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# Copyright (C) 2001-2017 Alan W. Irwin
# Contour plot demo.
#
# This file is part of PLplot.
#
# PLplot is free software; you can redistribute it and/or modify
# it under the terms of the GNU Library General Public License as published
# by the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# PLplot is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General Public License
# along with PLplot; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
#
from numpy import *
XPTS = 35
YPTS = 46
XSPA = 2./(XPTS-1)
YSPA = 2./(YPTS-1)
#polar plot data
PERIMETERPTS = 100
RPTS = 40
THETAPTS = 40
#potential plot data
PPERIMETERPTS = 100
PRPTS = 40
PTHETAPTS = 64
tr = array((XSPA, 0.0, -1.0, 0.0, YSPA, -1.0))
def mypltr(x, y, data):
result0 = data[0] * x + data[1] * y + data[2]
result1 = data[3] * x + data[4] * y + data[5]
return array((result0, result1))
def polar(w):
#polar contour plot example.
w.plenv(-1., 1., -1., 1., 0, -2,)
w.plcol0(1)
# Perimeter
t = (2.*pi/(PERIMETERPTS-1))*arange(PERIMETERPTS)
px = cos(t)
py = sin(t)
w.plline(px, py)
# create data to be contoured.
r = arange(RPTS)/float(RPTS-1)
r.shape = (-1,1)
theta = (2.*pi/float(THETAPTS-1))*arange(THETAPTS-1)
xg = r*cos(theta)
yg = r*sin(theta)
zg = r*ones(THETAPTS-1)
lev = 0.05 + 0.10*arange(10)
w.plcol0(2)
w.plcont(zg, lev, w.pltr2, xg, yg, 2)
# ^-- :-). Means: "2nd coord is wrapped."
w.plcol0(1)
w.pllab("", "", "Polar Contour Plot")
def potential(w):
#shielded potential contour plot example.
# create data to be contoured.
r = 0.5 + arange(PRPTS)
r.shape = (-1,1)
theta = (2.*pi/float(PTHETAPTS-1))*(0.5+arange(PTHETAPTS-1))
xg = r*cos(theta)
yg = r*sin(theta)
rmax = max(r.flat)
xmin = min(xg.flat)
xmax = max(xg.flat)
ymin = min(yg.flat)
ymax = max(yg.flat)
x0 = (xmin + xmax)/2.
y0 = (ymin + ymax)/2.
#perturbed (expanded) limits
peps = 0.05
xpmin = xmin - abs(xmin)*peps
xpmax = xmax + abs(xmax)*peps
ypmin = ymin - abs(ymin)*peps
ypmax = ymax + abs(ymax)*peps
# Potential inside a conducting cylinder (or sphere) by method of images.
# Charge 1 is placed at (d1, d1), with image charge at (d2, d2).
# Charge 2 is placed at (d1, -d1), with image charge at (d2, -d2).
# Also put in smoothing term at small distances.
eps = 2.
q1 = 1.
d1 = rmax/4.
q1i = - q1*rmax/d1
d1i = rmax**2/d1
q2 = -1.
d2 = rmax/4.
q2i = - q2*rmax/d2
d2i = rmax**2/d2
div1 = sqrt((xg-d1)**2 + (yg-d1)**2 + eps**2)
div1i = sqrt((xg-d1i)**2 + (yg-d1i)**2 + eps**2)
div2 = sqrt((xg-d2)**2 + (yg+d2)**2 + eps**2)
div2i = sqrt((xg-d2i)**2 + (yg+d2i)**2 + eps**2)
zg = q1/div1 + q1i/div1i + q2/div2 + q2i/div2i
zmin = min(zg.flat)
zmax = max(zg.flat)
# print "%.15g %.15g %.15g %.15g %.15g %.15g %.15g %.15g \n" % \
# (q1, d1, q1i, d1i, q2, d2, q2i, d2i)
# print "%.15g %.15g %.15g %.15g %.15g %.15g \n" % \
# (xmin, xmax, ymin, ymax, zmin, zmax)
# Positive and negative contour levels.
nlevel = 20
dz = (zmax-zmin)/float(nlevel)
clevel = zmin + (arange(20)+0.5)*dz
clevelpos = compress(clevel > 0., clevel)
clevelneg = compress(clevel <= 0., clevel)
#Colours!
ncollin = 11
ncolbox = 1
ncollab = 2
#Finally start plotting this page!
w.pladv(0)
w.plcol0(ncolbox)
w.plvpas(0.1, 0.9, 0.1, 0.9, 1.0)
w.plwind(xpmin, xpmax, ypmin, ypmax)
w.plbox("", 0., 0, "", 0., 0)
w.plcol0(ncollin)
# Negative contours
w.pllsty(2)
w.plcont(zg, clevelneg, w.pltr2, xg, yg, 2)
# Positive contours
w.pllsty(1)
w.plcont(zg, clevelpos, w.pltr2, xg, yg, 2)
# Draw outer boundary
t = (2.*pi/(PPERIMETERPTS-1))*arange(PPERIMETERPTS)
px = x0 + rmax*cos(t)
py = y0 + rmax*sin(t)
w.plcol0(ncolbox)
w.plline(px, py)
w.plcol0(ncollab)
w.pllab("", "", "Shielded potential of charges in a conducting sphere")
def main(w):
mark = 1500
space = 1500
clevel = -1. + 0.2*arange(11)
xx = (arange(XPTS) - XPTS//2) / float((XPTS//2))
yy = (arange(YPTS) - YPTS//2) / float((YPTS//2)) - 1.
