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MatrixTimesMatrix-j.eps
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MatrixTimesMatrix-j.eps
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%%Title: (Illustrations-j)
%%Creator: (PowerPoint: cgpdftops CUPS filter)
%%CreationDate: (Saturday, August 13 2022 12:39:12 JST)
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counttomark 2 idiv
%dup (number of ld's = )print == flush % *** how many
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/W{clip newpath}bd
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pop pop pop % pop off the search results
true
}{
pop % previous search result
(hp) anchorsearch{
pop pop true
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{
{ % charCode Wx Wy
pop pop % charCode
(0)dup 0 4 -1 roll put
F charpath
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}
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{
pop
<<
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<< /ImageType 1
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currentdict/Interpolate known
{/Interpolate Interpolate}if
>>
>>
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{imagemask}{image}ifelse
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/t_array 0 def
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/t_c 1 string def
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exch t_array t_i get add exch moveto
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t_array t_i get add moveto
/t_i t_i 1 add store
}bd
/xy_proc{
% x y
t_array t_i 2 copy 1 add get 3 1 roll get
4 -1 roll add 3 1 roll add moveto
/t_i t_i 2 add store
}bd
/sop 0 def % don't bind sop
/cp_proc/x_proc ld % default moveto proc is for xwidths only
/base_charpath % string array
{
/t_array xs
/t_i 0 def
{ % char
t_c 0 3 -1 roll put
currentpoint
t_c cply sop
cp_proc
}forall
/t_array 0 def
}bd
/sop/stroke ld % default sop is stroke. Done here so we don't bind in /base_charpath
% default sop is stroke
/nop{}def
/xsp/base_charpath ld
/ysp{/cp_proc/y_proc ld base_charpath/cp_proc/x_proc ld}bd
/xysp{/cp_proc/xy_proc ld base_charpath/cp_proc/x_proc ld}bd
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/refnt{ % newname encoding fontname
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/Encoding 4 -1 roll put
definefont pop
}bd
/renmfont{ % newname fontname
findfont dup length dict copy definefont pop
}bd
L3? dup dup{save exch}if
% languagelevel2 ONLY code goes here
/Range 0 def
/DataSource 0 def
/val 0 def
/nRange 0 def
/mulRange 0 def
/d0 0 def
/r0 0 def
/di 0 def
/ri 0 def
/a0 0 def
/a1 0 def
/r1 0 def
/r2 0 def
/dx 0 def
/Nsteps 0 def
/sh3tp 0 def
/ymax 0 def
/ymin 0 def
/xmax 0 def
/xmin 0 def
/setupFunEval % funDict -- % this calculates and sets up a function dict for evaulation.
{
begin
/nRange Range length 2 idiv store
/mulRange % precompute the range data needed to map a sample value from the table to a range value
% this data looks like [ range0mul range0min range1mul range1min ... rangeN-1mul rangeN-1min ]
[
0 1 nRange 1 sub
{ % index
2 mul/nDim2 xd % 2*dimension# we are dealing with
Range nDim2 get % ymin
Range nDim2 1 add get % ymin ymax
1 index sub % ymin (ymax-ymin)
% xmin = 0, xmax = 255 (2^bitspersample - 1)
255 div % ymin (ymax-ymin)/(xmax - xmin)
exch % (ymax-ymin)/(xmax - xmin) ymin
}for
]store
end
}bd
/FunEval % val1 fundict -> comp1 comp2 ... compN
{
begin
% the value passed in is the base index into the table
nRange mul /val xd % compute the actual index to the table
% since there are nRange entries per base index
0 1 nRange 1 sub
{
dup 2 mul/nDim2 xd % dim
val % base value to use to do our lookup
add DataSource exch get % lookedupval
mulRange nDim2 get mul % lookedupval*(ymax-ymin)/(xmax-xmin)
mulRange nDim2 1 add get % lookedupval*(ymax-ymin)/(xmax-xmin) ymin
