pst-func 0.45

git-svn-id: svn://tug.org/texlive/trunk@1780 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 216 insertions, 5 deletions

diff --git a/Master/texmf-dist/dvips/pst-func/pst-func.pro b/Master/texmf-dist/dvips/pst-func/pst-func.pro
index 580e702c837..56b43d8c605 100644
--- a/Master/texmf-dist/dvips/pst-func/pst-func.pro
+++ b/Master/texmf-dist/dvips/pst-func/pst-func.pro
@@ -3,9 +3,9 @@
 %%
 %% IMPORTANT NOTICE:
 %%
-%% Package `pst-func.tex'
+%% Package `pst-func'
 %%
-%% Herbert Voss <voss _at_ perce.de>
+%% Herbert Voss <voss _at_ pstricks.de>
 %%
 %% This program can be redistributed and/or modified under the terms
 %% of the LaTeX Project Public License Distributed from CTAN archives
@@ -15,13 +15,70 @@
 %%   `pst-func' is a PSTricks package to plot special math functions
 %%
 %%
-%% version 0.02 / 2004-11-08  Herbert Voss <voss _at_ pstricks.de>
+%% version 0.06 / 2006-04-16  Herbert Voss <voss _at_ pstricks.de>
 %
-/tx@FuncDict 40 dict def
+/tx@FuncDict 100 dict def
 tx@FuncDict begin
 %
 /eps1 1.0e-05 def
 /eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n! 
+  dup 0 eq { 1 }{ 
+    dup 1 gt { dup 1 sub factorial mul } if }
+  ifelse } def 
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+  /n exch def /m exch def
+  n 0 eq { 1 }{
+    m n eq { 1 }{
+      m factorial n factorial m n sub factorial mul div } ifelse } ifelse 
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+  /arg exch def
+  /Sum arg def
+  /sign -1 def
+  /index 3 def
+  { 
+    arg index exp index div index factorial div sign mul 
+    dup abs eps8 lt { pop exit } if 
+    Sum add /Sum exch def
+    /sign sign neg def
+    /index index 2 add def
+  } loop
+  Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+  Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+  abs /arg exch def
+  arg 0 eq { 0 } { 
+    /argExp 1 def
+    /fact 1 def
+    /Sum CEuler arg ln add def
+    /sign -1 def
+    /index 2 def
+    { 
+      /argExp argExp arg arg mul mul def
+      /fact fact index 1 sub index mul mul def
+      argExp index div fact div sign mul 
+      dup abs exch Sum add /Sum exch def
+      eps8 lt { exit } if
+      /sign sign neg def
+      /index index 2 add def
+    } loop
+    Sum
+  } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+  dup Ci neg exch abs ln add CEuler add
+} def
+%
 /MaxIter 255 def
 /func { coeff Derivation FuncValue } def
 /func' { coeff Derivation 1 add FuncValue } def
@@ -54,7 +111,7 @@ tx@FuncDict begin
     y0 F sub /Phi exch def
     Phi func /F2 exch def
     F2 abs eps2 le { exit }{
-      Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add div /Diff exch def
+      Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
       y0 Diff sub /y0 exch def
       Diff abs eps1 le { exit } if
     } ifelse
@@ -113,5 +170,159 @@ tx@FuncDict begin
   } for
 } def
 %
+/Simpson { % on stack must be a b M 
+% /SFunc must be defined 
+  /M ED /b ED /a ED
+  /h b a sub M 2 mul div def
+  /s1 0 def
+  /s2 0 def
+  1 1 M {
+    /k exch def
+    /x k 2 mul 1 sub h mul a add def
+    /s1 s1 x SFunc add def
+  } for
+  1 1 M 1 sub {
+    /k exch def
+    /x k 2 mul h mul a add def
+    /s2 s2 x SFunc add def
