Mercurial > hg > octave-lyh

annotate liboctave/numeric/oct-norm.cc @ 15271:648dabbb4c6b

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build: Refactor liboctave into multiple subdirectories. Move libcruft into liboctave. * array/Array-C.cc, array/Array-b.cc, array/Array-ch.cc, array/Array-d.cc, array/Array-f.cc, array/Array-fC.cc, array/Array-i.cc, array/Array-idx-vec.cc, array/Array-s.cc, array/Array-str.cc, array/Array-util.cc, array/Array-util.h, array/Array-voidp.cc, array/Array.cc, array/Array.h, array/Array2.h, array/Array3.h, array/ArrayN.h, array/CColVector.cc, array/CColVector.h, array/CDiagMatrix.cc, array/CDiagMatrix.h, array/CMatrix.cc, array/CMatrix.h, array/CNDArray.cc, array/CNDArray.h, array/CRowVector.cc, array/CRowVector.h, array/CSparse.cc, array/CSparse.h, array/DiagArray2.cc, array/DiagArray2.h, array/MArray-C.cc, array/MArray-d.cc, array/MArray-decl.h, array/MArray-defs.h, array/MArray-f.cc, array/MArray-fC.cc, array/MArray-i.cc, array/MArray-s.cc, array/MArray.cc, array/MArray.h, array/MArray2.h, array/MArrayN.h, array/MDiagArray2.cc, array/MDiagArray2.h, array/MSparse-C.cc, array/MSparse-d.cc, array/MSparse-defs.h, array/MSparse.cc, array/MSparse.h, array/Matrix.h, array/MatrixType.cc, array/MatrixType.h, array/PermMatrix.cc, array/PermMatrix.h, array/Range.cc, array/Range.h, array/Sparse-C.cc, array/Sparse-b.cc, array/Sparse-d.cc, array/Sparse.cc, array/Sparse.h, array/boolMatrix.cc, array/boolMatrix.h, array/boolNDArray.cc, array/boolNDArray.h, array/boolSparse.cc, array/boolSparse.h, array/chMatrix.cc, array/chMatrix.h, array/chNDArray.cc, array/chNDArray.h, array/dColVector.cc, array/dColVector.h, array/dDiagMatrix.cc, array/dDiagMatrix.h, array/dMatrix.cc, array/dMatrix.h, array/dNDArray.cc, array/dNDArray.h, array/dRowVector.cc, array/dRowVector.h, array/dSparse.cc, array/dSparse.h, array/dim-vector.cc, array/dim-vector.h, array/fCColVector.cc, array/fCColVector.h, array/fCDiagMatrix.cc, array/fCDiagMatrix.h, array/fCMatrix.cc, array/fCMatrix.h, array/fCNDArray.cc, array/fCNDArray.h, array/fCRowVector.cc, array/fCRowVector.h, array/fColVector.cc, array/fColVector.h, array/fDiagMatrix.cc, array/fDiagMatrix.h, array/fMatrix.cc, array/fMatrix.h, array/fNDArray.cc, array/fNDArray.h, array/fRowVector.cc, array/fRowVector.h, array/idx-vector.cc, array/idx-vector.h, array/int16NDArray.cc, array/int16NDArray.h, array/int32NDArray.cc, array/int32NDArray.h, array/int64NDArray.cc, array/int64NDArray.h, array/int8NDArray.cc, array/int8NDArray.h, array/intNDArray.cc, array/intNDArray.h, array/module.mk, array/uint16NDArray.cc, array/uint16NDArray.h, array/uint32NDArray.cc, array/uint32NDArray.h, array/uint64NDArray.cc, array/uint64NDArray.h, array/uint8NDArray.cc, array/uint8NDArray.h: Moved from liboctave dir to array subdirectory. * cruft/Makefile.am, cruft/amos/README, cruft/amos/cacai.f, cruft/amos/cacon.f, cruft/amos/cairy.f, cruft/amos/casyi.f, cruft/amos/cbesh.f, cruft/amos/cbesi.f, cruft/amos/cbesj.f, cruft/amos/cbesk.f, cruft/amos/cbesy.f, cruft/amos/cbinu.f, cruft/amos/cbiry.f, cruft/amos/cbknu.f, cruft/amos/cbuni.f, cruft/amos/cbunk.f, cruft/amos/ckscl.f, cruft/amos/cmlri.f, cruft/amos/crati.f, cruft/amos/cs1s2.f, cruft/amos/cseri.f, cruft/amos/cshch.f, cruft/amos/cuchk.f, cruft/amos/cunhj.f, cruft/amos/cuni1.f, cruft/amos/cuni2.f, cruft/amos/cunik.f, cruft/amos/cunk1.f, cruft/amos/cunk2.f, cruft/amos/cuoik.f, cruft/amos/cwrsk.f, cruft/amos/dgamln.f, cruft/amos/gamln.f, cruft/amos/module.mk, cruft/amos/xzabs.f, cruft/amos/xzexp.f, cruft/amos/xzlog.f, cruft/amos/xzsqrt.f, cruft/amos/zacai.f, cruft/amos/zacon.f, cruft/amos/zairy.f, cruft/amos/zasyi.f, cruft/amos/zbesh.f, cruft/amos/zbesi.f, cruft/amos/zbesj.f, cruft/amos/zbesk.f, cruft/amos/zbesy.f, cruft/amos/zbinu.f, cruft/amos/zbiry.f, cruft/amos/zbknu.f, cruft/amos/zbuni.f, cruft/amos/zbunk.f, cruft/amos/zdiv.f, cruft/amos/zkscl.f, cruft/amos/zmlri.f, cruft/amos/zmlt.f, cruft/amos/zrati.f, cruft/amos/zs1s2.f, cruft/amos/zseri.f, cruft/amos/zshch.f, cruft/amos/zuchk.f, cruft/amos/zunhj.f, cruft/amos/zuni1.f, cruft/amos/zuni2.f, cruft/amos/zunik.f, cruft/amos/zunk1.f, cruft/amos/zunk2.f, cruft/amos/zuoik.f, cruft/amos/zwrsk.f, cruft/blas-xtra/cconv2.f, cruft/blas-xtra/cdotc3.f, cruft/blas-xtra/cmatm3.f, cruft/blas-xtra/csconv2.f, cruft/blas-xtra/dconv2.f, cruft/blas-xtra/ddot3.f, cruft/blas-xtra/dmatm3.f, cruft/blas-xtra/module