) (Matrix[T], error) {
if err != nil {
return Matrix[T]{}, err
}
// Calculate result submatrices

// --- 4. COMBINE ---
// Calculate result submatrices (C11, C12, C21, C22)
// C11 = M1 + M4 - M5 + M7
C11, err := A8.Subtract(M5)
if err != nil {
return Matrix[T]{}, err
}
// C12 = M3 + M5
C12, err := M3.Add(M5)
if err != nil {
return Matrix[T]{}, err
}
// C21 = M2 + M4
C21, err := M2.Add(M4)
if err != nil {
return Matrix[T]{}, err
}
// C22 = M1 - M2 + M3 + M6
C22, err := A10.Subtract(M2)
if err != nil {
return Matrix[T]{}, err
}

// Combine subMatrices into the result matrix
// Combine subMatrices into the final result matrix C
// C = | C11 C12 |
// | C21 C22 |
var zeroVal T
C := New(n, n, zeroVal)

for i := 0; i < mid; i++ {
for j := 0; j < mid; j++ {
// Set C11 (top-left quadrant)
val, err := C11.Get(i, j)
if err != nil {
return Matrix[T]{}, err
Expand All @@ -195,6 +235,7 @@ func (A Matrix[T]) StrassenMatrixMultiply(B Matrix[T]) (Matrix[T], error) {
return Matrix[T]{}, err
}

// Set C12 (top-right quadrant)
val, err = C12.Get(i, j)
if err != nil {
return Matrix[T]{}, err
Expand All @@ -204,6 +245,8 @@ func (A Matrix[T]) StrassenMatrixMultiply(B Matrix[T]) (Matrix[T], error) {
if err1 != nil {
return Matrix[T]{}, err1
}

// Set C21 (bottom-left quadrant)
val, err = C21.Get(i, j)
if err != nil {
return Matrix[T]{}, err
Expand All @@ -213,6 +256,8 @@ func (A Matrix[T]) StrassenMatrixMultiply(B Matrix[T]) (Matrix[T], error) {
if err2 != nil {
return Matrix[T]{}, err2
}

// Set C22 (bottom-right quadrant)
val, err = C22.Get(i, j)
if err != nil {
return Matrix[T]{}, err
Expand Down