Mercurial > octave
annotate libinterp/corefcn/stream-euler.cc @ 31605:e88a07dec498 stable
maint: Use macros to begin/end C++ namespaces.
* oct-conf-post-public.in.h: Define two macros (OCTAVE_BEGIN_NAMESPACE,
OCTAVE_END_NAMESPACE) that can be used to start/end a namespace.
* mk-opts.pl, build-env.h, build-env.in.cc, __betainc__.cc, __contourc__.cc,
__dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc,
__ichol__.cc, __ilu__.cc, __isprimelarge__.cc, __lin_interpn__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, auto-shlib.cc,
auto-shlib.h, balance.cc, base-text-renderer.cc, base-text-renderer.h,
besselj.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
call-stack.cc, call-stack.h, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc,
colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc,
defaults.cc, defaults.h, defun-int.h, defun.cc, det.cc, dirfns.cc, display.cc,
display.h, dlmread.cc, dmperm.cc, dot.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc,
ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.h,
event-manager.cc, event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc,
fcn-info.h, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
ft-text-renderer.cc, ft-text-renderer.h, gcd.cc, getgrent.cc, getpwent.cc,
getrusage.cc, givens.cc, gl-render.cc, gl-render.h, gl2ps-print.cc,
gl2ps-print.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc,
graphics.in.h, gsvd.cc, gtk-manager.cc, gtk-manager.h, hash.cc, help.cc,
help.h, hess.cc, hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h,
interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h,
inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, latex-text-renderer.cc,
latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h,
lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-oct-text.cc, ls-utils.cc,
ls-utils.h, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex-private.h,
mex.cc, mgorth.cc, nproc.cc, oct-fstrm.cc, oct-fstrm.h, oct-hdf5-types.cc,
oct-hdf5-types.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h,
oct-opengl.h, oct-prcstrm.cc, oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h,
oct-process.cc, oct-process.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h,
oct-strstrm.cc, oct-strstrm.h, oct-tex-lexer.in.ll, oct-tex-parser.yy,
ordqz.cc, ordschur.cc, pager.cc, pager.h, pinv.cc, pow2.cc, pr-flt-fmt.cc,
pr-output.cc, procstream.cc, procstream.h, psi.cc, qr.cc, quad.cc, quadcc.cc,
qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, settings.h,
sighandlers.cc, sighandlers.h, sparse-xdiv.cc, sparse-xdiv.h, sparse-xpow.cc,
sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc, stack-frame.cc, stack-frame.h,
stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc,
symbfact.cc, syminfo.cc, syminfo.h, symrcm.cc, symrec.cc, symrec.h,
symscope.cc, symscope.h, symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h,
text-engine.cc, text-engine.h, text-renderer.cc, text-renderer.h, time.cc,
toplev.cc, tril.cc, tsearch.cc, typecast.cc, url-handle-manager.cc,
url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc,
variables.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc, xpow.h,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, mk-build-env-features.sh,
mk-builtins.pl, cdef-class.cc, cdef-class.h, cdef-fwd.h, cdef-manager.cc,
cdef-manager.h, cdef-method.cc, cdef-method.h, cdef-object.cc, cdef-object.h,
cdef-package.cc, cdef-package.h, cdef-property.cc, cdef-property.h,
cdef-utils.cc, cdef-utils.h, ov-base.cc, ov-base.h, ov-bool-mat.cc,
ov-builtin.h, ov-cell.cc, ov-class.cc, ov-class.h, ov-classdef.cc,
ov-classdef.h, ov-complex.cc, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.h,
ov-java.cc, ov-java.h, ov-mex-fcn.h, ov-null-mat.cc, ov-oncleanup.cc,
ov-struct.cc, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h,
ov.cc, ov.h, octave.cc, octave.h, mk-ops.sh, op-b-b.cc, op-b-bm.cc,
op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc,
op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc,
op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-fcdm-fcdm.cc, op-fcm-fcm.cc,
op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc, op-fcs-fcm.cc,
op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fdm.cc, op-fm-fcm.cc,
op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc,
op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc,
op-i8-i8.cc, op-int-concat.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc,
op-m-scm.cc, op-m-sm.cc, op-mi.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc,
op-pm-template.cc, op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc,
op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc,
op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc,
op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc,
op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc,
op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, ops.h,
anon-fcn-validator.cc, anon-fcn-validator.h, bp-table.cc, bp-table.h,
comment-list.cc, comment-list.h, filepos.h, lex.h, lex.ll, oct-lvalue.cc,
oct-lvalue.h, oct-parse.yy, parse.h, profiler.cc, profiler.h,
pt-anon-scopes.cc, pt-anon-scopes.h, pt-arg-list.cc, pt-arg-list.h,
pt-args-block.cc, pt-args-block.h, pt-array-list.cc, pt-array-list.h,
pt-assign.cc, pt-assign.h, pt-binop.cc, pt-binop.h, pt-bp.cc, pt-bp.h,
pt-cbinop.cc, pt-cbinop.h, pt-cell.cc, pt-cell.h, pt-check.cc, pt-check.h,
pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc,
pt-const.h, pt-decl.cc, pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc,
pt-except.h, pt-exp.cc, pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-id.cc,
pt-id.h, pt-idx.cc, pt-idx.h, pt-jump.h, pt-loop.cc, pt-loop.h, pt-mat.cc,
pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc, pt-pr-code.h, pt-select.cc,
pt-select.h, pt-spmd.cc, pt-spmd.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc,
pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-vm-eval.cc, pt-walk.cc, pt-walk.h,
pt.cc, pt.h, token.cc, token.h, Range.cc, Range.h, idx-vector.cc, idx-vector.h,
range-fwd.h, CollocWt.cc, CollocWt.h, aepbalance.cc, aepbalance.h, chol.cc,
chol.h, gepbalance.cc, gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h,
lo-mappers.cc, lo-mappers.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h,
oct-convn.cc, oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h,
oct-rand.cc, oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc,
qrp.h, randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc,
randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h, sparse-lu.cc,
sparse-lu.h, sparse-qr.cc, sparse-qr.h, svd.cc, svd.h, child-list.cc,
child-list.h, dir-ops.cc, dir-ops.h, file-ops.cc, file-ops.h, file-stat.cc,
file-stat.h, lo-sysdep.cc, lo-sysdep.h, lo-sysinfo.cc, lo-sysinfo.h,
mach-info.cc, mach-info.h, oct-env.cc, oct-env.h, oct-group.cc, oct-group.h,
oct-password.cc, oct-password.h, oct-syscalls.cc, oct-syscalls.h, oct-time.cc,
oct-time.h, oct-uname.cc, oct-uname.h, action-container.cc, action-container.h,
base-list.h, cmd-edit.cc, cmd-edit.h, cmd-hist.cc, cmd-hist.h, f77-fcn.h,
file-info.cc, file-info.h, lo-array-errwarn.cc, lo-array-errwarn.h, lo-hash.cc,
lo-hash.h, lo-ieee.h, lo-regexp.cc, lo-regexp.h, lo-utils.cc, lo-utils.h,
