* Categories have been created for the following modules help pages: 51/8551/4
Sylvestre Ledru [Mon, 6 Aug 2012 08:02:17 +0000 (10:02 +0200)]
   - Linear algebra. See bug #11562

Change-Id: Ia15f8328dd25908896c5213d60724c2b80c09bf8

490 files changed:
scilab/CHANGES_5.4.X
scilab/modules/elementary_functions/help/en_US/matrixoperations/squeeze.xml [new file with mode: 0644]
scilab/modules/elementary_functions/help/en_US/symbolic/cmb_lin.xml [new file with mode: 0644]
scilab/modules/elementary_functions/help/fr_FR/matrixoperations/squeeze.xml [new file with mode: 0644]
scilab/modules/elementary_functions/help/fr_FR/symbolic/cmb_lin.xml [new file with mode: 0644]
scilab/modules/elementary_functions/help/ja_JP/matrixoperations/squeeze.xml [new file with mode: 0644]
scilab/modules/elementary_functions/help/ja_JP/symbolic/cmb_lin.xml [new file with mode: 0644]
scilab/modules/elementary_functions/help/pt_BR/matrixoperations/squeeze.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/aff2ab.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/balanc.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/bdiag.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/chol.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/classmarkov.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/cmb_lin.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/coff.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/colcomp.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/companion.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/cond.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/det.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/eigen/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/eigen/balanc.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/eigen/bdiag.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/eigen/gschur.xml [moved from scilab/modules/linear_algebra/help/en_US/gschur.xml with 100% similarity]
scilab/modules/linear_algebra/help/en_US/eigen/gspec.xml [moved from scilab/modules/linear_algebra/help/en_US/gspec.xml with 100% similarity]
scilab/modules/linear_algebra/help/en_US/eigen/hess.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/eigen/pbig.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/eigen/projspec.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/eigen/psmall.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/eigen/schur.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/eigen/spec.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/eigen/sva.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/eigen/svd.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/eigenmarkov.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/ereduc.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/expm.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/factorization/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/factorization/givens.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/factorization/householder.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/factorization/sqroot.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/fstair.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/fullrf.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/fullrfk.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/genmarkov.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/givens.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/glever.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/hess.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/householder.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/im_inv.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/inv.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/kernel.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/kernel/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/kernel/colcomp.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/kernel/fullrf.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/kernel/fullrfk.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/kernel/im_inv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/kernel/kernel.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/kernel/range.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/kernel/rowcomp.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/kroneck.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/linear/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/linear/aff2ab.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/linear/chol.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/linear/inv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/linear/linsolve.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/linear/lsq.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/linear/lu.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/linear/pinv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/linear/qr.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/linear/rankqr.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/linsolve.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/lsq.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/lu.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/lyap.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/markov/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/markov/classmarkov.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/markov/eigenmarkov.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/markov/genmarkov.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/matrix/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/matrix/cond.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/matrix/det.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/matrix/orth.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/matrix/rank.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/matrix/rcond.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/matrix/rref.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/matrix/trace.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/matrix_log/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/matrix_log/expm.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/matrix_log/polar.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/nlev.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/orth.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/pbig.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/pencan.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/pencil/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/pencil/companion.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/pencil/ereduc.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/pencil/fstair.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/pencil/glever.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/pencil/kroneck.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/pencil/lyap.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/pencil/pencan.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/pencil/penlaur.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/pencil/quaskro.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/pencil/randpencil.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/pencil/rowshuff.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/pencil/sylv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/penlaur.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/pinv.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/polar.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/projspec.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/psmall.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/qr.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/quaskro.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/randpencil.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/range.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/rank.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/rankqr.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/rcond.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/rowcomp.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/rowshuff.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/rref.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/schur.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/spaninter.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/spanplus.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/spantwo.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/spec.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/sqroot.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/squeeze.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/state_space/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/state_space/coff.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/state_space/nlev.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/subspaces/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/subspaces/spaninter.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/subspaces/spanplus.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/subspaces/spantwo.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/en_US/sva.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/svd.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/sylv.xml [deleted file]
scilab/modules/linear_algebra/help/en_US/trace.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/addchapter.sce
scilab/modules/linear_algebra/help/fr_FR/bdiag.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/chol.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/cmb_lin.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/coff.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/colcomp.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/companion.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/cond.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/det.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/eigen/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/eigen/bdiag.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/eigen/gspec.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/eigen/hess.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/eigen/pbig.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/eigen/spec.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/eigen/sva.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/eigen/svd.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/expm.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/factorization/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/factorization/givens.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/factorization/householder.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/factorization/sqroot.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/fullrf.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/fullrfk.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/givens.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/glever.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/gspec.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/hess.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/householder.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/inv.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/kernel.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/kernel/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/kernel/colcomp.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/kernel/fullrf.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/kernel/fullrfk.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/kernel/kernel.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/kernel/range.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/kernel/rowcomp.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/linear/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/linear/chol.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/linear/inv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/linear/linsolve.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/linear/lu.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/linear/pinv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/linear/qr.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/linsolve.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/lu.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/lyap.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/markov/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/matrix/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/matrix/cond.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/matrix/det.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/matrix/orth.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/matrix/rank.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/matrix/rcond.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/matrix/trace.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/matrix_log/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/matrix_log/expm.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/matrix_log/polar.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/nlev.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/orth.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/pbig.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/pencil/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/pencil/companion.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/pencil/glever.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/pencil/lyap.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/pinv.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/polar.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/proj.xml
scilab/modules/linear_algebra/help/fr_FR/qr.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/range.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/rank.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/rcond.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/rowcomp.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/spec.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/sqroot.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/squeeze.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/state_space/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/state_space/coff.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/state_space/nlev.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/subspaces/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/fr_FR/sva.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/svd.xml [deleted file]
scilab/modules/linear_algebra/help/fr_FR/trace.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/addchapter.sce
scilab/modules/linear_algebra/help/ja_JP/aff2ab.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/balanc.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/bdiag.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/chol.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/classmarkov.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/cmb_lin.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/coff.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/colcomp.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/companion.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/cond.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/det.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/eigen/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigen/balanc.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigen/bdiag.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigen/gschur.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigen/gspec.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigen/hess.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigen/pbig.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigen/projspec.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigen/psmall.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigen/schur.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigen/spec.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigen/sva.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigen/svd.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/eigenmarkov.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/ereduc.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/expm.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/factorization/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/factorization/givens.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/factorization/householder.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/factorization/sqroot.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/fstair.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/fullrf.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/fullrfk.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/genmarkov.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/givens.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/glever.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/gschur.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/gspec.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/hess.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/householder.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/im_inv.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/inv.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/kernel.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/kernel/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/kernel/colcomp.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/kernel/fullrf.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/kernel/fullrfk.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/kernel/im_inv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/kernel/kernel.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/kernel/range.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/kernel/rowcomp.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/kroneck.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/linear/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/linear/aff2ab.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/linear/chol.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/linear/inv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/linear/linsolve.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/linear/lsq.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/linear/lu.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/linear/pinv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/linear/qr.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/linear/rankqr.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/linsolve.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/lsq.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/lu.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/lyap.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/markov/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/markov/classmarkov.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/markov/eigenmarkov.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/markov/genmarkov.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/matrix/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/matrix/cond.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/matrix/det.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/matrix/orth.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/matrix/rank.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/matrix/rcond.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/matrix/rref.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/matrix/trace.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/matrix_log/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/matrix_log/expm.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/matrix_log/polar.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/nlev.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/orth.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/pbig.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/pencan.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/pencil/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/pencil/companion.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/pencil/ereduc.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/pencil/fstair.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/pencil/glever.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/pencil/kroneck.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/pencil/lyap.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/pencil/pencan.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/pencil/penlaur.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/pencil/quaskro.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/pencil/randpencil.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/pencil/rowshuff.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/pencil/sylv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/penlaur.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/pinv.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/polar.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/proj.xml
scilab/modules/linear_algebra/help/ja_JP/projspec.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/psmall.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/qr.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/quaskro.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/randpencil.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/range.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/rank.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/rankqr.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/rcond.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/rowcomp.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/rowshuff.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/rref.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/schur.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/spaninter.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/spanplus.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/spantwo.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/spec.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/sqroot.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/squeeze.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/state_space/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/state_space/coff.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/state_space/nlev.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/subspaces/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/subspaces/spaninter.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/subspaces/spanplus.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/subspaces/spantwo.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/ja_JP/sva.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/svd.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/sylv.xml [deleted file]
scilab/modules/linear_algebra/help/ja_JP/trace.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/addchapter.sce
scilab/modules/linear_algebra/help/pt_BR/aff2ab.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/balanc.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/bdiag.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/chol.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/classmarkov.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/cmb_lin.xml
scilab/modules/linear_algebra/help/pt_BR/coff.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/colcomp.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/companion.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/cond.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/det.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/eigen/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigen/balanc.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigen/bdiag.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigen/gschur.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigen/gspec.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigen/hess.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigen/pbig.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigen/projspec.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigen/psmall.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigen/schur.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigen/spec.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigen/sva.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigen/svd.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/eigenmarkov.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/ereduc.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/expm.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/factorization/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/factorization/givens.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/factorization/householder.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/factorization/sqroot.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/fstair.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/fullrf.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/fullrfk.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/genmarkov.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/givens.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/glever.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/gschur.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/gspec.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/hess.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/householder.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/im_inv.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/inv.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/kernel.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/kernel/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/kernel/colcomp.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/kernel/fullrf.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/kernel/fullrfk.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/kernel/im_inv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/kernel/kernel.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/kernel/range.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/kernel/rowcomp.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/kroneck.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/linear/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/linear/aff2ab.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/linear/chol.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/linear/inv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/linear/linsolve.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/linear/lsq.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/linear/lu.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/linear/pinv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/linear/qr.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/linear/rankqr.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/linsolve.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/lsq.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/lu.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/lyap.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/markov/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/markov/classmarkov.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/markov/eigenmarkov.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/markov/genmarkov.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/matrix/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/matrix/cond.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/matrix/det.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/matrix/orth.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/matrix/rank.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/matrix/rcond.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/matrix/rref.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/matrix/trace.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/matrix_log/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/matrix_log/expm.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/matrix_log/polar.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/nlev.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/orth.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/pbig.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/pencan.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/pencil/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/pencil/companion.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/pencil/ereduc.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/pencil/fstair.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/pencil/glever.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/pencil/kroneck.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/pencil/lyap.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/pencil/pencan.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/pencil/penlaur.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/pencil/quaskro.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/pencil/randpencil.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/pencil/rowshuff.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/pencil/sylv.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/penlaur.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/pinv.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/polar.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/proj.xml
scilab/modules/linear_algebra/help/pt_BR/projspec.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/psmall.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/qr.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/quaskro.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/randpencil.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/range.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/rank.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/rankqr.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/rcond.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/rowcomp.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/rowshuff.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/rref.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/schur.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/spaninter.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/spanplus.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/spantwo.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/spec.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/sqroot.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/squeeze.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/state_space/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/state_space/coff.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/state_space/nlev.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/subspaces/CHAPTER [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/subspaces/spaninter.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/subspaces/spanplus.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/subspaces/spantwo.xml [new file with mode: 0644]
scilab/modules/linear_algebra/help/pt_BR/sva.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/svd.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/sylv.xml [deleted file]
scilab/modules/linear_algebra/help/pt_BR/trace.xml [deleted file]

index 35a9cb9..25dbed8 100644 (file)
@@ -13,7 +13,8 @@ Documentation
 =============
 
 * Categories have been created for the following modules help pages:
-  - Functions: libraries sub-category (See bug #11642)
+    - Functions (libraries sub-category). See bug #11642.
+    - Linear algebra. See bug #11562.
 
 
 Bug Fixes
diff --git a/scilab/modules/elementary_functions/help/en_US/matrixoperations/squeeze.xml b/scilab/modules/elementary_functions/help/en_US/matrixoperations/squeeze.xml
new file mode 100644 (file)
index 0000000..c9f3952
--- /dev/null
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="squeeze">
+    <refnamediv>
+        <refname>squeeze</refname>
+        <refpurpose> squeeze</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>hypOut = squeeze(hypIn)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>hypIn</term>
+                <listitem>
+                    <para>hypermatrix or matrix of constant type.</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>hypOut</term>
+                <listitem>
+                    <para>hypermatrix or matrix of constant type.</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para> Remove singleton dimensions of a hypermatrix, that is any dimension for
+            which the size is 1. If the input is a matrix, it is unaffected.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+       M1 = zeros(2,1,5)
+       squeeze(M1)
+       squeeze(M1(:,:,1))
+       
+       M2 = hypermat([2 1 2 1],1:4)
+       squeeze(M2)
+       ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="hypermat">hypermat</link>
+            </member>
+            <member>
+                <link linkend="hypermatrices">hypermatrices</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/elementary_functions/help/en_US/symbolic/cmb_lin.xml b/scilab/modules/elementary_functions/help/en_US/symbolic/cmb_lin.xml
new file mode 100644 (file)
index 0000000..c8eb1bf
--- /dev/null
@@ -0,0 +1,40 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="cmb_lin">
+    <refnamediv>
+        <refname>cmb_lin</refname>
+        <refpurpose> symbolic linear combination</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[x]=cmb_lin(alfa,x,beta,y)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Evaluates <literal>alfa*x-beta*y</literal>. <literal> alfa, beta, x, y</literal> are character
+            strings. (low-level routine)
+        </para>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="mulf">mulf</link>
+            </member>
+            <member>
+                <link linkend="addf">addf</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/elementary_functions/help/fr_FR/matrixoperations/squeeze.xml b/scilab/modules/elementary_functions/help/fr_FR/matrixoperations/squeeze.xml
new file mode 100644 (file)
index 0000000..c9f3952
--- /dev/null
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="squeeze">
+    <refnamediv>
+        <refname>squeeze</refname>
+        <refpurpose> squeeze</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>hypOut = squeeze(hypIn)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>hypIn</term>
+                <listitem>
+                    <para>hypermatrix or matrix of constant type.</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>hypOut</term>
+                <listitem>
+                    <para>hypermatrix or matrix of constant type.</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para> Remove singleton dimensions of a hypermatrix, that is any dimension for
+            which the size is 1. If the input is a matrix, it is unaffected.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+       M1 = zeros(2,1,5)
+       squeeze(M1)
+       squeeze(M1(:,:,1))
+       
+       M2 = hypermat([2 1 2 1],1:4)
+       squeeze(M2)
+       ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="hypermat">hypermat</link>
+            </member>
+            <member>
+                <link linkend="hypermatrices">hypermatrices</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/elementary_functions/help/fr_FR/symbolic/cmb_lin.xml b/scilab/modules/elementary_functions/help/fr_FR/symbolic/cmb_lin.xml
new file mode 100644 (file)
index 0000000..c8eb1bf
--- /dev/null
@@ -0,0 +1,40 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="cmb_lin">
+    <refnamediv>
+        <refname>cmb_lin</refname>
+        <refpurpose> symbolic linear combination</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[x]=cmb_lin(alfa,x,beta,y)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Evaluates <literal>alfa*x-beta*y</literal>. <literal> alfa, beta, x, y</literal> are character
+            strings. (low-level routine)
+        </para>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="mulf">mulf</link>
+            </member>
+            <member>
+                <link linkend="addf">addf</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/elementary_functions/help/ja_JP/matrixoperations/squeeze.xml b/scilab/modules/elementary_functions/help/ja_JP/matrixoperations/squeeze.xml
new file mode 100644 (file)
index 0000000..c9f3952
--- /dev/null
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="squeeze">
+    <refnamediv>
+        <refname>squeeze</refname>
+        <refpurpose> squeeze</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>hypOut = squeeze(hypIn)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>hypIn</term>
+                <listitem>
+                    <para>hypermatrix or matrix of constant type.</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>hypOut</term>
+                <listitem>
+                    <para>hypermatrix or matrix of constant type.</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para> Remove singleton dimensions of a hypermatrix, that is any dimension for
+            which the size is 1. If the input is a matrix, it is unaffected.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+       M1 = zeros(2,1,5)
+       squeeze(M1)
+       squeeze(M1(:,:,1))
+       
+       M2 = hypermat([2 1 2 1],1:4)
+       squeeze(M2)
+       ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="hypermat">hypermat</link>
+            </member>
+            <member>
+                <link linkend="hypermatrices">hypermatrices</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/elementary_functions/help/ja_JP/symbolic/cmb_lin.xml b/scilab/modules/elementary_functions/help/ja_JP/symbolic/cmb_lin.xml
new file mode 100644 (file)
index 0000000..c8eb1bf
--- /dev/null
@@ -0,0 +1,40 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="cmb_lin">
+    <refnamediv>
+        <refname>cmb_lin</refname>
+        <refpurpose> symbolic linear combination</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[x]=cmb_lin(alfa,x,beta,y)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Evaluates <literal>alfa*x-beta*y</literal>. <literal> alfa, beta, x, y</literal> are character
+            strings. (low-level routine)
+        </para>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="mulf">mulf</link>
+            </member>
+            <member>
+                <link linkend="addf">addf</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/elementary_functions/help/pt_BR/matrixoperations/squeeze.xml b/scilab/modules/elementary_functions/help/pt_BR/matrixoperations/squeeze.xml
new file mode 100644 (file)
index 0000000..c9f3952
--- /dev/null
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="squeeze">
+    <refnamediv>
+        <refname>squeeze</refname>
+        <refpurpose> squeeze</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>hypOut = squeeze(hypIn)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>hypIn</term>
+                <listitem>
+                    <para>hypermatrix or matrix of constant type.</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>hypOut</term>
+                <listitem>
+                    <para>hypermatrix or matrix of constant type.</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para> Remove singleton dimensions of a hypermatrix, that is any dimension for
+            which the size is 1. If the input is a matrix, it is unaffected.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+       M1 = zeros(2,1,5)
+       squeeze(M1)
+       squeeze(M1(:,:,1))
+       
+       M2 = hypermat([2 1 2 1],1:4)
+       squeeze(M2)
+       ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="hypermat">hypermat</link>
+            </member>
+            <member>
+                <link linkend="hypermatrices">hypermatrices</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/aff2ab.xml b/scilab/modules/linear_algebra/help/en_US/aff2ab.xml
deleted file mode 100644 (file)
index 8ba357c..0000000
+++ /dev/null
@@ -1,150 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="aff2ab">
-  <refnamediv>
-    <refname>aff2ab</refname>
-    <refpurpose> linear (affine) function to A,b conversion</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[A,b]=aff2ab(afunction,dimX,D [,flag])</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>afunction</term>
-        <listitem>
-          <para>
-            a scilab function <literal> Y =fct(X,D) </literal> where <literal>X, D, Y</literal> are <literal>list</literal> of matrices
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>dimX</term>
-        <listitem>
-          <para>
-            a p x 2 integer matrix (<literal>p</literal> is the number of matrices in <literal>X</literal>)
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>D</term>
-        <listitem>
-          <para>
-            a <literal>list</literal> of real matrices (or any other valid Scilab object).
