.TH ZLAPLL 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME ZLAPLL - column vectors X and Y, let A = ( X Y ) .SH SYNOPSIS .TP 19 SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN ) .TP 19 .ti +4 INTEGER INCX, INCY, N .TP 19 .ti +4 DOUBLE PRECISION SSMIN .TP 19 .ti +4 COMPLEX*16 X( * ), Y( * ) .SH 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. .SH ARGUMENTS .TP 8 N (input) INTEGER The length of the vectors X and Y. .TP 8 X (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX) On entry, X contains the N-vector X. On exit, X is overwritten. .TP 8 INCX (input) INTEGER The increment between successive elements of X. INCX > 0. .TP 8 Y (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCY) On entry, Y contains the N-vector Y. On exit, Y is overwritten. .TP 8 INCY (input) INTEGER The increment between successive elements of Y. INCY > 0. .TP 8 SSMIN (output) DOUBLE PRECISION The smallest singular value of the N-by-2 matrix A = ( X Y ).