Matrix Transpose

题面

Write a program that transposes a matrix of 32-bit floating point numbers on a GPU. The transpose of a matrix switches its rows and columns. Given a matrix
𝐴
of dimensions
𝑟
𝑜
𝑤
𝑠
×
𝑐
𝑜
𝑙
𝑠
, the transpose
𝐴
𝑇
will have dimensions
𝑐
𝑜
𝑙
𝑠
×
𝑟
𝑜
𝑤
𝑠
. All matrices are stored in row-major format.

A
1
2
3
4
5
6
3 × 2
rows → cols
Aᵀ
1
3
5
2
4
6
2 × 3

Implementation Requirements

• Use only native features (external libraries are not permitted)
• The solve function signature must remain unchanged
• The final result must be stored in the matrix output

Examples

Example 1:

Input: 2×3 matrix
[
1.0
	
2.0
	
3.0


4.0
	
5.0
	
6.0
]
Output: 3×2 matrix
[
1.0
	
4.0


2.0
	
5.0


3.0
	
6.0
]

Example 2:

Input: 3×1 matrix
[
1.0


2.0


3.0
]
Output: 1×3 matrix
[
1.0
	
2.0
	
3.0
]

Constraints

• 1 ≤ rows, cols ≤ 8192
• Input matrix dimensions: rows × cols
• Output matrix dimensions: cols × rows
• Performance is measured with cols = 6,000, rows = 7,000