From 9b33046355238f56cda18493b8c757db736516a4 Mon Sep 17 00:00:00 2001 From: Urbain Vaes Date: Thu, 21 Sep 2023 18:37:50 +0200 Subject: Add worked example --- figures/2d_difficult_V.pdf | Bin 0 -> 80747 bytes figures/2d_difficult_observable.pdf | Bin 0 -> 76025 bytes figures/2d_difficult_optimal.pdf | Bin 0 -> 89775 bytes figures/2d_difficult_poisson.pdf | Bin 0 -> 86176 bytes figures/LR-eps-converted-to.pdf | Bin 0 -> 11627 bytes figures/LR.eps | 1200 ++++++++ figures/cusp.eps | 2807 +++++++++++++++++++ figures/dux5-eps-converted-to.pdf | Bin 0 -> 8262 bytes figures/dux5.eps | 854 ++++++ figures/error_diffusion-eps-converted-to.pdf | Bin 0 -> 11765 bytes figures/error_diffusion.eps | 1049 +++++++ figures/intro_position.pdf | Bin 0 -> 131584 bytes figures/intro_velocity.pdf | Bin 0 -> 133705 bytes figures/invariant_perturbed_ol.pdf | Bin 0 -> 10048 bytes figures/mobility_Langevin-eps-converted-to.pdf | Bin 0 -> 7685 bytes figures/mobility_Langevin.eps | 836 ++++++ figures/osc_shear-eps-converted-to.pdf | Bin 0 -> 5763 bytes figures/osc_shear.eps | 552 ++++ figures/ux5-eps-converted-to.pdf | Bin 0 -> 36444 bytes figures/ux5.eps | 3557 ++++++++++++++++++++++++ 20 files changed, 10855 insertions(+) create mode 100644 figures/2d_difficult_V.pdf create mode 100644 figures/2d_difficult_observable.pdf create mode 100644 figures/2d_difficult_optimal.pdf create mode 100644 figures/2d_difficult_poisson.pdf create mode 100644 figures/LR-eps-converted-to.pdf create mode 100644 figures/LR.eps create mode 100644 figures/cusp.eps create mode 100644 figures/dux5-eps-converted-to.pdf create mode 100644 figures/dux5.eps create mode 100644 figures/error_diffusion-eps-converted-to.pdf create mode 100644 figures/error_diffusion.eps create mode 100644 figures/intro_position.pdf create mode 100644 figures/intro_velocity.pdf create mode 100644 figures/invariant_perturbed_ol.pdf create mode 100644 figures/mobility_Langevin-eps-converted-to.pdf create mode 100644 figures/mobility_Langevin.eps create mode 100644 figures/osc_shear-eps-converted-to.pdf create mode 100644 figures/osc_shear.eps create mode 100644 figures/ux5-eps-converted-to.pdf create mode 100644 figures/ux5.eps (limited to 'figures') diff --git a/figures/2d_difficult_V.pdf b/figures/2d_difficult_V.pdf new file mode 100644 index 0000000..085bde1 Binary files /dev/null and b/figures/2d_difficult_V.pdf differ diff --git a/figures/2d_difficult_observable.pdf b/figures/2d_difficult_observable.pdf new file mode 100644 index 0000000..8e256fe Binary files /dev/null and b/figures/2d_difficult_observable.pdf differ diff --git a/figures/2d_difficult_optimal.pdf b/figures/2d_difficult_optimal.pdf new file mode 100644 index 0000000..359cd34 Binary files /dev/null and b/figures/2d_difficult_optimal.pdf differ diff --git a/figures/2d_difficult_poisson.pdf b/figures/2d_difficult_poisson.pdf new file mode 100644 index 0000000..932db14 Binary files /dev/null and b/figures/2d_difficult_poisson.pdf 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stroke} def +/TriDW {stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V Opaque stroke} def +/PentW {stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + Opaque stroke grestore} def +/CircW {stroke [] 0 setdash + hpt 0 360 arc Opaque stroke} def +/BoxFill {gsave Rec 1 setgray fill grestore} def +/Density { + /Fillden exch def + currentrgbcolor + /ColB exch def /ColG exch def /ColR exch def + /ColR ColR Fillden mul Fillden sub 1 add def + /ColG ColG Fillden mul Fillden sub 1 add def + /ColB ColB Fillden mul Fillden sub 1 add def + ColR ColG ColB setrgbcolor} def +/BoxColFill {gsave Rec PolyFill} def +/PolyFill {gsave Density fill grestore grestore} def +/h {rlineto rlineto rlineto gsave closepath fill grestore} bind def +% +% PostScript Level 1 Pattern Fill routine for rectangles +% Usage: x y w h s a XX PatternFill +% x,y = lower left corner of box to be filled +% w,h = width and height of box +% a = angle in degrees between lines and x-axis +% XX = 0/1 for no/yes cross-hatch +% +/PatternFill {gsave /PFa [ 9 2 roll ] def + PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate + PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec + gsave 1 setgray fill grestore clip + currentlinewidth 