Matlab生成哈達瑪矩陣的C語言實現

Matlab生成哈達瑪矩陣函數hadamard()的C語言實現

• matlab源代碼
• C語言實現

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項目	下屬項目	測試用例數量
Matlab源代碼	無	1
C語言實現	無	1

Matlab源代碼

參考以下代碼1：

function H = hadamard(n,classname)
%HADAMARD Hadamard matrix.
%   HADAMARD(N) is a Hadamard matrix of order N, that is,
%   a matrix H with elements 1 or -1 such that H'*H = N*EYE(N).
%   An N-by-N Hadamard matrix with N > 2 exists only if REM(N,4)=0.
%   This function handles only the cases where N, N/12 or N/20
%   is a power of 2.
%
%   HADAMARD(N,CLASSNAME) produces a matrix of class CLASSNAME.
%   CLASSNAME must be either 'single' or 'double' (the default).

%   Nicholas J. Higham
%   Copyright 1984-2005 The MathWorks, Inc.

%   Reference:
%   S. W. Golomb and L. D. Baumert, The search for Hadamard matrices,
%   Amer. Math. Monthly, 70 (1963) pp. 12-17.

if nargin < 2, classname = 'double'; end

[f,e] = log2([n n/12 n/20]);
k = find(f==1/2 & e>0);
if min(size(n)) > 1 || isempty(k)
   error(message('MATLAB:hadamard:InvalidInput'));
end
e = e(k)-1;

if k == 1        % N = 1 * 2^e;
   H = ones(classname);

elseif k == 2    % N = 12 * 2^e;
   H = [ones(1,12,classname); ones(11,1,classname) ...
        toeplitz([-1 -1 1 -1 -1 -1 1 1 1 -1 1],[-1 1 -1 1 1 1 -1 -1 -1 1 -1])];

elseif k == 3    % N = 20 * 2^e;
   H = [ones(1,20,classname); ones(19,1,classname)   ...
        hankel([-1 -1 1 1 -1 -1 -1 -1 1 -1 1 -1 1 1 1 1 -1 -1 1], ...
               [1 -1 -1 1 1 -1 -1 -1 -1 1 -1 1 -1 1 1 1 1 -1 -1])];
end

%  Kronecker product construction.
for i = 1:e
    H = [H  H
         H -H]; %#ok
end

C語言實現

此處僅給出哈達瑪矩陣列數爲2的N次方的實現2：

參考以下代碼

int ** myHardmard(int n)//僅產生簡單的哈達瑪矩陣
{
    int i = 0;
    int j = 0;
    int k = 0;
    int findFlag = 0;
    int finalI = 0;
    int nLimit = (int)pow(2.0, 10.0);
    if (n>nLimit)
    {
        printf("無法產生那麼大的哈達瑪矩陣,請手動關閉本程序\n");
        system("pause");
    }
    for (i = 0; i <= 10; i++)
    {
        if (n == myPow(2,i))
        {
            findFlag = 1;
            finalI = i;
            break;
        }
    }
    if (findFlag != 1)
    {
        printf("你輸入的哈達瑪矩陣列數n不是2的N次方,請手動關閉本程序\n");
        system("pause");
    }
    int **H = (int **)malloc(n*sizeof(int *));
    for (i = 0; i < n; i++)
        H[i] = (int *)malloc(n*sizeof(int));
    int row = myPow(2, finalI);
    int col = row;
    for (i = 0; i < row; i++)
    {
        for (j = 0; j < col; j++)
        {
            if (i == 0 && j == 0)
                H[i][j] = 1;
            else for (k = 0; k <= 10; k++)
            {
                int tmpLimit = myPow(2, k);
                if ((i >= tmpLimit) && (j >= tmpLimit))
                {
                    H[i][j] = -H[i - tmpLimit][j - tmpLimit];
                    //break;
                }
                if ((i >= tmpLimit) && (j < tmpLimit))
                {
                    H[i][j] = H[i - tmpLimit][j];
                    //break;
                }
                if ((i<tmpLimit) && (j >= tmpLimit))
                {
                    H[i][j] = H[i][j - tmpLimit];
                    //break;
                }
            }
        }
    }
    printf("生成的哈達瑪矩陣是：\n");
    for (i = 0; i < row; i++)
    {
        for (j = 0; j < col; j++)
        {
            printf("%-3d ", H[i][j]);
        }
        printf("\n");
    }
    printf("\n");
    return H;
}

事實上，以上代碼還可以拓展和簡化，功能上已經實現基本的哈達瑪矩陣了。改進算法將在以後添加。

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1. 源代碼來源於matlab R2016a ↩
2. 本次函數改寫源於一種圖像恢復算法的需求 ↩