1DLAPLL(1)           LAPACK auxiliary routine (version 3.1)           DLAPLL(1)
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NAME

6       DLAPLL - column vectors X and Y, let   A = ( X Y )
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SYNOPSIS

9       SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN )
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11           INTEGER        INCX, INCY, N
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13           DOUBLE         PRECISION SSMIN
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15           DOUBLE         PRECISION X( * ), Y( * )
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PURPOSE

18       Given two column vectors X and Y, let
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20       The subroutine first computes the QR factorization of A = Q*R, and then
21       computes the SVD of the 2-by-2 upper triangular matrix R.  The  smaller
22       singular value of R is returned in SSMIN, which is used as the measure‐
23       ment of the linear dependency of the vectors X and Y.
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ARGUMENTS

27       N       (input) INTEGER
28               The length of the vectors X and Y.
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30       X       (input/output) DOUBLE PRECISION array,
31               dimension (1+(N-1)*INCX) On entry, X contains the  N-vector  X.
32               On exit, X is overwritten.
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34       INCX    (input) INTEGER
35               The increment between successive elements of X. INCX > 0.
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37       Y       (input/output) DOUBLE PRECISION array,
38               dimension  (1+(N-1)*INCY)  On entry, Y contains the N-vector Y.
39               On exit, Y is overwritten.
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41       INCY    (input) INTEGER
42               The increment between successive elements of Y. INCY > 0.
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44       SSMIN   (output) DOUBLE PRECISION
45               The smallest singular value of the N-by-2 matrix A = ( X Y ).
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49 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       DLAPLL(1)