.mk, cruft/blas-xtra/sconv2.f, cruft/blas-xtra/sdot3.f, cruft/blas-xtra/smatm3.f, cruft/blas-xtra/xcdotc.f, cruft/blas-xtra/xcdotu.f, cruft/blas-xtra/xddot.f, cruft/blas-xtra/xdnrm2.f, cruft/blas-xtra/xdznrm2.f, cruft/blas-xtra/xerbla.f, cruft/blas-xtra/xscnrm2.f, cruft/blas-xtra/xsdot.f, cruft/blas-xtra/xsnrm2.f, cruft/blas-xtra/xzdotc.f, cruft/blas-xtra/xzdotu.f, cruft/blas-xtra/zconv2.f, cruft/blas-xtra/zdconv2.f, cruft/blas-xtra/zdotc3.f, cruft/blas-xtra/zmatm3.f, cruft/daspk/datv.f, cruft/daspk/dcnst0.f, cruft/daspk/dcnstr.f, cruft/daspk/ddasic.f, cruft/daspk/ddasid.f, cruft/daspk/ddasik.f, cruft/daspk/ddaspk.f, cruft/daspk/ddstp.f, cruft/daspk/ddwnrm.f, cruft/daspk/dfnrmd.f, cruft/daspk/dfnrmk.f, cruft/daspk/dhels.f, cruft/daspk/dheqr.f, cruft/daspk/dinvwt.f, cruft/daspk/dlinsd.f, cruft/daspk/dlinsk.f, cruft/daspk/dmatd.f, cruft/daspk/dnedd.f, cruft/daspk/dnedk.f, cruft/daspk/dnsd.f, cruft/daspk/dnsid.f, cruft/daspk/dnsik.f, cruft/daspk/dnsk.f, cruft/daspk/dorth.f, cruft/daspk/dslvd.f, cruft/daspk/dslvk.f, cruft/daspk/dspigm.f, cruft/daspk/dyypnw.f, cruft/daspk/module.mk, cruft/dasrt/ddasrt.f, cruft/dasrt/drchek.f, cruft/dasrt/droots.f, cruft/dasrt/module.mk, cruft/dassl/ddaini.f, cruft/dassl/ddajac.f, cruft/dassl/ddanrm.f, cruft/dassl/ddaslv.f, cruft/dassl/ddassl.f, cruft/dassl/ddastp.f, cruft/dassl/ddatrp.f, cruft/dassl/ddawts.f, cruft/dassl/module.mk, cruft/fftpack/cfftb.f, cruft/fftpack/cfftb1.f, cruft/fftpack/cfftf.f, cruft/fftpack/cfftf1.f, cruft/fftpack/cffti.f, cruft/fftpack/cffti1.f, cruft/fftpack/fftpack.doc, cruft/fftpack/module.mk, cruft/fftpack/passb.f, cruft/fftpack/passb2.f, cruft/fftpack/passb3.f, cruft/fftpack/passb4.f, cruft/fftpack/passb5.f, cruft/fftpack/passf.f, cruft/fftpack/passf2.f, cruft/fftpack/passf3.f, cruft/fftpack/passf4.f, cruft/fftpack/passf5.f, cruft/fftpack/zfftb.f, cruft/fftpack/zfftb1.f, cruft/fftpack/zfftf.f, cruft/fftpack/zfftf1.f, cruft/fftpack/zffti.f, cruft/fftpack/zffti1.f, cruft/fftpack/zpassb.f, cruft/fftpack/zpassb2.f, cruft/fftpack/zpassb3.f, cruft/fftpack/zpassb4.f, cruft/fftpack/zpassb5.f, cruft/fftpack/zpassf.f, cruft/fftpack/zpassf2.f, cruft/fftpack/zpassf3.f, cruft/fftpack/zpassf4.f, cruft/fftpack/zpassf5.f, cruft/lapack-xtra/crsf2csf.f, cruft/lapack-xtra/module.mk, cruft/lapack-xtra/xclange.f, cruft/lapack-xtra/xdlamch.f, cruft/lapack-xtra/xdlange.f, cruft/lapack-xtra/xilaenv.f, cruft/lapack-xtra/xslamch.f, cruft/lapack-xtra/xslange.f, cruft/lapack-xtra/xzlange.f, cruft/lapack-xtra/zrsf2csf.f, cruft/link-deps.mk, cruft/misc/blaswrap.c, cruft/misc/cquit.c, cruft/misc/d1mach-tst.for, cruft/misc/d1mach.f, cruft/misc/f77-extern.cc, cruft/misc/f77-fcn.c, cruft/misc/f77-fcn.h, cruft/misc/i1mach.f, cruft/misc/lo-error.c, cruft/misc/lo-error.h, cruft/misc/module.mk, cruft/misc/quit.cc, cruft/misc/quit.h, cruft/misc/r1mach.f, cruft/mkf77def.in, cruft/odepack/cfode.f, cruft/odepack/dlsode.f, cruft/odepack/ewset.f, cruft/odepack/intdy.f, cruft/odepack/module.mk, cruft/odepack/prepj.f, cruft/odepack/scfode.f, cruft/odepack/sewset.f, cruft/odepack/sintdy.f, cruft/odepack/slsode.f, cruft/odepack/solsy.f, cruft/odepack/sprepj.f, cruft/odepack/ssolsy.f, cruft/odepack/sstode.f, cruft/odepack/stode.f, cruft/odepack/svnorm.f, cruft/odepack/vnorm.f, cruft/ordered-qz/README, cruft/ordered-qz/dsubsp.f, cruft/ordered-qz/exchqz.f, cruft/ordered-qz/module.mk, cruft/ordered-qz/sexchqz.f, cruft/ordered-qz/ssubsp.f, cruft/quadpack/dqagi.f, cruft/quadpack/dqagie.f, cruft/quadpack/dqagp.f, cruft/quadpack/dqagpe.f, cruft/quadpack/dqelg.f, cruft/quadpack/dqk15i.f, cruft/quadpack/dqk21.f, cruft/quadpack/dqpsrt.f, cruft/quadpack/module.mk, cruft/quadpack/qagi.f, cruft/quadpack/qagie.f, cruft/quadpack/qagp.f, cruft/quadpack/qagpe.f, cruft/quadpack/qelg.f, cruft/quadpack/qk15i.f, cruft/quadpack/qk21.f, cruft/quadpack/qpsrt.f, cruft/quadpack/xerror.f, cruft/ranlib/Basegen.doc, cruft/ranlib/HOWTOGET, cruft/ranlib/README, cruft/ranlib/advnst.f, cruft/ranlib/genbet.f, cruft/ranlib/genchi.f, cruft/ranlib/genexp.f, cruft/ranlib/genf.f, cruft/ranlib/gengam.f, cruft/ranlib/genmn.f, cruft/ranlib/genmul.f, cruft/ranlib/gennch.f, cruft/ranlib/gennf.f, cruft/ranlib/gennor.f, cruft/ranlib/genprm.f, cruft/ranlib/genunf.f, cruft/ranlib/getcgn.f, cruft/ranlib/getsd.f, cruft/ranlib/ignbin.f, cruft/ranlib/ignlgi.f, cruft/ranlib/ignnbn.f, cruft/ranlib/ignpoi.f, cruft/ranlib/ignuin.f, cruft/ranlib/initgn.f, cruft/ranlib/inrgcm.f, cruft/ranlib/lennob.f, cruft/ranlib/mltmod.f, cruft/ranlib/module.mk, cruft/ranlib/phrtsd.f, cruft/ranlib/qrgnin.f, cruft/ranlib/randlib.chs, cruft/ranlib/randlib.fdoc, cruft/ranlib/ranf.f, cruft/ranlib/setall.f, cruft/ranlib/setant.f, cruft/ranlib/setgmn.f, cruft/ranlib/setsd.f, cruft/ranlib/sexpo.f, cruft/ranlib/sgamma.f, cruft/ranlib/snorm.f, cruft/ranlib/tstbot.for, cruft/ranlib/tstgmn.for, cruft/ranlib/tstmid.for, cruft/ranlib/wrap.f, cruft/slatec-err/fdump.f, cruft/slatec-err/ixsav.f, cruft/slatec-err/j4save.f, cruft/slatec-err/module.mk, cruft/slatec-err/xerclr.f, cruft/slatec-err/xercnt.f, cruft/slatec-err/xerhlt.f, cruft/slatec-err/xermsg.f, cruft/slatec-err/xerprn.f, cruft/slatec-err/xerrwd.f, cruft/slatec-err/xersve.f, cruft/slatec-err/xgetf.f, cruft/slatec-err/xgetua.f, cruft/slatec-err/xsetf.f, cruft/slatec-err/xsetua.f, cruft/slatec-fn/acosh.f, cruft/slatec-fn/albeta.f, cruft/slatec-fn/algams.f, cruft/slatec-fn/alngam.f, cruft/slatec-fn/alnrel.f, cruft/slatec-fn/asinh.f, cruft/slatec-fn/atanh.f, cruft/slatec-fn/betai.f, cruft/slatec-fn/csevl.f, cruft/slatec-fn/d9gmit.f, cruft/slatec-fn/d9lgic.f, cruft/slatec-fn/d9lgit.f, cruft/slatec-fn/d9lgmc.f, cruft/slatec-fn/dacosh.f, cruft/slatec-fn/dasinh.f, cruft/slatec-fn/datanh.f, cruft/slatec-fn/dbetai.f, cruft/slatec-fn/dcsevl.f, cruft/slatec-fn/derf.f, cruft/slatec-fn/derfc.in.f, cruft/slatec-fn/dgami.f, cruft/slatec-fn/dgamit.f, cruft/slatec-fn/dgamlm.f, cruft/slatec-fn/dgamma.f, cruft/slatec-fn/dgamr.f, cruft/slatec-fn/dlbeta.f, cruft/slatec-fn/dlgams.f, cruft/slatec-fn/dlngam.f, cruft/slatec-fn/dlnrel.f, cruft/slatec-fn/dpchim.f, cruft/slatec-fn/dpchst.f, cruft/slatec-fn/erf.f, cruft/slatec-fn/erfc.in.f, cruft/slatec-fn/gami.f, cruft/slatec-fn/gamit.f, cruft/slatec-fn/gamlim.f, cruft/slatec-fn/gamma.f, cruft/slatec-fn/gamr.f, cruft/slatec-fn/initds.f, cruft/slatec-fn/inits.f, cruft/slatec-fn/module.mk, cruft/slatec-fn/pchim.f, cruft/slatec-fn/pchst.f, cruft/slatec-fn/r9gmit.f, cruft/slatec-fn/r9lgic.f, cruft/slatec-fn/r9lgit.f, cruft/slatec-fn/r9lgmc.f, cruft/slatec-fn/xacosh.f, cruft/slatec-fn/xasinh.f, cruft/slatec-fn/xatanh.f, cruft/slatec-fn/xbetai.f, cruft/slatec-fn/xdacosh.f, cruft/slatec-fn/xdasinh.f, cruft/slatec-fn/xdatanh.f, cruft/slatec-fn/xdbetai.f, cruft/slatec-fn/xderf.f, cruft/slatec-fn/xderfc.f, cruft/slatec-fn/xdgami.f, cruft/slatec-fn/xdgamit.f, cruft/slatec-fn/xdgamma.f, cruft/slatec-fn/xerf.f, cruft/slatec-fn/xerfc.f, cruft/slatec-fn/xgamma.f, cruft/slatec-fn/xgmainc.f, cruft/slatec-fn/xsgmainc.f: Moved from top-level libcruft to cruft directory below liboctave. * numeric/CmplxAEPBAL.cc, numeric/CmplxAEPBAL.h, numeric/CmplxCHOL.cc, numeric/CmplxCHOL.h, numeric/CmplxGEPBAL.cc, numeric/CmplxGEPBAL.h, numeric/CmplxHESS.cc, numeric/CmplxHESS.h, numeric/CmplxLU.cc, numeric/CmplxLU.h, numeric/CmplxQR.cc, numeric/CmplxQR.h, numeric/CmplxQRP.cc, numeric/CmplxQRP.h, numeric/CmplxSCHUR.cc, numeric/CmplxSCHUR.h, numeric/CmplxSVD.cc, numeric/CmplxSVD.h, numeric/CollocWt.cc, numeric/CollocWt.h, numeric/DAE.h, numeric/DAEFunc.h, numeric/DAERT.h, numeric/DAERTFunc.h, numeric/DASPK-opts.in, numeric/DASPK.cc, numeric/DASPK.h, numeric/DASRT-opts.in, numeric/DASRT.cc, numeric/DASRT.h, numeric/DASSL-opts.in, numeric/DASSL.cc, numeric/DASSL.h, numeric/DET.h, numeric/EIG.cc, numeric/EIG.h, numeric/LSODE-opts.in, numeric/LSODE.cc, numeric/LSODE.h, numeric/ODE.h, numeric/ODEFunc.h, numeric/ODES.cc, numeric/ODES.h, numeric/ODESFunc.h, numeric/Quad-opts.in, numeric/Quad.cc, numeric/Quad.h, numeric/SparseCmplxCHOL.cc, numeric/SparseCmplxCHOL.h, numeric/SparseCmplxLU.cc, numeric/SparseCmplxLU.h, numeric/SparseCmplxQR.cc, numeric/SparseCmplxQR.h, numeric/SparseQR.cc, numeric/SparseQR.h, numeric/SparsedbleCHOL.cc, numeric/SparsedbleCHOL.h, numeric/SparsedbleLU.cc, numeric/SparsedbleLU.h, numeric/base-aepbal.h, numeric/base-dae.h, numeric/base-de.h, numeric/base-lu.cc, numeric/base-lu.h, numeric/base-min.h, numeric/base-qr.cc, numeric/base-qr.h, numeric/bsxfun-decl.h, numeric/bsxfun-defs.cc, numeric/bsxfun.h, numeric/dbleAEPBAL.cc, numeric/dbleAEPBAL.h, numeric/dbleCHOL.cc, numeric/dbleCHOL.h, numeric/dbleGEPBAL.cc, numeric/dbleGEPBAL.h, numeric/dbleHESS.cc, numeric/dbleHESS.h, numeric/dbleLU.cc, numeric/dbleLU.h, numeric/dbleQR.cc, numeric/dbleQR.h, numeric/dbleQRP.cc, numeric/dbleQRP.h, numeric/dbleSCHUR.cc, numeric/dbleSCHUR.h, numeric/dbleSVD.cc, numeric/dbleSVD.h, numeric/eigs-base.cc, numeric/fCmplxAEPBAL.cc, numeric/fCmplxAEPBAL.h, numeric/fCmplxCHOL.cc, numeric/fCmplxCHOL.h, numeric/fCmplxGEPBAL.cc, numeric/fCmplxGEPBAL.h, numeric/fCmplxHESS.cc, numeric/fCmplxHESS.h, numeric/fCmplxLU.cc, numeric/fCmplxLU.h, numeric/fCmplxQR.cc, numeric/fCmplxQR.h, numeric/fCmplxQRP.cc, numeric/fCmplxQRP.h, numeric/fCmplxSCHUR.cc, numeric/fCmplxSCHUR.h, numeric/fCmplxSVD.cc, numeric/fCmplxSVD.h, numeric/fEIG.cc, numeric/fEIG.h, numeric/floatAEPBAL.cc, numeric/floatAEPBAL.h, numeric/floatCHOL.cc, numeric/floatCHOL.h, numeric/floatGEPBAL.cc, numeric/floatGEPBAL.h, numeric/floatHESS.cc, numeric/floatHESS.h, numeric/floatLU.cc, numeric/floatLU.h, numeric/floatQR.cc, numeric/floatQR.h, numeric/floatQRP.cc, numeric/floatQRP.h, numeric/floatSCHUR.cc, numeric/floatSCHUR.h, numeric/floatSVD.cc, numeric/floatSVD.h, numeric/lo-mappers.cc, numeric/lo-mappers.h, numeric/lo-specfun.cc, numeric/lo-specfun.h, numeric/module.mk, numeric/oct-convn.cc, numeric/oct-convn.h, numeric/oct-fftw.cc, numeric/oct-fftw.h, numeric/oct-norm.cc, numeric/oct-norm.h, numeric/oct-rand.cc, numeric/oct-rand.h, numeric/oct-spparms.cc, numeric/oct-spparms.h, numeric/randgamma.c, numeric/randgamma.h, numeric/randmtzig.c, numeric/randmtzig.h, numeric/randpoisson.c, numeric/randpoisson.h, numeric/sparse-base-chol.cc, numeric/sparse-base-chol.h, numeric/sparse-base-lu.cc, numeric/sparse-base-lu.h, numeric/sparse-dmsolve.cc: Moved from liboctave dir to numeric subdirectory. * operators/Sparse-diag-op-defs.h, operators/Sparse-op-defs.h, operators/Sparse-perm-op-defs.h, operators/config-ops.sh, operators/mk-ops.awk, operators/module.mk, operators/mx-base.h, operators/mx-defs.h, operators/mx-ext.h, operators/mx-inlines.cc, operators/mx-op-decl.h, operators/mx-op-defs.h, operators/mx-ops, operators/sparse-mk-ops.awk, operators/sparse-mx-ops, operators/vx-ops: Moved from liboctave dir to operators subdirectory. * system/dir-ops.cc, system/dir-ops.h, system/file-ops.cc, system/file-ops.h, system/file-stat.cc, system/file-stat.h, system/lo-sysdep.cc, system/lo-sysdep.h, system/mach-info.cc, system/mach-info.h, system/module.mk, system/oct-env.cc, system/oct-env.h, system/oct-group.cc, system/oct-group.h, system/oct-openmp.h, system/oct-passwd.cc, system/oct-passwd.h, system/oct-syscalls.cc, system/oct-syscalls.h, system/oct-time.cc, system/oct-time.h, system/oct-uname.cc, system/oct-uname.h, system/pathlen.h, system/sysdir.h, system/syswait.h, system/tempnam.c, system/tempname.c: Moved from liboctave dir to system subdirectory. * util/base-list.h, util/byte-swap.h, util/caseless-str.h, util/cmd-edit.cc, util/cmd-edit.h, util/cmd-hist.cc, util/cmd-hist.h, util/data-conv.cc, util/data-conv.h, util/f2c-main.c, util/functor.h, util/glob-match.cc, util/glob-match.h, util/kpse.cc, util/lo-array-gripes.cc, util/lo-array-gripes.h, util/lo-cieee.c, util/lo-cutils.c, util/lo-cutils.h, util/lo-ieee.cc, util/lo-ieee.h, util/lo-macros.h, util/lo-math.h, util/lo-traits.h, util/lo-utils.cc, util/lo-utils.h, util/module.mk, util/oct-alloc.cc, util/oct-alloc.h, util/oct-base64.cc, util/oct-base64.h, util/oct-binmap.h, util/oct-cmplx.h, util/oct-glob.cc, util/oct-glob.h, util/oct-inttypes.cc, util/oct-inttypes.h, util/oct-locbuf.cc, util/oct-locbuf.h, util/oct-md5.cc, util/oct-md5.h, util/oct-mem.h, util/oct-mutex.cc, util/oct-mutex.h, util/oct-refcount.h, util/oct-rl-edit.c, util/oct-rl-edit.h, util/oct-rl-hist.c, util/oct-rl-hist.h, util/oct-shlib.cc, util/oct-shlib.h, util/oct-sort.cc, util/oct-sort.h, util/oct-sparse.h, util/pathsearch.cc, util/pathsearch.h, util/regexp.cc, util/regexp.h, util/singleton-cleanup.cc, util/singleton-cleanup.h, util/sparse-sort.cc, util/sparse-sort.h, util/sparse-util.cc, util/sparse-util.h, util/statdefs.h, util/str-vec.cc, util/str-vec.h, util/sun-utils.h: Moved from liboctave dir to util subdirectory. * Makefile.am: Eliminate reference to top-level liboctave directory. * autogen.sh: cd to new liboctave/operators directory to run config-ops.sh. * build-aux/common.mk: Eliminate LIBCRUFT references. * configure.ac: Eliminate libcruft top-level references. Switch test programs to find files in liboctave/cruft subdirectory. * OctaveFAQ.texi, install.txi, mkoctfile.1: Eliminate references to libcruft in docs. * libgui/src/Makefile.am, libinterp/Makefile.am, src/Makefile.am: Update include file