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-rw-r--r--Master/texmf-dist/dvips/pst-ode/pst-ode.pro209
1 files changed, 126 insertions, 83 deletions
diff --git a/Master/texmf-dist/dvips/pst-ode/pst-ode.pro b/Master/texmf-dist/dvips/pst-ode/pst-ode.pro
index 02ea9f726e5..e1de2a52680 100644
--- a/Master/texmf-dist/dvips/pst-ode/pst-ode.pro
+++ b/Master/texmf-dist/dvips/pst-ode/pst-ode.pro
@@ -1,7 +1,7 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% PostScript prologue for pst-ode.tex.
-% Version 0.6, 2013/11/26
+% Version 0.7, 2014/03/27
%
% Alexander Grahn (C) 2012, 2013
%
@@ -12,102 +12,145 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/tx@odeDict 1 dict def
tx@odeDict begin
-%some constants for step size calculation
-/sfty 0.9 def /pgrow -0.2 def /pshrink -0.25 def
-%helper functions
-/addvect { % [1 2 3] [4 5 6] addvect => [5 7 9]
- aload pop xlength1 -1 roll {xlength1 -1 roll add} forall
- xlength array astore
-} bind def
-/subvect { % [1 2 3] [4 5 6] subvect => [-3 -3 -3]
- aload pop xlength1 -1 roll {xlength1 -1 roll sub} forall
- xlength array astore
-} bind def
-/mulvect { % [1 2 3] 4 mulvect => [4 8 12]
- /mul cvx 2 array astore cvx forall xlength array astore
-} bind def
-/edivvect { % [1 2 3] [4 5 6] edivvect => [0.25 0.4 0.5]
- aload pop xlength1 -1 roll {xlength1 -1 roll div} forall
- xlength array astore
-} bind def
-/eabsvect { % [-1 2 -3] eabsvect => [1 2 3]
- {abs} forall xlength array astore
-} bind def
-%/revstack { % (a) (b) (c) (d) 3 revstack => (a) (d) (c) (b)
-% -1 2 {dup 1 sub neg roll} for
-%} bind def
-/min { 2 copy gt { exch } if pop } bind def
-/max { 2 copy lt { exch } if pop } bind def
-%coefficient table (Butcher table) of RKF45
-/a41 25 216 div def /a43 1408 2565 div def
-/a44 2197 4104 div def /a45 1 5 div neg def
-/a51 16 135 div def /a53 6656 12825 div def
-/a54 28561 56430 div def /a55 9 50 div neg def
-/a56 2 55 div def
-/b21 1 4 div def /b31 3 32 div def /b32 9 32 div def
-/b41 1932 2197 div def /b42 7200 2197 div neg def /b43 7296 2197 div def
-/b51 439 216 div def /b52 8 neg def /b53 3680 513 div def
-/b54 845 4104 div neg def /b61 8 27 div neg def /b62 2 def
-/b63 3544 2565 div neg def /b64 1859 4104 div def /b65 11 40 div neg def
+/ode@@dict 1 dict def
+/ode@dict {ode@@dict begin} bind def
+ode@dict
+ %some constants for step size calculation
+ /sfty 0.9 def /pgrow -0.2 def /pshrink -0.25 def
+ %helper functions
+ /addvect { % [1 2 3] [4 5 6] addvect => [5 7 9]
+ ode@dict
+ aload pop xlength1 -1 roll {xlength1 -1 roll add} forall
+ xlength array astore
+ end
+ } bind def
+ /subvect { % [1 2 3] [4 5 6] subvect => [-3 -3 -3]
+ ode@dict
+ aload pop xlength1 -1 roll {xlength1 -1 roll sub} forall
+ xlength array astore
+ end
+ } bind def
+ /mulvect { % [1 2 3] 4 mulvect => [4 8 12]
+ ode@dict /mul cvx 2 array astore cvx forall xlength array astore end
+ } bind def
+ /edivvect { % [1 2 3] [4 5 6] edivvect => [0.25 0.4 0.5]
+ ode@dict
+ aload pop xlength1 -1 roll {xlength1 -1 roll div} forall