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>flag</term>
-        <listitem>
-          <para>
-            optional parameter (<literal>flag='f'</literal> or <literal>flag='sp'</literal>)
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>A</term>
-        <listitem>
-          <para>a real matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>b</term>
-        <listitem>
-          <para>
-            a real vector having same row dimension as <literal>A</literal>
-          </para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      <literal>aff2ab</literal>  returns the matrix representation of an affine
-      function (in the canonical basis).
-    </para>
-    <para>
-      <literal>afunction</literal> is a function with imposed syntax:
-      <literal> Y=afunction(X,D) </literal> where <literal> X=list(X1,X2,...,Xp) </literal> is
-      a list of p real matrices, and <literal> Y=list(Y1,...,Yq) </literal> is
-      a list of q real real matrices which depend linearly of
-      the <literal> Xi</literal>'s. The (optional) input <literal> D</literal> contains 
-      parameters needed to compute Y as a function of X. 
-      (It is generally a list of matrices).
-    </para>
-    <para>
-      <literal> dimX</literal> is a p x 2 matrix: <literal>dimX(i)=[nri,nci]</literal>
-      is the actual number of rows and columns of matrix <literal>Xi</literal>.
-      These dimensions determine <literal>na</literal>, the column dimension of 
-      the resulting matrix <literal>A</literal>: <literal>na=nr1*nc1 +...+ nrp*ncp</literal>.
-    </para>
-    <para>
-      If the optional parameter <literal>flag='sp'</literal> the resulting <literal>A</literal>
-      matrix is returned as a sparse matrix.
-    </para>
-    <para>
-      This function is useful to solve a system of linear equations
-      where the unknown variables are matrices.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-// Lyapunov equation solver (one unknown variable, one constraint)
-deff('Y=lyapunov(X,D)','[A,Q]=D(:);Xm=X(:); Y=list(A''*Xm+Xm*A-Q)')
-A=rand(3,3);Q=rand(3,3);Q=Q+Q';D=list(A,Q);dimX=[3,3];
-[Aly,bly]=aff2ab(lyapunov,dimX,D);
-[Xl,kerA]=linsolve(Aly,bly); Xv=vec2list(Xl,dimX); lyapunov(Xv,D)
-Xm=Xv(:); A'*Xm+Xm*A-Q
-
-// Lyapunov equation solver with redundant constraint X=X'
-// (one variable, two constraints) D is global variable
-deff('Y=ly2(X,D)','[A,Q]=D(:);Xm=X(:); Y=list(A''*Xm+Xm*A-Q,Xm''-Xm)')
-A=rand(3,3);Q=rand(3,3);Q=Q+Q';D=list(A,Q);dimX=[3,3];
-[Aly,bly]=aff2ab(ly2,dimX,D);
-[Xl,kerA]=linsolve(Aly,bly); Xv=vec2list(Xl,dimX); ly2(Xv,D)
-
-// Francis equations
-// Find matrices X1 and X2 such that:
-// A1*X1 - X1*A2 + B*X2 -A3 = 0
-// D1*X1 -D2 = 0 
-deff('Y=bruce(X,D)','[A1,A2,A3,B,D1,D2]=D(:),...
-[X1,X2]=X(:);Y=list(A1*X1-X1*A2+B*X2-A3,D1*X1-D2)')
-A1=[-4,10;-1,2];A3=[1;2];B=[0;1];A2=1;D1=[0,1];D2=1;
-D=list(A1,A2,A3,B,D1,D2);
-[n1,m1]=size(A1);[n2,m2]=size(A2);[n3,m3]=size(B);
-dimX=[[m1,n2];[m3,m2]];
-[Af,bf]=aff2ab(bruce,dimX,D);
-[Xf,KerAf]=linsolve(Af,bf);Xsol=vec2list(Xf,dimX)
-bruce(Xsol,D)
-
-// Find all X which commute with A
-deff('y=f(X,D)','y=list(D(:)*X(:)-X(:)*D(:))')
-A=rand(3,3);dimX=[3,3];[Af,bf]=aff2ab(f,dimX,list(A));
-[Xf,KerAf]=linsolve(Af,bf);[p,q]=size(KerAf);
-Xsol=vec2list(Xf+KerAf*rand(q,1),dimX);
-C=Xsol(:); A*C-C*A
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="linsolve">linsolve</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/balanc.xml b/scilab/modules/linear_algebra/help/en_US/balanc.xml
deleted file mode 100644 (file)
index 0409bbd..0000000
+++ /dev/null
@@ -1,106 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="balanc">
-  <refnamediv>
-    <refname>balanc</refname>
-    <refpurpose> matrix or pencil balancing</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[Ab,X]=balanc(A)
-      [Eb,Ab,X,Y]=balanc(E,A)
-    </synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>A:  </term>
-        <listitem>
-          <para>a real square matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>X:  </term>
-        <listitem>
-          <para>a real square invertible matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>E:  </term>
-        <listitem>
-          <para>
-            a real square matrix (same dimension as <literal>A</literal>)
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Y:  </term>
-        <listitem>
-          <para>a real square invertible matrix.</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      Balance a square matrix to improve
-      its condition number.
-    </para>
-    <para>
-      <literal>[Ab,X] = balanc(A)</literal> finds a similarity transformation
-      <literal>X</literal> such that
-    </para>
-    <para>
-      <literal>Ab = inv(X)*A*X</literal> has approximately equal row and column norms.
-    </para>
-    <para>
-      For matrix pencils,balancing is done for improving the
-      generalized eigenvalue problem.
-    </para>
-    <para>
-      <literal>[Eb,Ab,X,Y] = balanc(E,A)</literal> returns left and right transformations <literal>X</literal> and <literal>Y</literal>
-      such that <literal>Eb=inv(X)*E*Y,  Ab=inv(X)*A*Y</literal>
-    </para>
-  </refsection>
-  <refsection>
-    <title>Remark</title>
-    <para>
-      Balancing is made in the functions <literal>bdiag</literal> and <literal>spec</literal>.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-A=[1/2^10,1/2^10;2^10,2^10];
-[Ab,X]=balanc(A);
-norm(A(1,:))/norm(A(2,:))
-norm(Ab(1,:))/norm(Ab(2,:))
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="bdiag">bdiag</link>
-      </member>
-      <member>
-        <link linkend="spec">spec</link>
-      </member>
-      <member>
-        <link linkend="schur">schur</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/bdiag.xml b/scilab/modules/linear_algebra/help/en_US/bdiag.xml
deleted file mode 100644 (file)
index 2c982f5..0000000
+++ /dev/null
@@ -1,103 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="bdiag">
-  <refnamediv>
-    <refname>bdiag</refname>
-    <refpurpose> block diagonalization, generalized eigenvectors</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[Ab [,X [,bs]]]=bdiag(A [,rmax])</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>A</term>
-        <listitem>
-          <para>real or complex square matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>rmax</term>
-        <listitem>
-          <para>real number</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Ab</term>
-        <listitem>
-          <para>real or complex square matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>X</term>
-        <listitem>
-          <para>real or complex non-singular matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>bs</term>
-        <listitem>
-          <para>vector of integers</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <programlisting role=""><![CDATA[ 
-[Ab [,X [,bs]]]=bdiag(A [,rmax]) 
- ]]></programlisting>
-    <para>
-      performs the block-diagonalization of matrix <literal>A</literal>.  bs
-      gives the structure of the blocks (respective sizes of the
-      blocks).  <literal>X</literal> is the change of basis i.e 
-      <literal>Ab = inv(X)*A*X</literal>is block diagonal.
-    </para>
-    <para>
-      <literal>rmax</literal> controls the conditioning of <literal>X</literal>; the
-      default value is the l1 norm of <literal>A</literal>.
-    </para>
-    <para>
-      To get a diagonal form (if it exists) choose a large value for
-      <literal>rmax</literal> (<literal>rmax=1/%eps</literal> for example).
-      Generically (for real random A) the blocks are (1x1) and (2x2) and
-      <literal>X</literal> is the matrix of eigenvectors.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-//Real case: 1x1 and 2x2 blocks
-a=rand(5,5);[ab,x,bs]=bdiag(a);ab
-
-//Complex case: complex 1x1 blocks
-[ab,x,bs]=bdiag(a+%i*0);ab
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="schur">schur</link>
-      </member>
-      <member>
-        <link linkend="sylv">sylv</link>
-      </member>
-      <member>
-        <link linkend="spec">spec</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/chol.xml b/scilab/modules/linear_algebra/help/en_US/chol.xml
deleted file mode 100644 (file)
index 44c24da..0000000
+++ /dev/null
@@ -1,81 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="chol">
-  <refnamediv>
-    <refname>chol</refname>
-    <refpurpose> Cholesky factorization</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[R]=chol(X)</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>X</term>
-        <listitem>
-          <para>a symmetric positive definite real or complex matrix.</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      If <literal>X</literal> is positive definite, then <literal>R = chol(X)</literal> produces an upper 
-      triangular matrix <literal>R</literal> such that <literal>R'*R = X</literal>.
-    </para>
-    <para>
-      <literal>chol(X)</literal> uses only the diagonal and upper triangle of <literal>X</literal>.
-      The lower triangular is assumed to be the (complex conjugate) 
-      transpose of the upper.
-    </para>
-  </refsection>
-  <refsection>
-    <title>References</title>
-    <para>
-      Cholesky decomposition is based on  the Lapack routines
-      DPOTRF for  real matrices and  ZPOTRF for the complex case.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-W=rand(5,5)+%i*rand(5,5);
-X=W*W';
-R=chol(X);
-norm(R'*R-X)
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="spchol">spchol</link>
-      </member>
-      <member>
-        <link linkend="qr">qr</link>
-      </member>
-      <member>
-        <link linkend="svd">svd</link>
-      </member>
-      <member>
-        <link linkend="bdiag">bdiag</link>
-      </member>
-      <member>
-        <link linkend="fullrf">fullrf</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/classmarkov.xml b/scilab/modules/linear_algebra/help/en_US/classmarkov.xml
deleted file mode 100644 (file)
index 1847697..0000000
+++ /dev/null
@@ -1,93 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="classmarkov">
-  <refnamediv>
-    <refname>classmarkov</refname>
-    <refpurpose> recurrent and transient classes of Markov matrix</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[perm,rec,tr,indsRec,indsT]=classmarkov(M)</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>M</term>
-        <listitem>
-          <para>real N x N Markov matrix. Sum of entries in each row should add to one.</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>perm</term>
-        <listitem>
-          <para>integer permutation vector.</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>rec, tr</term>
-        <listitem>
-          <para>integer vector, number (number of states in each recurrent classes, number of transient states).</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>indsRec,indsT</term>
-        <listitem>
-          <para>integer vectors. (Indexes of recurrent and transient states).</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      Returns a permutation vector <literal>perm</literal> such that
-    </para>
-    <programlisting role=""><![CDATA[ 
-M(perm,perm) = [M11 0 0 0 0   0]
-               [0 M22 0 0     0]
-               [0 0 M33       0]
-               [      ...      ]
-               [0 0       Mrr 0]
-               [* *        *  Q]
- ]]></programlisting>
-    <para>
-      Each <literal>Mii</literal> is a Markov matrix of dimension <literal>rec(i)  i=1,..,r</literal>.
-      <literal>Q</literal> is sub-Markov matrix of dimension <literal>tr</literal>.
-      States 1 to sum(rec) are recurrent and states from r+1 to n
-      are transient. 
