diff options
| -rw-r--r-- | Master/texmf-dist/doc/generic/pst-ode/ChangeLog | 4 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/generic/pst-ode/README | 2 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/generic/pst-ode/pst-ode-doc.pdf | bin | 125572 -> 125368 bytes | |||
| -rw-r--r-- | Master/texmf-dist/dvips/pst-ode/pst-ode.pro | 209 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/generic/pst-ode/pst-ode.tex | 34 |
5 files changed, 150 insertions, 99 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-ode/ChangeLog b/Master/texmf-dist/doc/generic/pst-ode/ChangeLog index 9ac21a7df39..2b1e5106c62 100644 --- a/Master/texmf-dist/doc/generic/pst-ode/ChangeLog +++ b/Master/texmf-dist/doc/generic/pst-ode/ChangeLog @@ -1,3 +1,7 @@ +2014-03-27 + * version 0.7 + * change: internal variable defs put into dict for protection + 2013-11-26 * version 0.6 * fix: Postscript error with Distiller if errmax .eq. 0 diff --git a/Master/texmf-dist/doc/generic/pst-ode/README b/Master/texmf-dist/doc/generic/pst-ode/README index 428d9b6d409..35e40e5fbb3 100644 --- a/Master/texmf-dist/doc/generic/pst-ode/README +++ b/Master/texmf-dist/doc/generic/pst-ode/README @@ -11,5 +11,5 @@ of Ordinary Differential Equations (ODE) using the Runge-Kutta-Fehlberg This material is subject to the LaTeX Project Public License. See - http://www.ctan.org/tex-archive/help/Catalogue/licenses.lppl.html + http://mirror.ctan.org/help/Catalogue/licenses.lppl.html for the details of that license. diff --git a/Master/texmf-dist/doc/generic/pst-ode/pst-ode-doc.pdf b/Master/texmf-dist/doc/generic/pst-ode/pst-ode-doc.pdf Binary files differindex 86c45ba5f7b..ed6cb24694c 100644 --- a/Master/texmf-dist/doc/generic/pst-ode/pst-ode-doc.pdf +++ b/Master/texmf-dist/doc/generic/pst-ode/pst-ode-doc.pdf 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 diff --git a/Master/texmf-dist/tex/generic/pst-ode/pst-ode.tex b/Master/texmf-dist/tex/generic/pst-ode/pst-ode.tex index 29b43916228..ffcb24358f0 100644 --- a/Master/texmf-dist/tex/generic/pst-ode/pst-ode.tex +++ b/Master/texmf-dist/tex/generic/pst-ode/pst-ode.tex @@ -11,8 +11,8 @@ %% ODEs using the Runge-Kutta-Fehlberg (RKF45) method with automatic %% step size adjustment %% -\def\fileversion{0.6} -\def\filedate{2013/11/26} +\def\fileversion{0.7} +\def\filedate{2014/03/27} \csname PSTODELoaded\endcsname \let\PSTODELoaded\endinput @@ -119,13 +119,15 @@ %process arguments \ifPstODE@saveData /statefile (#1.dat) (\filemode) file def \fi \ifPstODE@algebraicT - /tStart tx@Dict begin (\expandafter\ode@zapspace\ode@ta\@nil) AlgParser cvx exec end def - /tEnd tx@Dict begin (\expandafter\ode@zapspace\ode@tb\@nil) AlgParser cvx exec end def + tx@Dict begin (\expandafter\ode@zapspace\ode@ta\@nil) + AlgParser cvx exec end ode@dict /tStart exch def end + tx@Dict begin (\expandafter\ode@zapspace\ode@tb\@nil) + AlgParser cvx exec end ode@dict /tEnd exch def end \else - /tStart tx@Dict begin 1 dict begin #3 end end def - /tEnd tx@Dict begin 1 dict begin #4 end end def + tx@Dict begin 1 dict begin #3 end end ode@dict /tStart exch def end + tx@Dict begin 1 dict begin #4 end end ode@dict /tEnd exch def end \fi - /dt tEnd tStart sub #5\space 1 sub div def % output step size + ode@dict /dt tEnd tStart sub #5\space 1 sub div def end % output step size \ifx\@empty#6\@empty\else \ifPstODE@algebraicIC true setglobal globaldict /ode@laststate [ @@ -138,16 +140,16 @@ false setglobal \fi \fi% - /xlength ode@laststate length def % number of equations - /xlength1 xlength 1 add def % number of equations plus 1 + ode@dict /xlength ode@laststate length def end % number of equations + ode@dict /xlength1 xlength 1 add def end % number of equations plus 1 \ifPst@algebraic /ode@rpn tx@Dict begin (\expandafter\ode@zapspace\ode@arg\@nil) AlgParser end cvx bind def /ODESET {%system of ODEs - /x exch def /y x def tx@Dict begin ode@rpn end xlength array astore + /x exch def /y x def tx@Dict begin ode@rpn end ode@dict xlength end array astore } bind def \else /ODESET { - aload pop tx@Dict begin ode@foo begin #7 end end xlength array astore + aload pop tx@Dict begin ode@foo begin #7 end end ode@dict xlength end array astore } bind def %ensure local scope of user defined variables in #7, from BlueBook, p. 133 /ODESET load 4 1 dict put @@ -155,16 +157,18 @@ \ifPstODE@algebraicOutputFormat /ode@fmtrpn tx@Dict begin (\expandafter\ode@zapspace\ode@fmt\@nil) AlgParser end cvx bind def /formatoutput {% - ode@laststate /x exch def /y x def /t tcur def + ode@laststate /x exch def /y x def /t ode@dict tcur end def tx@Dict begin ode@fmtrpn end } bind def \else /formatoutput {[#2] assembleresult} def \fi% %perform ode integration (\string\n pstODEsolve RKF45 method; '-' failed step, '+' successful step, % 'o' output step : \string\n) odeprint - /tcur tStart def % current parameter t value - /tout tStart dt add def % next output t - /ddt dt def % initial integration step size + ode@dict + /tcur tStart def % current parameter t value + /tout tStart dt add def % next output t + /ddt dt def % initial integration step size + end \ifPstODE@append\else [ [formatoutput] |