+ xlength array astore
+ end
+ } bind def
+ /eabsvect { % [-1 2 -3] eabsvect => [1 2 3]
+ ode@dict {abs} forall xlength array astore end
+ } bind def
+ %/revstack { % (a) (b) (c) (d) 3 revstack => (a) (d) (c) (b)
+ % -1 2 {dup 1 sub neg roll} for
+ %} bind def
+ /min { 2 copy gt { exch } if pop } bind def
+ /max { 2 copy lt { exch } if pop } bind def
+ %coefficient table (Butcher table) of RKF45
+ /a41 25 216 div def /a43 1408 2565 div def
+ /a44 2197 4104 div def /a45 1 5 div neg def
+ /a51 16 135 div def /a53 6656 12825 div def
+ /a54 28561 56430 div def /a55 9 50 div neg def
+ /a56 2 55 div def
+ /b21 1 4 div def /b31 3 32 div def /b32 9 32 div def
+ /b41 1932 2197 div def /b42 7200 2197 div neg def /b43 7296 2197 div def
+ /b51 439 216 div def /b52 8 neg def /b53 3680 513 div def
+ /b54 845 4104 div neg def /b61 8 27 div neg def /b62 2 def
+ /b63 3544 2565 div neg def /b64 1859 4104 div def /b65 11 40 div neg def
+end
%Runge-Kutta-Fehlberg (RKF45) method
%performs one integration step over tentative step size ddt
%[state vector x(t)] RKF45 => [x(t)] [x(t+ddt) by RKF4] errmax
/RKF45 {
- /t tcur def
- dup ODESET ddt mulvect /k1 exch def
- /t tcur ddt 4 div add def
- dup k1 b21 mulvect addvect ODESET ddt mulvect /k2 exch def
- /t tcur ddt 3 mul 8 div add def
- dup k1 b31 mulvect addvect k2 b32 mulvect addvect ODESET ddt mulvect
- /k3 exch def
- /t tcur ddt 12 mul 13 div add def
- dup k1 b41 mulvect addvect k2 b42 mulvect addvect k3 b43 mulvect addvect
- ODESET ddt mulvect /k4 exch def
- /t tcur ddt add def
- dup k1 b51 mulvect addvect k2 b52 mulvect addvect k3 b53 mulvect addvect
- k4 b54 mulvect addvect ODESET ddt mulvect /k5 exch def
- /t tcur ddt 2 div add def
- dup k1 b61 mulvect addvect k2 b62 mulvect addvect k3 b63 mulvect addvect
- k4 b64 mulvect addvect k5 b65 mulvect addvect ODESET ddt mulvect
- /k6 exch def % => [x(t)]
- %fourth order solution (increment dx)
- dup dup k1 a41 mulvect k3 a43 mulvect addvect k4 a44 mulvect addvect
- k5 a45 mulvect addvect dup
- % => [x(t)] [x(t)] [x(t)] [dx by RKF4] [dx by RKF4]
- %fifth order solution (abs. error)
- k1 a51 mulvect k3 a53 mulvect addvect k4 a54 mulvect addvect
- k5 a55 mulvect addvect k6 a56 mulvect addvect subvect
- % => [x(t)] [x(t)] [x(t)] [dx by RKF4] [err]
- 5 1 roll addvect 4 -2 roll % => [x(t)] [x(t+ddt) by RKF4] [err] [x(t)]
- %scaling vector for step size adjustment (Numerical Recipies)
- eabsvect k1 eabsvect addvect {1e-30 add} forall xlength array astore
- % => [x(t)] [x(t+ddt) by RKF4] [err] [xscale]
- %maximum rel. error
- /errmax 0 def
- edivvect {abs dup errmax gt {/errmax exch def}{pop} ifelse} forall errmax
- % => [x(t)] [x(t+ddt) by RKF4] errmax
+ dup
+ ode@dict tcur end /t exch def
+ ODESET
+ ode@dict
+ ddt mulvect /k1 exch def
+ dup k1 b21 mulvect addvect
+ tcur ddt 4 div add
+ end
+ /t exch def
+ ODESET
+ ode@dict
+ ddt mulvect /k2 exch def
+ dup k1 b31 mulvect addvect k2 b32 mulvect addvect
+ tcur ddt 3 mul 8 div add
+ end
+ /t exch def
