new pstricks package pst-ode (16aug12)

git-svn-id: svn://tug.org/texlive/trunk@27431 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 136 insertions, 0 deletions

diff --git a/Master/texmf-dist/dvips/pst-ode/pst-ode.pro b/Master/texmf-dist/dvips/pst-ode/pst-ode.pro
new file mode 100644
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+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% PostScript prologue for pst-ode.tex.
+% Version 0.1, 2012/07/20
+%
+% Alexander Grahn (C) 2012
+%
+% This program can be redistributed and/or modified under the terms
+% of the LaTeX Project Public License Distributed from CTAN archives
+% in directory macros/latex/base/lppl.txt.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/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
+%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
+} 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
+  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
+    ODEINT %repeat step with new ddt
+  }{
+    %success
+    3 -1 roll pop % remove previous state vector
+    /tcur tcur ddt add def
+    pgrow exp 5 min sfty mul ddt mul /ddt exch def
+    %output step completed?
+    tcur tout sub dt mul 0 ge {
+      (o) odeprint /tcur tout def /tout tout dt add def
+    }{
+      (+) odeprint ODEINT %continue integration
+    } ifelse
+  }ifelse
+} bind def
+/writeresult { %assembles state vector for output into file + writes it
+  outvect {
+       dup (t) eq {
+         pop tcur 20 string cvs statefile exch writestring
+       }{
+         ode@laststate exch get 20 string cvs statefile exch writestring
+       } ifelse
+       statefile ( ) writestring
+  } forall
+  statefile (\n) writestring
+} bind def
+/assembleresult { %assembles state vector for building table of results
+  outvect {
+       dup (t) eq {
+         pop tcur
+       }{
+         ode@laststate exch get
+       } ifelse
+  } forall
+} bind def
+end