如何将向量归一化/去正化到范围[-1;1]

How can I normalize a vector to the range [-1;1]

如何将向量归一化到量程[-1;1]

I would like to use function norm, because it will be faster.

我想用函数范数，因为它会更快。

Also let me know how I can denormalize that vector after normalization?

还要让我知道如何在归一化后去规范化那个向量?

3 个解决方案

#1

norm normalizes a vector so that its sum of squares are 1.

范数使一个向量标准化，使其平方和为1。

If you want to normalize the vector so that all its elements are between 0 and 1, you need to use the minimum and maximum value, which you can then use to denormalize again.

如果要使向量标准化，使其所有元素都在0和1之间，那么就需要使用最小值和最大值，然后再用它来重新规格化。

%# generate some vectorvec = randn(10,1);%# get max and minmaxVec = max(vec);minVec = min(vec);%# normalize to -1...1vecN = ((vec-minVec)./(maxVec-minVec) - 0.5 ) *2;%# to "de-normalize", apply the calculations in reversevecD = (vecN./2+0.5) * (maxVec-minVec) + minVec

#2

An extended answer that was built on the answer by Jonas is below. It allows for automated normalization based on if negative and positive numbers are present in the vector or manual selection of the type of normalization desired. Below the function is a test script.

以下是建立在乔纳斯回答基础上的扩展答案。它允许基于在向量或手动选择所需的规范化类型中存在负数和正数的情况下进行自动规范化。函数下面是一个测试脚本。

Normalization function

归一化函数

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 argumentsnumvarargs = length(varargin);if numvarargs > 1    error('Requires at most 1 optional input');end% Set defaults for optional inputsoptargs = {0};% Overwrite default values if new values providedoptargs(1:numvarargs) = varargin;% Set input to variable names[setNorm] = optargs{:};%% Normalize input vector% get max and minmaxVec = 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;    endelseif 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

Script to test the function

脚本测试函数

% Define vectorx=linspace(0,4*pi,25);y = sin(x);ya=sin(x); yb=y+10; yc=y-10;% Normalize vectorya0=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 resultsfigure(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]')

#3

An up-to-date answer would be to use the rescale function introduced in Matlab R2017b. To normalise the vector A to the range -1:1, you'd run:

一个最新的答案将是使用在Matlab R2017b中引入的rescale函数。为了将向量A归一化到-1:1的范围，你可以这样做:

A = rescale(A, -1, 1);

You could undo this by saving the minimum and maximum beforehand then running rescale again:

您可以通过预先保存最小和最大值，然后再次运行重新缩放来取消这个操作:

maxA = max(A(:));minA = min(A(:));A = rescale(A, -1, 1);% use the normalised AA = rescale(A, minA, maxA);