locations. Stop linking against libcruft. * libinterp/corefcn/module.mk: Update location of OPT_INC files which are now in numeric/ subdirectory. * libinterp/dldfcn/config-module.awk: Stop linking against libcruft. * libinterp/interpfcn/toplev.cc: Remove reference to LIBCRUFT. * libinterp/link-deps.mk, liboctave/link-deps.mk: Add GNULIB_LINK_DEPS to link dependencies. * libinterp/oct-conf.in.h: Remove reference to OCTAVE_CONF_LIBCRUFT. * liboctave/Makefile.am: Overhaul to use convenience libraries in subdirectories. * scripts/miscellaneous/mkoctfile.m: Eliminate reference to LIBCRUFT. * src/mkoctfile.in.cc, src/mkoctfile.in.sh: Stop linking againt libcruft. Eliminate references to LIBCRUFT.
author Rik <rik@octave.org>
date Fri, 31 Aug 2012 20:00:20 -0700
parents liboctave/oct-norm.cc@c4ed0fdf2b62
children
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1 /*
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2
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72c96de7a403 maint: update copyright notices for 2012
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3 Copyright (C) 2008-2012 VZLU Prague, a.s.
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 // author: Jaroslav Hajek <highegg@gmail.com>
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24
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25 #ifdef HAVE_CONFIG_H
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26 #include <config.h>
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27 #endif
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28
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29 #include <cassert>
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30 #include <cfloat>
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31 #include <cmath>
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32
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33 #include <iostream>
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34 #include <vector>
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35
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36 #include "oct-cmplx.h"
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37 #include "lo-error.h"
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38 #include "lo-ieee.h"
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39 #include "Array.h"
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40 #include "Array-util.h"
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41 #include "CMatrix.h"
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42 #include "dMatrix.h"
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43 #include "fCMatrix.h"
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44 #include "fMatrix.h"
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45 #include "CColVector.h"
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46 #include "dColVector.h"
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47 #include "CRowVector.h"
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48 #include "dRowVector.h"
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49 #include "fCColVector.h"
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50 #include "fColVector.h"
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51 #include "fCRowVector.h"
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52 #include "fRowVector.h"
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53 #include "CSparse.h"
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54 #include "dSparse.h"
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55 #include "dbleSVD.h"
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56 #include "CmplxSVD.h"
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57 #include "floatSVD.h"
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58 #include "fCmplxSVD.h"
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59
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60 // Theory: norm accumulator is an object that has an accum method able
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61 // to handle both real and complex element, and a cast operator
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62 // returning the intermediate norm. Reference: Higham, N. "Estimating
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63 // the Matrix p-Norm." Numer. Math. 62, 539-555, 1992.
