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//
// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2001 - Bruno PINCON
// Copyright (C) 2005 - INRIA - Pierre MARECHAL <pierre.marechal@inria.fr>
//
// This file is distributed under the same license as the Scilab package.
//
function [xr,yr,zr,xi,yi,zi] = CmplxFacets(R,e,TypeDomain,TypeCut,n,StrFunc)
// A function to compute the facets for drawing a complex function
// on a square or a disk with branch(es) cut(s) on Ox or Oy
//
// TypeDomain : "Square" or "Disk"
// TypeCut : "Ox" or "Oy"
// R : length of half a side of the square or radius of the disk
// e : thin layer to avoid the branch(es) cut(s)
// n : a scalar (for Square) or a 2-vector = [ntheta, nr]
// (for Disk) for discretization
// StrFunc : the string which names the complex function (this is
// because primitive don't pass as function argument)
//
// Bruno (10/10/2001): macros for the complex function dem
if TypeDomain == "Square" then
if TypeCut == "Ox" then
x1 = linspace(-R, R, n);
y1 = linspace( e, R, floor(n/2));
else // for TypeCut = "Oy" ...
x1 = linspace( e, R, floor(n/2));
y1 = linspace(-R, R, n);
end
X1 = ones(y1')*x1 ; Y1 = y1'*ones(x1);
else // for TypeDomain = "Disk"
r = linspace(0,R, n(2));
if TypeCut == "Ox" then
theta = linspace(0,%pi,n(1))';
X1 = cos(theta)*r;
Y1 = e + sin(theta)*r;
else // for TypeCut = "Oy"
theta = linspace(-%pi/2,%pi/2,n(1))';
X1 = e + cos(theta)*r;
Y1 = sin(theta)*r;
end
end
X2 = -X1 ; Y2 = -Y1;
Z1 = evstr(StrFunc+"(X1 + %i*Y1)");
Z2 = evstr(StrFunc+"(X2 + %i*Y2)");
[xr1,yr1,zr1] = nf3d(X1,Y1,real(Z1));
[xr2,yr2,zr2] = nf3d(X2,Y2,real(Z2));
xr = [xr1 xr2]; yr = [yr1 yr2]; zr = [zr1 zr2];
[xi1,yi1,zi1] = nf3d(X1,Y1,imag(Z1));
[xi2,yi2,zi2] = nf3d(X2,Y2,imag(Z2));
xi = [xi1 xi2]; yi = [yi1 yi2]; zi = [zi1 zi2];
endfunction
function []=PlotCmplxFunc(R,e,TypeDomain,TypeCut,n,StrFunc,theta,alpha,DomReal)
// A function to draw on a square or a disk a complex function
// with branch(es) cut(s) on Ox or Oy
//
// TypeDomain : "Square" or "Disk"
// TypeCut : "Ox" or "Oy"
// R : length of half a side of the square or radius of the disk
// e : thin layer to avoid the branch(es) cut(s)
// n : a scalar (for Square) or a 2-vector = [ntheta, nr]
// (for Disk) for discretization
// StrFunc : the string which names the complex function (this is
// because primitive don't pass as function argument)
// theta,alpha : usual parameters for plot3d
// DomReal : interval for which the real restriction is drawn
// Bruno (10/10/2001): macros for the complex function dem
// Adapted for new graphic by Pierre MARECHAL ( 16/12/2005 )
// computes the facets
[xr,yr,zr,xi,yi,zi] = CmplxFacets(R,e,TypeDomain,TypeCut,n,StrFunc)
// draw
// ============================================
current_figure_hdl = scf(100001);
clf(current_figure_hdl,"reset");
drawlater();
// Title
// ============================================
my_title_axes = newaxes();
// make axes transparent
my_title_axes.filled = "off";
Rs = string(R);
if TypeDomain == "Square" then
end_title = " Function on [-"+Rs+","+Rs+"]x[-"+Rs+","+Rs+"]"
else
end_title = " Function on D(0,R="+Rs+")"
end
if StrFunc == "f" then
the_title = "Your Custom (named f) Complex" + end_title;
else
the_title = "The Complex " + StrFunc + end_title;
end
xtitle(the_title);
my_title_axes.title.text = the_title;
my_title_axes.title.font_size = 3;
my_title_axes.title.font_style = 2;
my_title_axes.margins = [ 0.08 0.08 0.08 0.08 ]
// plot Im(z)
// ============================================
subplot(1,2,1);
plot3d(xi,yi,zi,theta,alpha,"Re(z)@Im(z)@",[2 6 4]);
xtitle("Im("+StrFunc+"(z))");
// plot Re(z) + the real restriction
// ============================================
subplot(1,2,2);
plot3d(xr,yr,zr,theta,alpha,"Re(z)@Im(z)@",[ 2 6 4]);
xtitle("Re("+StrFunc+"(z))");
// real function in yellow
// ============================================
if DomReal(2) > DomReal(1) then
//xstring(0.1,-0.15," In yellow : the real "+StrFunc+" function")
xx = linspace(DomReal(1),DomReal(2),40)';
yy = zeros(xx);
zz = evstr(StrFunc+"(xx)");
param3d1(xx,yy,list(zz,32),theta,alpha,flag=[0,0]);
yellow_line = get("hdl");
yellow_line.thickness = 3;
captions(yellow_line, "the real "+StrFunc+" function", "lower_caption");
end
drawnow();
endfunction
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