为了您的学习，您需要比较经典的矩阵乘法算法和 Winograd-Strassen 算法。我不清楚为什么 Winograd-Strassen 算法比经典算法慢得多。据我所知，MatLab 对经典算法进行了更优化，尤其是对于超大型矩阵。使用 Winograd-Strassen 算法会浪费时间为中间矩阵等分配内存空间。但随着矩阵的大小，减速非常大 - 我将其附在图片中。图中，矩阵阶数为2^10的经典算法运行时间为几秒钟，而Winograd-Strassen算法则需要7分钟。
这是代码，可能算法没有正确理解它。只需使用 Strassen 和 Winograd-Strassen 算法调用一个函数就需要类型参数。好像没有更多的功能了
clc;
function AA = split_to_2x2_blocks(matrix) % разделение матрицы на 4 части
buf = width(matrix);
A11 = matrix(1:buf/2, 1:buf/2);
A12 = matrix(1:buf/2, buf/2+1:buf);
A21 = matrix(buf/2+1:buf, 1:buf/2);
A22 = matrix(buf/2+1:buf, buf/2+1:buf);
AA = {A11, A12
A21, A22};
end
function CC = strassen_mul_2x2(lb, rb, type) % умножение матрицы после разделения, рекурсивная чушь тут и все такое
d = strassen_mul(cell2mat(lb(1,1)) + cell2mat(lb(2,2)), cell2mat(rb(1,1)) + cell2mat(rb(2,2)), type);
d_1 = strassen_mul(cell2mat(lb(1,2)) - cell2mat(lb(2,2)), cell2mat(rb(2,1)) + cell2mat(rb(2,2)), type);
d_2 = strassen_mul(cell2mat(lb(2,1)) - cell2mat(lb(1,1)), cell2mat(rb(1,1)) + cell2mat(rb(1,2)), type);
left = strassen_mul(cell2mat(lb(2,2)), cell2mat(rb(2,1)) - cell2mat(rb(1,1)), type);
right = strassen_mul(cell2mat(lb(1,1)), cell2mat(rb(1,2)) - cell2mat(rb(2,2)), type);
top = strassen_mul(cell2mat(lb(1,1)) + cell2mat(lb(1,2)), cell2mat(rb(2,2)), type);
bottom = strassen_mul(cell2mat(lb(2,1)) + cell2mat(lb(2,2)), cell2mat(rb(1,1)), type);
c1 = d + d_1 + left - top;
c2 = right + top;
c3 = left + bottom;
c4 = d + d_2 + right - bottom;
CC = [c1, c2
c3, c4];
end
function CC = vinograd_strassen_mul_2x2(lb, rb, type)
s1 = cell2mat(lb(2,1)) + cell2mat(lb(2,2));
s2 = s1 - cell2mat(lb(1,1));
s3 = cell2mat(lb(1,1)) - cell2mat(lb(2,1));
s4 = cell2mat(lb(1,2)) - s2;
s5 = cell2mat(rb(1,2)) - cell2mat(rb(1,1));
s6 = cell2mat(rb(2,2)) - s5;
s7 = cell2mat(rb(2,2)) - cell2mat(rb(1,2));
s8 = s6 - cell2mat(rb(2,1));
p1 = strassen_mul(s2, s6, type);
p2 = strassen_mul(cell2mat(lb(1,1)), cell2mat(rb(1,1)), type);
p3 = strassen_mul(cell2mat(lb(1,2)), cell2mat(rb(2,1)), type);
p4 = strassen_mul(s3, s7, type);
p5 = strassen_mul(s1, s5, type);
p6 = strassen_mul(s4, cell2mat(rb(2,2)), type);
p7 = strassen_mul(cell2mat(lb(2,2)), s8, type);
t1 = p1 + p2;
t2 = t1 + p4;
CC = [p2 + p3, t1 + p5 + p6
t2 - p7, t2 + p5];
end
function c = default_mul(left, right) % классический метод умножения матриц
c = zeros(length(left));
for ii = 1:length(left)
for jj = 1:length(right)
for rr = 1:length(left)
c(ii, jj) = c(ii, jj) + left(ii, rr)* right(rr, jj);
end
end
end
end
function c = strassen_mul(left, right, type ) % типо сюда пихаем матрицу и её будущие части, а потом решаем
if length(left) == 2
c = default_mul(left, right);
else
%if type == 0
% c = strassen_mul_2x2(split_to_2x2_blocks(left), split_to_2x2_blocks(right), type);
%elseif type == 1
c = vinograd_strassen_mul_2x2(split_to_2x2_blocks(left), split_to_2x2_blocks(right), type);
%else
% disp('Не выбран вариант')
%end
end
end
%
% a = [1 2 3 4
% 5 6 7 8
% 9 10 11 12
% 13 14 15 16];
% b = [1 2 3 4
% 5 6 7 8
% 9 10 11 12
% 13 14 15 16];
% a = randi([1, 10], 8);
% b = randi([1, 10], 8);
% count_mas = [0, 0, 0]; % сложение, умножение, умножение матриц
% disp(a)
% disp(b)
% c = strassen_mul(a,b);
% disp(c)
% disp(sum)
% disp(umnoj)
% disp(umnoj_mat)
max_stepen = 6;
all_time = zeros(max_stepen, 2);
for t = 1:max_stepen
step = 2^t;
a = randi([1,10], step);
b = randi([1,10], step);
tic
c = default_mul(a, b);
all_time(t, 1) = toc;
tic
c = strassen_mul(a,b, 1);
all_time(t, 2) = toc;
end
t = 1:max_stepen;
hold on
grid on
title("График времени работы без фоновых процессов")
plot(t, all_time(:, 1),'-gs', 'LineWidth',2, 'MarkerSize',10,'Color', [0 0.4470 0.7410])
plot(t,all_time(:, 2),':gs','LineWidth',2,'MarkerSize',10, 'Color', [0.9290 0.6940 0.1250])
xlabel('Порядок матриц')
ylabel('Время работы')
legend("Классический метод", "Метод Винограда-Штрассена")