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designed_experiment_v2.py
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designed_experiment_v2.py
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# -*- coding: utf-8 -*-
#==============================================================================
# IMPORT
#------------------------------------------------------------------------------
import matplotlib.pyplot as plt
import numpy as np
import bearded_octo_wookie.RED.RedReader as RedReader
import bearded_octo_wookie.RED.POD as POD
from scipy.spatial import cKDTree
from scipy.interpolate import interp1d
from scipy.interpolate import UnivariateSpline
from wg.tools.function import fixargument
#==============================================================================
# CONFIGURE FIGURES
#------------------------------------------------------------------------------
plt.figure = fixargument(plt.figure, figsize=(20, 10))
#==============================================================================
# DEFINE FUNCTIONS DECORATORS
#------------------------------------------------------------------------------
class require:
def __init__(self, *args, **kargs):
for i,a in enumerate(args):
if not a:
raise "Rquired from-uppr argument number ", i , " failed"
pass
def __call__(self, func):
return func
#==============================================================================
#==============================================================================
# SETUP INPUT DATA
#------------------------------------------------------------------------------
fname0 = '/home/wgryglas/python/avio/naca0012/multi_sweapt_1/mach.65/input/fin_%d.dat'
geometryFile = '/home/wgryglas/python/avio/naca0012/multi_sweapt_1/all/name.get'
boundaryFile = '/home/wgryglas/python/avio/naca0012/multi_sweapt_1/all/boundary.dat'
kappa = 1.4
rtfs = [RedReader.RedTecplotFile(fname0%i) for i in range(1,10)]
#==============================================================================
# for rtf in rtfs:
# data = rtf.data
# p = (kappa-1.) * data[:,2] * ( data[:,3] - (data[:,4]**2 + data[:,5]**2) / data[:,2] / 2. )
# rtf.appendData('p', p)
#==============================================================================
num_modes = 9
modesH = POD.Modes(rtfs, num_modes=num_modes)
modesH.dumpAllModes('/tmp/test%d.vti')
mesh = cKDTree(modesH.baseRedFile.data[:, :2])
#==============================================================================
# SHOW RECONSTRUCTION
#==============================================================================
plt.figure()
for fid, field in enumerate(rtfs[0].variables[2:]):
plt.subplot(3, 2, fid+1)
plt.title(field)
for i, rtf in enumerate(rtfs):
shape = rtf.data[:, 2:].shape
shape1d = shape[0] * shape[1]
v0 = rtf.data[:, 2:].reshape((1, shape1d))
v = np.zeros_like(v0)
cs = list()
en = list()
for m in modesH.modes:
c = v0.dot(m.reshape(shape1d).T)[0, 0]
v = v + c * m.reshape(shape1d)
print v[:, fid]
e = np.max(np.abs(v[:, fid] - v0[:, fid]))
en.append(e)
plt.plot(en, label='m='+str(i))
print "EOF #############"
plt.show()
#==============================================================================
get = RedReader.GetReader(geometryFile)
boundary_nodes = np.loadtxt(boundaryFile)[:, :2]
boundary_nodes_params = np.array(get.getParamList(boundary_nodes[:, :2].tolist(), 1))
bids = mesh.query(boundary_nodes)[1]
#==============================================================================
#DISPLAY BOUNDARY NODES PARAMETRISATION
#==============================================================================
# plt.figure()
# xy = np.array( get.getXYList(np.linspace(0.,1.,200),1) )
# xxyy = np.array( get.getXYList(boundary_nodes_params,1) )
# plt.plot(xxyy[:,0],xxyy[:,1], 'o')
# plt.plot(xy[:,0],xy[:,1])
# plt.figure()
# plt.plot(modesH.baseRedFile.data[bids,0], modesH.baseRedFile.data[bids,1], 'o' )
# plt.plot(boundary_nodes[:,0], boundary_nodes[:,1] , 'x' )
#==============================================================================
work_on_param = 0
modes_interpolators = list()
for m in modesH.modes:
mt = np.squeeze(np.array(m[bids, work_on_param]))
mi = interp1d(boundary_nodes_params, mt, kind='cubic')
#mi = UnivariateSpline(boundary_nodes_params, mt)
#mi.set_smoothing_factor(0.)