0.5 mul setlinewidth + /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def + 0 0 M PFa 5 get rotate PFs -2 div dup translate + 0 1 PFs PFa 4 get div 1 add floor cvi + {PFa 4 get mul 0 M 0 PFs V} for + 0 PFa 6 get ne { + 0 1 PFs PFa 4 get div 1 add floor cvi + {PFa 4 get mul 0 2 1 roll M PFs 0 V} for + } if + stroke grestore} def +% +/languagelevel where + {pop languagelevel} {1} ifelse + 2 lt + {/InterpretLevel1 true def} + {/InterpretLevel1 Level1 def} + ifelse +% +% PostScript level 2 pattern fill definitions +% +/Level2PatternFill { +/Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} + bind def +/KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} +>> matrix makepattern +/Pat1 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke + 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} +>> matrix makepattern +/Pat2 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L + 8 8 L 8 0 L 0 0 L fill} +>> matrix makepattern +/Pat3 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L + 0 12 M 12 0 L stroke} +>> matrix makepattern +/Pat4 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L + 0 -4 M 12 8 L stroke} +>> matrix makepattern +/Pat5 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L + 0 12 M 8 -4 L 4 12 M 10 0 L stroke} +>> matrix makepattern +/Pat6 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L + 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} +>> matrix makepattern +/Pat7 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L + 12 0 M -4 8 L 12 4 M 0 10 L stroke} +>> matrix makepattern +/Pat8 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L + -4 0 M 12 8 L -4 4 M 8 10 L stroke} +>> matrix makepattern +/Pat9 exch def +/Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def +/Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def +/Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def +/Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def +/Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def +/Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def +/Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def +} def +% +% +%End of PostScript Level 2 code +% +/PatternBgnd { + TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse +} def +% +% Substitute for Level 2 pattern fill codes with +% grayscale if Level 2 support is not selected. +% +/Level1PatternFill { +/Pattern1 {0.250 Density} bind def +/Pattern2 {0.500 Density} bind def +/Pattern3 {0.750 Density} bind def +/Pattern4 {0.125 Density} bind def +/Pattern5 {0.375 Density} bind def +/Pattern6 {0.625 Density} bind def +/Pattern7 {0.875 Density} bind def +} def +% +% Now test for support of Level 2 code +% +Level1 {Level1PatternFill} {Level2PatternFill} ifelse +% +/Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont +dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall +currentdict end definefont pop +/MFshow { + { dup 5 get 3 ge + { 5 get 3 eq {gsave} {grestore} ifelse } + {dup dup 0 get findfont exch 1 get scalefont setfont + [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 + get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq + {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 + get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div + dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get + show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop + pop aload pop M} ifelse }ifelse }ifelse } + ifelse } + forall} def +/Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def +/MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } + {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont + 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def +/MLshow { currentpoint stroke M + 0 exch R + Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def +/MRshow { currentpoint stroke M + exch dup MFwidth neg 3 -1 roll R + Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def +/MCshow { currentpoint stroke M + exch dup MFwidth -2 div 3 -1 roll R + Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def +/XYsave { [( ) 1 2 true false 3 ()] } bind def +/XYrestore { [( ) 1 2 true false 4 ()] } bind def +end +%%EndProlog +gnudict begin +gsave +doclip +50 50 translate 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