 # 最小均方跟数据拟合*matlab代做

### 时间：2017-4-27 2:41:34 点击： 核心提示：最小均方跟数据拟合*matlab代做... function [ YI ] = lsq_lut_piecewise( x, y, XI )
% LSQ_LUT_PIECEWISE Piecewise linear interpolation for 1-D interpolation (table lookup)
%   YI = lsq_lut_piecewise( x, y, XI ) obtain optimal (least-square sense)
%   vector to be used with linear interpolation routine.
%   The target is finding Y given X the minimization of function
%           f = |y-interp1(XI,YI,x)|^2
%
%   INPUT
%       x measured data vector
%       y measured data vector
%       XI break points of 1-D table
%
%   OUTPUT
%       YI interpolation points of 1-D table
%           y = interp1(XI,YI,x)
%

if size(x,2) ~= 1
error('Vector x must have dimension n x 1.');
elseif size(y,2) ~= 1
error('Vector y must have dimension n x 1.');
elseif size(x,1) ~= size(x,1)
error('Vector x and y must have dimension n x 1.');
end

% matrix defined by x measurements
A = sparse([]);

% vector for y measurements
Y = [];

for j=2:length(XI)

% get index of points in bin [XI(j-1) XI(j)]
ix = x>=XI(j-1) & x<XI(j);

% check if we have data points in bin
if ~any(ix)
warning(sprintf('Bin [%f %f] has no data points, check estimation. Please re-define X vector accordingly.',XI(j-1),XI(j)));
end

% get x and y data subset
x_ = x(ix);
y_ = y(ix);

% create temporary matrix to be added to A
tmp = [(( -x_+XI(j-1) ) / ( XI(j)-XI(j-1) ) + 1) (( x_-XI(j-1) ) / ( XI(j)-XI(j-1) ))];

% build matrix of measurement with constraints
[m1,n1]=size(A);
[m2,n2]=size(tmp);
A = [[A zeros(m1,n2-1)];[zeros(m2,n1-1) tmp]];

% concatenate y measurements of bin
Y = [Y; y_];
end

% obtain least-squares Y estimation
YI=A\Y;

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