oct-base64.cc, oct-base64.h, oct-glob.cc, oct-glob.h, oct-inttypes.h,
oct-mutex.cc, oct-mutex.h, oct-refcount.h, oct-shlib.cc, oct-shlib.h,
oct-sparse.cc, oct-sparse.h, oct-string.h, octave-preserve-stream-state.h,
pathsearch.cc, pathsearch.h, quit.cc, quit.h, unwind-prot.cc, unwind-prot.h,
url-transfer.cc, url-transfer.h : Use new macros to begin/end C++ namespaces.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 01 Dec 2022 14:23:45 -0800 |
parents | a3d8915b9f87 |
children | aac27ad79be6 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 2019-2022 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
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25 |
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26 /* |
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27 |
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28 References: |
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29 |
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30 @article{ |
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31 title = {Particle Tracing Algorithms for 3D Curvilinear Grids}, |
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32 year = {2000}, |
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33 author = {Nielson, Gregory and Uller, H. and Sadarjoen, I. and Walsum, Theo and Hin, Andrea and Post, Frits} |
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34 } |
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35 |
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36 @article{ |
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37 title = {Sources of error in the graphical analysis of CFD results}, |
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38 publisher = {Journal of Scientific Computing}, |
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39 year = {1988}, |
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40 volume = {3}, |
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41 number = {2}, |
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42 pages = {149--164}, |
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43 author = {Buning, Pieter G.}, |
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44 } |
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45 |
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46 */ |
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47 |
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48 #if defined (HAVE_CONFIG_H) |
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49 # include "config.h" |
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50 #endif |
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51 |
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52 #include "defun.h" |
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53 #include "error.h" |
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54 #include "ovl.h" |
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55 |
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56 OCTAVE_BEGIN_NAMESPACE(octave) |
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57 |
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58 // Coordinates of a point in C-Space (unit square mesh) |
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59 |
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60 struct Vector2 |
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61 { |
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62 double x, y; |
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63 }; |
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64 |
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65 // The integer value and the fractional value from a point in C-Space. |
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66 // Equivalent to the cell index the point is located in and the local |
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67 // coordinates of the point in the cell. |
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68 |
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69 struct Cell2 |
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70 { |
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71 double fcx, fcy; |
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72 signed long idx, idy; |
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73 }; |
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74 |
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75 struct Vector3 |
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76 { |
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77 double x, y, z; |
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78 }; |
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79 |
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80 struct Cell3 |
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81 { |
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82 double fcx, fcy, fcz; |
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83 signed long idx, idy, idz; |
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84 }; |
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85 |
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86 static inline void |
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87 number_to_fractional (signed long *id, double *fc, const double u) |
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88 { |
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89 *id = floor (u); |
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90 *fc = u - *id; |
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91 } |
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92 |
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93 static inline octave_idx_type |
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94 handle_border_index (const octave_idx_type id, const octave_idx_type N) |
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95 { |
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96 return (id < N - 1 ? id : N - 2); |
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97 } |
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98 |
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99 static inline void |
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100 handle_border (octave_idx_type *id2, double *fc2, const octave_idx_type id1, |
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101 const double fc1, const octave_idx_type N) |
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102 { |
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103 if (id1 < N - 1) |
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104 { |
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105 *id2 = id1; |
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106 *fc2 = fc1; |
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107 } |
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108 else |
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109 { |
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110 *id2 = N - 2; |
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111 *fc2 = 1.0; |
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112 } |
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113 } |
