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author | julie <julielangou@users.noreply.github.com> | 2011-09-30 18:34:50 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2011-09-30 18:34:50 +0000 |
commit | 13acf3d65eb8df4cb8df221509bf0178396dcff1 (patch) | |
tree | e3adc3e2fab395b82d4e1bc5111ad5a74afe4be3 /SRC/dgesvj.f | |
parent | d3718a28ef2fad11da862ba0782d39ce506d249f (diff) | |
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Comments fix to be able to generate the new layout and the corresponding Doxygen documentation
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diff --git a/SRC/dgesvj.f b/SRC/dgesvj.f index 5b40d0f2..03ac060e 100644 --- a/SRC/dgesvj.f +++ b/SRC/dgesvj.f @@ -39,57 +39,6 @@ * of SIGMA are the singular values of A. The columns of U and V are the * left and the right singular vectors of A, respectively. * -* Further Details -* ~~~~~~~~~~~~~~~ -* The orthogonal N-by-N matrix V is obtained as a product of Jacobi plane -* rotations. The rotations are implemented as fast scaled rotations of -* Anda and Park [1]. In the case of underflow of the Jacobi angle, a -* modified Jacobi transformation of Drmac [4] is used. Pivot strategy uses -* column interchanges of de Rijk [2]. The relative accuracy of the computed -* singular values and the accuracy of the computed singular vectors (in -* angle metric) is as guaranteed by the theory of Demmel and Veselic [3]. -* The condition number that determines the accuracy in the full rank case -* is essentially min_{D=diag} kappa(A*D), where kappa(.) is the -* spectral condition number. The best performance of this Jacobi SVD -* procedure is achieved if used in an accelerated version of Drmac and -* Veselic [5,6], and it is the kernel routine in the SIGMA library [7]. -* Some tunning parameters (marked with [TP]) are available for the -* implementer. -* The computational range for the nonzero singular values is the machine -* number interval ( UNDERFLOW , OVERFLOW ). In extreme cases, even -* denormalized singular values can be computed with the corresponding -* gradual loss of accurate digits. -* -* Contributors -* ~~~~~~~~~~~~ -* Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) -* -* References -* ~~~~~~~~~~ -* [1] A. A. Anda and H. Park: Fast plane rotations with dynamic scaling. -* SIAM J. matrix Anal. Appl., Vol. 15 (1994), pp. 162-174. -* [2] P. P. M. De Rijk: A one-sided Jacobi algorithm for computing the -* singular value decomposition on a vector computer. -* SIAM J. Sci. Stat. Comp., Vol. 10 (1998), pp. 359-371. -* [3] J. Demmel and K. Veselic: Jacobi method is more accurate than QR. -* [4] Z. Drmac: Implementation of Jacobi rotations for accurate singular -* value computation in floating point arithmetic. -* SIAM J. Sci. Comp., Vol. 18 (1997), pp. 1200-1222. -* [5] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm I. -* SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1322-1342. -* LAPACK Working note 169. -* [6] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm II. -* SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1343-1362. -* LAPACK Working note 170. -* [7] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV, -* QSVD, (H,K)-SVD computations. -* Department of Mathematics, University of Zagreb, 2008. -* -* Bugs, Examples and Comments -* ~~~~~~~~~~~~~~~~~~~~~~~~~~~ -* Please report all bugs and send interesting test examples and comments to -* drmac@math.hr. Thank you. -* * Arguments * ========= * @@ -251,6 +200,60 @@ * of sweeps. The output may still be useful. See the * description of WORK. * +* Further Details +* =============== +* +* The orthogonal N-by-N matrix V is obtained as a product of Jacobi plane +* rotations. The rotations are implemented as fast scaled rotations of +* Anda and Park [1]. In the case of underflow of the Jacobi angle, a +* modified Jacobi transformation of Drmac [4] is used. Pivot strategy uses +* column interchanges of de Rijk [2]. The relative accuracy of the computed +* singular values and the accuracy of the computed singular vectors (in +* angle metric) is as guaranteed by the theory of Demmel and Veselic [3]. +* The condition number that determines the accuracy in the full rank case +* is essentially min_{D=diag} kappa(A*D), where kappa(.) is the +* spectral condition number. The best performance of this Jacobi SVD +* procedure is achieved if used in an accelerated version of Drmac and +* Veselic [5,6], and it is the kernel routine in the SIGMA library [7]. +* Some tunning parameters (marked with [TP]) are available for the +* implementer. +* The computational range for the nonzero singular values is the machine +* number interval ( UNDERFLOW , OVERFLOW ). In extreme cases, even +* denormalized singular values can be computed with the corresponding +* gradual loss of accurate digits. +* +* Contributors +* ============ +* +* Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) +* +* References +* ========== +* +* [1] A. A. Anda and H. Park: Fast plane rotations with dynamic scaling. +* SIAM J. matrix Anal. Appl., Vol. 15 (1994), pp. 162-174. +* [2] P. P. M. De Rijk: A one-sided Jacobi algorithm for computing the +* singular value decomposition on a vector computer. +* SIAM J. Sci. Stat. Comp., Vol. 10 (1998), pp. 359-371. +* [3] J. Demmel and K. Veselic: Jacobi method is more accurate than QR. +* [4] Z. Drmac: Implementation of Jacobi rotations for accurate singular +* value computation in floating point arithmetic. +* SIAM J. Sci. Comp., Vol. 18 (1997), pp. 1200-1222. +* [5] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm I. +* SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1322-1342. +* LAPACK Working note 169. +* [6] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm II. +* SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1343-1362. +* LAPACK Working note 170. +* [7] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV, +* QSVD, (H,K)-SVD computations. +* Department of Mathematics, University of Zagreb, 2008. +* +* Bugs, Examples and Comments +* =========================== +* Please report all bugs and send interesting test examples and comments to +* drmac@math.hr. Thank you. +* * ===================================================================== * * .. Local Parameters .. |