#Test Name: EISMINTRoundIceSheetStaticSIA
import numpy
from model import *
from roundmesh import *
from setmask import *
from parameterize import *
from setflowequation import *
from EnumDefinitions import *
from solve import *
from MatlabFuncs import *

"""
The aim of this program is to compare a model with an analytical solution given in SSA EISMINT : Lessons in Ice-Sheet Modeling.
"""

printingflag=False

numlayers=10
resolution=30000.

#To begin with the numerical model
md=model()
md=roundmesh(md,750000.,resolution)
md=setmask(md,'','')    #We can not test iceshelves nor ice rises with this analytical solution
md=parameterize(md,'../Par/RoundSheetStaticEISMINT.py')

#Calculation of the analytical 2d velocity field
constant=0.3
vx_obs=constant/2.*md.mesh.x*(md.geometry.thickness)**-1
vy_obs=constant/2.*md.mesh.y*(md.geometry.thickness)**-1
vel_obs=numpy.sqrt((md.inversion.vx_obs)**2+(md.inversion.vy_obs)**2)

#We extrude the model to have a 3d model
md.extrude(numlayers,1.);
md=setflowequation(md,'SIA','all')

#Spc the nodes on the bed
pos=numpy.nonzero(md.mesh.vertexonbase)
md.stressbalance.spcvx[pos]=0.
md.stressbalance.spcvy[pos]=0.
md.stressbalance.spcvz[pos]=0.

#Now we can solve the problem 
md.cluster=generic('name',oshostname(),'np',8)
md=solve(md,'StressbalanceSolution')

#Calculate the depth averaged velocity field (2d):
vx=md.results.StressbalanceSolution.Vx
vy=md.results.StressbalanceSolution.Vy
vel=numpy.zeros((md.mesh.numberofvertices2d,1))

for i in xrange(0,md.mesh.numberofvertices2d):
	node_vel=0.
	for j in xrange(0,md.mesh.numberoflayers-1):
		node_vel=node_vel+1./(2.*(md.mesh.numberoflayers-1))*\
			(numpy.sqrt(vx[i+(j+1)*md.mesh.numberofvertices2d,0]**2+vy[i+(j+1)*md.mesh.numberofvertices2d,0]**2)+\
			numpy.sqrt(vx[i+j*md.mesh.numberofvertices2d,0]**2+vy[i+j*md.mesh.numberofvertices2d,0]**2))
	vel[i,0]=node_vel

#Plot of the velocity from the exact and calculated solutions
#figure(1)
#set(gcf,'Position',[1 1 1580 1150])
#subplot(2,2,1)
#p=patch('Faces',md.mesh.elements2d,'Vertices',[md.mesh.x2d md.mesh.y2d],'FaceVertexCData',...
#vel,'FaceColor','interp','EdgeColor','none');
#title('Modelled velocity','FontSize',14,'FontWeight','bold')
#colorbar; 
#caxis([0 200]);
   
#subplot(2,2,2)
#p=patch('Faces',md.mesh.elements2d,'Vertices',[md.mesh.x2d md.mesh.y2d],'FaceVertexCData',...
#vel_obs,'FaceColor','interp','EdgeColor','none');
#title('Analytical velocity','FontSize',14,'FontWeight','bold')
#colorbar; 
#caxis([0 200]);

#subplot(2,2,3)
#hold on;
#plot(sqrt((md.mesh.x(1:md.mesh.numberofvertices2d)).^2+(md.mesh.y(1:md.mesh.numberofvertices2d)).^2),vel,'r.');
#plot(sqrt((md.mesh.x2d).^2+(md.mesh.y2d).^2),vel_obs,'b.');
#title('Analytical vs calculated velocity','FontSize',14,'FontWeight','bold');
#xlabel('distance to the center of the icesheet [m]','FontSize',14,'FontWeight','bold');
#ylabel('velocity [m/yr]','FontSize',14,'FontWeight','bold');
#legend('calculated velocity','exact velocity');
#axis([0 750000 0 200]);
#hold off;

#subplot(2,2,4)
#p=patch('Faces',md.mesh.elements2d,'Vertices',[md.mesh.x2d md.mesh.y2d],'FaceVertexCData',...
#abs(vel-vel_obs)./vel_obs*100,'FaceColor','interp','EdgeColor','none');
#title('Relative misfit [%]','FontSize',14,'FontWeight','bold')
#colorbar;
#caxis([0 100]);

if printingflag:
	pass
#	set(gcf,'Color','w')
#	printmodel('SIAstatic','png','margin','on','marginsize',25,'frame','off','resolution',0.7,'hardcopy','off');
#	system(['mv SIAstatic.png ' ISSM_DIR '/website/doc_pdf/validation/Images/EISMINT/IceSheet']);

#Fields and tolerances to track changes
field_names     =[ \
	'Vx','Vy','Vel', \
]
field_tolerances=[ \
	1e-13,1e-13,1e-13, \
]
field_values=[ \
	vx,vy,vel, \
]