add % interpolated result
}for % comp1 comp2 ... compN
end
}bd
/max % a b -> max(a, b)
{
2 copy lt
{exch pop}{pop}ifelse
}bd
/sh2
{ % emulation of shading type 2. Assumes shading dictionary is top dictionary on the dict stack
/Coords load aload pop % x0 y0 x1 y1
3 index 3 index translate % origin is now at beginning point of shading
% x0 y0 x1 y1
3 -1 roll sub % x0 x1 y1-y0
3 1 roll exch % y1-y0 x1 x0
sub % y1-y0 x1-x0
2 copy
dup mul exch dup mul add sqrt % length of segment between two points
dup
scale
atan % atan (dy/dx)
%dup (rotation angle = )print ==
rotate % now line between 0,0 and 1,0 is the line perpendicular to which the axial lines are drawn
/Function load setupFunEval % may need to setup function dictionary by calling setupFunEval
% this is now specific to axial shadings. Compute the maximum bounds to fill
clippath {pathbbox}stopped {0 0 0 0}if newpath % x0 y0 x1 y1
/ymax xs
/xmax xs
/ymin xs
/xmin xs
currentdict/Extend known
{
/Extend load 0 get
{
0/Function load FunEval sc % evaluate the function to get a color and set it
xmin ymin xmin abs ymax ymin sub rectfill
}if
}if
% paint the rects. The sampling frequency is that of our table
/Nsteps/Function load/Size get 0 get 1 sub store
/dx 1 Nsteps div store
gsave
/di ymax ymin sub store
/Function load
% loop Nsteps + 1 times, incrementing the index by 1 each time
0 1 Nsteps
{
1 index FunEval sc
0 ymin dx di rectfill
dx 0 translate
}for
pop % pop our function
grestore % origin is back to start point
currentdict/Extend known
{
/Extend load 1 get
{
Nsteps/Function load FunEval sc % last element
1 ymin xmax 1 sub abs ymax ymin sub rectfill
}if
}if
}bd
/shp % this paints our shape for shading type 3
{ % x1 r1 x0 r0 -
4 copy
% fill interior arc
dup 0 gt{
0 exch a1 a0 arc
}{
pop 0 moveto
}ifelse
dup 0 gt{
0 exch a0 a1 arcn
}{
pop 0 lineto
}ifelse
fill
% fill exterior arc
dup 0 gt{
0 exch a0 a1 arc
}{
pop 0 moveto
}ifelse
dup 0 gt{
0 exch a1 a0 arcn
}{
pop 0 lineto
}ifelse
fill
}bd
/calcmaxs
{ % calculate maximum distance vector from origin to corner points
% of bbox
xmin dup mul ymin dup mul add sqrt % (xmin2 + ymin2)
xmax dup mul ymin dup mul add sqrt % (xmax2 + ymin2)
xmin dup mul ymax dup mul add sqrt % (xmin2 + ymax2)
xmax dup mul ymax dup mul add sqrt % (xmax2 + ymax2)
max max max % maximum value
}bd
/sh3
{ % emulation of shading type 3. Assumes shading dictionary is top dictionary on the dict stack
/Coords load aload pop % x0 y0 r1 x1 y1 r2
5 index 5 index translate % origin is now at first circle origin
3 -1 roll 6 -1 roll sub % y0 r1 y1 r2 dx
3 -1 roll 5 -1 roll sub % r1 r2 dx dy
2 copy dup mul exch dup mul add sqrt
/dx xs % r1 r2 dx dy
2 copy 0 ne exch 0 ne or
{
% r1 r2 dx dy
exch atan rotate % we are now rotated so dy is zero and positive values of dx move us as expected
}{
pop pop
}ifelse
% r1 r2
/r2 xs
/r1 xs
/Function load
dup/Size get 0 get 1 sub % this is the size of our table minus 1
/Nsteps xs % at some point we should optimize this better so NSteps is based on needed steps for the device
setupFunEval % may need to setup function dictionary by calling setupFunEval
% determine the case:
% case 0: circle1 inside circle2
% case 1: circle 2 inside circle 1
% case 2: r1 = r2
% case 3: r1 != r2
dx r2 add r1 lt{
% circle 2 inside of circle 1
0
}{
dx r1 add r2 le
{ % circle 1 inside of circle 2
1
}{ % circles don't contain each other
r1 r2 eq
{ % equal
2
}{ % r1 != r2
3
}ifelse
}ifelse
}ifelse
/sh3tp xs % sh3tp has the number of our different cases
clippath {pathbbox}stopped {0 0 0 0}if
newpath % x0 y0 x1 y1
/ymax xs
/xmax xs
/ymin xs
/xmin xs
% Arc angle atan( sqrt((dx*dx + dy*dy) - dr*dr), dr)
dx dup mul r2 r1 sub dup mul sub dup 0 gt
{
sqrt r2 r1 sub atan
/a0 exch 180 exch sub store
/a1 a0 neg store
}{
pop
/a0 0 store
/a1 360 store
}ifelse
currentdict/Extend known