+ ODESET
+ ode@dict
+ ddt mulvect /k3 exch def
+ dup k1 b41 mulvect addvect k2 b42 mulvect addvect k3 b43 mulvect addvect
+ tcur ddt 12 mul 13 div add
+ end
+ /t exch def
+ ODESET
+ ode@dict
+ ddt mulvect /k4 exch def
+ dup k1 b51 mulvect addvect k2 b52 mulvect addvect k3 b53 mulvect addvect
+ k4 b54 mulvect addvect
+ tcur ddt add
+ end
+ /t exch def
+ ODESET
+ ode@dict
+ ddt mulvect /k5 exch def
+ dup k1 b61 mulvect addvect k2 b62 mulvect addvect k3 b63 mulvect addvect
+ k4 b64 mulvect addvect k5 b65 mulvect addvect
+ tcur ddt 2 div add
+ end
+ /t exch def
+ ODESET
+ ode@dict
+ ddt mulvect /k6 exch def % => [x(t)]
+ %fourth order solution (increment dx)
+ dup dup k1 a41 mulvect k3 a43 mulvect addvect k4 a44 mulvect addvect
+ k5 a45 mulvect addvect dup
+ % => [x(t)] [x(t)] [x(t)] [dx by RKF4] [dx by RKF4]
+ %fifth order solution (abs. error)
+ k1 a51 mulvect k3 a53 mulvect addvect k4 a54 mulvect addvect
+ k5 a55 mulvect addvect k6 a56 mulvect addvect subvect
+ % => [x(t)] [x(t)] [x(t)] [dx by RKF4] [err]
+ 5 1 roll addvect 4 -2 roll % => [x(t)] [x(t+ddt) by RKF4] [err] [x(t)]
+ %scaling vector for step size adjustment (Numerical Recipies)
+ eabsvect k1 eabsvect addvect {1e-30 add} forall xlength array astore
+ % => [x(t)] [x(t+ddt) by RKF4] [err] [xscale]
+ %maximum rel. error
+ /errmax 0 def
+ edivvect {abs dup errmax gt {/errmax exch def}{pop} ifelse} forall errmax
+ % => [x(t)] [x(t+ddt) by RKF4] errmax
+ end
} bind def
/ODEINT { % performs integration over output step [t,t+dt]
% [ state vector x(t) ] ODEINT => [ state vector x(t+dt) ]
%decrease overshooting step size
- tcur ddt add tout sub tcur ddt add tout sub dt add mul 0 gt
- {/ddt tout tcur sub def} if
+ ode@dict
+ tcur ddt add tout sub tcur ddt add tout sub dt add mul 0 gt
+ {/ddt tout tcur sub def} if
+ end
RKF45
ode@tol div dup 1 gt {
%failed step -> reduce step size
- exch pop pshrink exp 0.1 max sfty mul ddt mul /ddt exch def
- (-) odeprint tcur ddt add tcur eq {
- (error: step size underflow in ODEINT) print quit
- } if
+ ode@dict
+ exch pop pshrink exp 0.1 max sfty mul ddt mul /ddt exch def
+ (-) odeprint ode@dict tcur ddt add tcur end eq {
+ (error: step size underflow in ODEINT) print quit
+ } if
+ end
ODEINT %repeat step with new ddt
}{
%success
3 -1 roll pop % remove previous state vector
- /tcur tcur ddt add def
- dup 0 ne {pgrow exp 5 min sfty mul ddt mul /ddt exch def}{pop} ifelse
- %output step completed?
- tcur tout sub dt mul 0 ge {
- (o) odeprint /tcur tout def /tout tout dt add def
+ ode@dict
+ /tcur tcur ddt add def
+ dup 0 ne {pgrow exp 5 min sfty mul ddt mul /ddt exch def}{pop} ifelse
+ %output step completed?
+ tcur tout sub dt mul
+ end
+ 0 ge {
+ (o) odeprint ode@dict /tcur tout def /tout tout dt add def end
}{
(+) odeprint ODEINT %continue integration
} ifelse
@@ -123,7 +166,7 @@ tx@odeDict begin
/assembleresult { %assembles state vector for building table of results
{
dup (t) eq {
- pop tcur
+ pop ode@dict tcur end
}{
ode@laststate exch get
} ifelse