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64
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65 // norm accumulator for the p-norm
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66 template <class R>
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67 class norm_accumulator_p
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68 {
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69 R p,scl,sum;
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70 public:
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71 norm_accumulator_p () {} // we need this one for Array
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72 norm_accumulator_p (R pp) : p(pp), scl(0), sum(1) {}
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73
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74 template<class U>
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75 void accum (U val)
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76 {
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77 octave_quit ();
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78 R t = std::abs (val);
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79 if (scl == t) // we need this to handle Infs properly
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80 sum += 1;
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81 else if (scl < t)
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82 {
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83 sum *= std::pow (scl/t, p);
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84 sum += 1;
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85 scl = t;
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86 }
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87 else if (t != 0)
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88 sum += std::pow (t/scl, p);
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89 }
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90 operator R () { return scl * std::pow (sum, 1/p); }
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91 };
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92
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93 // norm accumulator for the minus p-pseudonorm
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94 template <class R>
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95 class norm_accumulator_mp
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96 {
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97 R p,scl,sum;
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98 public:
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99 norm_accumulator_mp () {} // we need this one for Array
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100 norm_accumulator_mp (R pp) : p(pp), scl(0), sum(1) {}
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101
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102 template<class U>
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103 void accum (U val)
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104 {
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105 octave_quit ();
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106 R t = 1 / std::abs (val);
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107 if (scl == t)
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108 sum += 1;
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109 else if (scl < t)
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110 {
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111 sum *= std::pow (scl/t, p);
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112 sum += 1;
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113 scl = t;
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114 }
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115 else if (t != 0)
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116 sum += std::pow (t/scl, p);
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117 }
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118 operator R () { return scl * std::pow (sum, -1/p); }
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119 };
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120
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121 // norm accumulator for the 2-norm (euclidean)
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122 template <class R>
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123 class norm_accumulator_2
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124 {
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125 R scl,sum;
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126 static R pow2 (R x) { return x*x; }
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127 public:
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128 norm_accumulator_2 () : scl(0), sum(1) {}
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129
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130 void accum (R val)
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131 {
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132 R t = std::abs (val);
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133 if (scl == t)
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134 sum += 1;
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135 else if (scl < t)
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136 {
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137 sum *= pow2 (scl/t);
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138 sum += 1;
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139 scl = t;
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140 }
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141 else if (t != 0)
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142 sum += pow2 (t/scl);
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143 }
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144
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145 void accum (std::complex<R> val)
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146 {
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147 accum (val.real ());
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148 accum (val.imag ());
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149 }
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150
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151 operator R () { return scl * std::sqrt (sum); }
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152 };
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153
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154 // norm accumulator for the 1-norm (city metric)
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155 template <class R>
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156 class norm_accumulator_1
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157 {
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158 R sum;
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159 public:
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160 norm_accumulator_1 () : sum (0) {}
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161 template<class U>
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162 void accum (U val)
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163 {
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164 sum += std::abs (val);
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165 }
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166 operator R () { return sum; }
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167 };
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168
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169 // norm accumulator for the inf-norm (max metric)
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170 template <class R>
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171 class norm_accumulator_inf
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172 {
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173 R max;
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174 public:
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175 norm_accumulator_inf () : max (0) {}
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176 template<class U>
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177 void accum (U val)
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178 {
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179 max = std::max (max, std::abs (val));
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180 }
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181 operator R () { return max; }
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182 };
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183
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184 // norm accumulator for the -inf pseudonorm (min abs value)
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185 template <class R>
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186 class norm_accumulator_minf
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187 {
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188 R min;
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189 public:
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190 norm_accumulator_minf () : min (octave_Inf) {}
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191 template<class U>
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192 void accum (U val)
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193 {
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194 min = std::min (min, std::abs (val));
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195 }
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196 operator R () { return min; }
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197 };
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198
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199 // norm accumulator for the 0-pseudonorm (hamming distance)
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200 template <class R>
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201 class norm_accumulator_0
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202 {
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203 unsigned int num;
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204 public:
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205 norm_accumulator_0 () : num (0) {}
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206 template<class U>
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207 void accum (U val)
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208 {
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209 if (val != static_cast<U> (0)) ++num;
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210 }
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211 operator R () { return num; }
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212 };
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213
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214
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215 // OK, we're armed :) Now let's go for the fun
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216
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217 template <class T, class R, class ACC>
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218 inline void vector_norm (const Array<T>& v, R& res, ACC acc)
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219 {
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220 for (octave_idx_type i = 0; i < v.numel (); i++)
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221 acc.accum (v(i));
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222
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223 res = acc;
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224 }
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225
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226 // dense versions
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227 template <class T, class R, class ACC>
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228 void column_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
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229 {
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230 res = MArray<R> (dim_vector (1, m.columns ()));
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231 for (octave_idx_type j = 0; j < m.columns (); j++)
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232 {
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233 ACC accj = acc;
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234 for (octave_idx_type i = 0; i < m.rows (); i++)
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235 accj.accum (m(i, j));
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236
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237 res.xelem (j) = accj;
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238 }
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239 }
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240
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241 template <class T, class R, class ACC>
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242 void row_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
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243 {
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244 res = MArray<R> (dim_vector (m.rows (), 1));
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245 std::vector<ACC> acci (m.rows (), acc);
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246 for (octave_idx_type j = 0; j < m.columns (); j++)
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247 {
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248 for (octave_idx_type i = 0; i < m.rows (); i++)
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249 acci[i].accum (m(i, j));
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250 }
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251
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252 for (octave_idx_type i = 0; i < m.rows (); i++)
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253 res.xelem (i) = acci[i];
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254 }
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255
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256 // sparse versions
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257 template <class T, class R, class ACC>
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258 void column_norms (const MSparse<T>& m, MArray<R>& res, ACC acc)
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259 {
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260 res = MArray<R> (dim_vector (1, m.columns ()));
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261 for (octave_idx_type j = 0; j < m.columns (); j++)
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262 {
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263 ACC accj = acc;
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264 for (octave_idx_type k = m.cidx (j); k < m.cidx (j+1); k++)
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265 accj.accum (m.data (k));
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266
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267 res.xelem (j) = accj;
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268 }
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269 }
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270
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271 template <class T, class R, class ACC>
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272 void row_norms (const MSparse<T>& m, MArray<R>& res, ACC acc)
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273 {
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274 res = MArray<R> (dim_vector (m.rows (), 1));
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275 std::vector<ACC> acci (m.rows (), acc);
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276 for (octave_idx_type j = 0; j < m.columns (); j++)
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277 {
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278 for (octave_idx_type k = m.cidx (j); k < m.cidx (j+1); k++)
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279 acci[m.ridx (k)].accum (m.data (k));
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280 }
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281
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282 for (octave_idx_type i = 0; i < m.rows (); i++)
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283 res.xelem (i) = acci[i];
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284 }
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285
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286 // now the dispatchers
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287 #define DEFINE_DISPATCHER(FUNC_NAME, ARG_TYPE, RES_TYPE) \
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288 template <class T, class R> \
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289 RES_TYPE FUNC_NAME (const ARG_TYPE& v, R p) \
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290 { \
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291 RES_TYPE res; \
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292 if (p == 2) \
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293 FUNC_NAME (v, res, norm_accumulator_2<R> ()); \
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294 else if (p == 1) \
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295 FUNC_NAME (v, res, norm_accumulator_1<R> ()); \
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296 else if (lo_ieee_isinf (p)) \
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297 { \
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298 if (p > 0) \
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299 FUNC_NAME (v, res, norm_accumulator_inf<R> ()); \
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300 else \
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301 FUNC_NAME (v, res, norm_accumulator_minf<R> ()); \
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302 } \
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303 else if (p == 0) \
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304 FUNC_NAME (v, res, norm_accumulator_0<R> ()); \
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305 else if (p > 0) \
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306 FUNC_NAME (v, res, norm_accumulator_p<R> (p)); \
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307 else \
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308 FUNC_NAME (v, res, norm_accumulator_mp<R> (p)); \
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309 return res; \
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310 }
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311
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312 DEFINE_DISPATCHER (vector_norm, MArray<T>, R)
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313 DEFINE_DISPATCHER (column_norms, MArray<T>, MArray<R>)
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314 DEFINE_DISPATCHER (row_norms, MArray<T>, MArray<R>)
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315 DEFINE_DISPATCHER (column_norms, MSparse<T>, MArray<R>)
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316 DEFINE_DISPATCHER (row_norms, MSparse<T>, MArray<R>)
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317
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318 // The approximate subproblem in Higham's method. Find lambda and mu such that
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319 // norm ([lambda, mu], p) == 1 and norm (y*lambda + col*mu, p) is maximized.