{
/Extend load 0 get r1 0 gt and % no need to extend if the radius of the first end is 0
{
0/Function load FunEval sc % evaluate the function to get a color and set it
% case 0: circle1 inside circle2
% case 1: circle 2 inside circle 1
% case 2: circles don't contain each other and r1 == r2
% case 3: circles don't contain each other and r1 != r2
{
{ % case 0
dx 0 r1 360 0 arcn
xmin ymin moveto
xmax ymin lineto
xmax ymax lineto
xmin ymax lineto
xmin ymin lineto
eofill % for the bigger radius we fill everything except our circle
}
{ % case 1
r1 0 gt{0 0 r1 0 360 arc fill}if
}
{ % case 2
% r1 == r2, extend 0
% r3 = r, x3 = -(abs(minx) + r), x1 = 0
% x(i+1) r(i+1) x(i) r(i) shp
0 r1 xmin abs r1 add neg r1 shp
}
{ % case 3
% no containment, r1 != r2
r2 r1 gt{ % the endpoint we are drawing is that with a circle of zero radius
% x(i+1) r(i+1) x(i) r(i) shp
0 r1
r1 neg r2 r1 sub div dx mul % this is point of beginning circle
0 % point of ending circle
shp % takes x(i+1) r(i+1) x(i) r(i)
}{ % the first circle is the bigger of the two
% we find a circle on our line which is outside the bbox in the
% negative direction
% x(i+1) r(i+1) x(i) r(i) shp
0 r1 calcmaxs % 0 r1 maxs
dup
% calculating xs: (-(maxs+r2)*x2)/(x2-(r1-r2))
r2 add dx mul dx r1 r2 sub sub div
neg % maxs xs'
exch 1 index % xs' maxs xs'
abs exch sub
shp
}ifelse
}
}sh3tp get exec % execute the extend at beginning proc for our shading type
}if
}if
% now do the shading
/d0 0 store
/r0 r1 store
/di dx Nsteps div store
/ri r2 r1 sub Nsteps div store
/Function load
0 1 Nsteps
{ % function t(i)
1 index FunEval sc
d0 di add r0 ri add d0 r0 shp
{
% fill interior arc
d0 0 r0 a1 a0 arc
d0 di add 0 r0 ri add a0 a1 arcn
fill
% fill exterior arc
d0 0 r0 a0 a1 arc
d0 di add 0 r0 ri add a1 a0 arcn
fill
}pop
% advance to next
/d0 d0 di add store
/r0 r0 ri add store
}for
pop % pop our function dict
% handle Extend
currentdict/Extend known
{
/Extend load 1 get r2 0 gt and % no need to extend if the radius of the last end is 0
{
Nsteps/Function load FunEval sc % last element
% case 0: circle1 inside circle2
% case 1: circle 2 inside circle 1
% case 2: circles don't contain each other and r1 == r2
% case 3: circles don't contain each other and r1 != r2
{
{
dx 0 r2 0 360 arc fill
}
{
dx 0 r2 360 0 arcn
xmin ymin moveto
xmax ymin lineto
xmax ymax lineto
xmin ymax lineto
xmin ymin lineto
eofill % for the bigger radius we fill everything except our circle
}
{ % r1 == r2, extend 1
% r3 = r, x3 = (abs(xmax) + r), x1 = dx
% x(i+1) r(i+1) x(i) r(i) shp
xmax abs r1 add r1 dx r1 shp
}
{ % no containment, r1 != r2
r2 r1 gt{
% we find a circle on our line which is outside the bbox in the
% positive direction
% x(i+1) r(i+1) x(i) r(i) shp
calcmaxs dup % maxs maxs
% calculating xs: ((maxs+r1)*x2)/(x2-(r2-r1))
r1 add dx mul dx r2 r1 sub sub div % maxs xs
exch 1 index % xs maxs xs
exch sub
dx r2
shp
}{ % the endpoint we are drawing is that with a circle of zero radius
% x(i+1) r(i+1) x(i) r(i) shp
r1 neg r2 r1 sub div dx mul % this is point of ending circle
0 % radius of ending circle
dx % point of starting circle
r2 % radius of starting circle
shp
}ifelse
}
}
sh3tp get exec % execute the extend at end proc for our shading type
}if
}if
}bd
/sh % emulation of shfill operator for type 2 and type 3 shadings based on type 0 functions
{ % shadingDict --
begin
/ShadingType load dup dup 2 eq exch 3 eq or
{ % shadingtype
gsave
newpath
/ColorSpace load scs
currentdict/BBox known
{
/BBox load aload pop % llx lly urx ury
2 index sub % llx lly urx ury-lly
3 index % llx lly urx ury-lly llx
3 -1 roll exch sub
exch rectclip
}if
2 eq
{sh2}{sh3}ifelse
grestore
}{
% shadingtype
pop
(DEBUG: shading type unimplemented\n)print flush
}ifelse
end
}bd
% end of language level 2 ONLY code
{restore}if not dup{save exch}if
% languagelevel3 ONLY code goes here
