import numpy as npy
from GetNodalFunctionsCoeff import GetNodalFunctionsCoeff
from results import results

def mechanicalproperties(md,vx,vy):
	"""
	MECHANICALPROPERTIES - compute stress and strain rate for a goven velocity
	
   this routine computes the components of the stress tensor
   strain rate tensor and their respective principal directions.
   the results are in the model md: md.results
	
   Usage:
      md=mechanicalproperties(md,vx,vy)
	
   Example:
      md=mechanicalproperties(md,md.initialization.vx,md.initialization.vy)
      md=mechanicalproperties(md,md.inversion.vx_obs,md.inversion.vy_obs)
	"""

	#some checks
	if len(vx)!=md.mesh.numberofvertices or len(vy)!=md.mesh.numberofvertices:
		raise ValueError('the input velocity should be of size ' + md.mesh.numberofvertices)

	if md.mesh.dimension!=2:
		raise StandardError('only 2D model supported currently')

	if npy.any(md.flowequation.element_equation!=2):
		print 'Warning: the model has some non SSA elements. These will be treated like SSA elements'
	
	#initialization
	numberofelements=md.mesh.numberofelements
	index=md.mesh.elements
	summation=npy.array([[1],[1],[1]])
	directionsstress=npy.zeros((numberofelements,4))
	directionsstrain=npy.zeros((numberofelements,4))
	valuesstress=npy.zeros((numberofelements,2))
	valuesstrain=npy.zeros((numberofelements,2))
	
	#compute nodal functions coefficients N(x,y)=alpha x + beta y +gamma
	alpha,beta=GetNodalFunctionsCoeff(index,md.mesh.x,md.mesh.y)[0:2]
	
	#compute shear
	vxlist=vx[index-1]/md.constants.yts
	vylist=vy[index-1]/md.constants.yts
	ux=npy.dot((vxlist*alpha),summation).reshape(-1,)
	uy=npy.dot((vxlist*beta),summation).reshape(-1,)
	vx=npy.dot((vylist*alpha),summation).reshape(-1,)
	vy=npy.dot((vylist*beta),summation).reshape(-1,)
	uyvx=(vx+uy)/2.
	#clear vxlist vylist
	
	#compute viscosity
	nu=npy.zeros((numberofelements,))
	B_bar=npy.dot(md.materials.rheology_B[index-1],summation/3.).reshape(-1,)
	power=(md.materials.rheology_n-1.)/(2.*md.materials.rheology_n)
	second_inv=(ux**2.+vy**2.+((uy+vx)**2.)/4.+ux*vy).reshape(-1,)
	
	#some corrections
	location=npy.nonzero(npy.logical_and(second_inv==0,power!=0))
	nu[location]=10^18 	#arbitrary maximum viscosity to apply where there is no effective shear
	
	if 'matice' in md.materials.__module__:
		location=npy.nonzero(second_inv)
		nu[location]=B_bar[location]/(second_inv[location]**power[location])
		location=npy.nonzero(npy.logical_and(second_inv==0,power==0))
		nu[location]=B_bar[location]
	elif 'matdamageice' in md.materials.__module__:
		Zinv=npy.dot(md.materials.rheology_Z[index-1],summation/3.).reshape(-1,)
		location=npy.nonzero(second_inv)
		nu[location]=Zinv[location]*B_bar[location]/npy.power(second_inv[location],power[location])
		location=npy.nonzero(npy.logical_and(second_inv==0,power==0))
		nu[location]=Zinv[location]*B_bar[location]
		#clear Zinv
	else:
		raise StandardError('class of md.materials (' + md.materials.__module__ + ') not recognized or not supported')
	
	#compute stress
	tau_xx=nu*ux
	tau_yy=nu*vy
	tau_xy=nu*uyvx
	
	#compute principal properties of stress
	for i in npy.arange(numberofelements):
	
		#compute stress and strainrate matrices
		stress=npy.array([ [tau_xx[i], tau_xy[i]], [tau_xy[i], tau_yy[i]] ])
		strain=npy.array([ [ux[i], uyvx[i]], [uyvx[i], vy[i]] ])
	
		#eigenvalues and vectors for stress
		value,directions=npy.linalg.eig(stress);
		idx=abs(value).argsort()[::-1] # sort in descending order
		value=value[idx]
		directions=directions[:,idx]
		valuesstress[i,:]=[value[0],value[1]]
		directionsstress[i,:]=directions.transpose().flatten()

		#eigenvalues and vectors for strain
		value,directions=npy.linalg.eig(strain);
		idx=abs(value).argsort()[::-1] # sort in descending order
		value=value[idx]
		directions=directions[:,idx]
		valuesstrain[i,:]=[value[0],value[1]]
		directionsstrain[i,:]=directions.transpose().flatten()

	##plug onto the model
	##NB: Matlab sorts the eigen value in increasing order, we want the reverse
	stress=results()
	stress.xx=tau_xx
	stress.yy=tau_yy
	stress.xy=tau_xy
	stress.principalvalue1=valuesstress[:,0]
	stress.principalaxis1=directionsstress[:,0:2]
	stress.principalvalue2=valuesstress[:,1]
	stress.principalaxis2=directionsstress[:,2:4]
	stress.effectivevalue=1./npy.sqrt(2.)*npy.sqrt(stress.xx**2+stress.yy**2+2.*stress.xy**2)
	md.results.stress=stress
	
	strainrate=results()
	strainrate.xx=ux*md.constants.yts #strain rate in 1/a instead of 1/s
	strainrate.yy=vy*md.constants.yts 
	strainrate.xy=uyvx*md.constants.yts 
	strainrate.principalvalue1=valuesstrain[:,0]*md.constants.yts 
	strainrate.principalaxis1=directionsstrain[:,0:2]
	strainrate.principalvalue2=valuesstrain[:,1]*md.constants.yts 
	strainrate.principalaxis2=directionsstrain[:,2:4]
	strainrate.effectivevalue=1./npy.sqrt(2.)*npy.sqrt(strainrate.xx**2+strainrate.yy**2+2.*strainrate.xy**2)
	md.results.strainrate=strainrate
	
	deviatoricstress=results()
	deviatoricstress.xx=tau_xx
	deviatoricstress.yy=tau_yy
	deviatoricstress.xy=tau_xy
	deviatoricstress.principalvalue1=valuesstress[:,0]
	deviatoricstress.principalaxis1=directionsstress[:,1:2]
	deviatoricstress.principalvalue2=valuesstress[:,1]
	deviatoricstress.principalaxis2=directionsstress[:,2:4]
	deviatoricstress.effectivevalue=1./npy.sqrt(2.)*npy.sqrt(stress.xx**2+stress.yy**2+2.*stress.xy**2)
	md.results.deviatoricstress=deviatoricstress

	return md
