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## man page of LAPACK-3

### LAPACK-3: two column vectors X and Y, let A = ( X Y )

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## NAME

LAPACK-3 - two column vectors X and Y, let A = ( X Y )## SYNOPSIS

SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN ) INTEGER INCX, INCY, N DOUBLE PRECISION SSMIN COMPLEX*16 X( * ), Y( * )## PURPOSE

Given two column vectors X and Y, let 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.ARGUMENTS

N (input) INTEGER The length of the vectors X and Y. X (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX) On entry, X contains the N-vector X. On exit, X is overwritten. INCX (input) INTEGER The increment between successive elements of X. INCX > 0. Y (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCY) On entry, Y contains the N-vector Y. On exit, Y is overwritten. 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 auxiliary routine (versionMarch 2011 LAPACK-3(3)

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