--- rpl/lapack/lapack/dlasq1.f 2010/08/13 21:03:52 1.6 +++ rpl/lapack/lapack/dlasq1.f 2023/08/07 08:38:59 1.19 @@ -1,12 +1,112 @@ - SUBROUTINE DLASQ1( N, D, E, WORK, INFO ) +*> \brief \b DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* -- LAPACK routine (version 3.2) -- +*> \htmlonly +*> Download DLASQ1 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLASQ1( N, D, E, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), E( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLASQ1 computes the singular values of a real N-by-N bidiagonal +*> matrix with diagonal D and off-diagonal E. The singular values +*> are computed to high relative accuracy, in the absence of +*> denormalization, underflow and overflow. The algorithm was first +*> presented in +*> +*> "Accurate singular values and differential qd algorithms" by K. V. +*> Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, +*> 1994, +*> +*> and the present implementation is described in "An implementation of +*> the dqds Algorithm (Positive Case)", LAPACK Working Note. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of rows and columns in the matrix. N >= 0. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> On entry, D contains the diagonal elements of the +*> bidiagonal matrix whose SVD is desired. On normal exit, +*> D contains the singular values in decreasing order. +*> \endverbatim +*> +*> \param[in,out] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N) +*> On entry, elements E(1:N-1) contain the off-diagonal elements +*> of the bidiagonal matrix whose SVD is desired. +*> On exit, E is overwritten. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (4*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: the algorithm failed +*> = 1, a split was marked by a positive value in E +*> = 2, current block of Z not diagonalized after 100*N +*> iterations (in inner while loop) On exit D and E +*> represent a matrix with the same singular values +*> which the calling subroutine could use to finish the +*> computation, or even feed back into DLASQ1 +*> = 3, termination criterion of outer while loop not met +*> (program created more than N unreduced blocks) +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* -- Contributed by Osni Marques of the Lawrence Berkeley National -- -* -- Laboratory and Beresford Parlett of the Univ. of California at -- -* -- Berkeley -- -* -- November 2008 -- +*> \ingroup auxOTHERcomputational +* +* ===================================================================== + SUBROUTINE DLASQ1( N, D, E, WORK, INFO ) * +* -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * @@ -17,50 +117,6 @@ DOUBLE PRECISION D( * ), E( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DLASQ1 computes the singular values of a real N-by-N bidiagonal -* matrix with diagonal D and off-diagonal E. The singular values -* are computed to high relative accuracy, in the absence of -* denormalization, underflow and overflow. The algorithm was first -* presented in -* -* "Accurate singular values and differential qd algorithms" by K. V. -* Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, -* 1994, -* -* and the present implementation is described in "An implementation of -* the dqds Algorithm (Positive Case)", LAPACK Working Note. -* -* Arguments -* ========= -* -* N (input) INTEGER -* The number of rows and columns in the matrix. N >= 0. -* -* D (input/output) DOUBLE PRECISION array, dimension (N) -* On entry, D contains the diagonal elements of the -* bidiagonal matrix whose SVD is desired. On normal exit, -* D contains the singular values in decreasing order. -* -* E (input/output) DOUBLE PRECISION array, dimension (N) -* On entry, elements E(1:N-1) contain the off-diagonal elements -* of the bidiagonal matrix whose SVD is desired. -* On exit, E is overwritten. -* -* WORK (workspace) DOUBLE PRECISION array, dimension (4*N) -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* > 0: the algorithm failed -* = 1, a split was marked by a positive value in E -* = 2, current block of Z not diagonalized after 30*N -* iterations (in inner while loop) -* = 3, termination criterion of outer while loop not met -* (program created more than N unreduced blocks) -* * ===================================================================== * * .. Parameters .. @@ -85,7 +141,7 @@ * INFO = 0 IF( N.LT.0 ) THEN - INFO = -2 + INFO = -1 CALL XERBLA( 'DLASQ1', -INFO ) RETURN ELSE IF( N.EQ.0 ) THEN @@ -130,7 +186,7 @@ CALL DCOPY( N-1, E, 1, WORK( 2 ), 2 ) CALL DLASCL( 'G', 0, 0, SIGMX, SCALE, 2*N-1, 1, WORK, 2*N-1, $ IINFO ) -* +* * Compute the q's and e's. * DO 30 I = 1, 2*N - 1 @@ -145,6 +201,17 @@ D( I ) = SQRT( WORK( I ) ) 40 CONTINUE CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, D, N, IINFO ) + ELSE IF( INFO.EQ.2 ) THEN +* +* Maximum number of iterations exceeded. Move data from WORK +* into D and E so the calling subroutine can try to finish +* + DO I = 1, N + D( I ) = SQRT( WORK( 2*I-1 ) ) + E( I ) = SQRT( WORK( 2*I ) ) + END DO + CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, D, N, IINFO ) + CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, E, N, IINFO ) END IF * RETURN