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114 |
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115 static inline double |
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116 bilinear (const double u11, const double u21, const double u12, |
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117 const double u22, const double x, const double y) |
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118 { |
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119 return (u11 * (1-x) * (1-y) + |
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120 u21 * x * (1-y) + |
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121 u12 * (1-x) * y + |
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122 u22 * x * y); |
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123 } |
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124 |
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125 static inline Cell2 |
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126 vector_to_cell2d (const Vector2 X) |
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127 { |
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128 Cell2 Z; |
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129 |
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130 number_to_fractional (&Z.idx, &Z.fcx, X.x); |
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131 number_to_fractional (&Z.idy, &Z.fcy, X.y); |
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132 |
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133 return (Z); |
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134 } |
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135 |
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136 static inline bool |
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137 is_in_definition_set2d (const Cell2 X, const octave_idx_type cols, |
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138 const octave_idx_type rows) |
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139 { |
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140 return ( (((X.idx >= 0) && (X.idx < cols-1)) || |
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141 ((X.idx == cols-1) && (X.fcx == 0.0))) && |
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142 (((X.idy >= 0) && (X.idy < rows-1)) || |
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143 ((X.idy == rows-1) && (X.fcy == 0.0))) ); |
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144 } |
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145 |
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146 static inline Vector2 |
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147 add2d (const Cell2 X, const Vector2 Y) |
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148 { |
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149 Vector2 Z = {X.idx + X.fcx + Y.x, |
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150 X.idy + X.fcy + Y.y}; |
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151 |
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152 return (Z); |
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153 } |
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154 |
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155 static inline Vector2 |
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156 vector_interpolation2d (const Cell2 X, const Matrix& u, const Matrix& v, |
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157 const octave_idx_type cols, const octave_idx_type rows) |
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158 { |
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159 Vector2 V; |
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160 double fcx, fcy; |
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161 octave_idx_type idx, idy; |
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162 |
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163 handle_border (&idx, &fcx, X.idx, X.fcx, cols); |
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164 handle_border (&idy, &fcy, X.idy, X.fcy, rows); |
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165 |
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166 V.x = bilinear (u(idy, idx), u(idy, idx+1), u(idy+1, idx), |
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167 u(idy+1, idx+1), fcx, fcy); |
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168 V.y = bilinear (v(idy, idx), v(idy, idx+1), v(idy+1, idx), |
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169 v(idy+1, idx+1), fcx, fcy); |
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170 |
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171 return (V); |
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172 } |
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173 |
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174 // Apply the Jacobian matrix on the vector V. |
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175 // The step vector length is set to h. |
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176 |
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177 static inline Vector2 |
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178 calculate_step_vector2d (const Cell2 X, const Vector2 V, |
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179 const RowVector& tx, const RowVector& ty, |
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180 const octave_idx_type cols, const octave_idx_type rows, |
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181 const double h) |
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182 { |
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183 Vector2 S; |
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184 |
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185 const octave_idx_type idx = handle_border_index (X.idx, cols); |
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186 const octave_idx_type idy = handle_border_index (X.idy, rows); |
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187 |
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188 const double x = V.x * tx(idx); |
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189 const double y = V.y * ty(idy); |
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190 const double n = 1.0 / sqrt (x*x + y*y); |
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191 S.x = h * n * x; |
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192 S.y = h * n * y; |
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193 |
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194 return (S); |
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195 } |
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196 |
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197 static inline bool |
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198 is_singular2d (const Vector2 V) |
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199 { |
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200 return ((math::isnan (V.x) || math::isnan (V.y)) || |
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201 ((V.x == 0) && (V.y == 0))); |
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202 } |
