生成矩陣

命名模塊，配置編譯選項(xiàng)

-module(matrix_test).
-compile(export_all).

隨機(jī)生成M*N矩陣

%% 隨機(jī)產(chǎn)生M*N矩陣
generateMatrix(M,N) ->
    row(M,N,[]).

row(M,N,Result) ->
    case 0 =:= M of
        true -> Result;
        false -> row(M-1,N,Result++[column(N,[])])
    end.

column(N,Result) ->
    case 0 =:= N of
        true -> Result;
        false -> column(N-1,Result++[random:uniform(2)])
    end.

測試,在erlang shell輸入:

1> c(matrix_test).
 [2,1,2,2,2]]
{ok,matrix_test}
2> matrix_test:generateMatrix(5,5).
[[2,1,1,1,1],
[2,2,1,1,2],
[1,2,2,1,2],
[1,1,2,2,2],

單線程實(shí)現(xiàn)

%% 單線程
matrixMultiply(A,B) ->
    R = lists:foldl(fun(Element,Acc) -> Acc++[rowMultiplyColumn(Element,B,[],1)] end, [], A),
    printMatrix(R,'C').

%%@param 
 % A,B:list
 % Result:存放結(jié)果，初始為[]
 % Count:控制列數(shù),初始為1
 % Result：存放結(jié)果，初始為[]   
%%將某一行A與矩陣B相乘，得出一組向量 
rowMultiplyColumn(A,B,Result,Count) ->
    case Count =:= length(lists:nth(1,B))+1 of
        true -> Result;
        false -> 
            rowMultiplyColumn(A,B,Result ++ [multiply(A,getMatrixColumn(B,Count),0)],Count+1)
    end.

%% 得到矩陣B的第Num列
getMatrixColumn(B,Num) ->
    lists:foldl(fun(A,Acc) -> Acc++[lists:nth(Num, A)] end, [],B).

%% 計(jì)算兩個(gè)向量List的數(shù)量積
multiply([H1|T1],[H2|T2],Sum)  when length(T1) =:= length(T2)  ->
multiply(T1,T2,Sum+H1*H2);
multiply([],[],Sum) -> Sum.

為便于查看,按一定格式打印矩陣

% ????????
printMatrix(A,Name) ->
% P = fun(A, AccIn) -> io:format("~p ~n", [A]) end,
io:format("Matrix ~p is :~n",[Name]),
lists:foldl(fun printRow/2, [], A).
% ????????
printRow(Row, AccIn) ->
io:format("| "),
P = fun(Row,AccIn) -> io:format(" ~p ", [Row]) end,
lists:foldl(P, [], Row),
io:format("| ~n").

測試入口:

%%????????
    io:format("Single Thread:~p[ms]~n",[Time/1000]).
test(M,N,R) ->
A = generateMatrix(M,N),
B = generateMatrix(N,R),
printMatrix(A,'A'),
printMatrix(B,'B'),
{Time,Value} = timer:tc(matrix_test,matrixMultiply,[A,B]),

測試,在erlang shell輸入:

1> c(matrix_test).
matrix_test.erl:10: Warning: variable 'Value' is unused
{ok,matrix_test}
2> matrix_test:test(5,5,5).
Matrix 'A' is :
|12211|
|12212|
|12111|
|12112|
|12221|
Matrix 'B' is :
|11122|
|21111|
|12212|
|22112|
|21211|
Matrix 'C' is :
| 11 10 10 8 11 |
| 13 11 12 9 12 |
| 10 8 8 7 9|
| 12 9 10 8 10|
| 13 12 11 9 13 |
Single Thread:0.619[ms]
ok

5*5矩陣相乘的單線程實(shí)現(xiàn)時(shí)間為0.619ms ,經(jīng)檢驗(yàn),計(jì)算結(jié)果也正確。

多線程實(shí)現(xiàn)

由于要比較串行運(yùn)算與并行運(yùn)算的時(shí)間花銷，所以將matrixMultiply的打印結(jié)果語句去掉，改為：

 %% 單線程
matrixMultiply(A,B) ->
    R = lists:foldl(fun(Element,Acc) -> Acc++[rowMultiplyColumn(Element,B,[],1)] end, [], A).

