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Annotation of rpl/lapack/lapack/zlapll.f, revision 1.14

1.11      bertrand    1: *> \brief \b ZLAPLL measures the linear dependence of two vectors.
1.8       bertrand    2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
                      5: * Online html documentation available at 
                      6: *            http://www.netlib.org/lapack/explore-html/ 
                      7: *
                      8: *> \htmlonly
                      9: *> Download ZLAPLL + dependencies 
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlapll.f"> 
                     11: *> [TGZ]</a> 
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlapll.f"> 
                     13: *> [ZIP]</a> 
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlapll.f"> 
                     15: *> [TXT]</a>
                     16: *> \endhtmlonly 
                     17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN )
                     22: * 
                     23: *       .. Scalar Arguments ..
                     24: *       INTEGER            INCX, INCY, N
                     25: *       DOUBLE PRECISION   SSMIN
                     26: *       ..
                     27: *       .. Array Arguments ..
                     28: *       COMPLEX*16         X( * ), Y( * )
                     29: *       ..
                     30: *  
                     31: *
                     32: *> \par Purpose:
                     33: *  =============
                     34: *>
                     35: *> \verbatim
                     36: *>
                     37: *> Given two column vectors X and Y, let
                     38: *>
                     39: *>                      A = ( X Y ).
                     40: *>
                     41: *> The subroutine first computes the QR factorization of A = Q*R,
                     42: *> and then computes the SVD of the 2-by-2 upper triangular matrix R.
                     43: *> The smaller singular value of R is returned in SSMIN, which is used
                     44: *> as the measurement of the linear dependency of the vectors X and Y.
                     45: *> \endverbatim
                     46: *
                     47: *  Arguments:
                     48: *  ==========
                     49: *
                     50: *> \param[in] N
                     51: *> \verbatim
                     52: *>          N is INTEGER
                     53: *>          The length of the vectors X and Y.
                     54: *> \endverbatim
                     55: *>
                     56: *> \param[in,out] X
                     57: *> \verbatim
                     58: *>          X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
                     59: *>          On entry, X contains the N-vector X.
                     60: *>          On exit, X is overwritten.
                     61: *> \endverbatim
                     62: *>
                     63: *> \param[in] INCX
                     64: *> \verbatim
                     65: *>          INCX is INTEGER
                     66: *>          The increment between successive elements of X. INCX > 0.
                     67: *> \endverbatim
                     68: *>
                     69: *> \param[in,out] Y
                     70: *> \verbatim
                     71: *>          Y is COMPLEX*16 array, dimension (1+(N-1)*INCY)
                     72: *>          On entry, Y contains the N-vector Y.
                     73: *>          On exit, Y is overwritten.
                     74: *> \endverbatim
                     75: *>
                     76: *> \param[in] INCY
                     77: *> \verbatim
                     78: *>          INCY is INTEGER
                     79: *>          The increment between successive elements of Y. INCY > 0.
                     80: *> \endverbatim
                     81: *>
                     82: *> \param[out] SSMIN
                     83: *> \verbatim
                     84: *>          SSMIN is DOUBLE PRECISION
                     85: *>          The smallest singular value of the N-by-2 matrix A = ( X Y ).
                     86: *> \endverbatim
                     87: *
                     88: *  Authors:
                     89: *  ========
                     90: *
                     91: *> \author Univ. of Tennessee 
                     92: *> \author Univ. of California Berkeley 
                     93: *> \author Univ. of Colorado Denver 
                     94: *> \author NAG Ltd. 
                     95: *
1.11      bertrand   96: *> \date September 2012
1.8       bertrand   97: *
                     98: *> \ingroup complex16OTHERauxiliary
                     99: *
                    100: *  =====================================================================
1.1       bertrand  101:       SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN )
                    102: *
1.11      bertrand  103: *  -- LAPACK auxiliary routine (version 3.4.2) --
1.1       bertrand  104: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    105: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.11      bertrand  106: *     September 2012
1.1       bertrand  107: *
                    108: *     .. Scalar Arguments ..
                    109:       INTEGER            INCX, INCY, N
                    110:       DOUBLE PRECISION   SSMIN
                    111: *     ..
                    112: *     .. Array Arguments ..
                    113:       COMPLEX*16         X( * ), Y( * )
                    114: *     ..
                    115: *
                    116: *  =====================================================================
                    117: *
                    118: *     .. Parameters ..
                    119:       DOUBLE PRECISION   ZERO
                    120:       PARAMETER          ( ZERO = 0.0D+0 )
                    121:       COMPLEX*16         CONE
                    122:       PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
                    123: *     ..
                    124: *     .. Local Scalars ..
                    125:       DOUBLE PRECISION   SSMAX
                    126:       COMPLEX*16         A11, A12, A22, C, TAU
                    127: *     ..
                    128: *     .. Intrinsic Functions ..
                    129:       INTRINSIC          ABS, DCONJG
                    130: *     ..
                    131: *     .. External Functions ..
                    132:       COMPLEX*16         ZDOTC
                    133:       EXTERNAL           ZDOTC
                    134: *     ..
                    135: *     .. External Subroutines ..
                    136:       EXTERNAL           DLAS2, ZAXPY, ZLARFG
                    137: *     ..
                    138: *     .. Executable Statements ..
                    139: *
                    140: *     Quick return if possible
                    141: *
                    142:       IF( N.LE.1 ) THEN
                    143:          SSMIN = ZERO
                    144:          RETURN
                    145:       END IF
                    146: *
                    147: *     Compute the QR factorization of the N-by-2 matrix ( X Y )
                    148: *
                    149:       CALL ZLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU )
                    150:       A11 = X( 1 )
                    151:       X( 1 ) = CONE
                    152: *
                    153:       C = -DCONJG( TAU )*ZDOTC( N, X, INCX, Y, INCY )
                    154:       CALL ZAXPY( N, C, X, INCX, Y, INCY )
                    155: *
                    156:       CALL ZLARFG( N-1, Y( 1+INCY ), Y( 1+2*INCY ), INCY, TAU )
                    157: *
                    158:       A12 = Y( 1 )
                    159:       A22 = Y( 1+INCY )
                    160: *
                    161: *     Compute the SVD of 2-by-2 Upper triangular matrix.
                    162: *
                    163:       CALL DLAS2( ABS( A11 ), ABS( A12 ), ABS( A22 ), SSMIN, SSMAX )
                    164: *
                    165:       RETURN
                    166: *
                    167: *     End of ZLAPLL
                    168: *
                    169:       END