-      One has <literal>perm=[indsRec,indsT]</literal> where indsRec is a  vector of size sum(rec) 
-      and indsT is a vector of size tr.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-//P has two recurrent classes (with 2 and 1 states) 2 transient states
-P=genmarkov([2,1],2,'perm')
-[perm,rec,tr,indsRec,indsT]=classmarkov(P);
-P(perm,perm)
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="genmarkov">genmarkov</link>
-      </member>
-      <member>
-        <link linkend="eigenmarkov">eigenmarkov</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/cmb_lin.xml b/scilab/modules/linear_algebra/help/en_US/cmb_lin.xml
deleted file mode 100644 (file)
index 0e7122a..0000000
+++ /dev/null
@@ -1,40 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="cmb_lin">
-  <refnamediv>
-    <refname>cmb_lin</refname>
-    <refpurpose> symbolic linear combination</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[x]=cmb_lin(alfa,x,beta,y)</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Description</title>
-    <para>
-      Evaluates <literal>alfa*x-beta*y</literal>. <literal> alfa, beta, x, y</literal> are character
-      strings. (low-level routine)
-    </para>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="mulf">mulf</link>
-      </member>
-      <member>
-        <link linkend="addf">addf</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/coff.xml b/scilab/modules/linear_algebra/help/en_US/coff.xml
deleted file mode 100644 (file)
index 22371c9..0000000
+++ /dev/null
@@ -1,97 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="coff">
-  <refnamediv>
-    <refname>coff</refname>
-    <refpurpose> resolvent (cofactor method)  </refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[N,d]=coff(M [,var])</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>M</term>
-        <listitem>
-          <para>square real matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>var</term>
-        <listitem>
-          <para>character string</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>N</term>
-        <listitem>
-          <para>
-            polynomial matrix (same size as <literal>M</literal>)
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>d</term>
-        <listitem>
-          <para>
-            polynomial (characteristic polynomial <literal>poly(A,'s')</literal>)
-          </para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      <literal>coff</literal> computes R=<literal>(s*eye()-M)^-1</literal> for <literal>M</literal> a real matrix. 
-      R is given by <literal>N/d</literal>.
-    </para>
-    <para>
-      <literal>N</literal> = numerator polynomial matrix.
-    </para>
-    <para>
-      <literal>d</literal> = common denominator.
-    </para>
-    <para>
-      <literal>var</literal> character string ('<literal>s</literal>' if omitted)
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-M=[1,2;0,3];
-[N,d]=coff(M)
-N/d
-inv(%s*eye()-M)
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="coffg">coffg</link>
-      </member>
-      <member>
-        <link linkend="ss2tf">ss2tf</link>
-      </member>
-      <member>
-        <link linkend="nlev">nlev</link>
-      </member>
-      <member>
-        <link linkend="poly">poly</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/colcomp.xml b/scilab/modules/linear_algebra/help/en_US/colcomp.xml
deleted file mode 100644 (file)
index bdec81f..0000000
+++ /dev/null
@@ -1,106 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="colcomp">
-  <refnamediv>
-    <refname>colcomp</refname>
-    <refpurpose> column compression, kernel, nullspace</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[W,rk]=colcomp(A [,flag] [,tol])</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>A</term>
-        <listitem>
-          <para>real or complex matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>flag</term>
-        <listitem>
-          <para>character string</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>tol</term>
-        <listitem>
-          <para>real number</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>W</term>
-        <listitem>
-          <para>square non-singular matrix (change of basis)</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>rk</term>
-        <listitem>
-          <para>
-            integer (rank of <literal>A</literal>)
-          </para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      Column compression of <literal>A</literal>: <literal>Ac = A*W</literal> is 
-      column compressed i.e
-    </para>
-    <para>
-      <literal>Ac=[0,Af]</literal> with <literal>Af</literal> full column rank, 
-      rank(<literal>Af</literal>) = rank(<literal>A</literal>) = <literal>rk</literal>.
-    </para>
-    <para>
-      <literal>flag</literal> and <literal>tol</literal> are optional parameters: <literal>flag = 'qr'</literal> 
-      or <literal>'svd'</literal> (default is <literal>'svd'</literal>).
-    </para>
-    <para>
-      <literal>tol</literal> = tolerance parameter (of order <literal>%eps</literal> as default value).
-    </para>
-    <para>
-      The <literal>ma-rk</literal> first columns of <literal>W</literal> span the kernel of <literal>A</literal> 
-      when <literal>size(A)=(na,ma)</literal>
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-A=rand(5,2)*rand(2,5);
-[X,r]=colcomp(A);
-norm(A*X(:,1:$-r),1)
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="rowcomp">rowcomp</link>
-      </member>
-      <member>
-        <link linkend="fullrf">fullrf</link>
-      </member>
-      <member>
-        <link linkend="fullrfk">fullrfk</link>
-      </member>
-      <member>
-        <link linkend="kernel">kernel</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/companion.xml b/scilab/modules/linear_algebra/help/en_US/companion.xml
deleted file mode 100644 (file)
index a050f64..0000000
+++ /dev/null
@@ -1,77 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="companion">
-  <refnamediv>
-    <refname>companion</refname>
-    <refpurpose> companion matrix</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>A=companion(p)</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>p</term>
-        <listitem>
-          <para>polynomial or vector of polynomials</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>A</term>
-        <listitem>
-          <para>square matrix</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      Returns a matrix <literal>A</literal> with characteristic polynomial equal
-      to <literal>p</literal> if <literal>p</literal> is monic. If <literal>p</literal> is not monic
-      the characteristic polynomial of <literal>A</literal> is equal to
-      <literal>p/c</literal> where <literal>c</literal> is the coefficient of largest degree
-      in <literal>p</literal>.
-    </para>
-    <para>
-      If <literal>p</literal> is a vector of monic polynomials, <literal>A</literal> is block diagonal,
-      and the characteristic polynomial of the ith block is <literal>p(i)</literal>.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-s=poly(0,'s');
-p=poly([1,2,3,4,1],'s','c')
-det(s*eye()-companion(p))
-roots(p)
-spec(companion(p))
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="spec">spec</link>
-      </member>
-      <member>
-        <link linkend="poly">poly</link>
-      </member>
-      <member>
-        <link linkend="randpencil">randpencil</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/cond.xml b/scilab/modules/linear_algebra/help/en_US/cond.xml
deleted file mode 100644 (file)
index e481250..0000000
+++ /dev/null
@@ -1,58 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="cond">
-  <refnamediv>
-    <refname>cond</refname>
-    <refpurpose> condition number</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>cond(X)</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>X</term>
-        <listitem>
-          <para>real or complex square matrix</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      Condition number in 2-norm.  <literal>cond(X)</literal> is the  ratio  of  the
-      largest singular value of  <literal>X</literal>  to the smallest.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-A=testmatrix('hilb',6);
-cond(A)
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="rcond">rcond</link>
-      </member>
-      <member>
-        <link linkend="svd">svd</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/det.xml b/scilab/modules/linear_algebra/help/en_US/det.xml
deleted file mode 100644 (file)
index bbd35c5..0000000
+++ /dev/null
@@ -1,87 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="det">
-  <refnamediv>
-    <refname>det</refname>
-    <refpurpose> determinant</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>det(X)
-      [e,m]=det(X)
-    </synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>X</term>
-        <listitem>
-          <para>real or complex square matrix, polynomial or rational matrix.</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>m</term>
-        <listitem>
-          <para>real or complex number, the determinant base 10 mantissae</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>e</term>
-        <listitem>
-          <para>integer, the determinant base 10 exponent</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      <literal>det(X)</literal> ( <literal>m*10^e</literal> is the determinant of the square matrix <literal>X</literal>.
-    </para>
-    <para>
-      For polynomial matrix <literal>det(X)</literal> is equivalent to <literal>determ(X)</literal>.
-    </para>
-    <para>
-      For rational matrices <literal>det(X)</literal> is equivalent to <literal>detr(X)</literal>.
-    </para>
-  </refsection>
-  <refsection>
-    <title>References</title>
-    <para>
-      det computations are based on the Lapack routines
-      DGETRF for  real matrices and  ZGETRF for the complex case.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-x=poly(0,'x');
-det([x,1+x;2-x,x^2])
-w=ssrand(2,2,4);roots(det(systmat(w))),trzeros(w)   //zeros of linear system
-A=rand(3,3);
-det(A), prod(spec(A))
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="detr">detr</link>
-      </member>
-      <member>
-        <link linkend="determ">determ</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/eigen/CHAPTER b/scilab/modules/linear_algebra/help/en_US/eigen/CHAPTER
new file mode 100644 (file)
index 0000000..88f8bc4
--- /dev/null
@@ -0,0 +1,2 @@
+title = Eigenvalue and Singular Value
+
diff --git a/scilab/modules/linear_algebra/help/en_US/eigen/balanc.xml b/scilab/modules/linear_algebra/help/en_US/eigen/balanc.xml
new file mode 100644 (file)
index 0000000..bcc2b93
--- /dev/null
@@ -0,0 +1,106 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="balanc">
+    <refnamediv>
+        <refname>balanc</refname>
+        <refpurpose> matrix or pencil balancing</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[Ab,X]=balanc(A)
+            [Eb,Ab,X,Y]=balanc(E,A)
+        </synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A:  </term>
+                <listitem>
+                    <para>a real square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>X:  </term>
+                <listitem>
+                    <para>a real square invertible matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>E:  </term>
+                <listitem>
+                    <para>
+                        a real square matrix (same dimension as <literal>A</literal>)
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Y:  </term>
+                <listitem>
+                    <para>a real square invertible matrix.</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Balance a square matrix to improve
+            its condition number.
+        </para>
+        <para>
+            <literal>[Ab,X] = balanc(A)</literal> finds a similarity transformation
+            <literal>X</literal> such that
+        </para>
+        <para>
+            <literal>Ab = inv(X)*A*X</literal> has approximately equal row and column norms.
+        </para>
+        <para>
+            For matrix pencils,balancing is done for improving the
+            generalized eigenvalue problem.
+        </para>
+        <para>
+            <literal>[Eb,Ab,X,Y] = balanc(E,A)</literal> returns left and right transformations <literal>X</literal> and <literal>Y</literal>
+            such that <literal>Eb=inv(X)*E*Y,  Ab=inv(X)*A*Y</literal>
+        </para>
+    </refsection>
+    <refsection>
+        <title>Remark</title>
+        <para>
+            Balancing is made in the functions <literal>bdiag</literal> and <literal>spec</literal>.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=[1/2^10,1/2^10;2^10,2^10];
+[Ab,X]=balanc(A);
+norm(A(1,:))/norm(A(2,:))
+norm(Ab(1,:))/norm(Ab(2,:))
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="bdiag">bdiag</link>
+            </member>
+            <member>
+                <link linkend="spec">spec</link>
+            </member>
+            <member>
+                <link linkend="schur">schur</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/eigen/bdiag.xml b/scilab/modules/linear_algebra/help/en_US/eigen/bdiag.xml
new file mode 100644 (file)
index 0000000..29102fe
--- /dev/null
@@ -0,0 +1,103 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="bdiag">
+    <refnamediv>
+        <refname>bdiag</refname>
+        <refpurpose> block diagonalization, generalized eigenvectors</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[Ab [,X [,bs]]]=bdiag(A [,rmax])</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>real or complex square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>rmax</term>
+                <listitem>
+                    <para>real number</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Ab</term>
+                <listitem>
+                    <para>real or complex square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>X</term>
+                <listitem>
+                    <para>real or complex non-singular matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>bs</term>
+                <listitem>
+                    <para>vector of integers</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <programlisting role=""><![CDATA[ 
+[Ab [,X [,bs]]]=bdiag(A [,rmax]) 
+ ]]></programlisting>
+        <para>
+            performs the block-diagonalization of matrix <literal>A</literal>.  bs
+            gives the structure of the blocks (respective sizes of the
+            blocks).  <literal>X</literal> is the change of basis i.e 
+            <literal>Ab = inv(X)*A*X</literal>is block diagonal.
+        </para>
+        <para>
+            <literal>rmax</literal> controls the conditioning of <literal>X</literal>; the
+            default value is the l1 norm of <literal>A</literal>.
+        </para>
+        <para>
+            To get a diagonal form (if it exists) choose a large value for
+            <literal>rmax</literal> (<literal>rmax=1/%eps</literal> for example).
+            Generically (for real random A) the blocks are (1x1) and (2x2) and
+            <literal>X</literal> is the matrix of eigenvectors.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+//Real case: 1x1 and 2x2 blocks
+a=rand(5,5);[ab,x,bs]=bdiag(a);ab
+
+//Complex case: complex 1x1 blocks
+[ab,x,bs]=bdiag(a+%i*0);ab
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="schur">schur</link>
+            </member>
+            <member>
+                <link linkend="sylv">sylv</link>
+            </member>
+            <member>
+                <link linkend="spec">spec</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/eigen/hess.xml b/scilab/modules/linear_algebra/help/en_US/eigen/hess.xml
new file mode 100644 (file)
index 0000000..f9cc5c5
--- /dev/null
@@ -0,0 +1,97 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="hess">
+    <refnamediv>
+        <refname>hess</refname>
+        <refpurpose> Hessenberg form</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>H = hess(A)
+            [U,H] = hess(A)
+        </synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>real or complex square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>H</term>
+                <listitem>
+                    <para>real or complex square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>U</term>
+                <listitem>
+                    <para>orthogonal or unitary square matrix</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            <literal>[U,H] = hess(A)</literal> produces a unitary matrix
+            <literal>U</literal> and a Hessenberg matrix <literal>H</literal> so that
+            <literal>A = U*H*U'</literal> and <literal>U'*U</literal> =
+            Identity.  By itself, <literal>hess(A)</literal> returns <literal>H</literal>.
+        </para>
+        <para>
+            The Hessenberg form of a matrix is zero below the first
+            subdiagonal. If the matrix is symmetric or Hermitian, the form is
+            tridiagonal.
+        </para>
+    </refsection>
+    <refsection>
+        <title>References</title>
+        <para>
+            hess function is based on the Lapack routines
+            DGEHRD, DORGHR for  real matrices and  ZGEHRD, ZORGHR for the complex case.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=rand(3,3);[U,H]=hess(A);
+and( abs(U*H*U'-A)<1.d-10 )
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="qr">qr</link>
+            </member>
+            <member>
+                <link linkend="contr">contr</link>
+            </member>
+            <member>
+                <link linkend="schur">schur</link>
+            </member>
+        </simplelist>
+    </refsection>
+    <refsection>
+        <title>Used Functions</title>
+        <para>
+            <literal>hess</literal> function is based on the Lapack routines
+            DGEHRD, DORGHR for  real matrices and  ZGEHRD, ZORGHR for the
+            complex  case.
+        </para>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/eigen/pbig.xml b/scilab/modules/linear_algebra/help/en_US/eigen/pbig.xml
new file mode 100644 (file)
index 0000000..9291150
--- /dev/null
@@ -0,0 +1,125 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="pbig">
+    <refnamediv>
+        <refname>pbig</refname>
+        <refpurpose> eigen-projection</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[Q,M]=pbig(A,thres,flag)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>real square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>thres</term>
+                <listitem>
+                    <para>real number</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>flag</term>
+                <listitem>
+                    <para>
+                        character string (<literal>'c'</literal> or <literal>'d'</literal>)
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Q,M</term>
+                <listitem>
+                    <para>real matrices</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Projection on eigen-subspace associated with eigenvalues with real
+            part &gt;= <literal>thres</literal> (<literal>flag='c'</literal>) or
+            with magnitude &gt;= <literal>thres</literal>
+            (<literal>flag='d'</literal>).
+        </para>
+        <para>
+            The projection is defined by <literal>Q*M</literal>, <literal>Q</literal> is
+            full column rank, <literal>M</literal> is full row rank and
+            <literal>M*Q=eye</literal>.
+        </para>
+        <para>
+            If <literal>flag='c'</literal>, the eigenvalues of
+            <literal>M*A*Q</literal> = eigenvalues of <literal>A</literal> with real part
+            &gt;= <literal>thres</literal>.