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203 |
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204 static void |
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205 euler2d (const octave_idx_type cols, const octave_idx_type rows, |
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206 const Matrix& u, const Matrix& v, |
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207 const RowVector& tx, const RowVector& ty, |
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208 const double zeta, const double xi, |
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209 const double h, const octave_idx_type maxnverts, |
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210 Matrix& buffer, octave_idx_type *nverts) |
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211 { |
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212 Vector2 V0, V1, S0, X1, Xnxt, S1; |
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213 const Vector2 X0 = {zeta, xi}; |
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214 Cell2 X0f, X1f; |
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215 |
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216 octave_idx_type i = 0; |
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217 |
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218 buffer(i, 0) = X0.x; |
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219 buffer(i, 1) = X0.y; |
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220 |
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221 X0f = vector_to_cell2d (X0); |
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222 while (true) |
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223 { |
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224 if (! is_in_definition_set2d (X0f, cols, rows)) |
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225 break; |
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226 |
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227 V0 = vector_interpolation2d (X0f, u, v, cols, rows); |
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228 if (is_singular2d (V0)) |
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229 break; |
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230 |
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231 S0 = calculate_step_vector2d (X0f, V0, tx, ty, cols, rows, h); |
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232 |
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233 X1 = add2d (X0f, S0); |
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234 X1f = vector_to_cell2d (X1); |
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235 if (! is_in_definition_set2d (X1f, cols, rows)) |
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236 break; |
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237 |
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238 V1 = vector_interpolation2d (X1f, u, v, cols, rows); |
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239 if (is_singular2d (V1)) |
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240 break; |
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241 |
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242 S1 = calculate_step_vector2d (X1f, V1, tx, ty, cols, rows, h); |
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243 |
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244 // Runge Kutta - Heun's Scheme |
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245 const Vector2 S = {0.5 * (S0.x + S1.x), |
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246 0.5 * (S0.y + S1.y)}; |
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247 Xnxt = add2d (X0f, S); |
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248 |
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249 X0f = vector_to_cell2d (Xnxt); |
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250 if (! is_in_definition_set2d (X0f, cols, rows)) |
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251 break; |
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252 |
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253 i++; |
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254 buffer(i, 0) = Xnxt.x; |
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255 buffer(i, 1) = Xnxt.y; |
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256 |
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257 if (i + 1 >= maxnverts) |
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258 break; |
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259 } |
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260 |
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261 *nverts = i + 1; |
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262 } |
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263 |
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264 static inline double |
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265 trilinear (const double u111, const double u211, const double u121, |
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266 const double u221, const double u112, const double u212, |
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267 const double u122, const double u222, |
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268 const double x, const double y, const double z) |
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269 { |
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270 return (u111 * (1-x) * (1-y) * (1-z) + |
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271 u211 * x * (1-y) * (1-z) + |
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272 u121 * (1-x) * y * (1-z) + |
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273 u221 * x * y * (1-z) + |
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274 u112 * (1-x) * (1-y) * z + |
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275 u212 * x * (1-y) * z + |
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276 u122 * (1-x) * y * z + |
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277 u222 * x * y * z); |
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278 } |
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279 |
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280 static inline Cell3 |
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281 vector_to_cell3d (const Vector3 X) |
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282 { |
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283 Cell3 Z; |
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284 |
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285 number_to_fractional (&Z.idx, &Z.fcx, X.x); |
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286 number_to_fractional (&Z.idy, &Z.fcy, X.y); |
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287 number_to_fractional (&Z.idz, &Z.fcz, X.z); |
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288 |
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289 return (Z); |
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290 } |
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291 |
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292 static inline bool |
