如何将向量归一化到范围为[-1;1]
?
我想使用函数norm
,因为它会更快。
在归一化后,也请告诉我如何反归一化该向量?
如何将向量归一化到范围为[-1;1]
?
我想使用函数norm
,因为它会更快。
在归一化后,也请告诉我如何反归一化该向量?
norm
函数将一个向量规范化,以使其平方和为1。
如果您想将向量规范化,使其所有元素都介于0和1之间,则需要使用最小值和最大值,并且可以再次使用它们来进行反规范化。
%# generate some vector
vec = randn(10,1);
%# get max and min
maxVec = max(vec);
minVec = min(vec);
%# normalize to -1...1
vecN = ((vec-minVec)./(maxVec-minVec) - 0.5 ) *2;
%# to "de-normalize", apply the calculations in reverse
vecD = (vecN./2+0.5) * (maxVec-minVec) + minVec
rescale
函数。要将向量A
归一化到范围-1:1
,您可以运行以下命令:A = rescale(A, -1, 1);
您可以通过先保存最小值和最大值,然后再运行重新缩放来撤消此操作:
maxA = max(A(:));
minA = min(A(:));
A = rescale(A, -1, 1);
% use the normalised A
A = rescale(A, minA, maxA);
mapminmax
通过将行最小值和最大值映射到[-1, 1]来处理矩阵。
例子:
x1 = [1 2 4; 1 1 1; 3 2 2; 0 0 0]
[y1,PS] = mapminmax(x1)
在归一化后对该向量进行反规范化处理
x1_again = mapminmax('reverse',y1,PS)
function [vecN, vecD] = normVec(vec,varargin)
% Returns a normalize vector (vecN) and "de-nomralized" vector (vecD). The
% function detects if both positive and negative values are present or not
% and automatically normalizes between the appropriate range (i.e., [0,1],
% [-1,0], or [-1,-1].
% Optional argument allows control of normalization range:
% normVec(vec,0) => sets range based on positive/negative value detection
% normVec(vec,1) => sets range to [0,1]
% normVec(vec,2) => sets range to [-1,0]
% normVec(vec,3) => sets range to [-1,1]
%% Default Input Values
% Check for proper length of input arguments
numvarargs = length(varargin);
if numvarargs > 1
error('Requires at most 1 optional input');
end
% Set defaults for optional inputs
optargs = {0};
% Overwrite default values if new values provided
optargs(1:numvarargs) = varargin;
% Set input to variable names
[setNorm] = optargs{:};
%% Normalize input vector
% get max and min
maxVec = max(vec);
minVec = min(vec);
if setNorm == 0
% Automated normalization
if minVec >= 0
% Normalize between 0 and 1
vecN = (vec - minVec)./( maxVec - minVec );
vecD = minVec + vecN.*(maxVec - minVec);
elseif maxVec <= 0
% Normalize between -1 and 0
vecN = (vec - maxVec)./( maxVec - minVec );
vecD = maxVec + vecN.*(maxVec - minVec);
else
% Normalize between -1 and 1
vecN = ((vec-minVec)./(maxVec-minVec) - 0.5 ) *2;
vecD = (vecN./2+0.5) * (maxVec-minVec) + minVec;
end
elseif setNorm == 1
% Normalize between 0 and 1
vecN = (vec - minVec)./( maxVec - minVec );
vecD = minVec + vecN.*(maxVec - minVec);
elseif setNorm == 2
% Normalize between -1 and 0
vecN = (vec - maxVec)./( maxVec - minVec );
vecD = maxVec + vecN.*(maxVec - minVec);
elseif setNorm == 3
% Normalize between -1 and 1
vecN = ((vec-minVec)./(maxVec-minVec) - 0.5 ) *2;
vecD = (vecN./2+0.5) * (maxVec-minVec) + minVec;
else
error('Unrecognized input argument varargin. Options are {0,1,2,3}');
end
测试函数的脚本
% Define vector
x=linspace(0,4*pi,25);
y = sin(x);
ya=sin(x); yb=y+10; yc=y-10;
% Normalize vector
ya0=normVec(ya); yb0=normVec(yb); yc0=normVec(yc);
ya1=normVec(ya,1); yb1=normVec(yb,1); yc1=normVec(yc,1);
ya2=normVec(ya,2); yb2=normVec(yb,2); yc2=normVec(yc,2);
ya3=normVec(ya,3); yb3=normVec(yb,3); yc3=normVec(yc,3);
% Plot results
figure(1)
subplot(2,2,1)
plot(x,ya0,'k',x,yb0,'ro',x,yc0,'b^')
title('Auto Norm-Range')
subplot(2,2,2)
plot(x,ya1,'k',x,yb1,'ro',x,yc1,'b^')
title('Manual Norm-Range: [0,1]')
subplot(2,2,3)
plot(x,ya2,'k',x,yb2,'ro',x,yc2,'b^')
title('Manual Norm-Range: [-1,0]')
subplot(2,2,4)
plot(x,ya3,'k',x,yb3,'ro',x,yc3,'b^')
title('Manual Norm-Range: [-1,1]')
((vec-minVec)./(maxVec-minVec))
- Jonas