+        </para>
+        <para>
+            If <literal>flag='d'</literal>, the eigenvalues of
+            <literal>M*A*Q</literal> = eigenvalues of <literal>A</literal> with magnitude
+            &gt;= <literal>thres</literal>.
+        </para>
+        <para>
+            If <literal>flag='c'</literal> and if <literal>[Q1,M1]</literal> =
+            full rank factorization (<literal>fullrf</literal>) of
+            <literal>eye()-Q*M</literal> then eigenvalues of <literal>M1*A*Q1</literal> =
+            eigenvalues of <literal>A</literal> with real part &lt;
+            <literal>thres</literal>.
+        </para>
+        <para>
+            If <literal>flag='d'</literal> and if <literal>[Q1,M1]</literal> =
+            full rank factorization (<literal>fullrf</literal>) of
+            <literal>eye()-Q*M</literal> then eigenvalues of <literal>M1*A*Q1</literal> =
+            eigenvalues of <literal>A</literal> with magnitude &lt;
+            <literal>thres</literal>.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X;
+[Q,M]=pbig(A,1.5,'d');
+spec(M*A*Q)
+[Q1,M1]=fullrf(eye()-Q*M);
+spec(M1*A*Q1)
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="psmall">psmall</link>
+            </member>
+            <member>
+                <link linkend="projspec">projspec</link>
+            </member>
+            <member>
+                <link linkend="fullrf">fullrf</link>
+            </member>
+            <member>
+                <link linkend="schur">schur</link>
+            </member>
+        </simplelist>
+    </refsection>
+    <refsection>
+        <title>Used Functions</title>
+        <para>
+            <literal>pbig</literal> is based on the ordered schur form (scilab
+            function <literal>schur</literal>).
+        </para>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/eigen/projspec.xml b/scilab/modules/linear_algebra/help/en_US/eigen/projspec.xml
new file mode 100644 (file)
index 0000000..9612a11
--- /dev/null
@@ -0,0 +1,90 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="projspec">
+    <refnamediv>
+        <refname>projspec</refname>
+        <refpurpose> spectral operators</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[S,P,D,i]=projspec(A)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>S, P, D</term>
+                <listitem>
+                    <para>square matrices</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>i</term>
+                <listitem>
+                    <para>
+                        integer (index of the zero eigenvalue of <literal>A</literal>).
+                    </para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Spectral characteristics of <literal>A</literal> at 0.
+        </para>
+        <para>
+            <literal>S</literal> = reduced resolvent at 0 (<literal>S</literal> = -Drazin_inverse(<literal>A</literal>)).
+        </para>
+        <para>
+            <literal>P</literal> = spectral projection at 0.
+        </para>
+        <para>
+            <literal>D</literal> = nilpotent operator at 0.
+        </para>
+        <para>
+            <literal>index</literal> = index of the 0 eigenvalue.
+        </para>
+        <para>
+            One has <literal>(s*eye()-A)^(-1) = D^(i-1)/s^i +... + D/s^2 + P/s - S - s*S^2 -...</literal>
+            around the singularity s=0.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+deff('j=jdrn(n)','j=zeros(n,n);for k=1:n-1;j(k,k+1)=1;end')
+A=sysdiag(jdrn(3),jdrn(2),rand(2,2));X=rand(7,7);
+A=X*A*inv(X);
+[S,P,D,index]=projspec(A);
+index   //size of J-block
+trace(P)  //sum of dimensions of J-blocks
+A*S-(eye()-P)
+norm(D^index,1)
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="coff">coff</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/eigen/psmall.xml b/scilab/modules/linear_algebra/help/en_US/eigen/psmall.xml
new file mode 100644 (file)
index 0000000..a4a27f3
--- /dev/null
@@ -0,0 +1,122 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="psmall">
+    <refnamediv>
+        <refname>psmall</refname>
+        <refpurpose> spectral projection</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[Q,M]=psmall(A,thres,flag)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>real square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>thres</term>
+                <listitem>
+                    <para>real number</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>flag</term>
+                <listitem>
+                    <para>
+                        character string (<literal>'c'</literal> or <literal>'d'</literal>)
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Q,M</term>
+                <listitem>
+                    <para>real matrices</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Projection on eigen-subspace associated with eigenvalues with real
+            part &lt; <literal>thres</literal> (<literal>flag='c'</literal>) or
+            with modulus &lt; <literal>thres</literal>
+            (<literal>flag='d'</literal>).
+        </para>
+        <para>
+            The projection is defined by <literal>Q*M</literal>, <literal>Q</literal> is
+            full column rank, <literal>M</literal> is full row rank and
+            <literal>M*Q=eye</literal>.
+        </para>
+        <para>
+            If <literal>flag='c'</literal>, the eigenvalues of
+            <literal>M*A*Q</literal> = eigenvalues of <literal>A</literal> with real part
+            &lt; <literal>thres</literal>.
+        </para>
+        <para>
+            If <literal>flag='d'</literal>, the eigenvalues of
+            <literal>M*A*Q</literal> = eigenvalues of <literal>A</literal> with magnitude
+            &lt; <literal>thres</literal>.
+        </para>
+        <para>
+            If <literal>flag='c'</literal> and if <literal>[Q1,M1]</literal> =
+            full rank factorization (<literal>fullrf</literal>) of
+            <literal>eye()-Q*M</literal> then eigenvalues of <literal>M1*A*Q1</literal> =
+            eigenvalues of <literal>A</literal> with real part &gt;=
+            <literal>thres</literal>.
+        </para>
+        <para>
+            If <literal>flag='d'</literal> and if <literal>[Q1,M1]</literal> =
+            full rank factorization (<literal>fullrf</literal>) of
+            <literal>eye()-Q*M</literal> then eigenvalues of <literal>M1*A*Q1</literal> =
+            eigenvalues of <literal>A</literal> with magnitude &gt;=
+            <literal>thres</literal>.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X;
+[Q,M]=psmall(A,2.5,'d');
+spec(M*A*Q)
+[Q1,M1]=fullrf(eye()-Q*M);
+spec(M1*A*Q1)
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="pbig">pbig</link>
+            </member>
+            <member>
+                <link linkend="proj">proj</link>
+            </member>
+            <member>
+                <link linkend="projspec">projspec</link>
+            </member>
+        </simplelist>
+    </refsection>
+    <refsection>
+        <title>Used Functions</title>
+        <para>
+            This function is  based on the ordered schur form (scilab
+            function <literal>schur</literal>).
+        </para>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/eigen/schur.xml b/scilab/modules/linear_algebra/help/en_US/eigen/schur.xml
new file mode 100644 (file)
index 0000000..c8043ea
--- /dev/null
@@ -0,0 +1,386 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="schur">
+    <refnamediv>
+        <refname>schur</refname>
+        <refpurpose> [ordered] Schur decomposition of matrix and pencils</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[U,T] = schur(A)
+            [U,dim [,T] ]=schur(A,flag)
+            [U,dim [,T] ]=schur(A,extern1)
+            
+            [As,Es [,Q,Z]]=schur(A,E)
+            [As,Es [,Z,dim]] = schur(A,E,flag)
+            [Z,dim] = schur(A,E,flag)
+            [As,Es [,Z,dim]]= schur(A,E,extern2)
+            [Z,dim]= schur(A,E,extern2)
+        </synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>real or complex square matrix.</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>E</term>
+                <listitem>
+                    <para>
+                        real or complex square matrix with same dimensions as <literal> A</literal>.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>flag</term>
+                <listitem>
+                    <para>
+                        character string (<literal>'c'</literal> or <literal>'d'</literal>)
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>extern1</term>
+                <listitem>
+                    <para>an ``external'', see below</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>extern2</term>
+                <listitem>
+                    <para>an ``external'', see below</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>U</term>
+                <listitem>
+                    <para>orthogonal or unitary square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Q</term>
+                <listitem>
+                    <para>orthogonal or unitary square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Z</term>
+                <listitem>
+                    <para>orthogonal or unitary square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>T</term>
+                <listitem>
+                    <para>upper triangular or quasi-triangular square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>As</term>
+                <listitem>
+                    <para>upper triangular or quasi-triangular square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Es</term>
+                <listitem>
+                    <para>upper triangular  square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>dim</term>
+                <listitem>
+                    <para>integer</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Schur forms, ordered Schur forms of matrices and pencils
+        </para>
+        <variablelist>
+            <varlistentry>
+                <term>MATRIX SCHUR FORM</term>
+                <listitem>
+                    <variablelist>
+                        <varlistentry>
+                            <term>Usual schur form:</term>
+                            <listitem>
+                                <para>
+                                    <literal>[U,T] = schur(A)</literal> produces a Schur matrix
+                                    <literal>T</literal> and a unitary matrix <literal>U</literal> so that
+                                    <literal>A = U*T*U'</literal> and <literal>U'*U =  eye(U)</literal>. By itself, schur(<literal>A</literal>) returns
+                                    <literal>T</literal>. If <literal>A</literal> is complex, the Complex
+                                    Schur Form is returned in matrix
+                                    <literal>T</literal>. The Complex Schur Form is upper triangular with
+                                    the eigenvalues of <literal>A</literal> on the diagonal. If
+                                    <literal>A</literal> is real, the Real Schur Form is returned.  The Real
+                                    Schur Form has the real eigenvalues on the diagonal and the
+                                    complex eigenvalues in 2-by-2 blocks on the diagonal.
+                                </para>
+                            </listitem>
+                        </varlistentry>
+                        <varlistentry>
+                            <term>Ordered Schur forms</term>
+                            <listitem>
+                                <para>
+                                    <literal>[U,dim]=schur(A,'c')</literal> returns an unitary
+                                    matrix <literal>U</literal> which transforms <literal>A</literal> into schur
+                                    form.  In addition, the dim first columns of <literal>U</literal> make
+                                    a basis of the eigenspace of <literal>A</literal> associated with
+                                    eigenvalues with negative real parts (stable "continuous
+                                    time" eigenspace).
+                                </para>
+                                <para>
+                                    <literal>[U,dim]=schur(A,'d')</literal> returns an unitary
+                                    matrix <literal>U</literal> which transforms <literal>A</literal> into schur
+                                    form.  In addition, the <literal>dim</literal> first columns of
+                                    <literal>U</literal> span a basis of the eigenspace of <literal>A</literal>
+                                    associated with eigenvalues with magnitude lower than 1 (stable
+                                    "discrete time" eigenspace).
+                                </para>
+                                <para>
+                                    <literal>[U,dim]=schur(A,extern1)</literal> returns an unitary matrix
+                                    <literal>U</literal> which transforms <literal>A</literal> into schur form.
+                                    In addition, the <literal>dim</literal> first columns of
+                                    <literal>U</literal> span a basis of the eigenspace of <literal>A</literal>
+                                    associated with the eigenvalues which are selected by the
+                                    external function <literal>extern1</literal> (see external for
+                                    details).  This external can be described by a Scilab function
+                                    or by C or Fortran procedure: 
+                                </para>
+                                <variablelist>
+                                    <varlistentry>
+                                        <term>a Scilab function</term>
+                                        <listitem>
+                                            <para>
+                                                If <literal>extern1</literal> is described by a Scilab function, it
+                                                should have the following calling sequence:
+                                                <literal>s=extern1(Ev)</literal>, where <literal>Ev</literal> is an eigenvalue and
+                                                <literal>s</literal> a boolean.
+                                            </para>
+                                        </listitem>
+                                    </varlistentry>
+                                    <varlistentry>
+                                        <term>a C or Fortran procedure</term>
+                                        <listitem>
+                                            <para>
+                                                If <literal>extern1</literal> is described by a C or Fortran function it
+                                                should have the following calling sequence:
+                                                <literal>int extern1(double *EvR, double *EvI)</literal>
+                                                where <literal>EvR</literal> and <literal>EvI</literal> are  eigenvalue real and complex parts.
+                                                a true or non zero returned value stands for selected eigenvalue.
+                                            </para>
+                                        </listitem>
+                                    </varlistentry>
+                                </variablelist>
+                            </listitem>
+                        </varlistentry>
+                    </variablelist>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>PENCIL SCHUR FORMS</term>
+                <listitem>
+                    <variablelist>
+                        <varlistentry>
+                            <term>Usual Pencil Schur form</term>
+                            <listitem>
+                                <para>
+                                    <literal>[As,Es] = schur(A,E)</literal> produces a quasi triangular
+                                    <literal>As</literal> matrix and a triangular <literal>Es</literal> matrix
+                                    which are the generalized Schur form of the pair <literal>A, E</literal>.
+                                </para>
+                                <para>
+                                    <literal>[As,Es,Q,Z] = schur(A,E)</literal>
+                                    returns in addition two unitary matrices
+                                    <literal>Q</literal> and <literal>Z</literal> such that
+                                    <literal>As=Q'*A*Z</literal> and <literal>Es=Q'*E*Z</literal>.
+                                </para>
+                            </listitem>
+                        </varlistentry>
+                        <varlistentry>
+                            <term>Ordered Schur forms:</term>
+                            <listitem>
+                                <para>
+                                    <literal>[As,Es,Z,dim] = schur(A,E,'c')</literal>
+                                    returns the real generalized
+                                    Schur form of the pencil <literal>s*E-A</literal>. In addition, the dim first columns 
+                                    of <literal>Z</literal> span a basis of the right eigenspace  associated with 
+                                    eigenvalues with negative real parts (stable "continuous
+                                    time" generalized eigenspace).
+                                </para>
+                                <para>
+                                    <literal>[As,Es,Z,dim] = schur(A,E,'d')</literal>
+                                </para>
+                                <para>
+                                    returns the real generalized
+                                    Schur form of the pencil <literal>s*E-A</literal>. In addition, the dim first columns 
+                                    of <literal>Z</literal> make a basis of the right eigenspace  associated with 
+                                    eigenvalues with magnitude lower than 1 (stable "discrete
+                                    time" generalized eigenspace).
+                                </para>
+                                <para>
+                                    <literal>[As,Es,Z,dim] = schur(A,E,extern2)</literal>
+                                </para>
+                                <para>
+                                    returns the real generalized Schur form of the pencil <literal>s*E-A</literal>. 
+                                    In addition, the dim first columns 
+                                    of <literal>Z</literal> make a basis of the right eigenspace  associated with 
+                                    eigenvalues of the pencil which are selected according to a
+                                    rule which is given by the function <literal>extern2</literal>. (see external
+                                    for details). This external can be described by a Scilab
+                                    function or by C or Fortran procedure:      
+                                </para>
+                                <variablelist>
+                                    <varlistentry>
+                                        <term>A Scilab function</term>
+                                        <listitem>
+                                            <para>
+                                                If <literal>extern2</literal> is described by a Scilab function, it should
+                                                have the following calling sequence:
+                                                <literal>s=extern2(Alpha,Beta)</literal>, where <literal>Alpha</literal> and
+                                                <literal>Beta</literal> defines a generalized eigenvalue and
+                                                <literal>s</literal> a boolean.
+                                            </para>
+                                        </listitem>
+                                    </varlistentry>
+                                    <varlistentry>
+                                        <term>C or Fortran procedure</term>
+                                        <listitem>
+                                            <para>
+                                                if external <literal>extern2</literal> is described by a C or a
+                                                Fortran procedure, it should have the following calling
+                                                sequence:
+                                            </para>
+                                            <para>
+                                                <literal>int extern2(double *AlphaR, double *AlphaI, double *Beta)</literal>
+                                            </para>
+                                            <para>
+                                                if <literal>A</literal> and <literal>E</literal> are real and
+                                            </para>
+                                            <para>
+                                                <literal>int extern2(double *AlphaR, double *AlphaI, double *BetaR, double *BetaI)</literal>
+                                            </para>
+                                            <para>
+                                                if <literal>A</literal> or <literal>E</literal> are complex.