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293 is_in_definition_set3d (const Cell3 X, const octave_idx_type nx, |
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294 const octave_idx_type ny, const octave_idx_type nz) |
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295 { |
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296 return ( (((X.idx >= 0) && (X.idx < nx-1)) || |
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297 ((X.idx == nx-1) && (X.fcx == 0.0))) && |
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298 (((X.idy >= 0) && (X.idy < ny-1)) || |
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299 ((X.idy == ny-1) && (X.fcy == 0.0))) && |
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300 (((X.idz >= 0) && (X.idz < nz-1)) || |
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301 ((X.idz == nz-1) && (X.fcz == 0.0))) ); |
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302 } |
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303 |
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304 static inline Vector3 |
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305 add3d (const Cell3 X, const Vector3 Y) |
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306 { |
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307 Vector3 Z = {X.idx + X.fcx + Y.x, |
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308 X.idy + X.fcy + Y.y, |
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309 X.idz + X.fcz + Y.z}; |
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310 |
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311 return (Z); |
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312 } |
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313 |
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314 static inline Vector3 |
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315 vector_interpolation3d (const Cell3 X, const NDArray& u, const NDArray& v, |
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316 const NDArray& w, const octave_idx_type nx, |
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317 const octave_idx_type ny, const octave_idx_type nz) |
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318 { |
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319 Vector3 V; |
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320 double fcx, fcy, fcz; |
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321 octave_idx_type idx, idy, idz; |
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322 |
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323 handle_border (&idx, &fcx, X.idx, X.fcx, nx); |
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324 handle_border (&idy, &fcy, X.idy, X.fcy, ny); |
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325 handle_border (&idz, &fcz, X.idz, X.fcz, nz); |
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326 |
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327 V.x = trilinear (u(idy, idx, idz), u(idy, idx+1, idz), |
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328 u(idy+1, idx, idz), u(idy+1, idx+1, idz), |
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329 u(idy, idx, idz+1), u(idy, idx+1, idz+1), |
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330 u(idy+1, idx, idz+1), u(idy+1, idx+1, idz+1), |
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331 fcx, fcy, fcz); |
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332 V.y = trilinear (v(idy, idx, idz), v(idy, idx+1, idz), |
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333 v(idy+1, idx, idz), v(idy+1, idx+1, idz), |
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334 v(idy, idx, idz+1), v(idy, idx+1, idz+1), |
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335 v(idy+1, idx, idz+1), v(idy+1, idx+1, idz+1), |
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336 fcx, fcy, fcz); |
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337 V.z = trilinear (w(idy, idx, idz), w(idy, idx+1, idz), |
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338 w(idy+1, idx, idz), w(idy+1, idx+1, idz), |
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339 w(idy, idx, idz+1), w(idy, idx+1, idz+1), |
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340 w(idy+1, idx, idz+1), w(idy+1, idx+1, idz+1), |
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341 fcx, fcy, fcz); |
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342 |
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343 return (V); |
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344 } |
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345 |
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346 static inline Vector3 |
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347 calculate_step_vector3d (const Cell3 X, const Vector3 V, |
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348 const RowVector& tx, const RowVector& ty, const RowVector& tz, |
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349 const octave_idx_type nx, const octave_idx_type ny, |
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350 const octave_idx_type nz, const double h) |
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351 { |
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352 Vector3 S; |
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353 |
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354 const octave_idx_type idx = handle_border_index (X.idx, nx); |
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355 const octave_idx_type idy = handle_border_index (X.idy, ny); |
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356 const octave_idx_type idz = handle_border_index (X.idz, nz); |
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357 |
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358 const double x = V.x * tx(idx); |
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359 const double y = V.y * ty(idy); |
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360 const double z = V.z * tz(idz); |
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361 const double n = 1.0 / sqrt (x*x + y*y + z*z); |
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362 S.x = h * n * x; |
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363 S.y = h * n * y; |
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364 S.z = h * n * z; |
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365 |
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366 return (S); |
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367 } |
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368 |
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369 static inline bool |
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370 is_singular3d (const Vector3 V) |
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371 { |
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372 return ((math::isnan (V.x) || math::isnan (V.y) || math::isnan (V.z)) || |
27759
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373 ((V.x == 0) && (V.y == 0) && (V.z == 0))); |
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374 } |
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375 |
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376 static void |
