写论文第五天：参数扫描法

1.parameterSweep函数

[respmax,varmax,resp,var] = parameterSweep(fun,range)

输出的4个变量依次是最优结果（比如最大夏普比例），最优结果对应的参数组合，所有扫描结果以及所有的参数组合。

输入两个变量，第一个是一个指向被扫描函数的function handle，第二个是一个cell类型，可以包含多个参数的范围。

>> type parameterSweep

function [respmax,varmax,resp,var] = parameterSweep(fun,range)
%PARAMETERSWEEP performs a parameters sweep for a given function
%   RESPMAX = PARAMETERSWEEP(FUN,RANGE) takes as input a function handle in
%   FUN and the range of allowable values for inputs in RANGE.
%
%   FUN is a function handle that accepts one input and returns one output,
%   F = FUN(X), where X is an array of size N x M.  N is the number of
%   observations (rows) and M is the number of variables (columns).  F is
%   the response of size N x 1, a column vector;
%
%   RANGE is a cell array of length M that contains a vector of ranges for
%   each variable.
%
%   [RESPMAX,VARMAX,RESP,VAR] = PARAMETERSWEEP(FUN,RANGE) returns the
%   maximum response value in RESPMAX, the location of the maximum value in
%   VARMAX, an N-D array of the response values in RESP, and and N-D array
%   where the size of the N-D array depends upon the values in RANGE.
%   NDGRID is used to generate the arrays.
%
%   Examples:
%   % Example 1: peaks function
%     range = {-3:0.1:3, -3:0.2:3};  % range of x and y variables
%     fun = @(x) deal( peaks(x(:,1),x(:,2)) ); % peaks as a function handle
%     [respmax,varmax,resp,var] = parameterSweep(fun,range);
%     surf(var{1},var{2},resp)
%     hold on, grid on
%     plot3(varmax(1),varmax(2),respmax,...
%         'MarkerFaceColor','k', 'MarkerEdgeColor','k',...
%         'Marker','pentagram', 'LineStyle','none',...
%         'MarkerSize',20, 'Color','k');
%     hold off
%     xlabel('x'),ylabel('y')
%     legend('Surface','Max Value','Location','NorthOutside')
%
%   See also ndgrid

%%
% Copyright 2010, The MathWorks, Inc.
% All rights reserved.

%% Check inputs
if nargin == 0
example(1)
else
%% Generate expression for ndgrid
N = length(range);
if N == 1
var = range;
else
in = ''; out = '';
for i = 1:N
in  = [in,'range{',num2str(i),'},'];
out = [out,'var{',num2str(i),'},'];
end
in(end)  = []; % remove last commas
out(end) = [];

%% Evaluate ndgrid
eval( ['[',out,'] = ndgrid(',in,');'] );
end
%% Perform parameter sweep
sz = size(var{1});
for i = 1:N
var{i} = var{i}(:);
end
resp = fun(cell2mat(var));

%% Find maximum value and location
[respmax,idx]   = max(resp);
for i = 1:N
varmax(i) = var{i}(idx);
end

%% Reshape output only if requested
if nargout > 2
resp = reshape(resp,sz);
for i = 1:N
var{i} = reshape(var{i},sz);
end
end %if

end %if

%% Examples
function example(ex)
for e = 1:length(ex)
for e = 1:length(ex)
switch ex(e)
case 1
figure(1), clf
range = {-3:0.1:3, -3:0.2:3};  % range of x and y variables
fun = @(x) deal( peaks(x(:,1),x(:,2)) ); % peaks as a function handle
[respmax,varmax,resp,var] = parameterSweep(fun,range);
surf(var{1},var{2},resp)
hold on, grid on
plot3(varmax(1),varmax(2),respmax,...
'MarkerFaceColor','k', 'MarkerEdgeColor','k',...
'Marker','pentagram', 'LineStyle','none',...
'MarkerSize',20, 'Color','k');
hold off
xlabel('x'),ylabel('y')
legend('Surface','Max Value','Location','NorthOutside')
end %switch
end %for
end %for

2.rsiFun函数

>> type rsiFun

function sh = rsifun(x,data,scaling,cost)
% define rsi to accept vectorized inputs and return only sharpe ratio
%%
% Copyright 2010, The MathWorks, Inc.
% All rights reserved.
row = size(x,1);
sh = zeros(row,1);
parfor i = 1:row
[~,~,sh(i)] = rsi(data,[x(i,1),x(i,2)],x(i,3),scaling,cost);
end

3.size函数

size（）：获取矩阵的行数和列数

（1）s=size(A),

当只有一个输出参数时，返回一个行向量，该行向量的第一个元素时矩阵的行数，第二个元素是矩阵的列数。

（2）[r,c]=size(A),

当有两个输出参数时，size函数将矩阵的行数返回到第一个输出变量r，将矩阵的列数返回到第二个输出变量c。

（3）size(A,n)如果在size函数的输入参数中再添加一项n，并用1或2为n赋值，则 size将返回矩阵的行数或列数。其中r=size(A,1)该语句返回的时矩阵A的行数， c=size(A,2) 该语句返回的时矩阵A的列数。

另外，length()=max(size()).