+                                                <literal>Alpha</literal>, and <literal>Beta</literal> defines the generalized eigenvalue.
+                                                a true or non zero returned value stands for selected generalized eigenvalue.
+                                            </para>
+                                        </listitem>
+                                    </varlistentry>
+                                </variablelist>
+                            </listitem>
+                        </varlistentry>
+                    </variablelist>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>References</title>
+        <para>
+            Matrix schur form computations are based on the Lapack routines DGEES and ZGEES.
+        </para>
+        <para>
+            Pencil schur form computations are based on the Lapack routines DGGES and ZGGES.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+//SCHUR FORM OF A MATRIX
+//----------------------
+A=diag([-0.9,-2,2,0.9]);X=rand(A);A=inv(X)*A*X;
+[U,T]=schur(A);T
+
+[U,dim,T]=schur(A,'c');
+T(1:dim,1:dim)      //stable cont. eigenvalues
+
+function t=mytest(Ev),t=abs(Ev)<0.95,endfunction
+[U,dim,T]=schur(A,mytest);
+T(1:dim,1:dim)  
+
+// The same function in C (a Compiler is required)
+cd TMPDIR;
+C=['int mytest(double *EvR, double *EvI) {' //the C code
+   'if (*EvR * *EvR + *EvI * *EvI < 0.9025) return 1;'
+   'else return 0; }';]
+mputl(C,TMPDIR+'/mytest.c')
+
+
+//build and link
+lp=ilib_for_link('mytest','mytest.c',[],'c');
+link(lp,'mytest','c'); 
+
+//run it
+[U,dim,T]=schur(A,'mytest');
+//SCHUR FORM OF A PENCIL
+//----------------------
+F=[-1,%s, 0,   1;
+    0,-1,5-%s, 0;
+    0, 0,2+%s, 0;
+    1, 0, 0, -2+%s];
+A=coeff(F,0);E=coeff(F,1);
+[As,Es,Q,Z]=schur(A,E);
+Q'*F*Z //It is As+%s*Es
+
+
+[As,Es,Z,dim] = schur(A,E,'c')
+function t=mytest(Alpha,Beta),t=real(Alpha)<0,endfunction
+[As,Es,Z,dim] = schur(A,E,mytest)
+
+//the same function in Fortran (a Compiler is required)
+ftn=['integer function mytestf(ar,ai,b)' //the fortran code
+     'double precision ar,ai,b'
+     'mytestf=0'
+     'if(ar.lt.0.0d0) mytestf=1'
+     'end']
+mputl('      '+ftn,TMPDIR+'/mytestf.f')
+
+//build and link
+lp=ilib_for_link('mytestf','mytestf.f',[],'F');
+link(lp,'mytestf','f'); 
+
+//run it
+
+[As,Es,Z,dim] = schur(A,E,'mytestf')
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="spec">spec</link>
+            </member>
+            <member>
+                <link linkend="bdiag">bdiag</link>
+            </member>
+            <member>
+                <link linkend="ricc">ricc</link>
+            </member>
+            <member>
+                <link linkend="pbig">pbig</link>
+            </member>
+            <member>
+                <link linkend="psmall">psmall</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/eigen/spec.xml b/scilab/modules/linear_algebra/help/en_US/eigen/spec.xml
new file mode 100644 (file)
index 0000000..20bd852
--- /dev/null
@@ -0,0 +1,301 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:id="spec" xml:lang="en">
+    <refnamediv>
+        <refname>spec</refname>
+        <refpurpose>eigenvalues of matrices and pencils</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>evals=spec(A)
+            [R,diagevals]=spec(A)
+            
+            evals=spec(A,B)
+            [alpha,beta]=spec(A,B)
+            [alpha,beta,Z]=spec(A,B)
+            [alpha,beta,Q,Z]=spec(A,B)
+        </synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>real or complex square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>B</term>
+                <listitem>
+                    <para>real or complex square matrix with same dimensions as
+                        <literal> A</literal>
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>evals</term>
+                <listitem>
+                    <para>real or complex vector, the eigenvalues</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>diagevals</term>
+                <listitem>
+                    <para>real or complex diagonal matrix (eigenvalues along the
+                        diagonal)
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>alpha</term>
+                <listitem>
+                    <para>real or complex vector, al./be gives the eigenvalues</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>beta</term>
+                <listitem>
+                    <para>real vector, al./be gives the eigenvalues</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>R</term>
+                <listitem>
+                    <para>real or complex invertible square matrix, matrix right
+                        eigenvectors.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>L</term>
+                <listitem>
+                    <para>real or complex invertible square matrix, pencil left
+                        eigenvectors.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>R</term>
+                <listitem>
+                    <para>real or complex invertible square matrix, pencil right
+                        eigenvectors.
+                    </para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <variablelist>
+            <varlistentry>
+                <term>evals=spec(A)</term>
+                <listitem>
+                    <para>
+                        returns in vector <literal>evals</literal> the
+                        eigenvalues.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>[R,diagevals] =spec(A)</term>
+                <listitem>
+                    <para>
+                        returns in the diagonal matrix <literal>evals</literal> the
+                        eigenvalues and in <literal>R</literal> the right
+                        eigenvectors.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>evals=spec(A,B)</term>
+                <listitem>
+                    <para>returns the spectrum of the matrix pencil A - s B, i.e. the
+                        roots of the polynomial matrix s B - A.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>[alpha,beta] = spec(A,B)</term>
+                <listitem>
+                    <para>
+                        returns the spectrum of the matrix pencil <literal>A- s
+                            B
+                        </literal>
+                        ,i.e. the roots of the polynomial matrix <literal>A - s
+                            B
+                        </literal>
+                        .Generalized eigenvalues alpha and beta are so that the
+                        matrix <literal>A - alpha./beta B</literal> is a singular matrix.
+                        The eigenvalues are given by <literal>al./be</literal> and if
+                        <literal>beta(i) = 0</literal> the ith eigenvalue is at infinity.
+                        (For <literal>B = eye(A), alpha./beta</literal> is
+                        <literal>spec(A)</literal>). It is usually represented as the pair
+                        (alpha,beta), as there is a reasonable interpretation for beta=0,
+                        and even for both being zero.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>[alpha,beta,R] = spec(A,B)</term>
+                <listitem>
+                    <para>
+                        returns in addition the matrix <literal>R</literal> of
+                        generalized right eigenvectors of the pencil.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>[al,be,L,R] = spec(A,B)</term>
+                <listitem>
+                    <para>
+                        returns in addition the matrix <literal>L</literal> and
+                        <literal>R</literal> of generalized left and right eigenvectors of
+                        the pencil.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>[al,be,Z] = spec(A,E)</term>
+                <listitem>
+                    <para>
+                        returns the matrix <literal>Z</literal> of right
+                        generalized eigen vectors.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>[al,be,Q,Z] = spec(A,E)</term>
+                <listitem>
+                    <para>
+                        returns the matrices <literal>Q</literal>
+                        and <literal>Z</literal> of right and left generalized
+                        eigen vectors.
+                    </para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+        <para>For big full / sparse matrix, you can use the Arnoldi module.</para>
+    </refsection>
+    <refsection>
+        <title>References</title>
+        <para>Matrix eigenvalues computations are based on the Lapack
+            routines
+        </para>
+        <itemizedlist>
+            <listitem>
+                <para>DGEEV and ZGEEV when the matrix are not symmetric,</para>
+            </listitem>
+            <listitem>
+                <para>DSYEV and ZHEEV when the matrix are symmetric.</para>
+            </listitem>
+        </itemizedlist>
+        <para>A complex symmetric matrix has conjugate offdiagonal terms and real
+            diagonal terms.
+        </para>
+        <para>Pencil eigenvalues computations are based on the Lapack routines
+            DGGEV and ZGGEV.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Real and complex matrices</title>
+        <para>It must be noticed that the type of the output variables, such as
+            evals or R for example, is not necessarily the same as the type of the
+            input matrices A and B. In the following paragraph, we analyse the type of
+            the output variables in the case where one computes the eigenvalues and
+            eigenvectors of one single matrix A.
+        </para>
+        <itemizedlist>
+            <listitem>
+                <para>Real A matrix</para>
+                <itemizedlist>
+                    <listitem>
+                        <para>Symetric</para>
+                        <para>The eigenvalues and the eigenvectors are real.</para>
+                    </listitem>
+                    <listitem>
+                        <para>Not symmetric</para>
+                        <para>The eigenvalues and eigenvectors are complex.</para>
+                    </listitem>
+                </itemizedlist>
+            </listitem>
+            <listitem>
+                <para>Complex A matrix</para>
+                <itemizedlist>
+                    <listitem>
+                        <para>Symetric</para>
+                        <para>The eigenvalues are real but the eigenvectors are
+                            complex.
+                        </para>
+                    </listitem>
+                    <listitem>
+                        <para>Not symmetric</para>
+                        <para>The eigenvalues and the eigenvectors are complex.</para>
+                    </listitem>
+                </itemizedlist>
+            </listitem>
+        </itemizedlist>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+// MATRIX EIGENVALUES
+A=diag([1,2,3]);
+X=rand(3,3);
+A=inv(X)*A*X;
+spec(A)
+
+x=poly(0,'x');
+pol=det(x*eye()-A)
+roots(pol)
+
+[S,X]=bdiag(A);
+clean(inv(X)*A*X)
+
+// PENCIL EIGENVALUES
+A=rand(3,3);
+[al,be,R] = spec(A,eye(A));
+al./be
+clean(inv(R)*A*R)  //displaying the eigenvalues (generic matrix)
+A=A+%i*rand(A);
+E=rand(A);
+roots(det(A-%s*E))   //complex case
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="poly">poly</link>
+            </member>
+            <member>
+                <link linkend="det">det</link>
+            </member>
+            <member>
+                <link linkend="schur">schur</link>
+            </member>
+            <member>
+                <link linkend="bdiag">bdiag</link>
+            </member>
+            <member>
+                <link linkend="colcomp">colcomp</link>
+            </member>
+            <member>
+                <link linkend="dsaupd">dsaupd</link>
+            </member>
+            <member>
+                <link linkend="dnaupd">dnaupd</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/eigen/sva.xml b/scilab/modules/linear_algebra/help/en_US/eigen/sva.xml
new file mode 100644 (file)
index 0000000..77d0a4c
--- /dev/null
@@ -0,0 +1,84 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="sva">
+    <refnamediv>
+        <refname>sva</refname>
+        <refpurpose> singular value approximation</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[U,s,V]=sva(A,k)
+            [U,s,V]=sva(A,tol)
+        </synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>real or complex matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>k</term>
+                <listitem>
+                    <para>integer</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>tol</term>
+                <listitem>
+                    <para>nonnegative real number</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Singular value approximation.
+        </para>
+        <para>
+            <literal>[U,S,V]=sva(A,k)</literal> with <literal>k</literal> an integer
+            &gt;=1, returns <literal>U,S</literal> and <literal>V</literal> such that
+            <literal>B=U*S*V'</literal> is the best L2 approximation of
+            <literal>A</literal> with rank(<literal>B</literal>)=<literal>k</literal>.
+        </para>
+        <para>
+            <literal>[U,S,V]=sva(A,tol)</literal> with <literal>tol</literal> a real
+            number, returns <literal>U,S</literal> and <literal>V</literal> such that
+            <literal>B=U*S*V'</literal> such that L2-norm of <literal>A-B</literal>
+            is at most <literal>tol</literal>.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=rand(5,4)*rand(4,5);
+[U,s,V]=sva(A,2);
+B=U*s*V';
+svd(A)
+svd(B)
+clean(svd(A-B))
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="svd">svd</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/eigen/svd.xml b/scilab/modules/linear_algebra/help/en_US/eigen/svd.xml
new file mode 100644 (file)
index 0000000..105a3c8
--- /dev/null
@@ -0,0 +1,126 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="svd">
+    <refnamediv>
+        <refname>svd</refname>
+        <refpurpose>  singular value decomposition</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>s=svd(X)
+            [U,S,V]=svd(X)
+            [U,S,V]=svd(X,0) (obsolete)
+            [U,S,V]=svd(X,"e")
+            [U,S,V,rk]=svd(X [,tol])
+        </synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>X</term>
+                <listitem>
+                    <para>a real or complex matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>s</term>
+                <listitem>
+                    <para>real vector (singular values)</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>S</term>
+                <listitem>
+                    <para>real diagonal matrix (singular values)</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>U,V</term>
+                <listitem>
+                    <para>orthogonal or unitary square matrices (singular vectors).</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>tol</term>
+                <listitem>
+                    <para>real number</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            <literal>[U,S,V] = svd(X)</literal> produces a diagonal matrix
+            <literal>S</literal> , of the same dimension as <literal>X</literal> and with
+            nonnegative diagonal elements in decreasing order, and unitary
+            matrices <literal>U</literal> and <literal>V</literal> so that <literal>X = U*S*V'</literal>.
+        </para>
+        <para>
+            <literal>[U,S,V] = svd(X,0)</literal> produces the "economy
+            size" decomposition. If <literal>X</literal> is m-by-n with m &gt;
+            n, then only the first n columns of <literal>U</literal> are computed
+            and <literal>S</literal> is n-by-n.
+        </para>
+        <para>
+            <literal>s= svd(X)</literal> by itself, returns a vector <literal>s</literal>
+            containing the singular values.
+        </para>
+        <para>
+            <literal>[U,S,V,rk]=svd(X,tol)</literal> gives in addition <literal>rk</literal>, the numerical rank of <literal>X</literal> i.e. the number of 
+            singular values larger than <literal>tol</literal>.
+        </para>
+        <para>
+            The default value of <literal>tol</literal> is the same as in <literal>rank</literal>.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+X=rand(4,2)*rand(2,4)
+svd(X)
+sqrt(spec(X*X'))
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="rank">rank</link>
+            </member>
+            <member>
+                <link linkend="qr">qr</link>
+            </member>
+            <member>
+                <link linkend="colcomp">colcomp</link>
+            </member>
+            <member>
+                <link linkend="rowcomp">rowcomp</link>
+            </member>
+            <member>
+                <link linkend="sva">sva</link>
+            </member>
+            <member>
+                <link linkend="spec">spec</link>
+            </member>
+        </simplelist>
+    </refsection>
+    <refsection>
+        <title>Used Functions</title>
+        <para>
+            svd decompositions are based on  the Lapack routines DGESVD for
+            real matrices and  ZGESVD for the complex case.
+        </para>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/eigenmarkov.xml b/scilab/modules/linear_algebra/help/en_US/eigenmarkov.xml
deleted file mode 100644 (file)
index 8bce049..0000000
+++ /dev/null
@@ -1,81 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="eigenmarkov">
-  <refnamediv>
-    <refname>eigenmarkov</refname>
-    <refpurpose> normalized left and right Markov eigenvectors</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[M,Q]=eigenmarkov(P)</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>P</term>
-        <listitem>
-          <para>real N x N Markov matrix. Sum of entries in each row should add to one.</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>M</term>
-        <listitem>
-          <para>real matrix with N columns.</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Q</term>
-        <listitem>
-          <para>real matrix with N rows.</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      Returns normalized left and right eigenvectors
-      associated with the eigenvalue 1 of the Markov transition matrix P.