modes_interpolators.append(mi)
#==============================================================================
# DISPLAY POD VECTORS VALUES INTERPOLATION ON BOUNDARY
#==============================================================================
# plt.figure()
# l = np.linspace(0.,1., 5000)
# for m, mi in zip(modesH.modes, modes_interpolators):
# plt.plot(boundary_nodes_params, m[bids,0], 'o')
# plt.plot(l, mi(l))
#==============================================================================
#testpoints = boundary_nodes_params#np.linspace(0.,1., num_test_points)
#num_test_points = len(testpoints)
#
#
#make test matrix
@require(
num_modes>0,
not 'A' in locals(),
not 'A' in globals(),
'modes_interpolators' in locals()
)
def getInformationMatric(test_points_):
A = np.zeros((len(test_points_),num_modes))
for pid, point in enumerate(test_points_):
for mid, mi in enumerate(modes_interpolators):
A[pid, mid] = mi(point)
return A
@require(
num_modes>0,
not 'A' in locals(),
not 'A' in globals(),
'modes_interpolators' in locals()
)
def getInformationMatric_ComputeSingleCol(test_points_, pid):
A = np.zeros((len(test_points_),num_modes))
point = test_points_[pid]
for mid, mi in enumerate(modes_interpolators):
A[pid, mid] = mi(point)
return A
#==============================================================================
# TEST THE MATRIX
#==============================================================================
# num_test_points = 15
# testpoints = np.linspace(0.,1., num_test_points)
#
# A = getInformationMatric(testpoints)
#
# ## fake experimanta data
# experiment_values_interpolate = interp1d(boundary_nodes_params, np.array(rtfs[0].data[bids,2+work_on_param]), kind='cubic')
# experiment_values = experiment_values_interpolate(testpoints)
#
# #reconstruct coefficents
# cs_A = np.linalg.solve(A.T.dot(A),A.T.dot(experiment_values))
#
# #reconstruct coeficients ased on whole solution
# shape = rtfs[0].data[:,2:].shape
# shape1d = shape[0] * shape[1]
# v0 = rtfs[0].data[:,2:].reshape((1,shape1d))
# cs_org = list()
#
# for m in modesH.modes:
# cs_org.append(v0.dot(m.reshape(shape1d).T)[0,0])
#
# cs_org = np.array(cs_org)
#
#
# #profile is aligned with XY coordinate system
# profile_length_param = boundary_nodes[:,0]
#
# #reconstruct full field, basing on modes. recon SHOULD BE EXACT, reconA contains error
# recon = np.squeeze(np.array(modesH.modes).T.dot(cs_org.reshape((1,9,1))))
# reconA = np.squeeze(np.array(modesH.modes).T.dot(cs_A.reshape((1,9,1))))
#
# #plot beutifully
# for fid, field in enumerate(rtfs[0].variables[2:]):
# print fid,field
# plt.subplot(3,2,fid+1)
# plt.title(field)
# values = rtfs[0].data[bids,2+fid]
# # plt.plot(profile_length_param, values)
# v = np.zeros_like(profile_length_param)
# plt.plot(profile_length_param, recon[fid,bids],'o')
# plt.plot(profile_length_param, reconA[fid,bids],'rx')
# plt.twinx()
# err = np.absolute(recon[fid,bids] - reconA[fid,bids])
# plt.semilogy(profile_length_param, err,'k-')
#==============================================================================
#==============================================================================
# SHOW HOW SINGLE POINT MOVEMENT WRT TO ORIGINAL POSITION CHANGE cond(A)
#==============================================================================
# num_test_points = 15
# plt.figure()
# testpoints = np.linspace(0.,1., num_test_points)
#
# for move_point in range(1,num_test_points-1):
#
# maxmove = 0.9*(testpoints[move_point+1] - testpoints[move_point-1])
# move = np.linspace(-maxmove/2.,maxmove/2., 40)
# test_new_positions = testpoints[move_point] + move
#
# testpoints_modified = np.array([ testpoints for t in test_new_positions ])
# testpoints_modified[:,move_point] = test_new_positions
#
# Amodified = [ getInformationMatric(t) for t in testpoints_modified ]
#
# Aoptimality = np.array([ np.trace(np.linalg.inv(AA.T.dot(AA))) for AA in Amodified ])
# Aoptimality = Aoptimality
# plt.semilogy(move,Aoptimality)
#
# plt.grid(which='both')
#==============================================================================
@require(
not 'A' in locals(),
not 'A' in globals()
)
def getTraceOfInverse(A):
D = np.linalg.eigvalsh(A)
return np.sum(1./ D)
#==============================================================================
# SHOW HOW SINGLE EXTRA POINT ALONG PROFILE CHENGE cond(A)
#==============================================================================
num_test_points = 1
testpoints = np.linspace(0., 1., num_test_points)
testpoints0 = np.copy(testpoints)
Aoptim_min = list()
Aoptim_uniform = list()
for extrapoint in range(25):
num_test_points = num_test_points + 1
_testpoints = np.array(testpoints)
testpoints = np.zeros(num_test_points)
testpoints[:-1] = _testpoints
test_new_positions = np.linspace(0.,1., 3 * num_test_points)
testpoints_modified = np.array([ testpoints for t in test_new_positions ])
testpoints_modified[:,-1] = test_new_positions
#Amodified = [ getInformationMatric(t) for t in testpoints_modified ]
A0 = getInformationMatric(testpoints_modified[0])
A0[-1,:] = 0
Amodified = [ A0 + getInformationMatric_ComputeSingleCol(t,num_test_points-1) for t in testpoints_modified ]
Aoptimality = np.array([ getTraceOfInverse(AA.T.dot(AA)) for AA in Amodified ])
Aoptimality = Aoptimality
plt.semilogy(test_new_positions,Aoptimality)
#plt.semilogy(testpoints[:-1],np.ones_like(testpoints[:-1])*np.average(Aoptimality), 'o')
plt.grid(which='both')
print np.max(Aoptimality)
print np.min(Aoptimality)
sorte = np.argsort(Aoptimality)
optim = 0
for optim_ in sorte:
print "check point ", optim_
if not test_new_positions[optim_] in testpoints[:-1]:
optim = optim_
print " ok point ", optim_
break
else:
print " repeated point ", optim_
testpoints[-1] = test_new_positions[optim]
plt.semilogy(testpoints[-1],Aoptimality[optim], 'o')
Aoptim_min.append( Aoptimality[optim] )
Aunif = getInformationMatric(np.linspace(0,1.,num_test_points))
Aoptim_uniform.append(getTraceOfInverse(Aunif.T.dot(Aunif)))
testpoints = np.unique(testpoints)
testpoints_uniform = np.linspace(0,1.,len(testpoints))
testpoints_xy = np.array(get.getXYList(testpoints,1))
testpoints0_xy = np.array(get.getXYList(testpoints0,1))
testpoints_uniform_xy = np.array(get.getXYList(testpoints_uniform,1))
plt.figure()
plt.semilogy(Aoptim_uniform, 'k')
plt.semilogy(Aoptim_min, 'r')
plt.figure()
plt.plot(testpoints_xy[:,0], testpoints_xy[:,1],'ro', ms=30)
plt.plot(testpoints0_xy[:,0], testpoints0_xy[:,1],'ko' , ms=20)
plt.plot(testpoints_uniform_xy[:,0], testpoints_uniform_xy[:,1],'bo' , ms=10)
plt.figure()
A = getInformationMatric(testpoints)
A0 = getInformationMatric(testpoints0)
A_uniform = getInformationMatric(testpoints_uniform)
experiment_values_interpolate = interp1d(boundary_nodes_params, np.array(rtfs[0].data[bids,2+work_on_param]), kind='cubic')
experiment_values = experiment_values_interpolate(testpoints)
experiment_values0 = experiment_values_interpolate(testpoints0)
experiment_values_uniform = experiment_values_interpolate(testpoints_uniform)
#reconstruct coefficents
cs_A = np.linalg.solve(A.T.dot(A),A.T.dot(experiment_values))
initial_is_singular = False
try:
cs_A0 = np.linalg.solve(A0.T.dot(A0),A0.T.dot(experiment_values0))
except np.linalg.linalg.LinAlgError:
print "======================================================="
print "INITIAL DISTRIBUTION MATRIX IS SINGULAR!!!!!!!!!!!!!!!!"