L3?{ % we do these loads conditionally or else they will fail on a level 2 printer
/sh/shfill ld
/csq/clipsave ld
/csQ/cliprestore ld
}if
{restore}if
%currentdict dup maxlength exch length sub (number of extra slots in md = )print == flush % *** how many entries are free
end
setpacking
% count 0 ne { pstack(***extras on stack during prolog execution***\n)print flush}if % *** BARK if anything is left on stack
%%EndFile
%%EndProlog
%%BeginSetup
% Disable CTRL-D as an end-of-file marker...
userdict dup(\004)cvn{}put (\004\004)cvn{}put
[{
%%BeginFeature: *OKMultiOutputMode False
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *Collate True
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKAboutDriver Name
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKAlwaysKToner True
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKBlackFinish Gloss
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKColorBrightness 0
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKColorContrast 0
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKColorRenderStyle Auto
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKControl Auto
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKDrumCleaning False
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKDuplex None
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKHardCollate True
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKLongEdgeFeed True
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKMPTPaperSizeCheck True
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKMediaType PrinterDefault
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKOptionTray 0
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKOutputToFile False
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKPaperSizeCheck True
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKPaperSource Auto
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKPhotoMode False
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKResolution 600x600dpi
<< /HWResolution [600 600] >> setpagedevice
<< /cupsColorOrder 0/cupsColorSpace 1/cupsBitsPerColor 8 >> setpagedevice
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *OKTraySwitch True
%%EndFeature
} stopped cleartomark
[{
%%BeginFeature: *PageSize A4
<</PageSize[595 842]/ImagingBBox null>>setpagedevice
%%EndFeature
} stopped cleartomark
userdict/ESPrc/rectclip where{pop/rectclip load}
{{newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
neg 0 rlineto closepath clip newpath}bind}ifelse put
userdict/ESPrf/rectfill where{pop/rectfill load}
{{gsave newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
neg 0 rlineto closepath fill grestore}bind}ifelse put
userdict/ESPrs/rectstroke where{pop/rectstroke load}
{{gsave newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
neg 0 rlineto closepath stroke grestore}bind}ifelse put
userdict/ESPwl{}bind put
%%EndSetup
%%Page: 7 1
%%PageBoundingBox: 0 0 595 842
%%BeginPageSetup
%%EndPageSetup
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00>] def
/CharStrings 22 dict dup begin
/.notdef 0 def
/gid38 1 def
/gid44 2 def
/gid45 3 def
/gid46 4 def
/gid47 5 def
/gid48 6 def
/gid49 7 def
/gid50 8 def
/gid62 9 def
/gid63 10 def
/gid64 11 def
/gid65 12 def
/gid67 13 def
/gid68 14 def
/gid69 15 def
/gid70 16 def
/gid71 17 def
/gid80 18 def
/gid82 19 def
/gid83 20 def
/gid84 21 def
end readonly def
currentdict dup/FontName get exch definefont pop end
%APLsfntEnd
42/FontType resourcestatus{pop pop true}{false}ifelse
{currentfile 0(%APLT1End\n)/SubFileDecode filter flushfile}if
/FontType 1 def
/FontMatrix [ 0.00048828125 0 0 0.00048828125 0 0 ] readonly def
/FontBBox {-3020 -5046 5873 6383} readonly def
/UniqueID 4480348 def
currentdict end
currentfile eexec
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