-      If the multiplicity of this eigenvalue is m and P
-      is N x N, M is a m x N matrix and Q a N x m matrix.
-      M(k,:) is the probability distribution vector associated with the kth
-      ergodic set (recurrent class). M(k,x) is zero if x is not in the
-      k-th recurrent class.
-      Q(x,k) is the probability to end in the k-th recurrent class starting
-      from x. If <literal>P^k</literal> converges for large <literal>k</literal> (no eigenvalues on the
-      unit circle except 1), then the limit is <literal>Q*M</literal> (eigenprojection).
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-//P has two recurrent classes (with 2 and 1 states) 2 transient states
-P=genmarkov([2,1],2) 
-[M,Q]=eigenmarkov(P);
-P*Q-Q
-Q*M-P^20
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="genmarkov">genmarkov</link>
-      </member>
-      <member>
-        <link linkend="classmarkov">classmarkov</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/ereduc.xml b/scilab/modules/linear_algebra/help/en_US/ereduc.xml
deleted file mode 100644 (file)
index 147918d..0000000
+++ /dev/null
@@ -1,114 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="ereduc">
-  <refnamediv>
-    <refname>ereduc</refname>
-    <refpurpose> computes  matrix column echelon form by qz transformations</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[E,Q,Z [,stair [,rk]]]=ereduc(X,tol)</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>X</term>
-        <listitem>
-          <para>m x n matrix with real  entries.</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>tol</term>
-        <listitem>
-          <para>real positive scalar.</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>E</term>
-        <listitem>
-          <para>column echelon form matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Q</term>
-        <listitem>
-          <para>m x m unitary matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Z</term>
-        <listitem>
-          <para>n x n unitary matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>stair</term>
-        <listitem>
-          <para>vector of indexes,</para>
-          <variablelist>
-            <varlistentry>
-              <term>*  </term>
-              <listitem>
-                <para>
-                  <literal>ISTAIR(i) = + j</literal>  if the boundary element <literal>E(i,j)</literal> is a   corner point.
-                </para>
-              </listitem>
-            </varlistentry>
-            <varlistentry>
-              <term>*  </term>
-              <listitem>
-                <para>
-                  <literal>ISTAIR(i) = - j</literal>   if the boundary element <literal>E(i,j)</literal> is not a corner point.
-                </para>
-              </listitem>
-            </varlistentry>
-          </variablelist>
-          <para>
-            <literal>(i=1,...,M)</literal>
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>rk</term>
-        <listitem>
-          <para>integer, estimated rank of the matrix</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      Given an <literal>m x n</literal> matrix <literal>X</literal> (not necessarily regular) the function 
-      ereduc computes a unitary transformed matrix <literal>E=Q*X*Z</literal> which is in 
-      column echelon form (trapezoidal form). Furthermore the rank of
-      matrix <literal>X</literal> is determined.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-X=[1 2 3;4 5 6]
-[E,Q,Z ,stair ,rk]=ereduc(X,1.d-15)
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="fstair">fstair</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/expm.xml b/scilab/modules/linear_algebra/help/en_US/expm.xml
deleted file mode 100644 (file)
index 6cacde0..0000000
+++ /dev/null
@@ -1,75 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="expm">
-  <refnamediv>
-    <refname>expm</refname>
-    <refpurpose> square matrix exponential</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>expm(X)</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>X</term>
-        <listitem>
-          <para>square matrix with real or complex entries.</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      <literal>X</literal> is a square matrix <literal>expm(X)</literal> is the matrix
-    </para>
-    <para>
-      <literal>expm(X) = I + X + X^2 /2 + ...</literal>
-    </para>
-    <para>
-      The computation is performed by first 
-      block-diagonalizing <literal>X</literal> and then applying a Pade approximation 
-      on each block.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-X=[1 2;3 4]
-expm(X)
-logm(expm(X))    
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="logm">logm</link>
-      </member>
-      <member>
-        <link linkend="bdiag">bdiag</link>
-      </member>
-      <member>
-        <link linkend="coff">coff</link>
-      </member>
-      <member>
-        <link linkend="log">log</link>
-      </member>
-      <member>
-        <link linkend="exp">exp</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/factorization/CHAPTER b/scilab/modules/linear_algebra/help/en_US/factorization/CHAPTER
new file mode 100644 (file)
index 0000000..e6daeb8
--- /dev/null
@@ -0,0 +1,2 @@
+title = Factorization
+
diff --git a/scilab/modules/linear_algebra/help/en_US/factorization/givens.xml b/scilab/modules/linear_algebra/help/en_US/factorization/givens.xml
new file mode 100644 (file)
index 0000000..4c6b6e2
--- /dev/null
@@ -0,0 +1,84 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="givens">
+    <refnamediv>
+        <refname>givens</refname>
+        <refpurpose> Givens transformation</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>U=givens(xy)
+            U=givens(x,y)
+            [U,c]=givens(xy)
+            [U,c]=givens(x,y)
+        </synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>x,y</term>
+                <listitem>
+                    <para>two real or complex numbers</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>xy</term>
+                <listitem>
+                    <para> real or complex size 2 column vector</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>U</term>
+                <listitem>
+                    <para>2x2 unitary matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>c</term>
+                <listitem>
+                    <para> real or complex size 2 column vector</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            <literal>U= givens(x, y)</literal> or <literal>U = givens(xy)</literal> with <literal>xy = [x;y]</literal>
+            returns a <literal>2</literal>x<literal>2</literal> unitary matrix <literal>U</literal> such that:
+        </para>
+        <para>
+            <literal>U*xy=[r;0]=c</literal>.
+        </para>
+        <para>
+            Note that <literal>givens(x,y)</literal> and <literal>givens([x;y])</literal> are equivalent.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=[3,4;5,6];
+U=givens(A(:,1));
+U*A
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="qr">qr</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/factorization/householder.xml b/scilab/modules/linear_algebra/help/en_US/factorization/householder.xml
new file mode 100644 (file)
index 0000000..04113d9
--- /dev/null
@@ -0,0 +1,70 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="householder">
+    <refnamediv>
+        <refname>householder</refname>
+        <refpurpose> Householder orthogonal reflexion matrix</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>u=householder(v [,w])</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>v</term>
+                <listitem>
+                    <para>real or complex column vector</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>w</term>
+                <listitem>
+                    <para>
+                        real or complex column vector with same size as <literal>v</literal>. Default value is <literal>eye(v)</literal>
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>u</term>
+                <listitem>
+                    <para>real or complex column vector</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            given 2 column vectors <literal>v</literal>, <literal> w</literal> of same size, <literal>householder(v,w)</literal> returns a unitary 
+            column vector <literal>u</literal>, such that <literal> (eye()-2*u*u')*v</literal> is proportional to <literal>w</literal>.
+            <literal>(eye()-2*u*u')</literal> is the orthogonal Householder reflexion matrix .
+        </para>
+        <para>
+            <literal>w</literal> default value is <literal> eye(v)</literal>. In this case vector <literal> (eye()-2*u*u')*v</literal> is the 
+            vector  <literal> eye(v)*norm(v)</literal>.
+        </para>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="qr">qr</link>
+            </member>
+            <member>
+                <link linkend="givens">givens</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/factorization/sqroot.xml b/scilab/modules/linear_algebra/help/en_US/factorization/sqroot.xml
new file mode 100644 (file)
index 0000000..0ab7a1d
--- /dev/null
@@ -0,0 +1,62 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="sqroot">
+    <refnamediv>
+        <refname>sqroot</refname>
+        <refpurpose> W*W' hermitian factorization</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>sqroot(X)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>X</term>
+                <listitem>
+                    <para>symmetric non negative definite real or complex matrix</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            returns W such that  <literal>X=W*W'</literal> (uses SVD).
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+X=rand(5,2)*rand(2,5);X=X*X';
+W=sqroot(X)
+norm(W*W'-X,1)
+
+X=rand(5,2)+%i*rand(5,2);X=X*X';
+W=sqroot(X)
+norm(W*W'-X,1)
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="chol">chol</link>
+            </member>
+            <member>
+                <link linkend="svd">svd</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/fstair.xml b/scilab/modules/linear_algebra/help/en_US/fstair.xml
deleted file mode 100644 (file)
index 250b980..0000000
+++ /dev/null
@@ -1,157 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="fstair">
-  <refnamediv>
-    <refname>fstair</refname>
-    <refpurpose> computes  pencil  column echelon form by qz transformations</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[AE,EE,QE,ZE,blcks,muk,nuk,muk0,nuk0,mnei]=fstair(A,E,Q,Z,stair,rk,tol)</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>A</term>
-        <listitem>
-          <para>m x n matrix with real  entries.</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>tol</term>
-        <listitem>
-          <para>real positive scalar.</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>E</term>
-        <listitem>
-          <para>column echelon form matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Q</term>
-        <listitem>
-          <para>m x m unitary matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Z</term>
-        <listitem>
-          <para>n x n unitary matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>stair</term>
-        <listitem>
-          <para>vector of indexes (see ereduc)</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>rk</term>
-        <listitem>
-          <para>integer, estimated rank of the matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>AE</term>
-        <listitem>
-          <para>m x n matrix with real  entries.</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>EE</term>
-        <listitem>
-          <para>column echelon form matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>QE</term>
-        <listitem>
-          <para>m x m unitary matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>ZE</term>
-        <listitem>
-          <para>n x n unitary matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>nblcks</term>
-        <listitem>
-          <para>
-            is the number of submatrices having full row rank &gt;= 0  detected in matrix  <literal>A</literal>.
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>muk:  </term>
-        <listitem>
-          <para>integer array of dimension (n). Contains the column dimensions mu(k)  (k=1,...,nblcks) of the submatrices having full column  rank in the pencil sE(eps)-A(eps)</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>nuk:  </term>
-        <listitem>
-          <para>integer array of dimension (m+1). Contains the row dimensions nu(k)  (k=1,...,nblcks) of the submatrices having full row  rank in the pencil sE(eps)-A(eps)</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>muk0:  </term>
-        <listitem>
-          <para>integer array of dimension (n). Contains the column dimensions mu(k)  (k=1,...,nblcks) of the submatrices having full column  rank in the pencil sE(eps,inf)-A(eps,inf)</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>nuk:  </term>
-        <listitem>
-          <para>integer array of dimension (m+1). Contains the row dimensions nu(k)  (k=1,...,nblcks) of the submatrices having full row  rank in the pencil sE(eps,inf)-A(eps,inf)</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>mnei:  </term>
-        <listitem>
-          <para>integer array of dimension (4). mnei(1) = row dimension of sE(eps)-A(eps)</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      Given a pencil <literal>sE-A</literal> where matrix <literal>E</literal> is in column echelon form the
-      function  <literal>fstair</literal> computes according to the wishes of the user a
-      unitary transformed pencil <literal>QE(sEE-AE)ZE</literal> which is more or less similar
-      to the generalized Schur form of the pencil <literal>sE-A</literal>.
-      The function  yields also part of the Kronecker structure of
-      the given pencil.
-    </para>
-    <para>
-      <literal>Q,Z</literal> are the unitary matrices used to compute the pencil where E
-      is in column echelon form (see ereduc)
-    </para>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="quaskro">quaskro</link>
-      </member>
-      <member>
-        <link linkend="ereduc">ereduc</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/fullrf.xml b/scilab/modules/linear_algebra/help/en_US/fullrf.xml
deleted file mode 100644 (file)
index 3697535..0000000
+++ /dev/null
@@ -1,101 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="fullrf">
-  <refnamediv>
-    <refname>fullrf</refname>
-    <refpurpose> full rank factorization</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[Q,M,rk]=fullrf(A,[tol])</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>A</term>
-        <listitem>
-          <para>real or complex matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>tol</term>
-        <listitem>
-          <para>real number (threshold for rank determination)</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Q,M</term>
-        <listitem>
-          <para>real or complex matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>rk</term>
-        <listitem>
-          <para>
-            integer (rank of <literal>A</literal>)
-          </para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      Full rank factorization : <literal>fullrf</literal> returns <literal>Q</literal> and <literal>M</literal> such
-      that <literal>A = Q*M</literal>
-      with range(<literal>Q</literal>)=range(<literal>A</literal>) and ker(<literal>M</literal>)=ker(<literal>A</literal>),
-      <literal>Q</literal> full column rank , <literal>M</literal> full row rank,
-      <literal>rk = rank(A) = #columns(Q) = #rows(M)</literal>.
-    </para>
-    <para>
-      <literal>tol</literal> is an optional real parameter (default value is <literal>sqrt(%eps)</literal>).
-      The rank <literal>rk</literal> of <literal>A</literal> is defined as the number of singular values
-      larger than <literal>norm(A)*tol</literal>.
-    </para>
-    <para>
-      If A is symmetric, <literal>fullrf</literal> returns <literal>M=Q'</literal>.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-A=rand(5,2)*rand(2,5);
-[Q,M]=fullrf(A);
-norm(Q*M-A,1)
-[X,d]=rowcomp(A);Y=X';
-svd([A,Y(:,1:d),Q])        //span(Q) = span(A) = span(Y(:,1:2))
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="svd">svd</link>
-      </member>
-      <member>
-        <link linkend="qr">qr</link>
-      </member>
-      <member>
-        <link linkend="fullrfk">fullrfk</link>
-      </member>
-      <member>
-        <link linkend="rowcomp">rowcomp</link>
-      </member>
-      <member>
-        <link linkend="colcomp">colcomp</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/fullrfk.xml b/scilab/modules/linear_algebra/help/en_US/fullrfk.xml
deleted file mode 100644 (file)
index 5e2ec36..0000000
+++ /dev/null
@@ -1,74 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="fullrfk">
-  <refnamediv>
-    <refname>fullrfk</refname>
-    <refpurpose> full rank factorization of A^k</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[Bk,Ck]=fullrfk(A,k)</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>A</term>
-        <listitem>
-          <para>real or complex matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>k</term>
-        <listitem>
-          <para>integer</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Bk,Ck</term>
-        <listitem>
-          <para>real or complex matrices</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      This function computes the full rank factorization of <literal>A^k</literal> i.e.
-      <literal>Bk*Ck=A^k</literal> where <literal>Bk</literal> is full column rank and <literal>Ck</literal> full row rank.
-      One has range(<literal>Bk</literal>)=range(<literal>A^k</literal>) and ker(<literal>Ck</literal>)=ker(<literal>A^k</literal>).
-    </para>
-    <para>
-      For <literal>k=1</literal>, <literal>fullrfk</literal> is equivalent to <literal>fullrf</literal>.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-A=rand(5,2)*rand(2,5);[Bk,Ck]=fullrfk(A,3);
-norm(Bk*Ck-A^3,1)
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="fullrf">fullrf</link>
-      </member>
-      <member>
-        <link linkend="range">range</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/genmarkov.xml b/scilab/modules/linear_algebra/help/en_US/genmarkov.xml
deleted file mode 100644 (file)
index 5052c5e..0000000
+++ /dev/null
@@ -1,83 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="genmarkov">
-  <refnamediv>
-    <refname>genmarkov</refname>
-    <refpurpose> generates random markov matrix with recurrent and transient classes</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>M=genmarkov(rec,tr)
-      M=genmarkov(rec,tr,flag)
-    </synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>rec</term>
-        <listitem>
-          <para>integer row vector (its dimension is the number of recurrent classes).</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>tr</term>
-        <listitem>
-          <para>integer (number of transient states)</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>M</term>
-        <listitem>
-          <para>real Markov matrix. Sum of entries in each row should add to one.</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>flag</term>
-        <listitem>
-          <para>
-            string <literal>'perm'</literal>. If given, a random permutation of the states is done.