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320 // Real version. As in Higham's paper.
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321 template <class ColVectorT, class R>
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322 static void
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323 higham_subp (const ColVectorT& y, const ColVectorT& col,
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324 octave_idx_type nsamp, R p, R& lambda, R& mu)
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325 {
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326 R nrm = 0;
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327 for (octave_idx_type i = 0; i < nsamp; i++)
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328 {
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329 octave_quit ();
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330 R fi = i*M_PI/nsamp, lambda1 = cos (fi), mu1 = sin (fi);
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331 R lmnr = std::pow (std::pow (std::abs (lambda1), p) +
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332 std::pow (std::abs (mu1), p), 1/p);
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333 lambda1 /= lmnr; mu1 /= lmnr;
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334 R nrm1 = vector_norm (lambda1 * y + mu1 * col, p);
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335 if (nrm1 > nrm)
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336 {
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337 lambda = lambda1;
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338 mu = mu1;
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339 nrm = nrm1;
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340 }
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341 }
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342 }
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343
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344 // Complex version. Higham's paper does not deal with complex case, so we use a simple
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345 // extension. First, guess the magnitudes as in real version, then try to rotate lambda
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346 // to improve further.
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347 template <class ColVectorT, class R>
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348 static void
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349 higham_subp (const ColVectorT& y, const ColVectorT& col,
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350 octave_idx_type nsamp, R p,
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351 std::complex<R>& lambda, std::complex<R>& mu)
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352 {
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353 typedef std::complex<R> CR;
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354 R nrm = 0;
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355 lambda = 1.0;
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356 CR lamcu = lambda / std::abs (lambda);
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357 // Probe magnitudes
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358 for (octave_idx_type i = 0; i < nsamp; i++)
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359 {
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360 octave_quit ();
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361 R fi = i*M_PI/nsamp, lambda1 = cos (fi), mu1 = sin (fi);
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362 R lmnr = std::pow (std::pow (std::abs (lambda1), p) +
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363 std::pow (std::abs (mu1), p), 1/p);
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364 lambda1 /= lmnr; mu1 /= lmnr;
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365 R nrm1 = vector_norm (lambda1 * lamcu * y + mu1 * col, p);
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366 if (nrm1 > nrm)
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367 {
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368 lambda = lambda1 * lamcu;
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369 mu = mu1;
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370 nrm = nrm1;
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371 }
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372 }
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373 R lama = std::abs (lambda);
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374 // Probe orientation
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375 for (octave_idx_type i = 0; i < nsamp; i++)
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376 {
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377 octave_quit ();
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378 R fi = i*M_PI/nsamp;
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379 lamcu = CR (cos (fi), sin (fi));
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380 R nrm1 = vector_norm (lama * lamcu * y + mu * col, p);
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381 if (nrm1 > nrm)
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382 {
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383 lambda = lama * lamcu;
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384 nrm = nrm1;
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385 }
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386 }
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387 }
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388
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389 // the p-dual element (should work for both real and complex)
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390 template <class T, class R>
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391 inline T elem_dual_p (T x, R p)
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392 {
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393 return signum (x) * std::pow (std::abs (x), p-1);
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394 }
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395
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396 // the VectorT is used for vectors, but actually it has to be
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397 // a Matrix type to allow all the operations. For instance SparseMatrix
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398 // does not support multiplication with column/row vectors.
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399 // the dual vector
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400 template <class VectorT, class R>
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401 VectorT dual_p (const VectorT& x, R p, R q)
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402 {
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403 VectorT res (x.dims ());
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404 for (octave_idx_type i = 0; i < x.numel (); i++)
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405 res.xelem (i) = elem_dual_p (x(i), p);
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406 return res / vector_norm (res, q);
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407 }
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408
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409 // Higham's hybrid method
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410 template <class MatrixT, class VectorT, class R>
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411 R higham (const MatrixT& m, R p, R tol, int maxiter,
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412 VectorT& x)
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413 {
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414 x.resize (m.columns (), 1);
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415 // the OSE part
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416 VectorT y(m.rows (), 1, 0), z(m.rows (), 1);
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417 typedef typename VectorT::element_type RR;
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418 RR lambda = 0, mu = 1;
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419 for (octave_idx_type k = 0; k < m.columns (); k++)
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420 {
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421 octave_quit ();
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422 VectorT col (m.column (k));
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423 if (k > 0)
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424 higham_subp (y, col, 4*k, p, lambda, mu);
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425 for (octave_idx_type i = 0; i < k; i++)
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426 x(i) *= lambda;
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427 x(k) = mu;
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428 y = lambda * y + mu * col;
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429 }
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430
8303
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431 // the PM part
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432 x = x / vector_norm (x, p);
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433 R q = p/(p-1);
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434
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435 R gamma = 0, gamma1;
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436 int iter = 0;
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437 while (iter < maxiter)
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438 {
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439 octave_quit ();
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440 y = m*x;
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441 gamma1 = gamma;
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442 gamma = vector_norm (y, p);
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443 z = dual_p (y, p, q);
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444 z = z.hermitian ();
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445 z = z * m;
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446
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447 if (iter > 0 && (vector_norm (z, q) <= gamma
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448 || (gamma - gamma1) <= tol*gamma))
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449 break;
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450
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451 z = z.hermitian ();
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452 x = dual_p (z, q, p);
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453 iter ++;
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parents:
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454 }
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455
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456 return gamma;
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457 }
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458
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459 // derive column vector and SVD types
8303
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460
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461 static const char *p_less1_gripe = "xnorm: p must be at least 1";
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462
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parents:
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463 // Static constant to control the maximum number of iterations. 100 seems to be a good value.
