def det_tau_r(E_f, V_f, m_list, mu_xi, dp_tau, dp_r, tau_range, r_range, sV0):
w_arr = np.linspace(0, 20, 300)
tau_arr = np.linspace(tau_range[0], tau_range[1], dp_tau)
r_arr = np.linspace(r_range[0], r_range[1], dp_tau)
e_arr = orthogonalize([tau_arr, r_arr])
x_axis = e_arr[0]
y_axis = e_arr[1]
for mi in m_list:
res_array = np.zeros((dp_tau, dp_r))
for i_tau, taui in enumerate(tau_arr):
for i_r, ri in enumerate(r_arr):
s = get_scale(mu_xi, mi, taui, ri)
print s
#sV0 = float(s * (pi * mu_r ** 2) ** (1. / mi))
T = 2. * taui / ri
s0 = ((T * (mi + 1) * sV0 ** mi) / (2. * E_f * pi * ri ** 2)) ** (1. / (mi + 1))
print s0
k = np.sqrt(T / E_f)
ef0 = k * np.sqrt(w_arr)
G = 1 - np.exp(-(ef0 / s0) ** (mi + 1))
mu_int = ef0 * E_f * V_f * (1 - G)
I = s0 * gamma(1 + 1. / (mi + 1)) * gammainc(1 + 1. / (mi + 1), (ef0 / s0) ** (mi + 1))
mu_broken = E_f * V_f * I / (mi + 1)
result = mu_int + mu_broken
sigma_c = np.max(result)
if sigma_c == result[-1]:
print "w_arr too short"
pass
res_array[i_tau, i_r] = sigma_c
mlab.surf(x_axis, y_axis, res_array / 100.)
mlab.xlabel("det tau")
mlab.ylabel("det r")
mlab.zlabel("sigma")
mlab.show()
def rand_r_det_tau( E_f, V_f, tau_range, CoV_r_range, mu_r , dp_tau, dp_r, sV0 ):
m = m_list[0]
s0 = ( ( mu_tau * ( m + 1 ) * sV0 ** m ) / ( E_f * pi * mu_r ** 3 ) ) ** ( 1. / ( m + 1 ) )
mu_xi = s0 * gamma( 1. + 1. / ( 1. + m ) )
#loop with rand tau and rand r
for mi in m_list:
##############
Pf = RV( 'uniform', loc = 0.0, scale = 1.0 )
w_arr = np.linspace( 0, 2.0, 30 )
cb = CBResidual( include_pullout = True )
tau_arr = np.linspace( tau_range[0], tau_range[1], dp_tau )
CoV_r_arr = np.linspace( 0.0001, 0.5, dp_r )
loc_r_arr = mu_r - CoV_r_arr * mu_r * 3 ** 0.5
scale_r_arr = 2 * mu_r - 2 * loc_r_arr
e_arr = orthogonalize( [tau_arr, CoV_r_arr] )
x_axis = e_arr[0]
y_axis = e_arr[1]
stats_r = []
for s in range( dp_r ):
stats_r.append( RV( 'uniform', loc = loc_r_arr[s], scale = scale_r_arr[s] ) )
#gen Tuple of [loc,scale]
res_array = np.zeros( ( dp_tau, dp_r ) )
for i_tau, taui in enumerate( tau_arr ):
for i_r, ri in enumerate( stats_r ):
s0i = mu_xi / gamma( 1. + 1. / ( 1. + mi ) )
sV0i = ( ( s0i ** ( mi + 1 ) * E_f * pi * mu_r ** 3. ) / ( taui * ( mi + 1. ) ) ) ** ( 1. / mi )
total = SPIRRID( q = cb,
sampling_type = 'MCS',
evars = dict( w = w_arr ),
tvars = dict( tau = taui, E_f = E_f, V_f = V_f, r = ri,
m = mi, sV0 = sV0i, Pf = Pf ),
n_int = 60 )
if isinstance( ri, RV ):
r_arr = np.linspace( ri.ppf( 0.001 ), ri.ppf( 0.999 ), 200 )
Er = np.trapz( r_arr ** 2 * ri.pdf( r_arr ), r_arr )
else:
Er = ri ** 2
result = total.mu_q_arr / Er
sigma_c = np.max( result )
if sigma_c == result[-1]:
print "w_arr too short"
pass
res_array[i_tau, i_r] = sigma_c
#mayaviplot
print np.max( res_array )
mlab.surf( x_axis, y_axis, res_array )
#
mlab.view( 0., 0. )
mlab.xlabel( "det tau" )
mlab.ylabel( "rand r" )
mlab.zlabel( "sigma" )
mlab.show()
def rand_tau_det_r( E_f, V_f, CoV_tau_range, r_range, mu_tau , dp_tau, dp_r, sV0 ):
m = m_list[0]
s0 = ( ( mu_tau * ( m + 1 ) * sV0 ** m ) / ( E_f * pi * mu_r ** 3 ) ) ** ( 1. / ( m + 1 ) )
mu_xi = s0 * gamma( 1. + 1. / ( 1. + m ) )
for mi in m_list:
#######################################
Pf = RV( 'uniform', loc = 0.0, scale = 1.0 )