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377 euler3d (const octave_idx_type nx, const octave_idx_type ny, const octave_idx_type nz, |
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378 const NDArray& u, const NDArray& v, const NDArray& w, |
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379 const RowVector& tx, const RowVector& ty, const RowVector& tz, |
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380 const double zeta, const double xi, const double rho, |
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381 const double h, const octave_idx_type maxnverts, |
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382 Matrix& buffer, octave_idx_type *nverts) |
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383 { |
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384 Vector3 V0, V1, S0, X1, Xnxt, S1; |
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385 const Vector3 X0 = {zeta, xi, rho}; |
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386 Cell3 X0f, X1f; |
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387 |
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388 octave_idx_type i = 0; |
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389 buffer(i, 0) = X0.x; |
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390 buffer(i, 1) = X0.y; |
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391 buffer(i, 2) = X0.z; |
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392 |
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393 X0f = vector_to_cell3d (X0); |
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394 while (true) |
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395 { |
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396 if (! is_in_definition_set3d (X0f, nx, ny, nz)) |
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397 break; |
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398 |
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399 V0 = vector_interpolation3d (X0f, u, v, w, nx, ny, nz); |
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400 if (is_singular3d (V0)) |
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401 break; |
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402 |
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403 S0 = calculate_step_vector3d (X0f, V0, tx, ty, tz, nx, ny, nz, h); |
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404 |
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405 X1 = add3d (X0f, S0); |
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406 |
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407 X1f = vector_to_cell3d (X1); |
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408 if (! is_in_definition_set3d (X1f, nx, ny, nz)) |
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409 break; |
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410 |
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411 V1 = vector_interpolation3d (X1f, u, v, w, nx, ny, nz); |
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412 if (is_singular3d (V1)) |
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413 break; |
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414 |
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415 S1 = calculate_step_vector3d (X1f, V1, tx, ty, tz, nx, ny, nz, h); |
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416 |
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417 // Runge Kutta - Heun's Scheme |
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418 const Vector3 S = {0.5 * (S0.x + S1.x), |
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419 0.5 * (S0.y + S1.y), |
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420 0.5 * (S0.z + S1.z)}; |
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421 Xnxt = add3d (X0f, S); |
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422 |
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423 X0f = vector_to_cell3d (Xnxt); |
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424 if (! is_in_definition_set3d (X0f, nx, ny, nz)) |
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425 break; |
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426 |
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427 i++; |
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428 buffer(i, 0) = Xnxt.x; |
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429 buffer(i, 1) = Xnxt.y; |
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430 buffer(i, 2) = Xnxt.z; |
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|
431 |
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432 if (i + 1 >= maxnverts) |
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|
433 break; |
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|
434 |
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|
435 } |
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436 |
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437 *nverts = i + 1; |
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438 } |
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439 |
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440 static octave_value |
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441 streameuler2d_internal (const octave_value_list& args) |
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442 { |
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443 |
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444 const int nargin = args.length (); |
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445 if (nargin != 8) |
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446 print_usage (); |
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447 |
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448 const Matrix U = args(0).matrix_value (); |
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449 const Matrix V = args(1).matrix_value (); |
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450 const RowVector TX = args(2).row_vector_value (); |
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451 const RowVector TY = args(3).row_vector_value (); |
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452 const double zeta = args(4).double_value (); |
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453 const double xi = args(5).double_value (); |
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454 const double h = args(6).double_value (); |
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455 const octave_idx_type maxnverts = args(7).idx_type_value (); |
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456 |
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457 const octave_idx_type rows = U.rows (); |
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458 const octave_idx_type cols = U.columns (); |
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459 |
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460 octave_idx_type nverts; |
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461 Matrix buffer (maxnverts, 2); |
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462 |
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463 euler2d (cols, rows, U, V, TX, TY, zeta, xi, h, maxnverts, |