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parents:
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464 // Eventually, we can provide a means to change this constant from Octave.
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465 static int max_norm_iter = 100;
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466
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467 // version with SVD for dense matrices
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468 template <class MatrixT, class VectorT, class SVDT, class R>
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469 R matrix_norm (const MatrixT& m, R p, VectorT, SVDT)
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470 {
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471 R res = 0;
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472 if (p == 2)
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473 {
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474 SVDT svd (m, SVD::sigma_only);
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475 res = svd.singular_values () (0,0);
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476 }
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477 else if (p == 1)
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478 res = xcolnorms (m, 1).max ();
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479 else if (lo_ieee_isinf (p))
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480 res = xrownorms (m, 1).max ();
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481 else if (p > 1)
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482 {
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483 VectorT x;
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484 const R sqrteps = std::sqrt (std::numeric_limits<R>::epsilon ());
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485 res = higham (m, p, sqrteps, max_norm_iter, x);
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486 }
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487 else
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488 (*current_liboctave_error_handler) (p_less1_gripe);
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489
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490 return res;
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491 }
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492
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493 // SVD-free version for sparse matrices
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494 template <class MatrixT, class VectorT, class R>
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495 R matrix_norm (const MatrixT& m, R p, VectorT)
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496 {
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497 R res = 0;
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498 if (p == 1)
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499 res = xcolnorms (m, 1).max ();
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500 else if (lo_ieee_isinf (p))
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501 res = xrownorms (m, 1).max ();
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502 else if (p > 1)
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503 {
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504 VectorT x;
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505 const R sqrteps = std::sqrt (std::numeric_limits<R>::epsilon ());
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506 res = higham (m, p, sqrteps, max_norm_iter, x);
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507 }
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508 else
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509 (*current_liboctave_error_handler) (p_less1_gripe);
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510
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511 return res;
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512 }
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513
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parents:
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514 // and finally, here's what we've promised in the header file
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515
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516 #define DEFINE_XNORM_FUNCS(PREFIX, RTYPE) \
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517 OCTAVE_API RTYPE xnorm (const PREFIX##ColumnVector& x, RTYPE p) \
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518 { return vector_norm (x, p); } \
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519 OCTAVE_API RTYPE xnorm (const PREFIX##RowVector& x, RTYPE p) \
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520 { return vector_norm (x, p); } \
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parents: 8309
diff changeset
521 OCTAVE_API RTYPE xnorm (const PREFIX##Matrix& x, RTYPE p) \
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522 { return matrix_norm (x, p, PREFIX##Matrix (), PREFIX##SVD ()); } \
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parents: 8309
diff changeset
523 OCTAVE_API RTYPE xfrobnorm (const PREFIX##Matrix& x) \
8303
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524 { return vector_norm (x, static_cast<RTYPE> (2)); }
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parents:
diff changeset
525
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parents:
diff changeset
526 DEFINE_XNORM_FUNCS(, double)
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parents:
diff changeset
527 DEFINE_XNORM_FUNCS(Complex, double)
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parents:
diff changeset
528 DEFINE_XNORM_FUNCS(Float, float)
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parents:
diff changeset
529 DEFINE_XNORM_FUNCS(FloatComplex, float)
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parents:
diff changeset
530
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parents:
diff changeset
531 // this is needed to avoid copying the sparse matrix for xfrobnorm
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parents:
diff changeset
532 template <class T, class R>
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parents:
diff changeset
533 inline void array_norm_2 (const T* v, octave_idx_type n, R& res)
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parents:
diff changeset
534 {
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parents:
diff changeset
535 norm_accumulator_2<R> acc;
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parents:
diff changeset
536 for (octave_idx_type i = 0; i < n; i++)
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parents:
diff changeset
537 acc.accum (v[i]);
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parents:
diff changeset
538
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parents:
diff changeset
539 res = acc;
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parents:
diff changeset
540 }
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
541
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parents:
diff changeset
542 #define DEFINE_XNORM_SPARSE_FUNCS(PREFIX, RTYPE) \
8319
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Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
543 OCTAVE_API RTYPE xnorm (const Sparse##PREFIX##Matrix& x, RTYPE p) \
8303
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parents:
diff changeset
544 { return matrix_norm (x, p, PREFIX##Matrix ()); } \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
545 OCTAVE_API RTYPE xfrobnorm (const Sparse##PREFIX##Matrix& x) \
8303
b11c31849b44 improve norm computation capabilities
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parents:
diff changeset
546 { \
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parents:
diff changeset
547 RTYPE res; \
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
548 array_norm_2 (x.data (), x.nnz (), res); \
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parents:
diff changeset
549 return res; \
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parents:
diff changeset
550 }
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parents:
diff changeset
551
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
552 DEFINE_XNORM_SPARSE_FUNCS(, double)
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
553 DEFINE_XNORM_SPARSE_FUNCS(Complex, double)
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
554
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parents:
diff changeset
555 #define DEFINE_COLROW_NORM_FUNCS(PREFIX, RPREFIX, RTYPE) \
8319
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Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
556 extern OCTAVE_API RPREFIX##RowVector xcolnorms (const PREFIX##Matrix& m, RTYPE p) \
8303
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parents:
diff changeset
557 { return column_norms (m, p); } \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
558 extern OCTAVE_API RPREFIX##ColumnVector xrownorms (const PREFIX##Matrix& m, RTYPE p) \
8303
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parents:
diff changeset
559 { return row_norms (m, p); } \
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parents:
diff changeset
560
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parents:
diff changeset
561 DEFINE_COLROW_NORM_FUNCS(, , double)
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parents:
diff changeset
562 DEFINE_COLROW_NORM_FUNCS(Complex, , double)
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
563 DEFINE_COLROW_NORM_FUNCS(Float, Float, float)
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
564 DEFINE_COLROW_NORM_FUNCS(FloatComplex, Float, float)
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
565
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
566 DEFINE_COLROW_NORM_FUNCS(Sparse, , double)
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
567 DEFINE_COLROW_NORM_FUNCS(SparseComplex, , double)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
568