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Annotation of rpl/lapack/lapack/dlapll.f, revision 1.7

1.1       bertrand    1:       SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN )
                      2: *
                      3: *  -- LAPACK auxiliary routine (version 3.2) --
                      4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                      5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                      6: *     November 2006
                      7: *
                      8: *     .. Scalar Arguments ..
                      9:       INTEGER            INCX, INCY, N
                     10:       DOUBLE PRECISION   SSMIN
                     11: *     ..
                     12: *     .. Array Arguments ..
                     13:       DOUBLE PRECISION   X( * ), Y( * )
                     14: *     ..
                     15: *
                     16: *  Purpose
                     17: *  =======
                     18: *
                     19: *  Given two column vectors X and Y, let
                     20: *
                     21: *                       A = ( X Y ).
                     22: *
                     23: *  The subroutine first computes the QR factorization of A = Q*R,
                     24: *  and then computes the SVD of the 2-by-2 upper triangular matrix R.
                     25: *  The smaller singular value of R is returned in SSMIN, which is used
                     26: *  as the measurement of the linear dependency of the vectors X and Y.
                     27: *
                     28: *  Arguments
                     29: *  =========
                     30: *
                     31: *  N       (input) INTEGER
                     32: *          The length of the vectors X and Y.
                     33: *
                     34: *  X       (input/output) DOUBLE PRECISION array,
                     35: *                         dimension (1+(N-1)*INCX)
                     36: *          On entry, X contains the N-vector X.
                     37: *          On exit, X is overwritten.
                     38: *
                     39: *  INCX    (input) INTEGER
                     40: *          The increment between successive elements of X. INCX > 0.
                     41: *
                     42: *  Y       (input/output) DOUBLE PRECISION array,
                     43: *                         dimension (1+(N-1)*INCY)
                     44: *          On entry, Y contains the N-vector Y.
                     45: *          On exit, Y is overwritten.
                     46: *
                     47: *  INCY    (input) INTEGER
                     48: *          The increment between successive elements of Y. INCY > 0.
                     49: *
                     50: *  SSMIN   (output) DOUBLE PRECISION
                     51: *          The smallest singular value of the N-by-2 matrix A = ( X Y ).
                     52: *
                     53: *  =====================================================================
                     54: *
                     55: *     .. Parameters ..
                     56:       DOUBLE PRECISION   ZERO, ONE
                     57:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
                     58: *     ..
                     59: *     .. Local Scalars ..
                     60:       DOUBLE PRECISION   A11, A12, A22, C, SSMAX, TAU
                     61: *     ..
                     62: *     .. External Functions ..
                     63:       DOUBLE PRECISION   DDOT
                     64:       EXTERNAL           DDOT
                     65: *     ..
                     66: *     .. External Subroutines ..
                     67:       EXTERNAL           DAXPY, DLARFG, DLAS2
                     68: *     ..
                     69: *     .. Executable Statements ..
                     70: *
                     71: *     Quick return if possible
                     72: *
                     73:       IF( N.LE.1 ) THEN
                     74:          SSMIN = ZERO
                     75:          RETURN
                     76:       END IF
                     77: *
                     78: *     Compute the QR factorization of the N-by-2 matrix ( X Y )
                     79: *
                     80:       CALL DLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU )
                     81:       A11 = X( 1 )
                     82:       X( 1 ) = ONE
                     83: *
                     84:       C = -TAU*DDOT( N, X, INCX, Y, INCY )
                     85:       CALL DAXPY( N, C, X, INCX, Y, INCY )
                     86: *
                     87:       CALL DLARFG( N-1, Y( 1+INCY ), Y( 1+2*INCY ), INCY, TAU )
                     88: *
                     89:       A12 = Y( 1 )
                     90:       A22 = Y( 1+INCY )
                     91: *
                     92: *     Compute the SVD of 2-by-2 Upper triangular matrix.
                     93: *
                     94:       CALL DLAS2( A11, A12, A22, SSMIN, SSMAX )
                     95: *
                     96:       RETURN
                     97: *
                     98: *     End of DLAPLL
                     99: *
                    100:       END