w_arr = np.linspace( 0, 5, 300 )
cb = CBResidual( include_pullout = True )
# CoV generation
CoV_tau_arr = np.linspace( CoV_tau_range[0], CoV_tau_range[1], dp_tau )
loc_tau_arr = mu_tau - CoV_tau_arr * mu_tau * 3 ** 0.5
scale_tau_arr = 2 * mu_tau - 2 * loc_tau_arr
r_arr = np.linspace( r_range[0], r_range[1], dp_r )
e_arr = orthogonalize( [CoV_tau_arr, r_arr] )
x_axis = e_arr[0]
y_axis = e_arr[1]
#TAU gen Tuple of [loc,scale]
stats_tau = []
for s in range( dp_tau ):
stats_tau.append( RV( 'uniform', loc = loc_tau_arr[s], scale = scale_tau_arr[s] ) )
#r gen Tuple of [loc,scale]
res_array = np.zeros( ( dp_tau, dp_r ) )
for i_tau, taui in enumerate( stats_tau ):
for i_r, ri in enumerate( r_arr ):
print i_tau, i_r
s0i = mu_xi / gamma( 1. + 1. / ( 1. + mi ) )
sV0i = ( ( s0i ** ( mi + 1 ) * E_f * pi * ri ** 3. ) / ( mu_tau * ( mi + 1. ) ) ) ** ( 1. / mi )
total = SPIRRID( q = cb,
sampling_type = 'MCS',
evars = dict( w = w_arr ),
tvars = dict( tau = taui, E_f = E_f, V_f = V_f, r = ri,
m = mi, sV0 = sV0i, Pf = Pf ),
n_int = 60 )
if isinstance( ri, RV ):
r_arr = np.linspace( ri.ppf( 0.001 ), ri.ppf( 0.999 ), 200 )
Er = np.trapz( r_arr ** 2 * ri.pdf( r_arr ), r_arr )
else:
Er = ri ** 2
#total(evars=dict(w=[3.]))
x = [2.]
x = np.array( x )
result = total.mu_q_arr / Er
sigma_c = np.max( result )
if sigma_c == result[-1]:
print "w_arr too short"
res_array[i_tau, i_r] = sigma_c
#mayaviplot
mlab.surf( x_axis, y_axis * 50, res_array, warpscale = 0.1 )
mlab.view( 0., 0. )
mlab.xlabel( "rand tau" )
mlab.ylabel( "det r" )
mlab.zlabel( "sigma" )
mlab.show()
def det_tau_r( E_f, V_f, m_list, dp_tau, dp_r, tau_range, r_range, sV0 ):
m = m_list[0]
s0 = ( ( mu_tau * ( m + 1 ) * sV0 ** m ) / ( E_f * pi * mu_r ** 3 ) ) ** ( 1. / ( m + 1 ) )
mu_xi = s0 * gamma( 1. + 1. / ( 1. + m ) )
################
w_arr = np.linspace( 0, 100, 300 )
tau_arr = np.linspace( tau_range[0], tau_range[1], dp_tau )
r_arr = np.linspace( r_range[0], r_range[1], dp_tau )
e_arr = orthogonalize( [tau_arr, r_arr] )
x_axis = e_arr[0]
y_axis = e_arr[1]
for i_m, mi in enumerate( m_list ):
res_array = np.zeros( ( dp_tau, dp_r ) )
for i_tau, taui in enumerate( tau_arr ):
for i_r, ri in enumerate( r_arr ):
s0i = mu_xi / gamma( 1. + 1. / ( 1. + mi ) )
sV0i = ( ( s0i ** ( mi + 1 ) * E_f * pi * ri ** 3. ) / ( taui * ( mi + 1. ) ) ) ** ( 1. / mi )
T = 2. * taui / ri
s0 = ( ( T * ( mi + 1 ) * sV0i ** mi ) / ( 2. * E_f * pi * ri ** 2 ) ) ** ( 1. / ( mi + 1 ) )
k = np.sqrt( T / E_f )
ef0 = k * np.sqrt( w_arr )
G = 1 - np.exp( -( ef0 / s0 ) ** ( mi + 1 ) )
mu_int = ef0 * E_f * V_f * ( 1 - G )
I = s0 * gamma( 1 + 1. / ( mi + 1 ) ) * gammainc( 1 + 1. / ( mi + 1 ), ( ef0 / s0 ) ** ( mi + 1 ) )
mu_broken = E_f * V_f * I / ( mi + 1 )
result = mu_int + mu_broken
sigma_c = np.max( result )
if sigma_c == result[-1]:
print "w_arr too short"
pass
res_array[i_tau, i_r] = sigma_c
mlab.surf( x_axis, y_axis, res_array / 100. )
mlab.xlabel( "det tau" )
mlab.ylabel( "det r" )
mlab.zlabel( "sigma" )
mlab.show()
def rand_tau_r( E_f, V_f, mu_tau, mu_r, m_list, CoV_tau_range, CoV_r_range, dp_tau, dp_r, sV0 ):
#rand tau and rand r
m = m_list[0]
s0 = ( ( mu_tau * ( m + 1 ) * sV0 ** m ) / ( E_f * pi * mu_r ** 3 ) ) ** ( 1. / ( m + 1 ) )
