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DLAPLL(l)) DLAPLL(l)NAMEDLAPLL - two column vectors X and Y, let A = ( X Y )SYNOPSISSUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN ) INTEGER INCX, INCY, N DOUBLE PRECISION SSMIN DOUBLE PRECISION X( * ), Y( * )PURPOSEGiven two column vectors X and Y, let A = ( X Y ). The subroutine first computes the QR factorization of A = Q*R, and then computes the SVD of the 2-by-2 upper triangular matrix R. The smaller singular value of R is returned in SSMIN, which is used as the measurement of the linear dependency of the vectors X and Y.ARGUMENTSN (input) INTEGER The length of the vectors X and Y. X (input/output) DOUBLE PRECISION array, dimension (1+(N-1)*INCX) On entry, X contains the N-vector X. On exit, X is over- written. INCX (input) INTEGER The increment between successive elements of X. INCX > 0. Y (input/output) DOUBLE PRECISION array, dimension (1+(N-1)*INCY) On entry, Y contains the N-vector Y. On exit, Y is over- written. INCY (input) INTEGER The increment between successive elements of Y. INCY > 0. SSMIN (output) DOUBLE PRECISION The smallest singular value of the N-by-2 matrix A = ( X Y ).LAPACK version 3.015 June 2000 DLAPLL(l)

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