pcares
              Calculate residuals from principal component analysis.
 residuals = pcares (x, ndim) returns the residuals
 obtained by retaining ndim principal components of the 
 matrix x. Rows of x correspond to observations, columns of
 x correspond to variables.  ndim is a scalar and must be less
 than or equal to .  residuals is a matrix of the same size as
 x.  Use the data matrix, not the covariance matrix, with this function.
 [residuals, reconstructed] = pcares (x, ndim)
 returns the reconstructed observations, i.e. the approximation to x
 obtained by retaining its first ndim principal components.
 pcares does not normalize the columns of x.  Use
 pcares (zscore (x), ndim) in order to perform the
 principal components analysis based on standardized variables, i.e. based on
 correlations.  Use pcacov in order to perform principal components
 analysis directly on a covariance or correlation matrix without constructing
 residuals.
See also: factoran, pcacov, pca
Source Code: pcares
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 x = [ 7    26     6    60;
       1    29    15    52;
      11    56     8    20;
      11    31     8    47;
       7    52     6    33;
      11    55     9    22;
       3    71    17     6;
       1    31    22    44;
       2    54    18    22;
      21    47     4    26;
       1    40    23    34;
      11    66     9    12;
      10    68     8    12];
 ## As we increase the number of principal components, the norm
 ## of the residuals matrix will decrease
 r1 = pcares (x,1);
 n1 = norm (r1)
 r2 = pcares (x,2);
 n2 = norm (r2)
 r3 = pcares (x,3);
 n3 = norm (r3)
 r4 = pcares (x,4);
 n4 = norm (r4)
n1 = 28.460
n2 = 12.201
n3 = 1.6870
n4 = 4.2168e-14
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