多線程實(shí)現(xiàn)矩陣相乘

%% 多線程
multiThread(A,B) ->
    P = self(),
%%  啟動(dòng)矩陣A的行數(shù)個(gè)進(jìn)程，分別發(fā)送A的每一行，計(jì)算A的每一行與矩陣B的乘積
    lists:foldl(fun(Element,Acc) -> spawn(fun() -> P! {self(),Acc,rowMultiplyColumn(Element,B,[],1)} end)  end, 1, A),
%% 接收，當(dāng)前進(jìn)程如果收到了A行數(shù)個(gè)消息，表明已經(jīng)計(jì)算完畢
    loop(length(A)).
%% 統(tǒng)計(jì)當(dāng)前進(jìn)程是否已經(jīng)收到了Count條消息
    loop(Count) ->
        receive 
            {Pid,N,Result} ->
%%      io:format("Count=~p,Message=~w~n",[Count,{Pid,N,Result}]),
                case 1=:= Count of
                    true -> io:format("Compute end~n");
                    false -> loop(Count-1)
                end
        end.

矩陣相乘結(jié)果的正確性已經(jīng)驗(yàn)證，打印高維矩陣意義不大，所以在測試入口將打印矩陣的語句去掉，并加入多線程運(yùn)算：

%%測試入口 
test(M,N,R) ->
    A = generateMatrix(M,N),
    B = generateMatrix(N,R),
    % 串行運(yùn)算
    {Time,Value} = timer:tc(matrix_test,matrixMultiply,[A,B]),
    io:format("Single Thread:~p[ms]~n",[Time/1000]),
    % 并行運(yùn)算
    {Time1,Value1} = timer:tc(matrix_test,multiThread,[A,B]),
    io:format("Multi Thread:~p[ms]~n",[Time1/1000]).

注意：為了你的筆記本，不要測試過高維的矩陣相乘。

測試，在erlang shell輸入：

14> c(matrix_test).
matrix_test.erl:11: Warning: variable 'Value' is unused
{ok,matrix_test}
15> matrix_test:test(5,5,5).
Single Thread:0.033[ms]
Compute end
Multi Thread:0.121[ms]
ok

5*5矩陣相乘的單線程實(shí)現(xiàn)時(shí)間為0.033ms，多線程計(jì)算時(shí)間為0.121ms，造成多線程時(shí)間花銷高于單線程的原因主要是計(jì)算量還較小，而建立線程的時(shí)間花銷大于并行計(jì)算節(jié)省的時(shí)間。

進(jìn)而測試100*100矩陣相乘：

19> matrix_test:test(100,100,100).
Single Thread:1507.563[ms]
Compute end
Multi Thread:836.394[ms]
ok

單線程實(shí)現(xiàn)時(shí)間為1507.563ms，多線程計(jì)算時(shí)間為836.394ms，由此可知多線程對高維矩陣運(yùn)算的計(jì)算速度有所提高。

測試200*200矩陣相乘：

20> matrix_test:test(200,200,200).
Single Thread:25639.889[ms]
Compute end
Multi Thread:15294.531[ms]
ok

單線程實(shí)現(xiàn)時(shí)間為25639.889ms，多線程計(jì)算時(shí)間為15294.531ms，隨著矩陣維度的增加，多線程的優(yōu)勢又下降了。

測試400*400矩陣相乘：

21> matrix_test:test(400,400,400).

當(dāng)運(yùn)行到多線程時(shí)，CPU負(fù)載達(dá)到400%以上，筆記本鋁合金外殼都發(fā)黑了，著實(shí)嚇出一身冷汗，迅速關(guān)閉終端，單線程運(yùn)行的結(jié)果也就很遺憾地沒有保存。所以大家還是不要在自己的筆記本上測試這個(gè)了。