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464 buffer, &nverts); |
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465 |
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466 Matrix xy = buffer.extract (0, 0, nverts-1, 1); |
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467 |
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468 return octave_value (xy); |
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469 } |
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470 |
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471 static octave_value |
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472 streameuler3d_internal (const octave_value_list& args, const char *fcn) |
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473 { |
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474 |
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475 const int nargin = args.length (); |
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476 if (nargin != 11) |
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477 print_usage (); |
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478 |
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479 const NDArray U = args(0).array_value (); |
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480 const NDArray V = args(1).array_value (); |
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481 const NDArray W = args(2).array_value (); |
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482 const RowVector TX = args(3).row_vector_value (); |
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483 const RowVector TY = args(4).row_vector_value (); |
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484 const RowVector TZ = args(5).row_vector_value (); |
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485 const double zeta = args(6).double_value (); |
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486 const double xi = args(7).double_value (); |
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487 const double rho = args(8).double_value (); |
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488 const double h = args(9).double_value (); |
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489 const octave_idx_type maxnverts = args(10).idx_type_value (); |
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490 |
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491 const dim_vector dims = args(0).dims (); |
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492 const int ndims = dims.ndims (); |
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493 if (ndims != 3) |
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494 error ("%s: dimension must be 3", fcn); |
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495 |
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496 octave_idx_type nverts; |
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497 Matrix buffer (maxnverts, 3); |
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498 |
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499 euler3d (dims(1), dims(0), dims(2), U, V, W, TX, TY, TZ, zeta, xi, rho, |
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500 h, maxnverts, buffer, &nverts); |
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501 |
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502 Matrix xyz = buffer.extract (0, 0, nverts-1, 2); |
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503 |
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504 return octave_value (xyz); |
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|
505 } |
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|
506 |
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507 DEFUN (__streameuler2d__, args, , |
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508 doc: /* -*- texinfo -*- |
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509 @deftypefn {} {@var{output} =} __streameuler2d__ (@var{U}, @var{V}, @var{TX}, @var{TY}, @var{ZETA}, @var{XI}, @var{H}, @var{MAXNVERTS}) |
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510 Calculate the streamline in a vector field @code{[@var{U}, @var{V}]} starting |
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|
511 from a seed point at position @code{[@var{ZETA}, @var{XI}]}. The integrator |
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512 used is Heun's Scheme. The step size can be controlled by @var{H}. The |
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|
513 Jacobian matrix can be defined for each grid cell by |
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|
514 @code{[@var{TX}, @var{TY}]}. |
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|
515 |
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516 @seealso{streamline, stream2, stream3, __streameuler3d__} |
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517 @end deftypefn */) |
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|
518 { |
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519 return streameuler2d_internal (args); |
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|
520 } |
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|
521 |
27808
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|
522 DEFUN (__streameuler3d__, args, , |
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|
523 doc: /* -*- texinfo -*- |
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|
524 @deftypefn {} {@var{output} =} __streameuler3d__ (@var{U}, @var{V}, @var{W}, @var{TX}, @var{TY}, @var{TZ}, @var{ZETA}, @var{XI}, @var{RHO}, @var{H}, @var{MAXNVERTS}) |
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|
525 Calculate the streamline in a vector field @code{[@var{U}, @var{V}, @var{W}]} |
27810
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|
526 starting from a seed point at position |
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|
527 @code{[@var{ZETA}, @var{XI}, @var{RHO}]}. The integrator used is Heun's |
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overhaul streamXXX.m series of functions.
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parents:
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diff
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|
528 Scheme. The step size can be controlled by @var{H}. The Jacobian matrix can |
f2b89a2e20b6
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|
529 be defined for each grid cell by @code{[@var{TX}, @var{TY}, @var{TZ}]}. |
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|
530 |
27808
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|
531 @seealso{streamline, stream2, stream3, __streameuler2d__} |
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|
532 @end deftypefn */) |
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|
533 { |
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|
534 return streameuler3d_internal (args, "__streameuler3d__"); |
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|
535 } |
992e702ef0d7
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diff
changeset
|
536 |
31605
e88a07dec498
maint: Use macros to begin/end C++ namespaces.
Rik <rik@octave.org>
parents:
31594
diff
changeset
|
537 OCTAVE_END_NAMESPACE(octave) |