print "======================================================="
initial_is_singular = True
cs_A0 = np.linalg.solve(A.T.dot(A),A.T.dot(experiment_values))
cs_A_uniform = np.linalg.solve(A_uniform.T.dot(A_uniform),A_uniform.T.dot(experiment_values_uniform))
#reconstruct coeficients ased on whole solution
shape = rtfs[0].data[:,2:].shape
shape1d = shape[0] * shape[1]
v0 = rtfs[0].data[:,2:].reshape((1,shape1d))
cs_org = list()
for m in modesH.modes:
cs_org.append(v0.dot(m.reshape(shape1d).T)[0,0])
cs_org = np.array(cs_org)
#profile is aligned with XY coordinate system
profile_length_param = boundary_nodes[:,0]
#reconstruct full field, basing on modes. recon SHOULD BE EXACT, reconA contains error
recon = np.squeeze(np.array(modesH.modes).T.dot(cs_org.reshape((1,num_modes,1))))
reconA = np.squeeze(np.array(modesH.modes).T.dot(cs_A.reshape((1,num_modes,1))))
reconA0 = np.squeeze(np.array(modesH.modes).T.dot(cs_A0.reshape((1,num_modes,1))))
reconA_uniform = np.squeeze(np.array(modesH.modes).T.dot(cs_A_uniform.reshape((1,num_modes,1))))
#plot beutifully
field = rtfs[0].variables[2+work_on_param]
plt.title(field)
v = np.zeros_like(profile_length_param)
plt.subplot(311)
plt.plot(profile_length_param, recon[work_on_param,bids],'-')
plt.plot(testpoints_xy[:,0], experiment_values,'ro')
plt.subplot(312)
plt.plot(profile_length_param, recon[work_on_param,bids],'-')
plt.plot(testpoints0_xy[:,0], experiment_values0,'ko')
plt.subplot(313)
plt.plot(profile_length_param, recon[work_on_param,bids],'-')
plt.plot(testpoints_uniform_xy[:,0], experiment_values_uniform,'bo')
plt.figure()
#plot beutifully
for fid, field in enumerate(rtfs[0].variables[2:]):
print fid,field
plt.subplot(3,2,fid+1)
plt.title(field)
values = rtfs[0].data[bids,2+fid]
# plt.plot(profile_length_param, values)
v = np.zeros_like(profile_length_param)
plt.plot(profile_length_param, recon[fid,bids],'o')
plt.plot(profile_length_param, reconA[fid,bids],'rx')
plt.plot(profile_length_param, reconA0[fid,bids],'kx')
plt.plot(profile_length_param, reconA_uniform[fid,bids],'bx')
plt.figure()
for fid, field in enumerate(rtfs[0].variables[2:]):
print fid,field
plt.subplot(3,2,fid+1)
plt.title(field)
err0 = np.absolute(recon[fid,bids] - reconA0[fid,bids])
plt.semilogy(profile_length_param, err0,'k-')
err = np.absolute(recon[fid,bids] - reconA[fid,bids])
plt.semilogy(profile_length_param, err,'r-')
err_unif = np.absolute(recon[fid,bids] - reconA_uniform[fid,bids])
plt.semilogy(profile_length_param, err_unif,'b-')
plt.figure()
for fid, field in enumerate(rtfs[0].variables[2:]):
print fid,field
plt.subplot(3,2,fid+1)
plt.title(field)
err = np.absolute(reconA0[fid,bids] - reconA[fid,bids])
plt.semilogy(profile_length_param, err,'ro-')
err_unif = np.absolute(reconA0[fid,bids] - reconA_uniform[fid,bids])
plt.semilogy(profile_length_param, err_unif,'bo-')
plt.show()