-          </para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      Returns in M a random Markov transition probability matrix
-      with <literal>size(rec,1)</literal> recurrent classes with <literal>rec(1),...rec($)</literal> 
-      entries respectively and tr transient states.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-//P has two recurrent classes (with 2 and 1 states) 2 transient states
-P=genmarkov([2,1],2,'perm')
-[perm,rec,tr,indsRec,indsT]=classmarkov(P);
-P(perm,perm)
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="classmarkov">classmarkov</link>
-      </member>
-      <member>
-        <link linkend="eigenmarkov">eigenmarkov</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/givens.xml b/scilab/modules/linear_algebra/help/en_US/givens.xml
deleted file mode 100644 (file)
index fd124a1..0000000
+++ /dev/null
@@ -1,84 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="givens">
-  <refnamediv>
-    <refname>givens</refname>
-    <refpurpose> Givens transformation</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>U=givens(xy)
-      U=givens(x,y)
-      [U,c]=givens(xy)
-      [U,c]=givens(x,y)
-    </synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>x,y</term>
-        <listitem>
-          <para>two real or complex numbers</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>xy</term>
-        <listitem>
-          <para> real or complex size 2 column vector</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>U</term>
-        <listitem>
-          <para>2x2 unitary matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>c</term>
-        <listitem>
-          <para> real or complex size 2 column vector</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      <literal>U= givens(x, y)</literal> or <literal>U = givens(xy)</literal> with <literal>xy = [x;y]</literal>
-      returns a <literal>2</literal>x<literal>2</literal> unitary matrix <literal>U</literal> such that:
-    </para>
-    <para>
-      <literal>U*xy=[r;0]=c</literal>.
-    </para>
-    <para>
-      Note that <literal>givens(x,y)</literal> and <literal>givens([x;y])</literal> are equivalent.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-A=[3,4;5,6];
-U=givens(A(:,1));
-U*A
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="qr">qr</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/glever.xml b/scilab/modules/linear_algebra/help/en_US/glever.xml
deleted file mode 100644 (file)
index 9fee48b..0000000
+++ /dev/null
@@ -1,118 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="glever">
-  <refnamediv>
-    <refname>glever</refname>
-    <refpurpose> inverse of matrix pencil</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[Bfs,Bis,chis]=glever(E,A [,s])</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>E, A</term>
-        <listitem>
-          <para>two real square matrices of same dimensions</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>s</term>
-        <listitem>
-          <para>
-            character string (default value '<literal>s</literal>')
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Bfs,Bis</term>
-        <listitem>
-          <para>two polynomial matrices</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>chis</term>
-        <listitem>
-          <para>polynomial</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      Computation of
-    </para>
-    <para>
-      <literal>(s*E-A)^-1</literal>
-    </para>
-    <para>
-      by generalized Leverrier's algorithm for a matrix pencil.
-    </para>
-    <programlisting role=""><![CDATA[ 
-(s*E-A)^-1 = (Bfs/chis) - Bis.
- ]]></programlisting>
-    <para>
-      <literal>chis</literal> = characteristic polynomial (up to a multiplicative constant).
-    </para>
-    <para>
-      <literal>Bfs</literal>  = numerator polynomial matrix.
-    </para>
-    <para>
-      <literal>Bis</literal>
-      = polynomial matrix ( - expansion of <literal>(s*E-A)^-1</literal> at infinity).
-    </para>
-    <para>
-      Note the - sign before <literal>Bis</literal>.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Caution</title>
-    <para>
-      This function uses <literal>cleanp</literal> to simplify <literal>Bfs,Bis</literal> and <literal>chis</literal>.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-s=%s;F=[-1,s,0,0;0,-1,0,0;0,0,s-2,0;0,0,0,s-1];
-[Bfs,Bis,chis]=glever(F)
-inv(F)-((Bfs/chis) - Bis)
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="rowshuff">rowshuff</link>
-      </member>
-      <member>
-        <link linkend="det">det</link>
-      </member>
-      <member>
-        <link linkend="invr">invr</link>
-      </member>
-      <member>
-        <link linkend="coffg">coffg</link>
-      </member>
-      <member>
-        <link linkend="pencan">pencan</link>
-      </member>
-      <member>
-        <link linkend="penlaur">penlaur</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/hess.xml b/scilab/modules/linear_algebra/help/en_US/hess.xml
deleted file mode 100644 (file)
index 59111d7..0000000
+++ /dev/null
@@ -1,97 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="hess">
-  <refnamediv>
-    <refname>hess</refname>
-    <refpurpose> Hessenberg form</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>H = hess(A)
-      [U,H] = hess(A)
-    </synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>A</term>
-        <listitem>
-          <para>real or complex square matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>H</term>
-        <listitem>
-          <para>real or complex square matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>U</term>
-        <listitem>
-          <para>orthogonal or unitary square matrix</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      <literal>[U,H] = hess(A)</literal> produces a unitary matrix
-      <literal>U</literal> and a Hessenberg matrix <literal>H</literal> so that
-      <literal>A = U*H*U'</literal> and <literal>U'*U</literal> =
-      Identity.  By itself, <literal>hess(A)</literal> returns <literal>H</literal>.
-    </para>
-    <para>
-      The Hessenberg form of a matrix is zero below the first
-      subdiagonal. If the matrix is symmetric or Hermitian, the form is
-      tridiagonal.
-    </para>
-  </refsection>
-  <refsection>
-    <title>References</title>
-    <para>
-      hess function is based on the Lapack routines
-      DGEHRD, DORGHR for  real matrices and  ZGEHRD, ZORGHR for the complex case.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-A=rand(3,3);[U,H]=hess(A);
-and( abs(U*H*U'-A)<1.d-10 )
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="qr">qr</link>
-      </member>
-      <member>
-        <link linkend="contr">contr</link>
-      </member>
-      <member>
-        <link linkend="schur">schur</link>
-      </member>
-    </simplelist>
-  </refsection>
-  <refsection>
-    <title>Used Functions</title>
-    <para>
-      <literal>hess</literal> function is based on the Lapack routines
-      DGEHRD, DORGHR for  real matrices and  ZGEHRD, ZORGHR for the
-      complex  case.
-    </para>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/householder.xml b/scilab/modules/linear_algebra/help/en_US/householder.xml
deleted file mode 100644 (file)
index 30cac74..0000000
+++ /dev/null
@@ -1,70 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="householder">
-  <refnamediv>
-    <refname>householder</refname>
-    <refpurpose> Householder orthogonal reflexion matrix</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>u=householder(v [,w])</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>v</term>
-        <listitem>
-          <para>real or complex column vector</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>w</term>
-        <listitem>
-          <para>
-            real or complex column vector with same size as <literal>v</literal>. Default value is <literal>eye(v)</literal>
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>u</term>
-        <listitem>
-          <para>real or complex column vector</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      given 2 column vectors <literal>v</literal>, <literal> w</literal> of same size, <literal>householder(v,w)</literal> returns a unitary 
-      column vector <literal>u</literal>, such that <literal> (eye()-2*u*u')*v</literal> is proportional to <literal>w</literal>.
-      <literal>(eye()-2*u*u')</literal> is the orthogonal Householder reflexion matrix .
-    </para>
-    <para>
-      <literal>w</literal> default value is <literal> eye(v)</literal>. In this case vector <literal> (eye()-2*u*u')*v</literal> is the 
-      vector  <literal> eye(v)*norm(v)</literal>.
-    </para>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="qr">qr</link>
-      </member>
-      <member>
-        <link linkend="givens">givens</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/im_inv.xml b/scilab/modules/linear_algebra/help/en_US/im_inv.xml
deleted file mode 100644 (file)
index db41431..0000000
+++ /dev/null
@@ -1,107 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="im_inv">
-  <refnamediv>
-    <refname>im_inv</refname>
-    <refpurpose> inverse image</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[X,dim]=im_inv(A,B [,tol])
-      [X,dim,Y]=im_inv(A,B, [,tol])
-    </synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>A,B</term>
-        <listitem>
-          <para>two real or complex matrices with equal number of columns</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>X</term>
-        <listitem>
-          <para>
-            orthogonal or unitary square matrix of order equal to the  number of columns of <literal>A</literal>
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>dim</term>
-        <listitem>
-          <para>integer (dimension of subspace)</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Y</term>
-        <listitem>
-          <para>
-            orthogonal matrix of order equal to the number of rows  of <literal>A</literal> and <literal>B</literal>.
-          </para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      <literal>[X,dim]=im_inv(A,B)</literal> computes <literal>(A^-1)(B)</literal>
-      i.e vectors whose image through <literal>A</literal> are in
-      range(<literal>B</literal>)
-    </para>
-    <para>
-      The <literal>dim</literal> first columns of <literal>X</literal> span
-      <literal>(A^-1)(B)</literal>
-    </para>
-    <para>
-      <literal>tol</literal> is a threshold used to test if subspace inclusion;
-      default value is <literal>tol = 100*%eps</literal>.
-      If <literal>Y</literal> is returned, then <literal>[Y*A*X,Y*B]</literal> is partitioned as follows:
-      <literal>[A11,A12;0,A22]</literal>,<literal>[B1;0]</literal>
-    </para>
-    <para>
-      where <literal>B1</literal> has full row rank (equals
-      <literal>rank(B)</literal>) and <literal>A22</literal> has full column rank
-      and has <literal>dim</literal> columns.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-A=[rand(2,5);[zeros(3,4),rand(3,1)]];B=[[1,1;1,1];zeros(3,2)];
-W=rand(5,5);A=W*A;B=W*B;
-[X,dim]=im_inv(A,B)
-svd([A*X(:,1:dim),B])   //vectors A*X(:,1:dim) belong to range(B)
-[X,dim,Y]=im_inv(A,B);[Y*A*X,Y*B]
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="rowcomp">rowcomp</link>
-      </member>
-      <member>
-        <link linkend="spaninter">spaninter</link>
-      </member>
-      <member>
-        <link linkend="spanplus">spanplus</link>
-      </member>
-      <member>
-        <link linkend="linsolve">linsolve</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/inv.xml b/scilab/modules/linear_algebra/help/en_US/inv.xml
deleted file mode 100644 (file)
index 17dd572..0000000
+++ /dev/null
@@ -1,105 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="inv">
-  <refnamediv>
-    <refname>inv</refname>
-    <refpurpose> matrix inverse</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>inv(X)</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>X</term>
-        <listitem>
-          <para>real or complex square matrix, polynomial matrix, rational matrix in transfer or state-space representation.</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      <literal>inv(X)</literal> is the inverse of the square matrix <literal>X</literal>. A warning
-      message is printed if <literal>X</literal> is badly scaled or nearly singular.
-    </para>
-    <para>
-      For polynomial matrices or rational matrices in transfer representation,
-      <literal>inv(X)</literal> is equivalent to <literal>invr(X)</literal>.
-    </para>
-    <para>
-      For linear systems in state-space representation (<literal>syslin</literal> list),
-      <literal>invr(X)</literal> is equivalent to <literal>invsyslin(X)</literal>.
-    </para>
-  </refsection>
-  <refsection>
-    <title>References</title>
-    <para>
-      <literal>inv</literal> function for matrices of numbers is  based on the Lapack routines
-      DGETRF, DGETRI for  real matrices and  ZGETRF, ZGETRI for the complex case.
-      For polynomial matrix and rational function matrix <literal>inv</literal> is based on the <literal>invr</literal>
-      Scilab function.
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-A=rand(3,3);inv(A)*A
-
-x=poly(0,'x');
-A=[x,1,x;x^2,2,1+x;1,2,3];inv(A)*A
-
-A=[1/x,2;2+x,2/(1+x)]
-inv(A)*A
-
-A=ssrand(2,2,3);
-W=inv(A)*A
-clean(ss2tf(W))
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="slash">slash</link>
-      </member>
-      <member>
-        <link linkend="backslash">backslash</link>
-      </member>
-      <member>
-        <link linkend="pinv">pinv</link>
-      </member>
-      <member>
-        <link linkend="qr">qr</link>
-      </member>
-      <member>
-        <link linkend="lufact">lufact</link>
-      </member>
-      <member>
-        <link linkend="lusolve">lusolve</link>
-      </member>
-      <member>
-        <link linkend="invr">invr</link>
-      </member>
-      <member>
-        <link linkend="coff">coff</link>
-      </member>
-      <member>
-        <link linkend="coffg">coffg</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/kernel.xml b/scilab/modules/linear_algebra/help/en_US/kernel.xml
deleted file mode 100644 (file)
index ab589d2..0000000
+++ /dev/null
@@ -1,92 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="kernel">
-  <refnamediv>
-    <refname>kernel</refname>
-    <refpurpose> kernel, nullspace</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>W=kernel(A [,tol,[,flag])</synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>A</term>
-        <listitem>
-          <para>full real or complex matrix or real sparse matrix</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>flag</term>
-        <listitem>
-          <para>
-            character string <literal>'svd'</literal> (default) or <literal>'qr'</literal>
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>tol</term>
-        <listitem>
-          <para>real number</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>W</term>
-        <listitem>
-          <para>full column rank matrix</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <title>Description</title>
-    <para>
-      <literal>W=kernel(A)</literal> returns the kernel (nullspace) of <literal>A</literal>. If A has full column rank then an empty matrix [] is returned.
-    </para>
-    <para>
-      <literal>flag</literal> and <literal>tol</literal> are optional parameters: <literal>flag = 'qr'</literal> 
-      or <literal>'svd'</literal> (default is <literal>'svd'</literal>).
-    </para>
-    <para>
-      <literal>tol</literal> = tolerance parameter (of order <literal>%eps</literal> as default value).
-    </para>
-  </refsection>
-  <refsection>
-    <title>Examples</title>
-    <programlisting role="example"><![CDATA[ 
-A=rand(3,1)*rand(1,3);
-A*kernel(A)
-A=sparse(A);
-clean(A*kernel(A))
- ]]></programlisting>
-  </refsection>
-  <refsection role="see also">
-    <title>See Also</title>
-    <simplelist type="inline">
-      <member>
-        <link linkend="colcomp">colcomp</link>
-      </member>
-      <member>
-        <link linkend="fullrf">fullrf</link>
-      </member>
-      <member>
-        <link linkend="fullrfk">fullrfk</link>
-      </member>
-      <member>
-        <link linkend="linsolve">linsolve</link>
-      </member>
-    </simplelist>
-  </refsection>
-</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/kernel/CHAPTER b/scilab/modules/linear_algebra/help/en_US/kernel/CHAPTER
new file mode 100644 (file)
index 0000000..be67920
--- /dev/null
@@ -0,0 +1,2 @@
+title = Kernel
+
diff --git a/scilab/modules/linear_algebra/help/en_US/kernel/colcomp.xml b/scilab/modules/linear_algebra/help/en_US/kernel/colcomp.xml
new file mode 100644 (file)
index 0000000..48c89e8
--- /dev/null
@@ -0,0 +1,106 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="colcomp">
+    <refnamediv>
+        <refname>colcomp</refname>
+        <refpurpose> column compression, kernel, nullspace</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[W,rk]=colcomp(A [,flag] [,tol])</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>real or complex matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>flag</term>
+                <listitem>
+                    <para>character string</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>tol</term>
+                <listitem>
+                    <para>real number</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>W</term>
+                <listitem>
+                    <para>square non-singular matrix (change of basis)</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>rk</term>
+                <listitem>
+                    <para>
+                        integer (rank of <literal>A</literal>)
+                    </para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Column compression of <literal>A</literal>: <literal>Ac = A*W</literal> is 
+            column compressed i.e
+        </para>
+        <para>
+            <literal>Ac=[0,Af]</literal> with <literal>Af</literal> full column rank, 
+            rank(<literal>Af</literal>) = rank(<literal>A</literal>) = <literal>rk</literal>.