mu_xi = s0 * gamma( 1. + 1. / ( 1. + m ) )
for i_m, mi in enumerate( m_list ):
s0i = mu_xi / gamma( 1. + 1. / ( 1. + mi ) )
sV0i = ( ( s0i ** ( mi + 1 ) * E_f * pi * mu_r ** 3. ) / ( mu_tau * ( mi + 1. ) ) ) ** ( 1. / mi )
#
#print 'Nr', i_m, 's0i', s0i, 'sV0i', sV0i, 'mu_xi', s0i * gamma(1. + 1. / (1. + mi))
#
#Pf = RV( 'uniform', loc = 0.0, scale = 1.0 )
#w_arr = np.linspace(0, 1.2, 30)
# loc scale generation for specific CoV
#CoVtau
CoV_tau_arr = np.linspace( CoV_tau_range[0], CoV_tau_range[1], dp_tau )
loc_tau_arr = mu_tau - CoV_tau_arr * mu_tau * 3 ** 0.5
scale_tau_arr = 2 * mu_tau - 2 * loc_tau_arr
#CoVr
CoV_r_arr = np.linspace( CoV_r_range[0], CoV_r_range[1], dp_r )
loc_r_arr = mu_r - CoV_r_arr * mu_r * 3 ** 0.5
scale_r_arr = 2 * mu_r - 2 * loc_r_arr
#shaping for mayavi
e_arr = orthogonalize( [CoV_tau_arr, CoV_r_arr] )
x_axis = e_arr[0]
y_axis = e_arr[1]
#TAU gen Tuple of [loc,scale]
stats_tau = []
for s in range( dp_tau ):
stats_tau.append( RV( 'uniform', loc = loc_tau_arr[s], scale = scale_tau_arr[s] ) )
stats_tau[0] = mu_tau
stats_r = []
for s in range( dp_r ):
stats_r.append( RV( 'uniform', loc = loc_r_arr[s], scale = scale_r_arr[s] ) )
stats_r[0] = mu_r
#r gen Tuple of [loc,scale]
sigma_array = np.zeros( ( dp_tau, dp_r ) )
w_array = np.zeros( ( dp_tau, dp_r ) )
##grid
sigma_array_grid = np.zeros( ( dp_tau, dp_r ) )
w_array_grid = np.zeros( ( dp_tau, dp_r ) )
for i_tau, taui in enumerate( stats_tau ):
for i_r, ri in enumerate( stats_r ):
total = SPIRRID( q = cb,
sampling_type = 'PGrid',
evars = dict(),
tvars = dict( tau = taui, E_f = E_f, V_f = V_f, r = ri,
m = mi, sV0 = sV0i ),
n_int = 70 )
if isinstance( ri, RV ):
r_arr = np.linspace( ri.ppf( 0.001 ), ri.ppf( 0.999 ), 200 )
Er = np.trapz( r_arr ** 2 * ri.pdf( r_arr ), r_arr )
else:
Er = ri ** 2
#Optimization taui, E_f, V_f, ri, mi, sV0i, Pf, Er
def spirrid_func( w_in, Er ):
w_arr = np.array( w_in )
#print 'w', w_arr
total.evars = dict( w = w_arr )
g = -1.*total.mu_q_arr / Er
#print 'res', g
total.evars = dict( w = w_arr )
return g
#w_test = np.linspace(0.001, 1, 1000)
#total.evars = dict(w=w_test)
# plt.plot(w_test, -1.*total.mu_q_arr / Er)
#plt.show()
print i_tau, 'von', dp_tau
#Optimierung
w_ult, sigma_ult, trash1, trash2, trash3 = fmin( spirrid_func, x0 = 0.1, args = [Er], ftol = 0.2, full_output = 1 )
sigma_array[i_tau, i_r] = np.float( -1.*sigma_ult )
w_array[i_tau, i_r] = np.float( w_ult )
#grid
w_grid = np.linspace( 0.2, 0.28, 50 )
res_grid = -1.* spirrid_func( w_grid, Er )
index_max_grid = np.argmax( res_grid )
sigma_array_grid[i_tau, i_r] = res_grid[index_max_grid]
w_array_grid[i_tau, i_r] = w_grid[index_max_grid]
#print w_grid[index_max_grid]
#print np.max( sigma_array )
s_dataname = 'sigmaOPT20_with_m{}.npy'.format( mi )
np.save( s_dataname, sigma_array )
w_dataname = 'wOPT20_with_m{}.npy'.format( mi )
np.save( w_dataname, w_array )
#Grid Datasave
s_gridname = 'sigmaGRID20_with_m{}.npy'.format( mi )
np.save( s_gridname , sigma_array_grid )
w_gridname = 'wGRID20_with_m{}.npy'.format( mi )
np.save( w_gridname, w_array_grid )
#mayaviplot
mlab.surf( x_axis, y_axis, w_array )
mlab.xlabel( "rand tau" )
mlab.ylabel( "rand r" )
mlab.zlabel( "sigma" )
mlab.show()