将这段c++代码转换为matlab代码def schmidt_orthogonality(matrix_org, debug=False): """ b1 = a1, b2 = a2 - kb1, b3 = a3 - k1b1 - k2b2 :param matrix_org: m x n matrix, m >= n 且满秩 :return: """ m, n = matrix_org.shape matrix_ortho = matrix_org.copy() matrix_ortho = np.asarray(matrix_ortho, dtype=np.float) coefficient = np.zeros(shape=(m, n)) # 系数矩阵k、k1、k2 coefficient[0, 0] = 1 # b1 = a1 for i in range(1, n): # 开始处理下一列 coefficient[i, i] = 1 for j in range(i): b_j = matrix_ortho[:, j] k_j = np.dot(b_j, matrix_org[:, i]) / np.dot(b_j, b_j) coefficient[j, i] = k_j matrix_ortho[:, i] -= k_j * b_j # 正交向量b1,b2...做正交化处理，系数也做相应的改变 for i in range(n): devider = np.dot(matrix_ortho[:, i], matrix_ortho[:, i]) if abs(devider) < 1e-16: # 避免除以0 matrix_ortho[:, i] *= 0 else: devider = np.sqrt(devider) matrix_ortho[:, i] /= devider coefficient[i, :] *= devider print('result:', matrix_ortho) return matrix_ortho, coefficient

下面是将该C++代码转换为MATLAB代码的实现：

function [matrix_ortho, coefficient] = schmidt_orthogonality(matrix_org, debug)
% matrix_org: m x n matrix, m >= n and full rank
% matrix_ortho: m x n matrix, orthogonal matrix
% coefficient: m x n matrix, coefficients k, k1, k2, ...
% debug: boolean, print debug information or not

[m,n] = size(matrix_org);
matrix_ortho = double(matrix_org);
coefficient = zeros(m,n);
coefficient(1,1) = 1;

for i = 2:n
    coefficient(i,i) = 1;
    for j = 1:i-1
        b_j = matrix_ortho(:,j);
        k_j = dot(b_j, matrix_org(:,i)) / dot(b_j, b_j);
        coefficient(j,i) = k_j;
        matrix_ortho(:,i) = matrix_ortho(:,i) - k_j * b_j;
    end
end

for i = 1:n
    devider = dot(matrix_ortho(:,i), matrix_ortho(:,i));
    if abs(devider) < 1e-16
        matrix_ortho(:,i) = matrix_ortho(:,i) * 0;
    else
        devider = sqrt(devider);
        matrix_ortho(:,i) = matrix_ortho(:,i) / devider;
        coefficient(i,:) = coefficient(i,:) * devider;
    end
end

if debug
    disp('result:');
    disp(matrix_ortho);
end

end

该函数会返回正交矩阵和系数矩阵。其中，正交矩阵按列排列，系数矩阵按行列顺序排列。若debug为true，则会输出结果。