qrdcomp(x) or qrdcomp(qr(x)), where x is a REAL matrix with no MISSING values |

qrdcomp(X) computes a QR decomposition without pivoting of M by N REAL matrix X with no MISSING values. It returns structure(q:Q,r:R), where Q and R are REAL matrices satisfying X = Q %*% R. When M >= N, Q is M by N orthonormal (Q' %*% Q = N by N identity matrix) and R is N by N upper triangular. When M < N, Q is M by M orthonormal and R is M by N with the first M columns an upper triangular matrix. qrdcomp() also works with the output from function qr(). That is qrdcomp(qr(X)) is the same as qrdcomp(X). Note: Computation of the QR decomposition without pivoting is not reliable when X is not of full rank. qrdcomp(X, pivot:T) or qrdcomp(qr(X, pivot:T)) a QR decomposition or X with pivoting and return a structure(q:Q,r:R,pivot:J), where J is a permutation of run(N), such that X[,J] = Q %*% R, where Q and R are as before. This usage is accurate even when X is not of full rank. See also qr()

Gary Oehlert 2003-01-15