+  } for
+  /I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
+} def
+
+%
+% subroutines for complex numbers, given as an array [a b] 
+% which is a+bi = Real+i Imag
+%
+/cxadd {		% [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+  dup 0 get		% [a1 b1] [a2 b2] a2
+  3 -1 roll		% [a2 b2] a2 [a1 b1]
+  dup 0 get		% [a2 b2] a2 [a1 b1] a1
+  3 -1 roll		% [a2 b2] [a1 b1] a1 a2
+  add			% [a2 b2] [a1 b1] a1+a2
+  3 1 roll		% a1+a2 [a2 b2] [a1 b1]
+  1 get			% a1+a2 [a2 b2] b1
+  exch 1 get		% a1+a2 b1 b2
+  add 2 array astore
+} def
+%
+/cxneg {		% [a b]
+  dup 1 get		% [a b] b
+  exch 0 get		% b a
+  neg exch neg		% -a -b
+  2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def  % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul {		% [a1 b1] [a2 b2]
+  dup 0 get		% [a1 b1] [a2 b2] a2
+  exch 1 get		% [a1 b1] a2 b2
+  3 -1 roll		% a2 b2 [a1 b1]
+  dup 0 get		% a2 b2 [a1 b1] a1
+  exch 1 get		% a2 b2 a1 b1
+  dup			% a2 b2 a1 b1 b1
+  5 -1 roll dup		% b2 a1 b1 b1 a2 a2
+  3 1 roll mul		% b2 a1 b1 a2 b1a2
+  5 -2 roll dup		% b1 a2 b1a2 b2 a1 a1
+  3 -1 roll dup		% b1 a2 b1a2 a1 a1 b2 b2
+  3 1 roll mul		% b1 a2 b1a2 a1 b2 a1b2
+  4 -1 roll add		% b1 a2 a1 b2 b3
+  4 2 roll mul		% b1 b2 b3 a1a2
+  4 2 roll mul sub	% b3 a3
+  exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr {		% [a b]   square root
+  dup 0 get exch 1 get	% a b
+  dup dup mul		% a b b^2
+  3 -1 roll		% b b^2 a
+  dup dup mul 		% b b^2 a a^2
+  3 -1 roll sub		% b a a2
+  3 1 roll mul 2 mul	% a2 b2	
+  2 array astore
+} def
+%
+/cxsqrt {		% [a b]
+%  dup cxnorm sqrt /r exch def
+%  cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2 
+  cxlog 		% log[a b]
+  2 cxrdiv 		% log[a b]/2
+  aload pop exch	% b a
+  2.781 exch exp	% b exp(a)
+  exch cxconv exch	% [Re +iIm] exp(a)
+  cxrmul		%
+} def
+%
+/cxarg { 		% [a b] 
+  aload pop 		% a b
+  exch atan 		% arctan b/a
+  DegtoRad 		% arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog {		% [a b]
+  dup 			% [a b][a b]
+  cxnorm 		% [a b] |z|
+  log 			% [a b] log|z|
+  exch 			% log|z|[a b]
+  cxarg 		% log|z| Theta
+  cxmake2 		% [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 {		% [a b]
+  dup 0 get exch 1 get	% a b
+  dup mul			% a b^2
+  exch dup mul add	% a^2+b^2
+} def
 %
+/cxnorm {		% [a b]
+  cxnorm2 sqrt
+} def
+%
+/cxconj {		% conjugent complex
+  dup 0 get exch 1 get	% a b
+  neg 2 array astore	% [a -b]
+} def
+%
+/cxre { 0 get } def	% real value
+/cxim { 1 get } def	% imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip {		% [a b]
+  dup cxnorm2 exch	% n2 [a b]
+  dup 0 get exch 1 get	% n2 a b
+  3 -1 roll		% a b n2
+  dup			% a b n2 n2
+  4 -1 roll exch div	% b n2 a/n2
+  3 1 roll div		% a/n2 b/n2
+  neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def	  % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul {		% [a b] r
+  exch aload pop	% r a b
+  3 -1 roll dup		% a b r r
+  3 1 roll mul		% a r b*r
+  3 1 roll mul		% b*r a*r
+  exch 2 array astore   % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv {		% [a b] r
+  1 exch div		% [a b] 1/r
+  cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv {		% theta
+  RadtoDeg dup sin exch cos cxmake2
+} def
 end