diff options
Diffstat (limited to 'Master/texmf-dist/dvips/pst-ode')
| -rw-r--r-- | Master/texmf-dist/dvips/pst-ode/pst-ode.pro | 209 |
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 |