4. parfor

【使用和关闭】

使用matlabpool 命令启动多个workers，使用parfor指令。自己的电脑上是4核4进程，开启4个workers：

matlabpool 4

关闭时用 matlabpool close

【语法】

parfor的语法和普通的for语法没有区别：

for i = 1:N

f(i);

end

parfor i = 1:N

f(i);

end

【并行】

for 语句是按照i的序列顺序执行的，而parfor是由多个worker同时执行i为不同值的结果

for i = 1:12 fprintf(' %d',i); end 的输出为：

1 2 3 4 5 6 7 8 9 10 11 12

parfor i = 1:12 fprintf(' %d',i); end的输出为：

2 1 10

4 3 11

6 5 12

8 7 9

5.rsi指标

参考:http://jingyan.baidu.com/article/ca00d56c54ff84e99eebcff4.html

RSI指标的计算方法

N日RSI=[A÷(A+B)]×100%

公式中，A——N日内收盘涨幅之和

B——N日内收盘跌幅之和(取正值)

N日RSI=100-100/(1+RS)

从计算公式上看，我们可以看到，RSI的计算非常简单，实际理解为：在某一阶段价格上涨所产生的波动占整个波动的半分比。

type rsi

function varargout = rsi(price,M,thresh,scaling,cost)
% RSI
%%
% Copyright 2010, The MathWorks, Inc.
% All rights reserved.
if ~exist('scaling','var')
scaling = 1;
end
if ~exist('M','var')
M = 0; % no detrending
else
if numel(M) > 1
N = M(2);
M = M(1);
else
N = M;
M = 15*M;
end
end
if ~exist('thresh','var')
thresh = [30 70]; % default threshold
else
if numel(thresh) == 1 % scalar value
thresh = [100-thresh, thresh];
else
if thresh(1) > thresh(2)
thresh= thresh(2:-1:1);
end
end
end

if ~exist('cost','var')
cost = 0; % default cost
end

%% Detrend with a moving average
if M == 0
ma = zeros(size(price));
else
ma = movavg(price,M,M,'e');
end
ri = rsindex(price - ma, N);

%% Position signal
s = zeros(size(price));
% Crossing the lower threshold
indx    = ri < thresh(1);
indx    = [false; indx(1:end-1) & ~indx(2:end)];
s(indx) = 1;
% Crossing the upper threshold
indx    = ri > thresh(2);
indx    = [false; indx(1:end-1) & ~indx(2:end)];
s(indx) = -1;
% Fill in zero values with prior position
for i = 2:length(s)
if  s(i) == 0
s(i) = s(i-1);
end
end

%% PNL Caclulation
r  = [0; s(1:end-1).*diff(price)-abs(diff(s))*cost/2];
sh = scaling*sharpe(r,0);

%% Plot if requested
if nargout == 0
ax(1) = subplot(3,1,1);
plot([price,ma]), grid on
legend('Price',['Moving Average ',num2str(M)])
title(['RSI Results, Sharpe Ratio = ',num2str(sh,3)])
ax(2) = subplot(3,1,2);
plot([ri,thresh(1)*ones(size(ri)),thresh(2)*ones(size(ri))])
grid on
legend(['RSI ',num2str(N)],'Lower Threshold','Upper Threshold')
title('RSI')
ax(3) = subplot(3,1,3);
plot([s,cumsum(r)]), grid on
legend('Position','Cumulative Return','Location','Best')
title(['Final Return = ',num2str(sum(r),3),' (',num2str(sum(r)/price(1)*100,3),'%)'])
linkaxes(ax,'x')
else
%% Return values
for i = 1:nargout
switch i
case 1
varargout{1} = s; % signal
case 2
varargout{2} = r; % return (pnl)
case 3
varargout{3} = sh; % sharpe ratio
case 4
varargout{4} = ri; % rsi signal
case 5
varargout{5} = ma; % moving average
case 6
varargout{6} = thresh; % threshold
otherwise
warning('RSI:OutputArg',...
'Too many output arguments requested, ignoring last ones');
end %switch
end %for
end %if

%% Examples

%% Supporting Functions
% Faster implementation of rsindex found in Financial Toolbox
function r=rsindex(x,N)
L = length(x);
dx = diff([0;x]);
up=dx;
down=abs(dx);
% up and down moves
I=dx<=0;
up(I) = 0;
down(~I)=0;
% calculate exponential moving averages
m1 = movavg(up,N,N,'e'); m2 = movavg(down,N,N,'e');
warning off
r = 100*m1./(m1+m2);
%r(isnan(r))=50;
I2=~((up+down)>0);
r(I2)=50;

6.