xx.shape = (-1,1)
z = (xx*xx)-(yy*yy)
# 2.*outerproduct(xx,yy) for new versions of Numeric which have outerproduct.
w_array = 2.*xx*yy
# Set up grids.
# Note *for the given* tr, mypltr(i,j,tr)[0] is only a function of i
# and mypltr(i,j,tr)[1] is only function of j.
xg0 = mypltr(arange(XPTS),0,tr)[0]
yg0 = mypltr(0,arange(YPTS),tr)[1]
distort = 0.4
cos_x = cos((pi/2.)*xg0)
cos_y = cos((pi/2.)*yg0)
xg1 = xg0 + distort*cos_x
yg1 = yg0 - distort*cos_y
# Need independent copy here so the shape changes for xg0t do not affect
# xg0.
xg0t = xg0.copy()
cos_x.shape = (-1,1)
xg0t.shape = (-1,1)
xg2 = xg0t + distort*cos_x*cos_y
yg2 = yg0 - distort*cos_x*cos_y
# Plot using mypltr (scaled identity) transformation used to create
# xg0 and yg0
# w.pl_setcontlabelparam(0.006, 0.3, 0.1, 0)
# w.plenv(-1.0, 1.0, -1.0, 1.0, 0, 0)
# w.plcol0(2)
# w.plcont(z, clevel, mypltr, tr)
# w.plstyl([mark], [space])
# w.plcol0(3)
# w.plcont(w, clevel, mypltr, tr)
# w.plstyl([], [])
# w.plcol0(1)
# w.pllab("X Coordinate", "Y Coordinate", "Streamlines of flow")
w.pl_setcontlabelformat(4,3)
w.pl_setcontlabelparam(0.006, 0.3, 0.1, 1)
w.plenv(-1.0, 1.0, -1.0, 1.0, 0, 0)
w.plcol0(2)
w.plcont(z, clevel, mypltr, tr)
w.plstyl([mark], [space])
w.plcol0(3)
w.plcont(w_array, clevel, mypltr, tr)
w.plstyl([], [])
w.plcol0(1)
w.pllab("X Coordinate", "Y Coordinate", "Streamlines of flow")
# Plot using 1D coordinate transformation.
w.pl_setcontlabelparam(0.006, 0.3, 0.1, 0)
w.plenv(-1.0, 1.0, -1.0, 1.0, 0, 0)
w.plcol0(2)
w.plcont(z, clevel, w.pltr1, xg1, yg1)
w.plstyl([mark], [space])
w.plcol0(3)
w.plcont(w_array, clevel, w.pltr1, xg1, yg1)
w.plstyl([], [])
w.plcol0(1)
w.pllab("X Coordinate", "Y Coordinate", "Streamlines of flow")
# w.pl_setcontlabelparam(0.006, 0.3, 0.1, 1)
# w.plenv(-1.0, 1.0, -1.0, 1.0, 0, 0)
# w.plcol0(2)
# w.plcont(z, clevel, w.pltr1, xg1, yg1)
# w.plstyl([mark], [space])
# w.plcol0(3)
# w.plcont(w, clevel, w.pltr1, xg1, yg1)
# w.plstyl([], [])
# w.plcol0(1)
# w.pllab("X Coordinate", "Y Coordinate", "Streamlines of flow")
# w.pl_setcontlabelparam(0.006, 0.3, 0.1, 0)
#
# Plot using 2D coordinate transformation.
w.plenv(-1.0, 1.0, -1.0, 1.0, 0, 0)
w.plcol0(2)
w.plcont(z, clevel, w.pltr2, xg2, yg2)
w.plstyl([mark], [space])
w.plcol0(3)
w.plcont(w_array, clevel, w.pltr2, xg2, yg2)
w.plstyl([], [])
w.plcol0(1)
w.pllab("X Coordinate", "Y Coordinate", "Streamlines of flow")
# w.pl_setcontlabelparam(0.006, 0.3, 0.1, 1)
# w.plenv(-1.0, 1.0, -1.0, 1.0, 0, 0)
# w.plcol0(2)
# w.plcont(z, clevel, w.pltr2, xg2, yg2)
# w.plstyl([mark], [space])
# w.plcol0(3)
# w.plcont(w, clevel, w.pltr2, xg2, yg2)
# w.plstyl([], [])
# w.plcol0(1)
# w.pllab("X Coordinate", "Y Coordinate", "Streamlines of flow")
#
# polar contour examples.
w.pl_setcontlabelparam(0.006, 0.3, 0.1, 0)
polar(w)
# w.pl_setcontlabelparam(0.006, 0.3, 0.1, 1)
# polar(w)
# potential contour examples.
w.pl_setcontlabelparam(0.006, 0.3, 0.1, 0)
potential(w)
# w.pl_setcontlabelparam(0.006, 0.3, 0.1, 1)
# potential(w)
# Restore defaults
w.pl_setcontlabelparam(0.006, 0.3, 0.1, 0)
# Must be done independently because otherwise this changes output files
# and destroys agreement with C examples.
#w.plcol0(1)