Commit 991332f6 authored by Paul Brown's avatar Paul Brown

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parent 3fe72982
/******************************************************************************
Author, date: Rick Wicklin, NOV2012
Macro name: NearestCorr
Description: implement the Higham projection method to obtain the nearest
correlation matrix to a given symmetric correlation/covariance matrix
Reference: http://blogs.sas.com/content/iml/2012/11/28/
computing-the-nearest-correlation-matrix.html
******************************************************************************/
%macro NearestCorr();
/* Project symmetric X onto S={positive semidefinite matrices}.
Replace any negative eigenvalues of X with zero */
start ProjS(X);
call eigen(D, Q, X); /* note X = Q*D*Q` */
V = choose(D>.0001, D, .0001); /*pmbrown: this line changed as per comment
at bottom of sas blog*/
W = Q#sqrt(V`); /* form Q*diag(V)*Q` */
return( W*W` ); /* W*W` = Q*diag(V)*Q` */
finish;
/* project square X onto U={matrices with unit diagonal}.
Return X with the diagonal elements replaced by ones. */
start ProjU(X);
n = nrow(X);
Y = X;
diagIdx = do(1, n*n, n+1);
Y[diagIdx] = 1; /* set diagonal elements to 1 */
return ( Y );
finish;
/* Helper function: the infinity norm is the max abs value of the row sums */
start MatInfNorm(A);
return( max(abs(A[,+])) );
finish;
/* Given a symmetric correlation matrix, A,
project A onto the space of positive semidefinite matrices.
The function uses the algorithm of Higham (2002) to return
the matrix X that is closest to A in the Frobenius norm. */
start NearestCorr(A);
maxIter = 100; tol = 1e-8; /* parameters...you can change these */
iter = 1; maxd = 1; /* initial values */
Yold = A; Xold = A; dS = 0;
do while( (iter <= maxIter) & (maxd > tol) );
R = Yold - dS; /* dS is Dykstra's correction */
X = ProjS(R); /* project onto S={positive semidefinite} */
dS = X - R;
Y = ProjU(X); /* project onto U={matrices with unit diagonal} */
/* How much has X changed? (Eqn 4.1) */
dx = MatInfNorm(X-Xold) / MatInfNorm(X);
dy = MatInfNorm(Y-Yold) / MatInfNorm(Y);
dxy = MatInfNorm(Y - X) / MatInfNorm(Y);
maxd = max(dx,dy,dxy);
iter = iter + 1;
Xold = X; Yold = Y; /* update matrices */
end;
return( X ); /* X is positive semidefinite */
finish;
%mend NearestCorr;
***end********************************************************;
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