+        </para>
+        <para>
+            <literal>flag</literal> and <literal>tol</literal> are optional parameters: <literal>flag = 'qr'</literal> 
+            or <literal>'svd'</literal> (default is <literal>'svd'</literal>).
+        </para>
+        <para>
+            <literal>tol</literal> = tolerance parameter (of order <literal>%eps</literal> as default value).
+        </para>
+        <para>
+            The <literal>ma-rk</literal> first columns of <literal>W</literal> span the kernel of <literal>A</literal> 
+            when <literal>size(A)=(na,ma)</literal>
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=rand(5,2)*rand(2,5);
+[X,r]=colcomp(A);
+norm(A*X(:,1:$-r),1)
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="rowcomp">rowcomp</link>
+            </member>
+            <member>
+                <link linkend="fullrf">fullrf</link>
+            </member>
+            <member>
+                <link linkend="fullrfk">fullrfk</link>
+            </member>
+            <member>
+                <link linkend="kernel">kernel</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/kernel/fullrf.xml b/scilab/modules/linear_algebra/help/en_US/kernel/fullrf.xml
new file mode 100644 (file)
index 0000000..be5baae
--- /dev/null
@@ -0,0 +1,101 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="fullrf">
+    <refnamediv>
+        <refname>fullrf</refname>
+        <refpurpose> full rank factorization</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[Q,M,rk]=fullrf(A,[tol])</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>real or complex matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>tol</term>
+                <listitem>
+                    <para>real number (threshold for rank determination)</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Q,M</term>
+                <listitem>
+                    <para>real or complex matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>rk</term>
+                <listitem>
+                    <para>
+                        integer (rank of <literal>A</literal>)
+                    </para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Full rank factorization : <literal>fullrf</literal> returns <literal>Q</literal> and <literal>M</literal> such
+            that <literal>A = Q*M</literal>
+            with range(<literal>Q</literal>)=range(<literal>A</literal>) and ker(<literal>M</literal>)=ker(<literal>A</literal>),
+            <literal>Q</literal> full column rank , <literal>M</literal> full row rank,
+            <literal>rk = rank(A) = #columns(Q) = #rows(M)</literal>.
+        </para>
+        <para>
+            <literal>tol</literal> is an optional real parameter (default value is <literal>sqrt(%eps)</literal>).
+            The rank <literal>rk</literal> of <literal>A</literal> is defined as the number of singular values
+            larger than <literal>norm(A)*tol</literal>.
+        </para>
+        <para>
+            If A is symmetric, <literal>fullrf</literal> returns <literal>M=Q'</literal>.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=rand(5,2)*rand(2,5);
+[Q,M]=fullrf(A);
+norm(Q*M-A,1)
+[X,d]=rowcomp(A);Y=X';
+svd([A,Y(:,1:d),Q])        //span(Q) = span(A) = span(Y(:,1:2))
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="svd">svd</link>
+            </member>
+            <member>
+                <link linkend="qr">qr</link>
+            </member>
+            <member>
+                <link linkend="fullrfk">fullrfk</link>
+            </member>
+            <member>
+                <link linkend="rowcomp">rowcomp</link>
+            </member>
+            <member>
+                <link linkend="colcomp">colcomp</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/kernel/fullrfk.xml b/scilab/modules/linear_algebra/help/en_US/kernel/fullrfk.xml
new file mode 100644 (file)
index 0000000..1063130
--- /dev/null
@@ -0,0 +1,74 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="fullrfk">
+    <refnamediv>
+        <refname>fullrfk</refname>
+        <refpurpose> full rank factorization of A^k</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[Bk,Ck]=fullrfk(A,k)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>real or complex matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>k</term>
+                <listitem>
+                    <para>integer</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Bk,Ck</term>
+                <listitem>
+                    <para>real or complex matrices</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            This function computes the full rank factorization of <literal>A^k</literal> i.e.
+            <literal>Bk*Ck=A^k</literal> where <literal>Bk</literal> is full column rank and <literal>Ck</literal> full row rank.
+            One has range(<literal>Bk</literal>)=range(<literal>A^k</literal>) and ker(<literal>Ck</literal>)=ker(<literal>A^k</literal>).
+        </para>
+        <para>
+            For <literal>k=1</literal>, <literal>fullrfk</literal> is equivalent to <literal>fullrf</literal>.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=rand(5,2)*rand(2,5);[Bk,Ck]=fullrfk(A,3);
+norm(Bk*Ck-A^3,1)
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="fullrf">fullrf</link>
+            </member>
+            <member>
+                <link linkend="range">range</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/kernel/im_inv.xml b/scilab/modules/linear_algebra/help/en_US/kernel/im_inv.xml
new file mode 100644 (file)
index 0000000..dba65dc
--- /dev/null
@@ -0,0 +1,107 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="im_inv">
+    <refnamediv>
+        <refname>im_inv</refname>
+        <refpurpose> inverse image</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[X,dim]=im_inv(A,B [,tol])
+            [X,dim,Y]=im_inv(A,B, [,tol])
+        </synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A,B</term>
+                <listitem>
+                    <para>two real or complex matrices with equal number of columns</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>X</term>
+                <listitem>
+                    <para>
+                        orthogonal or unitary square matrix of order equal to the  number of columns of <literal>A</literal>
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>dim</term>
+                <listitem>
+                    <para>integer (dimension of subspace)</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Y</term>
+                <listitem>
+                    <para>
+                        orthogonal matrix of order equal to the number of rows  of <literal>A</literal> and <literal>B</literal>.
+                    </para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            <literal>[X,dim]=im_inv(A,B)</literal> computes <literal>(A^-1)(B)</literal>
+            i.e vectors whose image through <literal>A</literal> are in
+            range(<literal>B</literal>)
+        </para>
+        <para>
+            The <literal>dim</literal> first columns of <literal>X</literal> span
+            <literal>(A^-1)(B)</literal>
+        </para>
+        <para>
+            <literal>tol</literal> is a threshold used to test if subspace inclusion;
+            default value is <literal>tol = 100*%eps</literal>.
+            If <literal>Y</literal> is returned, then <literal>[Y*A*X,Y*B]</literal> is partitioned as follows:
+            <literal>[A11,A12;0,A22]</literal>,<literal>[B1;0]</literal>
+        </para>
+        <para>
+            where <literal>B1</literal> has full row rank (equals
+            <literal>rank(B)</literal>) and <literal>A22</literal> has full column rank
+            and has <literal>dim</literal> columns.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=[rand(2,5);[zeros(3,4),rand(3,1)]];B=[[1,1;1,1];zeros(3,2)];
+W=rand(5,5);A=W*A;B=W*B;
+[X,dim]=im_inv(A,B)
+svd([A*X(:,1:dim),B])   //vectors A*X(:,1:dim) belong to range(B)
+[X,dim,Y]=im_inv(A,B);[Y*A*X,Y*B]
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="rowcomp">rowcomp</link>
+            </member>
+            <member>
+                <link linkend="spaninter">spaninter</link>
+            </member>
+            <member>
+                <link linkend="spanplus">spanplus</link>
+            </member>
+            <member>
+                <link linkend="linsolve">linsolve</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/kernel/kernel.xml b/scilab/modules/linear_algebra/help/en_US/kernel/kernel.xml
new file mode 100644 (file)
index 0000000..c2627af
--- /dev/null
@@ -0,0 +1,92 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="kernel">
+    <refnamediv>
+        <refname>kernel</refname>
+        <refpurpose> kernel, nullspace</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>W=kernel(A [,tol,[,flag])</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>full real or complex matrix or real sparse matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>flag</term>
+                <listitem>
+                    <para>
+                        character string <literal>'svd'</literal> (default) or <literal>'qr'</literal>
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>tol</term>
+                <listitem>
+                    <para>real number</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>W</term>
+                <listitem>
+                    <para>full column rank matrix</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            <literal>W=kernel(A)</literal> returns the kernel (nullspace) of <literal>A</literal>. If A has full column rank then an empty matrix [] is returned.
+        </para>
+        <para>
+            <literal>flag</literal> and <literal>tol</literal> are optional parameters: <literal>flag = 'qr'</literal> 
+            or <literal>'svd'</literal> (default is <literal>'svd'</literal>).
+        </para>
+        <para>
+            <literal>tol</literal> = tolerance parameter (of order <literal>%eps</literal> as default value).
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=rand(3,1)*rand(1,3);
+A*kernel(A)
+A=sparse(A);
+clean(A*kernel(A))
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="colcomp">colcomp</link>
+            </member>
+            <member>
+                <link linkend="fullrf">fullrf</link>
+            </member>
+            <member>
+                <link linkend="fullrfk">fullrfk</link>
+            </member>
+            <member>
+                <link linkend="linsolve">linsolve</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/kernel/range.xml b/scilab/modules/linear_algebra/help/en_US/kernel/range.xml
new file mode 100644 (file)
index 0000000..5ae81b7
--- /dev/null
@@ -0,0 +1,94 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="range">
+    <refnamediv>
+        <refname>range</refname>
+        <refpurpose> range (span) of A^k</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[X,dim]=range(A,k)</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>real square matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>k</term>
+                <listitem>
+                    <para>integer</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>X</term>
+                <listitem>
+                    <para>orthonormal real matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>dim</term>
+                <listitem>
+                    <para>integer (dimension of subspace)</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Computation of Range <literal>A^k</literal> ; the first dim rows of <literal>X</literal> span the
+            range of <literal>A^k</literal>. The last rows of <literal>X</literal> span the
+            orthogonal complement of the range. <literal>X*X'</literal> is the Identity matrix
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=rand(4,2)*rand(2,4);   // 4 column vectors, 2 independent.
+[X,dim]=range(A,1);dim   // compute the range
+
+y1=A*rand(4,1);          //a vector which is in the range of A
+y2=rand(4,1);            //a vector which is not  in the range of A
+norm(X(dim+1:$,:)*y1)    //the last entries are zeros, y1 is in the range of A
+norm(X(dim+1:$,:)*y2)    //the last entries are not zeros
+
+I=X(1:dim,:)'            //I is a basis of the range
+coeffs=X(1:dim,:)*y1     // components of y1 relative to the I basis
+
+norm(I*coeffs-y1)        //check
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="fullrfk">fullrfk</link>
+            </member>
+            <member>
+                <link linkend="rowcomp">rowcomp</link>
+            </member>
+        </simplelist>
+    </refsection>
+    <refsection>
+        <title>Used Functions</title>
+        <para>
+            The <literal>range</literal> function is based on the <link linkend="rowcomp">rowcomp</link> function
+            which uses the <link linkend="svd">svd</link> decomposition.
+        </para>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/kernel/rowcomp.xml b/scilab/modules/linear_algebra/help/en_US/kernel/rowcomp.xml
new file mode 100644 (file)
index 0000000..0f0db63
--- /dev/null
@@ -0,0 +1,123 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ * 
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution.  The terms
+ * are also available at    
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="rowcomp">
+    <refnamediv>
+        <refname>rowcomp</refname>
+        <refpurpose> row compression, range</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>[W,rk]=rowcomp(A [,flag [,tol]])</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>A</term>
+                <listitem>
+                    <para>real or complex matrix</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>flag</term>
+                <listitem>
+                    <para>optional character string, with possible values
+                        <literal>'svd'</literal> or <literal>'qr'</literal>. The default value is  <literal>'svd'</literal>.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>tol</term>
+                <listitem>
+                    <para>optional real non negative number. The default value is 
+                        <literal>sqrt(%eps)*norm(A,1)</literal>.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>W</term>
+                <listitem>
+                    <para>square non-singular matrix (change of basis)</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>rk</term>
+                <listitem>
+                    <para>
+                        integer (rank of <literal>A</literal>)
+                    </para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            Row compression of <literal>A</literal>. <literal>Ac = W*A</literal> is a row compressed matrix: i.e. 
+            <literal>Ac=[Af;0]</literal> with <literal>Af</literal> full row rank.
+        </para>
+        <para>
+            <literal>flag</literal> and <literal>tol</literal> are optional parameters: <literal>flag='qr'</literal> 
+            or <literal>'svd'</literal> (default <literal>'svd'</literal>).
+        </para>
+        <para>
+            <literal>tol</literal> is a tolerance parameter.
+        </para>
+        <para>
+            The <literal>rk</literal> first columns of <literal>W'</literal> span the range of
+            <literal>A</literal>.
+        </para>
+        <para>
+            The <literal>rk</literal> first (top) rows of <literal>W</literal> span the row
+            range of <literal>A</literal>.
+        </para>
+        <para>
+            A non zero vector <literal>x</literal> belongs to range(<literal>A</literal>) iff
+            <literal>W*x</literal> is row  compressed in accordance with <literal>Ac</literal>
+            i.e the norm of its last components is small w.r.t its first
+            components.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+A=rand(5,2)*rand(2,4);              // 4 col. vectors, 2 independent.
+[X,dim]=rowcomp(A);Xp=X';
+svd([Xp(:,1:dim),A])                //span(A) = span(Xp(:,1:dim)
+x=A*rand(4,1);                      //x belongs to span(A)
+y=X*x  
+norm(y(dim+1:$))/norm(y(1:dim))     // small
+ ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="colcomp">colcomp</link>
+            </member>
+            <member>
+                <link linkend="fullrf">fullrf</link>
+            </member>
+            <member>
+                <link linkend="fullrfk">fullrfk</link>
+            </member>
+        </simplelist>
+    </refsection>
+    <refsection>
+        <title>Used Functions</title>
+        <para>
+            The <literal>rowcomp</literal> function is based on the <link linkend="svd">svd</link> or
+            <link linkend="qr">qr</link> decompositions.
+        </para>
+    </refsection>
+</refentry>
diff --git a/scilab/modules/linear_algebra/help/en_US/kroneck.xml b/scilab/modules/linear_algebra/help/en_US/kroneck.xml
deleted file mode 100644 (file)
index 5318959..0000000
+++ /dev/null
@@ -1,159 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) 2008 - INRIA
- * 
- * This file must be used under the terms of the CeCILL.
- * This source file is licensed as described in the file COPYING, which
- * you should have received as part of this distribution.  The terms
- * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="kroneck">
-  <refnamediv>
-    <refname>kroneck</refname>
-    <refpurpose> Kronecker form of matrix pencil</refpurpose>
-  </refnamediv>
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-    <synopsis>[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F)
-      [Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(E,A)
-    </synopsis>
-  </refsynopsisdiv>
-  <refsection>
-    <title>Arguments</title>
-    <variablelist>
-      <varlistentry>
-        <term>F</term>
-        <listitem>
-          <para>
-            real matrix pencil <literal>F=s*E-A</literal>
-          </para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>E,A</term>
-        <listitem>
-          <para>two real matrices of same dimensions</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Q,Z</term>
-        <listitem>
-          <para>two square orthogonal matrices</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>Qd,Zd</term>
-        <listitem>
-          <para>two vectors of integers</para>
-        </listitem>
-      </varlistentry>
-      <varlistentry>
-        <term>numbeps,numeta</term>
-        <listitem>
-          <para>two vectors of integers</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-  <refsection>
-    <